Abstract:
Methods and configurations controlling a converter having controllable power semiconductors, compare actual and target state values to obtain control difference values for a control unit producing setting voltage values. Control electronics provide control signals according to setting voltage values and transmit them to power semiconductors. The control unit generates voltage values so control difference values become small. Current and converter energy controls and energy balancing are performed jointly, actual state values are calculated by an observing unit based on setting voltage values considering measured current values and actual state intermediate-circuit energy values are calculated by an estimating unit considering measured intermediate-circuit energy values of positive and negative voltage sources. The observing and estimating units model the converter so actual state current and intermediate-circuit steady-state energy values correspond to error-free current and intermediate-circuit energy values. A periodic time-variant gain controller receives error-free values.

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The invention relates to a method for controlling a converter having controllable power semiconductors, wherein actual state values {circumflex over (x)}(k) describing the state of the converter are compared with desired state values x  desired  (k), with control difference values being obtained, the control difference values are fed to a control unit, which generates actuating voltage values u(k) at its output, and control electronics provide control signals depending on the actuating voltage values u(k) and transmit said control signals to the power semiconductors of the converter, wherein the control unit generates actuating voltage values u(k) such that the control difference values become as small as possible. 
     Such a method is already known from WO 2008/067784 A1, for example. The method disclosed therein is provided for controlling a multilevel converter for high-voltage direct-current transmission, wherein the converter is a self-commutated converter comprising turn-off power semiconductors. Thus, the converter consists of a bridge circuit formed by power semiconductor valve branches, wherein each power semiconductor valve branch has a series circuit formed by submodules. Each submodule in turn has a power semiconductor circuit interconnected with a capacitor such that either the voltage dropped across the capacitor or else a zero voltage can be generated at the output terminals of each submodule. By virtue of the series circuit formed by the submodules, the voltage dropped across the power semiconductor valve can be set in steps, wherein the level of a step corresponds to the voltage dropped across the capacitor unit of a submodule. 
     BRIEF SUMMARY OF THE INVENTION 
     The invention is based on the object of proposing a method for controlling a converter having controllable power semiconductors by means of which the current control and the converter energy control and the energy balancing can be performed jointly. 
     In order to achieve this object, in a method of the type specified in the introduction, according to the invention the actual state values {circumflex over (x)}(k) are calculated by an observer unit proceeding from the actuating voltage values u(k) and taking account of measured current values x(k), actual state intermediate circuit energy values ŵ(k) are calculated by an estimator unit taking account of measured intermediate circuit energy values w(k) of the positive-side and of the negative-side three-phase voltage source of the converter, wherein the observer unit and the estimator unit model the converter, such that the calculated actual state current values {circumflex over (x)}(k) and actual state intermediate circuit energy values ŵ(k) in the steady state correspond to the fault-free current and intermediate circuit energy values, and the fault-free current and intermediate circuit energy values {circumflex over (x)}(k), ŵ(k) are fed to a control unit embodied as a periodic controller having a periodically time-variant gain. 
     What is essential to the method according to the invention is firstly the use of a model for the observer unit in the form of a mathematical state space model which structurally takes account of all converter currents. What is furthermore essential is the use of the estimator unit for estimating the intermediate circuit energies of the power semiconductor branches or phase modules of the converter, divided into the positive-side and the negative-side three-phase voltage source. One essential advantage of the method according to the invention is that all control aims for the converter are taken into account by said method. By virtue of the multi-variable control provided, superordinate converter energy control present in the prior art and the balancing of the intermediate circuit energies of the positive-side and of the negative-side three-phase voltage source can be obviated. By jointly pursuing all control aims, better control is also possible, which can be effected in a weighted manner in accordance with the importance of the control aims. As a result, the control is also additionally accelerated and a predefined behavior is obtained exactly. 
     On account of the accelerated control achieved, the intermediate circuit energy control and the balancing of the energies of the positive-side and of the negative-side three-phase voltage source can be improved such that either a smaller number of controllable power semiconductors or a lower capacitor capacitance of the converter suffices to control the same power supply system fault situations. This is manifested in lower converter costs. 
     Better control of power supply system fault situations also means a shorter failure time or a lower failure probability, which should be advantageous from an economic standpoint for power supply system operators. 
     In order to achieve the advantages indicated above, it is particularly expedient if an observer unit having a periodically time-variant system model is used, which model, proceeding from the general state equation
 
 {dot over (x)}=A·x+B·u  
 
with x as state variable, {dot over (x)} as time derivative of the state variable, A as system matrix, B as input matrix and u as input variable, has a time-invariant system matrix A PLTV  and a time-variant input matrix B PLTV (t) with
 
                   x   _     PLTV     =     (           x   _                 x   _       α   ⁢           ⁢   β                   x   _       dq     -   1                     w   _       α   ⁢           ⁢   β                   w   _       dq     -   1                   w   _           )       ,         
where x denotes the measured, Park-transformed current, x αβ  denotes the alpha-beta-transformed current and x dq     −1    denotes the doubly Park-inverse-transformed measured current (negative phase sequence system), w αβ  denotes the alpha-beta-transformed, measured intermediate circuit energy value sums of positive-side and negative-side three-phase voltage sources and w dq     −1    denotes the alpha-beta-transformed, measured intermediate circuit energy value differences between positive-side and negative-side three-phase voltage sources, and w denotes the measured intermediate circuit energy values of the entire converter.
 
     Advantageously, the desired state values are desired current values x desired (k) and desired intermediate circuit energy values w desired (k). 
     A further solution for achieving the object indicated above is seen in the fact that, proceeding from the prior art indicated in the introduction, according to the invention the actual state values {circumflex over (x)}(k) are calculated by an observer unit proceeding from the actuating voltage values u(k) and taking account of measured current values x(k), actual state intermediate circuit energy values ŵ(k) are calculated by an estimator unit taking account of measured intermediate circuit energy values w(k) of the positive-side and of the negative-side three-phase voltage source of the converter, wherein the observer unit and the estimator unit model the converter, such that the calculated actual state current values {circumflex over (x)}(k) and actual state intermediate circuit energy values ŵ(k) of the total energy of the converter and the difference in the state intermediate circuit energy values w(k) in the steady state correspond to the fault-free current and intermediate circuit energy values, and the fault-free current {circumflex over (x)}(k) and intermediate circuit energy values ŵ(k) are fed to a control unit embodied as a periodic controller having a periodically time-variant gain. 
     In this alternative solution, advantageously, the desired state values are desired current values x desired (k) and desired intermediate circuit energy values w desired (k). 
     A contribution is advantageously also made to the control accuracy of the method according to the invention if the desired state values are formed from predefined desired values by means of a periodically operating feedforward control unit. 
     The periodically time-variant gain can be achieved in various ways in the periodic controller. It is considered to be particularly advantageous if in the periodic controller the periodically time-variant gain is implemented by means of periodic changeover of controller matrices. 
     In order to obtain a particularly high control accuracy, the actual state values {circumflex over (x)}(k), are calculated by an observer unit proceeding from the actuating voltage values u(k) and the state measurement values y d (k) wherein the observer unit takes account of disturbance effects, such that the actual state values {circumflex over (x)}(k) in the steady state correspond to the undisturbed current measurement values freed of disturbance effects. 
     In this embodiment of the method according to the invention, the observer unit is designed such that the converter is transferred into a mathematical model that takes account of disturbance effects. In this case, the state of the converter is expediently described by the controlled variables, that is to say, for example, the power supply system, DC and circulating currents, wherein the controlled variables are combined in a state vector {circumflex over (x)}(k). The same correspondingly applies to the desired variables, which are likewise combined in a desired vector x desired (k). Proceeding from the actuating voltage values made available on the input side, the observer unit models the converter. In particular, the dynamic behavior of the converter is mathematically simulated, wherein expedient matrices are derived which are applied to the state vector or the vector of the manipulated variables u(k). On the output side of the observer unit, a set of actual state values {circumflex over (x)}(k) is then provided, wherein the actual state values {circumflex over (x)}(k) correspond to state measurement values which are free of disturbance effects in the steady state. The actual state values {circumflex over (x)}(k) correspond in the steady state in other words to undisturbed measurement values of the state of the converter and are fed to the control. According to the invention, the control can therefore be performed relatively precisely. 
     The disturbance effects can be based on power supply system faults, inter alia. Specifically, the input variables of the system have to be measured, wherein the measurement can be faulty. A faulty measurement can also be interpreted as a disturbance variable at the input of the system. 
     Furthermore, deviations in the actuating voltages can arise, which are likewise manifested as disturbance effects. 
     Disturbances at the output act as a disturbance directly on the controlled variables. 
     Component deviations also cause, in the steady-state case, constant deviations which are likewise taken into account as disturbances and compensated for in the method according to the invention. The deviations of the parameters cause a control error which can be mapped onto a steady-state disturbance of the system. 
     Harmonics were also interpreted as disturbances in the present context and corrected by the method according to the invention. 
     Expediently, the observer unit provides, besides the undisturbed actual state values {circumflex over (x)}(k), disturbed state model measurement values ŷ d (k) corresponding to measurable state measurement values y d (k), wherein the state model measurement values ŷ d (k) are compared with state measurement values y d (k) obtained by measurements, with a model measurement value deviation being obtained, the model measurement value deviation is fed to the observer unit on the input side and the modeling of the converter is carried out such that the model measurement value deviation is as small as possible. In accordance with this expedient further development, the modeling of the converter is effected with a feedback, wherein use is made of the fact that the chosen mathematical model of the converter yields not only the undisturbed actual state values {circumflex over (x)}(k) but also the state model measurement values beset by disturbance effects. The state model measurement values therefore correspond to the state measurement values obtainable by real measurements. A comparison of the state measurement values with the state model measurement values, that is to say in other words the formation of the model measurement value deviation between these two variables, therefore provides information about the quality of the modeling. The model measurement value deviation is fed to the observer unit as second input variable. Its minimization therefore improves the control method. In the ideal case, the model measurement value deviation is equal to zero. 
     For expedient further development in this regard, the model measurement value deviation is fed to the observer unit via a feedback unit, which expediently amplifies the model measurement value deviation. If the state of the converter is described by means of a state vector {circumflex over (x)}(k), for example a vector consisting of five currents of the converter, a vector for the model measurement value deviation also arises. In this case, the feedback unit applies a matrix consisting of constants to the vector of the model measurement value deviation. In other words, the model measurement value deviation is amplified by said matrix in a manner that is expedient for the further modeling of the converter with minimization of the model measurement value deviation. 
     Expediently, the converter is modeled with the aid of a state space model in accordance with
 
 {circumflex over (x)}′ ( k+ 1)=Φ {circumflex over (x)}′ ( k )+Γ u ( k )
 
 ŷ   d ( k )= H{circumflex over (x)}′ ( k )
 
wherein {circumflex over (x)}′(k) corresponds to a state vector of the converter including disturbed states, u(k) corresponds to a vector of the actuating voltages, Φ, Γ and H correspond to model matrices, and ŷ d (k) corresponds to a vector of state model measurement values beset by disturbances. k indicates the respective sampling step. The system model chosen is the discrete form of a time-continuous differential equation and is also designated as a difference equation.
 
     In the case of a multilevel converter comprising power semiconductor valve branches interconnected with one another to form a six-pulse bridge, wherein each power semiconductor valve branch consists of a series circuit formed by submodules, wherein each submodule has a power semiconductor circuit and also a capacitor, it suffices to describe the state of the converter with just five currents, since the other currents of the converter can be calculated from the five state variables. The currents occurring at the converter are, for example, power supply system currents, DC currents and also circulating currents between the valve branches of the converter. In order to be able to take account of disturbance effects in the model, the state vector {circumflex over (x)}′(k) is extended by the disturbed state measurement values ŷ d (k) to form {circumflex over (x)}′(k). 
     In order to increase the control accuracy even further, in one advantageous development of the method according to the invention, delay effects are additionally taken into account during the modeling of the observer unit, such that the actual state values {circumflex over (x)}(k) in the steady state correspond to undelayed and undisturbed current measurement values freed of delay effects. 
     A set of actual state values {circumflex over (x)}(k) is provided on the output side of the observer unit, wherein the actual state values {circumflex over (x)}(k), correspond to state measurement values that are free of disturbance and delay effects. The actual state values {circumflex over (x)}(k), correspond in other words to undelayed and undisturbed measurement values of the state of the converter and are fed to the control. According to the invention, therefore, the control can be performed more rapidly without instabilities having to be feared. 
     Expediently, the observer unit provides, besides the undisturbed and undelayed actual state values {circumflex over (x)}(k), disturbed and delayed state model measurement values ŷ d (k) corresponding to measurable state measurement values y d (k) wherein the state model measurement values ŷ d (k) are compared with state measurement values y d (k) obtained by measurements, with a model measurement value deviation being obtained, the model measurement value deviation is fed to the observer unit on the input side and the modeling of the converter is carried out such that the model measurement value deviation is as small as possible. 
     In accordance with this expedient further development, the modeling of the converter is effected with a feedback, wherein use is made of the fact that the chosen mathematical model of the converter yields not only the undisturbed and undelayed actual state values {circumflex over (x)}(k) but also the state model measurement values beset by disturbance and delay effects. The state model measurement values therefore correspond to the state measurement values obtainable by real measurements. A comparison of the state measurement values with the state model measurement values, that is to say in other words the formation of the model measurement value deviation between these two variables, therefore provides information about the quality of the modeling. The model measurement value deviation is fed to the observer unit as second input variable. Its minimization therefore improves the control method. In the ideal case, the model measurement value deviation is equal to zero. 
     In one preferred variant of the development of the method according to the invention, taking account of delay effects comprises taking account of measurement delays that arise during the digital detection of the electric currents of the converter and taking account of actuating delays caused by the control electronics. During the detection of the state measurement values, for example the currents of the converter are measured. The measurement signal obtained in this case is continuously sampled in sampling steps k, with samples being obtained. The samples are subsequently digitized. The modeling of the measurement delay established in this case is expediently effected under the assumption that the measurement delay corresponds to a time duration of four sampling steps. It has been found that such an assumption is expedient for a self-commutated multilevel converter for high-voltage direct-current transmission. 
     In accordance with a further configuration of the invention, an actuating delay τ is modeled in accordance with
 
τ=( l− 1)· T+τ′ 
 
wherein l corresponds to the number of sampling steps whose sum is less than the actuating delay τ. τ′ is designated as the remainder and is always shorter than the time duration between two sampling steps T. In this modeling of the actuating delay, a magnitude of l=2 has proved to be expedient for a multilayer self-commutated converter.
 
     In order to be able to take account of delay effects in the model, the state vector {circumflex over (x)}(k) is extended by the delayed state measurement values ŷ d (k) to form {circumflex over (x)}′(k). 
     In order to achieve a particularly fast control with good stability, in a further advantageous development of the method according to the invention, state intermediate circuit energy values are determined from measured intermediate circuit energy values by means of an estimator unit that has recourse to a signal model of the intermediate circuit energy values, wherein the estimator unit calculates the parameters of the signal model of the intermediate circuit energy values whilst determining in each case a DC variable representing state intermediate circuit energy values of the positive-side and of the negative-side three-phase voltage source of the converter, and state intermediate circuit energy values are fed to the control unit in addition to the state current values. 
     According to the invention, therefore, in addition to the observer unit an estimator unit is present, which is used to determine state intermediate circuit energy values in the form of DC variables by means of a signal model of the intermediate circuit energy values; the calculated state intermediate circuit energy values are combined to form a state intermediate circuit energy vector and are fed to the control unit in addition to the state current vector. The estimator unit therefore models the power semiconductor branches or phase modules or estimates the energy content of the phase modules. Desired intermediate circuit energy values are also combined to form a desired intermediate circuit energy vector. 
     A set of state current values {circumflex over (x)}(k) is provided on the output side of the observer unit, wherein the state current values {circumflex over (x)}(k) correspond to state current measurement values that are free of disturbance and, if appropriate, also delay effects. The state current values {circumflex over (x)}(k) correspond in other words to undelayed and/or undisturbed current measurement values of the converter and are fed to the control. According to the invention, therefore, with regard to the current control variables, the prerequisites for fast control are provided, without instabilities having to be feared in this regard. 
     At the output of the estimator unit, state intermediate circuit energies are present, which are likewise generated rapidly on account of their formation by means of estimation, such that no slow control behavior is caused by the intermediate circuit energy control variables either. 
     In this way, this development of the method according to the invention makes it possible to carry out the control of the converter on the basis of an integrated consideration whilst simultaneously taking account of all controlled variables that are relevant to the control, with an optimum control behavior being obtained, which also includes, in particular, a rapidly proceeding control. 
     In the method according to the invention, advantageously the state intermediate circuit energy values of the power semiconductor valve branches of the positive-side and of the negative-side three-phase voltage source of the converter are respectively individually detected; the parameters of a signal model of the intermediate energy values are calculated by means of a respective parameter estimator of the estimator unit, and the parameters of the positive-side and of the negative-side power semiconductor valve branches that respectively describe a DC component are respectively individually processed further to form the state intermediate circuit energy values. 
     Parameter estimators with a recursive algorithm are preferably used. Such algorithms include the recursive least squares algorithm, the recursive extended least squares algorithm, the recursive method of instrumental variables, the recursive prediction error method and the recursive maximum likelihood method or algorithm. 
     It is furthermore considered to be advantageous if, for determining the DC component of the intermediate circuit energy values, as estimator a parameter estimator with an oscillation model w(t) for the intermediate circuit energy values w(t)=A 0 +A k1 *cos(kωt)+A k2 *sin(kωt) for k=1 to n is used, in which A 0  indicates the DC component of the intermediate circuit energy values and A k1  and A k2  indicate further parameters of the oscillation model and ω indicates the angular frequency of an AC voltage power supply system connected to the converter. 
     The essential advantage of this configuration of the method according to the invention is that in this method the DC component of the intermediate circuit energy values can be determined rapidly on account of the use of the least squares estimator, which results in a good control behavior of the converter overall. This is because the DC component is required for controlling the intermediate circuit energy and for balancing the branches of the converter. If said DC component is determined exactly and rapidly, then as a result the control behavior of the converter overall is also good. If the control of the converter is effected digitally, which is preferred, then the invention makes it possible to achieve the effect that the DC component is respectively available at the present sampling incident or is even available after having already been estimated in advance for the following sampling point. 
     The DC component of the intermediate circuit energy values can be determined particularly rapidly if as estimator a parameter estimator with an oscillation model w(t) for the intermediate circuit energy values w(t)=A 0 +A 11 *cos(ωt)+A 12 *sin(ωt)+A 21 *cos(2ωt)+A 22 *sin(2ωt) is used, in which A 0  indicates the DC component of the intermediate circuit energy values and A 11  and A 22  indicate further parameters of the oscillation model and ω indicates the angular frequency of an AC voltage power supply system connected to the converter. 
     Parameters of different types can be estimated in the method according to the invention. In this case, it is advantageous for obtaining a high accuracy if an oscillation model with time-dependent parameters A 0 (t) to A 22 (t) is used. 
     In order to obtain an estimation that can be carried out relatively simply, it is furthermore advantageous if the time dependence of the parameters is predefined by a linear function or an exponential function. 
     Particularly simply, but possibly with a greater inaccuracy being accepted, the method according to the invention can be carried out with an oscillation model with temporally constant parameters A 0  to A 22 . If the model corresponds well to the actual signal, the method operates accurately even with the simple model. 
     In the context of the invention, the state variables can comprise not only pure current values but also voltages, in particular actuating voltages, or the like or other variables such as the temperature of specific components. In this case, the desired variables always correspond to the state variables since a comparison, that is to say formation of the difference between these variables, would not be possible otherwise. 
     The method according to the invention can be carried out particularly advantageously if the converter used is a multilevel converter having power semiconductor valve branches connected to one another to form a bridge circuit, wherein each power semiconductor valve branch consists of a series circuit formed by submodules and each submodule comprises a circuit formed by power semiconductors and also a capacitor unit arranged in parallel therewith. 
     The invention is also based on the object of developing an arrangement for controlling a converter such as is evident from the international application discussed in the introduction, or generally of a self-commutated converter, to an extent such that the arrangement has a clear control structure and exhibits fast control in conjunction with good stability of the control. 
     In order to achieve this object, the invention proceeds from an arrangement for controlling a converter having a bridge circuit formed by phase module branches each having a series circuit formed by submodules each having a semiconductor circuit with a connected capacitor, comprising a control unit connected by its input to the measurement value output of the converter, said control unit generating actuating voltage values u(k) at its output, and control electronics disposed downstream of the control unit, said control electronics providing control signals in a manner dependent on the actuating voltage values u(k) and transmitting said control signals to the power semiconductors of the converter. According to the invention, an observer unit is situated between the measurement value output of the converter and the input of the control unit ( 16 ), said observer unit calculating the actual state values {circumflex over (x)}(k), proceeding from the actuating voltage values u(k) and taking account of measured current values x(k), an estimator unit is situated between the measurement value output of the converter and the input of the control unit, said estimator unit calculating actual state intermediate circuit energy values ŵ(k), taking account of measured intermediate circuit energy values w(k) of the positive-side and of the negative-side three-phase voltage source of the converter, wherein the observer unit and the estimator unit model the converter, such that the calculated actual state current values {circumflex over (x)}(k) and actual state intermediate circuit energy values in the steady state correspond to the fault-free current and intermediate circuit energy values, and the fault-free current and intermediate circuit energy values {circumflex over (x)}(k), ŵ(k) are supplied to a control unit embodied as a periodic controller having a periodically time-variant gain. 
     Advantages of this arrangement are primarily that all controlled variables that are relevant to the control are taken into account simultaneously, whilst obtaining an optimum control behavior with rapidly proceeding control. 
     The arrangement is particularly advantageous when an observer unit having a periodically time-variant system model is used, which model, proceeding from the general state equation {dot over (x)}=A·x+B·u with x as state variable, {dot over (x)} as time derivative of the state variable, A as system matrix, B as input matrix and u as input variable, has a time-invariant system matrix A PLTV  and a time-variant input matrix B PLTV (t) with 
                   x   _     PLTV     =     (           x   _                 x   _       α   ⁢           ⁢   β                   x   _       dq     -   1                     w   _       α   ⁢           ⁢   β                   w   _       dq     -   1                   w   _           )       ,         
where x denotes the measured, Park-transformed current, x αβ  denotes the alpha-beta-transformed current and x dq     −1    denotes the doubly Park-inverse-transformed measured current (negative phase sequence system), w αβ  denotes the alpha-beta-transformed, measured intermediate circuit energy value sums of positive-side and negative-side three-phase voltage sources and w dq     −1    denotes the alpha-beta-transformed, measured intermediate circuit energy value differences between positive-side and negative-side three-phase voltage sources, and w denotes the measured intermediate circuit energy values of the entire converter.
 
     In a further solution for achieving the object indicated above, according to the invention, an observer unit is situated between the measurement value output of the converter and the input of the control unit, said observer unit calculating the actual state values {circumflex over (x)}(k), proceeding from the actuating voltage values u(k) and taking account of measured current values x(k); an estimator unit is situated between the measurement value output of the converter and the input of the control unit, said estimator unit calculating actual state intermediate circuit energy values ŵ(k), taking account of measured intermediate circuit energy values w(k) of the positive-side and of the negative-side three-phase voltage source of the converter, wherein the observer unit and the estimator unit model the converter, such that the calculated actual state current values {circumflex over (x)}(k) and state intermediate circuit energy values of the total energy of the converter and the difference in the intermediate circuit energy values w(k) of the positive-side and of the negative-side three-phase voltage source of the converter in the steady state correspond to the fault-free current and intermediate circuit energy values, and the fault-free current {circumflex over (x)}(k) and intermediate circuit energy values {circumflex over (x)}(k) are fed to a control unit embodied as a periodic controller having a periodically time-variant gain. 
     Advantages of this arrangement are likewise primarily that all controlled variables that are relevant to the control are taken into account simultaneously, whilst obtaining an optimum control behavior with rapidly proceeding control. 
     Particularly advantageously, in the arrangement according to the invention, a periodic feedforward control unit connected on the output side to a summing circuit disposed upstream of the periodic controller has a period corresponding to the period of the AC current. 
     Furthermore, it is considered to be advantageous if the periodic controller is designed such that its periodically time-variant gain is effected by means of periodic changeover of its controller matrices. 
     Preferably, the observer unit of the arrangement according to the invention is equipped such that it calculates actual state values {circumflex over (x)}(k) proceeding from the actuating voltage values u(k) and state measurement values y d (k) taking account of disturbance effects and/or delay effects in such a way that the actual state values {circumflex over (x)}(k) correspond to current measurement values that are freed of disturbance effects and/or undisturbed in the steady state. 
     In the arrangement according to the invention, preferably an estimator unit that simulates the signal model of intermediate circuit energy values (w(k)) is connected to the output of the converter, and the observer unit and the estimator unit are connected on the output side to actual inputs of the control unit. 
     In one particular advantageous embodiment of the arrangement according to the invention, the converter is a multilevel converter having power semiconductor valve branches connected to one another to form a bridge circuit, wherein each power semiconductor valve branch consists of a series circuit formed by submodules and each submodule comprises a circuit formed by power semiconductors and also a capacitor unit arranged in parallel therewith. 
     The invention and advantages thereof are described below on the basis of exemplary embodiments of the invention with reference to the figures of the drawing, wherein identical reference signs refer to identical components, and wherein 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
         FIGS. 1 to 3  show a schematic illustration of an exemplary converter which is controlled by the method according to the invention, 
         FIG. 4  shows an exemplary embodiment of an arrangement for carrying out the method according to the invention in an illustration of the principles, 
         FIG. 5  shows the same exemplary embodiment in a detailed illustration, 
         FIG. 6  shows an exemplary embodiment of a preferably used estimator unit with conditioning unit disposed downstream, 
         FIG. 7  shows an exemplary embodiment of an alternative conditioning unit, and 
         FIG. 8  shows an alternative configuration of the input part of the arrangement in accordance with  FIG. 4 . 
     
    
    
     DESCRIPTION OF THE INVENTION 
       FIG. 1  schematically shows the construction of a converter  1  to be controlled, said converter being provided for connection to an AC power supply system that is not illustrated pictorially in  FIG. 1 . The converter  1  has six power semiconductor valve branches  2  interconnected with one another to form a six-pulse bridge circuit. In this case, each power semiconductor valve branch  2  extends between an AC voltage connection  3  and a DC voltage connection  4 . Each AC voltage connection  3  is connected to a secondary winding  5  of a transformer (not completely illustrated pictorially), wherein the secondary windings  5  are interconnected with one another to form a star. The voltages U N1 , U N2  and U N3  are dropped across the secondary windings  5 . Furthermore, in each phase an ohmic resistor R, and an inductance L σ , are arranged between the AC voltage connection  3  and the secondary winding  5 , wherein the power supply system currents i N1 , i N2  and i N3  flow. Furthermore, inductances L Kr  and ohmic resistors R Kr  are arranged between each AC voltage connection and the associated phase module or power semiconductor valve branch  2 . The current flowing through the respective power semiconductor valve branch  2  is designated by i p1 , i p2 , i p3 , i n1 , i n2  and i n3 . The voltage dropped overall across the power semiconductor valve branches  2  is designated by u p1 , u p2 , u p3  and u n1 , u n2  and u n3 . The DC voltage connections  4  are part of a DC voltage circuit  6  in which a DC current i d  flows. 
     The positive pole of the DC voltage circuit  6 , said positive pole being illustrated at the top in  FIG. 1 , is connected to the negative pole, illustrated at the bottom, via an ohmic resistor R D , an inductance L D  and also a schematically indicated voltage source  7 . The voltage dropped between the positive pole and the negative pole of the DC voltage circuit  6  is U d0 , and the voltage dropped across the voltage source  7  is U q . 
     The construction of the power semiconductor valve branches  2  is illustrated more precisely in  FIG. 2 . It can be discerned that each power semiconductor valve branch  2  has a series circuit formed by submodules  8 , the construction of which is illustrated in  FIG. 3 . It can be discerned that each submodule  8  has a power semiconductor circuit  9 , which is connected to a submodule capacitor  10 , such that either the voltage U C,Sub  dropped across the submodule capacitor  10  or else a zero voltage can be generated at output terminals  11  and  12  of each submodule  8 . For this purpose, the power semiconductor circuit  9  has two turn-off power semiconductors S 1  and S 2 , which are designed for high voltages and are realized, for example, as IGBT, GTO or the like. A freewheeling diode  13  is connected in parallel in an opposite sense with respect to each turn-off power semiconductor S 1  and S 2 , respectively. 
       FIG. 4  shows an exemplary embodiment of the method according to the invention for controlling a converter in accordance with  FIGS. 1 to 3 . As is generally customary in closed-loop control systems, here as well desired values are compared with actual values, or in other words the difference between a desired value and an actual value is formed, wherein the control difference obtained in this way is subsequently fed to a control unit  16 , to which a feedforward control unit  14  and a mapping unit  14 ′ are assigned in the exemplary embodiments illustrated. The controlled variables of the converter shown in  FIG. 1  are the currents flowing in the converter  1 . In this case, however, it suffices to consider just five currents, since the remaining currents shown in  FIG. 1  can be calculated from the known five currents. 
     All current control variables are combined according to the invention in a state vector {circumflex over (x)}(k); the same correspondingly applies with regard to intermediate circuit energy control variables, which are combined in a state vector ŵ(k). The same correspondingly applies to the desired variables r(t), which are predefined with regard to the currents with the desired values x desired (t) and regarding the intermediate circuit energies with the desired values w(t). The desired values x desired (t) are firstly fed to the feedforward control unit  14 , which maps the desired values x desired (t) onto steady-state actuating voltages u SS (k). In the mapping unit  14 ′, desired state values w desired (k) are formed from the desired intermediate circuit energy values w desired (t). With the aid of the addition unit  15 , the difference between the desired values x desired (k) and w desired (k) and actual state current values {circumflex over (x)}(k) and actual state intermediate circuit energy values ŵ(k) is formed, wherein control difference values are generated, which are fed to the control unit  16 . On the output side, the control unit  16  provides actuating voltages for power semiconductor valve branches  2  of the converter  1  in accordance with  FIG. 1 . The steady-state actuating voltages u ss (k) are added to said actuating voltages by means of an adder  17  and an actual disturbance vector  ρ {circumflex over (ρ)}(k), is subtracted, wherein the actuating voltage vector u(k) is generated in a sampling step k. The actuating voltages of the actuating voltage vector u(k) are then converted into analog actuating voltages u(t) with the aid of a digital/analog converter  18   a  and are finally fed to control electronics  19 , which generate control signals for the power semiconductors S 1 , S 2  of each power semiconductor valve branch  2  in a manner dependent on the respective actuating voltage u(k) (cf.  FIGS. 1 and 3 ). The control signals are finally fed to the converter  1 , whereupon the desired currents and intermediate circuit energies are established, which are in turn symbolized by the state vector x(t) and w(t), respectively. The converter currents are measured by means of sensors (not illustrated), for example with the aid of current converters, wherein the analog/digital converter  18   b  samples the measured signal of the respective current converter and digitizes the samples obtained in this case, such that the state vectors x(k) and w(k) arise at the outputs of the analog/digital converter  18   b  at the sampling instant k, said state vectors comprising, for example, five different currents and intermediate circuit energies, such that the converter  1  is fully characterized. 
       FIG. 4  furthermore shows a disturbance unit  20 , which in the form of an equivalent circuit diagram takes account of the fact that the detected current measurement values are beset by disturbances. Therefore, y d (k) represents a state vector with disturbed current measurement values. This state vector y d (k) is fed to an observer unit  21 , which receives the actuating voltages u(k) as second input signal. The observer unit  21 , which will be discussed in more specific detail later, predicts, with the aid of a mathematical model of the converter  1  that takes account of disturbances, undisturbed actual current values {circumflex over (x)}(k) and provides the latter on the output side. The undisturbed actual current values {circumflex over (x)}(k) are then made available to the control unit  16  via a transformation component  21 ′ disposed downstream of the observer unit  21 . 
     The observer unit  21  furthermore generates at its output actual disturbance values  μ {circumflex over (ρ)}(k), which are processed in the adder  17  in such a way that they are subtracted. 
       FIG. 5  illustrates the exemplary embodiment in accordance with  FIG. 4  in a detailed fashion. 
     It can be discerned that the observer unit  21  has a model unit  22 , with the aid of which the converter  1  is modeled. At an output  22 A of the model unit  22 , a vector {circumflex over (x)}′(k) is provided, which comprises both the undisturbed actual current values {circumflex over (x)}(k), and current model measurement values beset by disturbances. At a further output  22 B of the model unit  22 , current model measurement values ŷ d (k) occur, which correspond to really measured current measurement values y d (k). In this case, the unit  23  cuts out from the vector {circumflex over (x)}′(k) only the disturbed current model measurement values ŷ d (k). Said current model measurement values ŷ d (k) will then be subtracted from the really measured measurement values y d (k) beset by disturbances by means of an adder  24 . The model measurement value deviation obtained in this way is finally fed to a feedback unit  25 , which applies a gain or feedback matrix L to the vector of the model measurement value deviation. The model measurement value deviations are thereby amplified. The amplified model measurement value deviations are finally fed to the model unit  22  at an input  22 C, wherein the feedback is effected such that ŷ d (k) and y d (k) converge. In other words, the modeling of the converter is effected such that the model measurement value deviation becomes minimal. 
     For cutting out the undelayed actual current values {circumflex over (x)}(k), from the state vector {circumflex over (x)}′(k), also comprising delayed measurement values, as output of the model unit  22 , a unit  26  is provided. The output of the unit  26  {circumflex over (x)}′(k) is fed to the adder  15  and thus taken as a basis for the further control. 
     Actual disturbance values {circumflex over (ρ)}(k) are also cut out from the state vector {circumflex over (x)}′(k) by means of a further unit  27  and are fed to the adder  17  such that a subtraction takes place there. 
     The mathematical model used is discussed below. For modeling disturbances, the state vector, that is to say the vector with the undisturbed actual current values, has to be extended by the disturbances. 
     In this case, firstly the conventional state equation is extended by a disturbance v which acts on the input in the system via the input matrix B. The following holds true:
 
 {dot over (x)}=Ax+Bu+Bv   (1)
 
in which x denotes the state variable and A denotes the system matrix.
 
     In addition, the system is intended to follow exactly one constant desired variable r in the steady state (cf.  FIG. 5 ). For the control error e, the following equation
 
 e=Hx−r   (2)
 
can then be established, in which H denotes the output matrix of the system with discretized consideration. In order to be able to design an observer for the disturbance variables, a mathematical model of the disturbance is necessary. A constant disturbance v can be described without problems by equation (3) and the desired variable r can be described by (4).
 
{dot over (v)}=0  (3)
 
{dot over (r)}=0  (4)
 
     In this case, equation (3) in terms of its statement is identical to the indication of the system matrices:
 
A=0 B=0 C=1  (5)
 
     If v and r then fulfill the same equation as in the above case, it is possible to find for the system an equivalent input signal ρ which likewise fulfills the equation. This results in the following:
 
 {dot over (x)}=Ax+B ( u +ρ)  (6)
 
and
 
e=Hx  (7)
 
     The state vector x is then extended by ρ to form 
                       x   _     ρ     =     (           ρ   _               x   _           )             (   8   )               
wherein the following holds true for ρ:
 
{dot over (ρ)}=0  (9)
 
     The situation is more complicated if a disturbance variable model for the positive, negative and zero phase sequence system is intended to be designed for the model unit  22  in order to correct DC current asymmetries or DC components. As is known, these DC disturbance variables appear as disturbances having single and double power supply system frequency after a Park transformation. 
     Therefore, a corresponding model is required for observing these disturbances. As described further above, the same model holds true for the modeling of the equivalent input signal ρ. Then, on the one hand, disturbances of this signal form in the steady state are exactly corrected; on the other hand, desired values of this signal form in the steady state are exactly adjusted by control. The oscillation model for the fundamental angular frequency ω 0  reads as follows in the state space: 
     
       
         
           
             
               
                 
                   
                     
                       
                         A 
                         _ 
                       
                       
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                       
                     
                     = 
                     
                       ( 
                       
                         
                           
                             0 
                           
                           
                             1 
                           
                         
                         
                           
                             
                               - 
                               
                                 ω 
                                 0 
                                 2 
                               
                             
                           
                           
                             0 
                           
                         
                       
                       ) 
                     
                   
                   , 
                   
                     
                       
                         B 
                         _ 
                       
                       
                         ω 
                         0 
                       
                     
                     = 
                     
                       ( 
                       
                         
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                         
                       
                       ) 
                     
                   
                   , 
                   
                     
                       
                         C 
                         _ 
                       
                       
                         ω 
                         0 
                       
                     
                     = 
                     
                       ( 
                       
                         
                           
                             1 
                           
                           
                             0 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     The input matrix B ω0  is zero because the disturbance cannot be influenced, that is to say is not controllable. A model for the observer design can then be established:
 
 {dot over (x)}   ρ   =A   ρ   x   ρ   +B   ρ   u, e=Cx   ρ   (11)
 
     The following holds true in this case: 
     
       
         
           
             
               
                 
                   
                     
                       
                         x 
                         _ 
                       
                       ρ 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               ρ 
                               _ 
                             
                           
                         
                         
                           
                             
                               x 
                               _ 
                             
                           
                         
                       
                       ) 
                     
                   
                   , 
                   
                     
                       ρ 
                       _ 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             ρ 
                           
                         
                         
                           
                             
                               ρ 
                               . 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     The system matrices are then established, which contain the system and disturbance variable model: 
     
       
         
           
             
               
                 
                   
                     
                       
                         A 
                         _ 
                       
                       ρ 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             0 
                           
                           
                             1 
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 ω 
                                 0 
                                 2 
                               
                             
                           
                           
                             0 
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               B 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               A 
                               _ 
                             
                           
                         
                       
                       ) 
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         B 
                         _ 
                       
                       ρ 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                         
                         
                           
                             
                               B 
                               _ 
                             
                           
                         
                       
                       ) 
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         C 
                         _ 
                       
                       ρ 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             
                               C 
                               _ 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     The model is then extended to all frequency ranges. The following is assumed for ρ: 
     
       
         
           
             
               
                 
                   
                     ρ 
                     _ 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             ρ 
                             _ 
                           
                         
                       
                       
                         
                           
                             ρ 
                             
                               ω 
                               0 
                             
                           
                         
                       
                       
                         
                           
                             ρ 
                             
                               2 
                               
                                 ω 
                                 0 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               ρ 
                               . 
                             
                             
                               ω 
                               0 
                             
                           
                         
                       
                       
                         
                           
                             
                               ρ 
                               . 
                             
                             
                               2 
                               
                                 ω 
                                 0 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     The following then holds true for the extended system model matrices: 
     
       
         
           
             
               
                 
                   
                     
                       
                         A 
                         _ 
                       
                       ρ 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                           
                             0 
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               - 
                               
                                 ω 
                                 0 
                                 2 
                               
                             
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             
                               
                                 - 
                                 4 
                               
                               ⁢ 
                               
                                 ω 
                                 0 
                                 2 
                               
                             
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               B 
                               _ 
                             
                           
                           
                             
                               B 
                               _ 
                             
                           
                           
                             
                               B 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               A 
                               _ 
                             
                           
                         
                       
                       ) 
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         B 
                         _ 
                       
                       ρ 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                         
                         
                           
                             
                               B 
                               _ 
                             
                           
                         
                       
                       ) 
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         C 
                         _ 
                       
                       ρ 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             
                               C 
                               _ 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     The model from equation (15) can be extended for the converter under discussion here. Firstly, in ρ all five input variables are combined: 
     
       
         
           
             
               
                 
                   
                     ρ 
                     _ 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             
                               ρ 
                               _ 
                             
                             _ 
                           
                         
                       
                       
                         
                           
                             
                               ρ 
                               _ 
                             
                             
                               ω 
                               0 
                             
                           
                         
                       
                       
                         
                           
                             
                               ρ 
                               _ 
                             
                             
                               2 
                               ⁢ 
                               
                                 ω 
                                 0 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 ρ 
                                 . 
                               
                               _ 
                             
                             
                               ω 
                               0 
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 ρ 
                                 _ 
                               
                               . 
                             
                             
                               2 
                               ⁢ 
                               
                                 ω 
                                 0 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     The elements of ρ then respectively again contain five elements, representative of the disturbances on the five manipulated variables. The system model becomes—with “I” as unit matrix: 
                         A   _     ρ     =     (           0   _           0   _           0   _           0   _           0   _           0   _               0   _           0   _           0   _           I   _           0   _           0   _               0   _           0   _           0   _           0   _           I   _           0   _               0   _             ω   _     0           0   _           0   _           0   _           0   _               0   _           0   _             ω   _     1           0   _           0   _           0   _               B   _           B   _           B   _           0   _           0   _           A   _           )       ,     
     ⁢         B   _     ρ     =     (           0   _               0   _               0   _               0   _               0   _               B   _           )       ,     
     ⁢         C   _     ρ     =     (           0   _           0   _           0   _           0   _           0   _           C   _           )               (   17   )               
wherein
 
ω 0 =−ω 0   2   ·I  and ω 1 =−4ω 0   2   ·I   (18)
 
     According to the same principle, besides positive and negative phase sequence systems, harmonics can also be compensated for by extending the disturbance model, wherein here by way of example
 
ω 2 =−16·ω 0   2   ·I, ω   3 =−25ω 0   2   ·I  and ω 4 =−36ω 0   2   ·I   (19)
 
are considered.
 
     
       
         
           
             
               
                 
                   
                     
                       A 
                       _ 
                     
                     ρ 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           … 
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           … 
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                       
                       
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           … 
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             I 
                             _ 
                           
                         
                         
                           … 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           … 
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           ⋱ 
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                       
                       
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           … 
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           … 
                         
                         
                           
                             I 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                       
                       
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             
                               ω 
                               _ 
                             
                             0 
                           
                         
                         
                           … 
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           … 
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                       
                       
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           ⋱ 
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           ⋱ 
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                       
                       
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           … 
                         
                         
                           
                             
                               ω 
                               _ 
                             
                             4 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           … 
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                       
                       
                         
                           
                             B 
                             _ 
                           
                         
                         
                           
                             B 
                             _ 
                           
                         
                         
                           … 
                         
                         
                           
                             B 
                             _ 
                           
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           … 
                         
                         
                           
                             0 
                             _ 
                           
                         
                         
                           
                             A 
                             _ 
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     This model can be discretized according to known methods, but this will not be presented here in detail, thus affording a system Φ ρ , Γ ρ , H ρ  with time-discrete model parameters that are accessible to practical processing in a data processing system. In this case, the time-discrete model parameter Φ ρ  corresponds to the continuous system parameter B, the time-discrete input matrix Γ ρ  corresponds to the input matrix B, and the time-discrete output matrix H ρ  corresponds to the output matrix C. 
     In order to explain the method developed according to the invention with additional correction of delays, reference is once again made to  FIG. 4  and firstly a situation in which solely delays are intended to be corrected; in this case, the block  20  symbolizes delays that arise unavoidably between the actual measurement instant of the currents of the converter  1  and the further processing and transmission of the current measurement values. These delays are designated as measurement delays or measurement dead times. y d (k) here then therefore represents a state vector with delayed current measurement values. The delayed current measurement values y d (k) are fed to the observer unit  21 , which receives the actuating voltages u(k) as second input signal. The observer unit  21 , which will be discussed in even more specific detail later, predicts, with the aid of a mathematical model for the converter  1  that takes account of both actuating delays and the measurement delays, the undelayed actual current values {circumflex over (x)}(k) and provides the latter on the output side. The undelayed actual current values {circumflex over (x)}(k) are then made available to the control unit  16 . 
     Referring to  FIG. 5 , it is furthermore evident that the model unit  22  provides a vector {circumflex over (x)}′(k) comprising both the undelayed actual current values {circumflex over (x)}(k) and current model measurement values which correspond to the actual current values but are beset with delays ŷ d (k). In other words, current model measurement values ŷ d (k) correspond to really measured current measurement values y d (k). The unit  23  cuts out from the output of the model unit  22  only the delayed current model measurement values ŷ d (k), wherein the current model measurement values ŷ d (k) are subtracted from the really measured measurement values y d (k) beset by delays by means of the adder  24 . The model measurement value deviation obtained in this way is finally fed to the feedback unit  25 , which applies a gain or feedback matrix L to the vector of the model measurement value deviation. The model measurement value deviations are thereby amplified. The amplified model measurement value deviations are finally fed to the model unit  22  as an input, wherein the feedback is effected such that ŷ d (k) and y d (k) converge. In other words, the modeling of the converter is effected such that the model measurement value deviation becomes minimal. 
     For cutting out the undelayed actual current values {circumflex over (x)}(k) from the state vector {circumflex over (x)}′(k), also comprising delayed measurement values, as output of the model unit  22 , the unit  26  is provided. The output of the unit  26  {circumflex over (x)}′(k) is fed to the adder  15  and thus taken as a basis for the further control. 
     The mathematical model used is discussed below. For modeling measurement delays, the state vector, that is to say the vector with the undelayed actual current values, has to be extended by the delayed measurement values. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           x 
                           ^ 
                         
                         _ 
                       
                       ′ 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             
                               
                                 x 
                                 ^ 
                               
                               _ 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   y 
                                   ^ 
                                 
                                 _ 
                               
                               
                                 1 
                                 ⁢ 
                                 d 
                               
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                       
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             
                               
                                 
                                   y 
                                   ^ 
                                 
                                 _ 
                               
                               nd 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     If ŷ d (k) is a vector of the delayed measurement variables, then the following holds true for the delay of one sampling step:
 
 y   1d ( k+ 1)= y ( k )  (22)
 
     In the case of delays of more than one sampling step, it furthermore holds true that
 
 y   2d ( k+ 1)= y   1d ( k )  (23)
 
and
 
 y   d ( k+ 1)= y   nd ( k )  (24)
 
     The following general model can be derived therefrom:
 
 x ( k+ 1)=Φ d   x ( k )+Γ d   u ( k )
 
 y   d ( k )= H   d   x ( k )  (25
 
     Furthermore, the following hold true—with “I” once again as unit matrix: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           Φ 
                           _ 
                         
                         d 
                       
                       = 
                       
                         ( 
                         
                           
                             
                               
                                 Φ 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               … 
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                           
                           
                             
                               
                                 H 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               … 
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                           
                           
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 I 
                                 _ 
                               
                             
                             
                               … 
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                           
                           
                             
                               ⋮ 
                             
                             
                               … 
                             
                             
                               ⋱ 
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                           
                         
                         ) 
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         Γ 
                         _ 
                       
                       d 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               Γ 
                               _ 
                             
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                         
                       
                       ) 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         H 
                         _ 
                       
                       d 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               I 
                               _ 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     Consequently, a system model is available which can be used to design the observer unit  21 . 
     The model unit  22  of the observer unit  21  uses, for modeling the converter  2 , the abovementioned system model in accordance with
 
 {circumflex over (x)}′ ( k+ 1)=Φ {circumflex over (x)}′ ( k )+Γ u ( k )  (27)
 
     The observation error can then be defined as
 
 {tilde over (x)}=x−{circumflex over (x)}′   (28)
 
     In order that the current model measurement values also converge toward the measured real current measurement values, a feedback matrix L is introduced, thus resulting in the following equation:
 
 {circumflex over (x)}′ ( k+ 1)=Φ {circumflex over (x)}′ ( k )+Γ u ( k )+ L ( y ( k )− H{circumflex over (x)}′ ( k ))  (29)
 
     For designing the feedback matrix it is necessary to consider the error equation
 
 {tilde over (x)} ( k+ 1)=(Φ− LH ) {tilde over (x)} ( k )  (30)
 
wherein the dynamic range (Φ−LH) is chosen such that the current model measurement values ŷ d (k) also converge toward the measured measurement values y d (k), to be precise more rapidly than the system dynamic range.
 
     For modeling actuating delays generated by the control electronics  19 , the following system is applied:
 
 x ( k+ 1)=Φ x ( k )+Γ 0   u ( k −( l− 1))+Γ 1   u ( k− 1)
 
     The following holds true for the actuating delay τ
 
τ=( l− 1)· T+τ′ 
 
     The system matrices read as follows: 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         Φ 
                         _ 
                       
                       = 
                       
                         ⅇ 
                         
                           
                             A 
                             _ 
                           
                           ⁢ 
                           T 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           Γ 
                           _ 
                         
                         0 
                       
                       = 
                       
                         
                           ∫ 
                           0 
                           
                             t 
                             - 
                             
                               τ 
                               ′ 
                             
                           
                         
                         ⁢ 
                         
                           
                             ⅇ 
                             
                               
                                 A 
                                 _ 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               t 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ⅆ 
                             s 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             B 
                             _ 
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           Γ 
                           _ 
                         
                         1 
                       
                       = 
                       
                         
                           
                             ⅇ 
                             
                               
                                 A 
                                 _ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   T 
                                   - 
                                   
                                     τ 
                                     ′ 
                                   
                                 
                                 ) 
                               
                             
                           
                           ⁢ 
                           
                             
                               ∫ 
                               0 
                               
                                 τ 
                                 ′ 
                               
                             
                             ⁢ 
                             
                               
                                 ⅇ 
                                 
                                   
                                     A 
                                     _ 
                                   
                                   ⁢ 
                                   x 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ⅆ 
                                 s 
                               
                               ⁢ 
                               
                                 
                                   B 
                                   _ 
                                 
                                 ⁢ 
                                 
                                   
 
                                 
                                 ( 
                                 
                                   
                                     
                                       
                                         
                                           x 
                                           _ 
                                         
                                         ⁡ 
                                         
                                           ( 
                                           
                                             k 
                                             + 
                                             1 
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                           u 
                                           _ 
                                         
                                         ⁡ 
                                         
                                           ( 
                                           
                                             k 
                                             - 
                                             
                                               ( 
                                               
                                                 l 
                                                 - 
                                                 1 
                                               
                                               ) 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                           u 
                                           _ 
                                         
                                         ⁡ 
                                         
                                           ( 
                                           
                                             k 
                                             - 
                                             
                                               ( 
                                               
                                                 l 
                                                 - 
                                                 2 
                                               
                                               ) 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                           u 
                                           _ 
                                         
                                         ⁡ 
                                         
                                           ( 
                                           
                                             k 
                                             - 
                                             1 
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                           u 
                                           _ 
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         = 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       Φ 
                                       _ 
                                     
                                   
                                   
                                     
                                       
                                         Γ 
                                         _ 
                                       
                                       1 
                                     
                                   
                                   
                                     
                                       
                                         Γ 
                                         _ 
                                       
                                       0 
                                     
                                   
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                 
                                 
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                   
                                     
                                       I 
                                       _ 
                                     
                                   
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                 
                                 
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                   
                                     
                                       I 
                                       _ 
                                     
                                   
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                 
                                 
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                   
                                     
                                       I 
                                       _ 
                                     
                                   
                                 
                                 
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     
                                       
                                         x 
                                         _ 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         u 
                                         _ 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         
                                           k 
                                           - 
                                           1 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         u 
                                         _ 
                                       
                                       ( 
                                       
                                         k 
                                         - 
                                         
                                           ( 
                                           
                                             l 
                                             - 
                                             1 
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         u 
                                         _ 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         
                                           k 
                                           - 
                                           2 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         u 
                                         _ 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         
                                           k 
                                           - 
                                           1 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                 
                                 
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                 
                                 
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                 
                                 
                                   
                                     
                                       0 
                                       _ 
                                     
                                   
                                 
                                 
                                   
                                     I 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               
                                 u 
                                 _ 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
           
         
       
     
     The converter can be completely modeled with measurement and actuating delays by combining the modelings shown above. The following arises as a direct representation of the difference equation of the modeled system:
 
 x   τ   d ( k+ 1)=Φ τ   d   x   τ   d ( k )+Γ τ   d   u ( k )
 
 y   d ( k )= H   τ   d   x   τ   d ( k )
 
     The system matrices are established here by way of example for a measurement delay d in sampling steps and an actuating delay of τ=(l−1)·T+τ′ wherein there are also actuating delays which are non-integral multiples of T. 
     
       
         
           
             
               
                 
                   
                     
                       
                         Φ 
                         _ 
                       
                       τ 
                       d 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               Φ 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               
                                 Γ 
                                 _ 
                               
                               1 
                             
                           
                           
                             
                               
                                 Γ 
                                 _ 
                               
                               0 
                             
                           
                           
                             … 
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               H 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               I 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               I 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             ⋮ 
                           
                           
                             ⋮ 
                           
                           
                             ⋮ 
                           
                           
                             ⋱ 
                           
                           
                             ⋮ 
                           
                           
                             ⋮ 
                           
                           
                             ⋮ 
                           
                           
                             ⋱ 
                           
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               I 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               I 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             ⋮ 
                           
                           
                             ⋮ 
                           
                           
                             ⋮ 
                           
                           
                             … 
                           
                           
                             ⋮ 
                           
                           
                             ⋮ 
                           
                           
                             ⋮ 
                           
                           
                             ⋱ 
                           
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               I 
                               _ 
                             
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                       
                       ) 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         x 
                         _ 
                       
                       τ 
                       d 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               
                                 
                                   x 
                                   ^ 
                                 
                                 _ 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 y 
                                 _ 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 y 
                                 _ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   k 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               
                                 y 
                                 _ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   k 
                                   - 
                                   d 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 u 
                                 _ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   k 
                                   - 
                                   l 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               
                                 u 
                                 _ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   k 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 u 
                                 _ 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   35 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         Γ 
                         _ 
                       
                       τ 
                       d 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               I 
                               _ 
                             
                           
                         
                       
                       ) 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       H 
                       τ 
                       d 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               I 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             … 
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     ( 
                     36 
                     ) 
                   
                   ) 
                 
               
             
           
         
       
     
     For the multilevel converter in accordance with  FIG. 1 , l=2 and d=4 are assumed. The following matrices then arise: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           Φ 
                           _ 
                         
                         MMC 
                       
                       = 
                       
                         ( 
                         
                           
                             
                               
                                 Φ 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 
                                   Γ 
                                   _ 
                                 
                                 1 
                               
                             
                             
                               
                                 
                                   Γ 
                                   _ 
                                 
                                 0 
                               
                             
                           
                           
                             
                               
                                 H 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                           
                           
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 I 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                           
                           
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 I 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                           
                           
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 I 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                           
                           
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 I 
                                 _ 
                               
                             
                           
                           
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                             
                               
                                 0 
                                 _ 
                               
                             
                           
                         
                         ) 
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         
                           
                             
                               x 
                               _ 
                             
                             ^ 
                           
                           ′ 
                         
                         MMC 
                       
                       = 
                       
                         ( 
                         
                           
                             
                               
                                 
                                   
                                     x 
                                     ^ 
                                   
                                   _ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   y 
                                   _ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   y 
                                   _ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   y 
                                   _ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   y 
                                   _ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     - 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   u 
                                   _ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   u 
                                   _ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         Γ 
                         _ 
                       
                       MMC 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               0 
                               _ 
                             
                           
                         
                         
                           
                             
                               I 
                               _ 
                             
                           
                         
                       
                       ) 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         H 
                         _ 
                       
                       MMC 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               I 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                           
                             
                               0 
                               _ 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   37 
                   ) 
                 
               
             
           
         
       
     
     With the modeling of the converter that is possible in this way, the undelayed actual current values can be calculated. 
     Assuming this, a system model is obtained which is used to compensate for disturbance variables and additionally measurement value delays by the two observer models described above being combined with one another, wherein the last row/column from the time-discrete model parameter Φ ρ —corresponding to system parameter A ρ  in accordance with equations (13) and (15)—together with the first row/column from the time-discrete model parameter Φ d —cf. equation (26)—overlap. 
     If Φ d   τ′  and Φ′ ρ  are the matrices without the row/column mentioned, then the following compact notation can be chosen for the observation model Φ b : 
     
       
         
           
             
               
                 
                   
                     
                       
                         Φ 
                         _ 
                       
                       b 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               
                                 Φ 
                                 _ 
                               
                               ′ 
                             
                           
                           
                             ⋮ 
                           
                           
                             
                                 
                             
                           
                         
                         
                           
                             … 
                           
                           
                             
                               Φ 
                               _ 
                             
                           
                           
                             … 
                           
                         
                         
                           
                             
                                 
                             
                           
                           
                             ⋮ 
                           
                           
                             
                               
                                 Φ 
                                 _ 
                               
                               d 
                               
                                 r 
                                 ′ 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       Γ 
                       b 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               Γ 
                               ρ 
                               ′ 
                             
                           
                         
                         
                           
                             0 
                           
                         
                         
                           
                             
                               Γ 
                               d 
                               
                                 r 
                                 ′ 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   38 
                   ) 
                 
               
             
           
         
       
     
     The observer design is accordingly standard; the observation equation holds true:
 
 {circumflex over (x)} ( k+ 1)=Φ b   {circumflex over (x)} ( k )+Γ b   u ( k )+ L ( y ( k )− H{circumflex over (x)} ( k )  (39)
 
     The control law is slightly modified; in order to suppress disturbances, the observed disturbance {circumflex over (ρ)} is subtracted from the manipulated variable:
 
 u ( k )= K ( k ) {circumflex over (x)} ( k )−{circumflex over (ρ)}( k )  (40)
 
     With corresponding output matrices it is possible to mask out {circumflex over (x)} and {circumflex over (ρ)} for the implementation:
 
 H   {circumflex over (x)} =(0 . . .  I . . .  0),  H   {circumflex over (ρ)} =( I . . .  0 . . . 0)  (41)
 
     The control loop then has the structure in accordance with  FIG. 5 . 
     As is furthermore shown in  FIG. 5 , intermediate circuit energy values w(t) are also measured here and fed to the input of the analog/digital converter  18   b ; the intermediate circuit energy values are determined by measurement of the voltages U C,Sub  at the submodules (cf.  FIG. 3 ) and via known calculation of the intermediate circuit energy values from said voltages. In this case, too, delays arise as a result of the further processing and transmission of the intermediate circuit energy values (cf. block  20 ). These delayed intermediate circuit energy values w d (k) are made available to an estimator unit  21 A, in which, by means of estimation (on the basis of a signal model of the intermediate circuit energy values), which will be explained in even greater detail below with reference to  FIG. 6 , actual state intermediate circuit energy values ŵ(k) are available at the output of the estimator unit  21 A. By means of a conditioning unit  21 A′ disposed downstream of the estimator unit  21 A, said actual state intermediate circuit energy values ŵ(k) are compared with desired intermediate circuit energy values ŵ desired (t) and the difference is fed to the control unit  16 . The state intermediate energy values w(k) that are wanted are thereupon established at the output of the converter  1 . 
     The estimator unit  21 A illustrated in  FIG. 6  is connected to all six power semiconductor valve branches  2  of the converter  1 , which is symbolized by the numeral “ 6 ” in the schematic illustration. In this case, the connection is effected such that the three respective positive-side (e.g. upper in  FIG. 2 ) power semiconductor valve branches  2  are fed to the estimator unit  21 A separately from the three respective negative-side (lower in  FIG. 2 ) power semiconductor valve branches  2 , in each case symbolized by the numeral “ 3 ”. 
     The estimator unit  21 A comprises a first estimator subunit  31  and a further estimator subunit  32 ; the estimator subunit  31  in turn is equipped with a respective estimator  33 ,  34  and  35 , which are connected to a respective positive-side power semiconductor valve branch  2  of the converter  1  and to which intermediate circuit energy values w 1   p  to w 3   p  of the positive-side power semiconductor valve branches  2  are thus applied. Intermediate circuit energy values win to w 3   n  of the negative-side power semiconductor valve branches  2  are correspondingly fed to estimators  36 ,  37  and  38  of the estimator subunit  32 . 
     The estimators  33  to  38  are in each case parameter estimators, for example least squares estimators. In the exemplary embodiment described here, an oscillation model of the intermediate energy values w(t) is predefined for each parameter estimator  33  to  38 , which model can be described mathematically by the following equation:
 
 w ( t )= A   0 ( t )+ A   11 ( t )*cos(ω t )+ A   12 ( t )*sin(ω t )+ A   21 ( t )*cos(2 ωt )+ A   22 ( t )*sin(2ω t )
 
     In this equation, A 0 (t) indicates the DC component of the intermediate circuit energy values w(t), and A 11 (t) to A 22 (t) indicate further parameters of the oscillation model; ω denotes the angular frequency of the AC voltage power supply system connected to the converter  1 . For the sake of better clarity,  FIG. 6  does not specifically illustrate how a measurement variable corresponding to the frequency of the AC voltage power supply system is applied to the individual least squares estimators. 
     In the oscillation model described by the above equation, time-dependent parameters A 0 (t) to A 22 (t) are used by the least squares estimators, which leads to a high accuracy of the estimation, but is also relatively complex. By way of example, a linear function or an exponential function can be chosen as time dependence. 
     The positive-side intermediate circuit energy values w 1p , w 2p  and w 3p  are accordingly applied to the least squares estimators  33  to  35  assigned to the positive-side three-phase voltage source  2 P. The same correspondingly applies with regard to the estimators  36  to  38 . The estimated intermediate circuit energy values  w   1p ,  w   2p  and  w   3p  and also  w   1n ,  w   2n  and  w   3n  and that occur on the output side are fed to the conditioning unit  21 A′, in which the intermediate circuit energy value sums w p  of the positive-side  2 P and w n  of the negative-side  2 N three-phase voltage source are respectively formed in summing units  39  and  40 . The intermediate circuit energy values  w   1p  and  w   3n  represent average values which, in principle, can also be formed in some other way. In a summing unit  41 , the intermediate circuit energy values  w   p1  to w n3  are added element by element, that is to say  w   p1  and  w   n1 ,  w   p2  and  w   n2  and also  w   p3  and  w   n3 . The three values thus obtained are subjected to an alpha-beta transformation in a transformation element  42 , such that the alpha-beta-transformed, measured intermediate circuit energy value sums w αβ  of the positive-side three-phase voltage source occur at the output of said transformation element. In a difference forming unit  43 , the intermediate circuit energy values  w   p1  to w n3  are subtracted from one another element by element and alpha-beta-transformed, measured intermediate circuit energy value differences w dq     −1    between positive- and negative-side three-phase voltage source  2 P and  2 N are formed therefrom in a further transformation element  44 . The variables, w αβ , w dq     −1   , w p  and w n  are fed together with the variables {circumflex over (x)}(k), {circumflex over (x)} αβ (k), {circumflex over (x)} dq     −1   (k) of the transformation component  21 ′ to the control unit  16  (cf. e.g.  FIG. 5 ) and processed therein. 
     With the conditioning unit  21 A″ illustrated in  FIG. 7 , it is possible to carry out the alternative embodiment of the method according to the invention using the total energy of the converter  1 . For this purpose, in the conditioning unit  21 A″, a further summing unit  45  and a further difference forming unit  46  are disposed downstream of the two summing units  39  and  40 ; at the output of the further summing unit  45 , the total energy w of the converter  1  results from the sum of the intermediate circuit energy values of the positive- and negative-side three-phase voltage source  2 P and  2 N, and, at the output of the further difference forming unit  46 , the difference Δw results from the values for  2 P and  2 N. 
     As shown in  FIGS. 4 and 5 , the output values of the transformation component  21 ′ and of the conditioning unit  21 A′ are fed via the adding unit  15  to the control unit  16 , which is formed by a periodic controller having a periodically time-variant gain. The way in which this controller is embodied in specific detail and the way in which balancing and converter control can be effected by means of the above-described method and arrangement according to the invention are explained below. 
     So-called horizontal balancing can be realized with the aid of DC current asymmetries or circulating DC currents of the converter  1 , without the power supply system or DC current being influenced thereby. Taking as a basis the sums of the energies w 1 , w 2 , w 3  in the three branches of the converter  1 , where w 1 =W p1 +W n1 , w 2 =W p2 +W n2  and w 3 =W p3 +W n3  (cf.  FIG. 6 ), the relationship (41) can then be established in the context of a power consideration: 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               w 
                               . 
                             
                             1 
                           
                         
                       
                       
                         
                           
                             
                               w 
                               . 
                             
                             2 
                           
                         
                       
                       
                         
                           
                             
                               w 
                               . 
                             
                             3 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               
                                 u 
                                 
                                   d 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   0 
                                 
                               
                               + 
                               
                                 
                                   u 
                                   _ 
                                 
                                 1 
                               
                             
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             
                               
                                 u 
                                 
                                   d 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   0 
                                 
                               
                               + 
                               
                                 
                                   u 
                                   _ 
                                 
                                 2 
                               
                             
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             
                               
                                 u 
                                 
                                   d 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   0 
                                 
                               
                               + 
                               
                                 
                                   u 
                                   _ 
                                 
                                 3 
                               
                             
                           
                         
                       
                       ) 
                     
                     · 
                     
                       ( 
                       
                         
                           
                             
                               
                                 i 
                                 _ 
                               
                               1 
                             
                           
                         
                         
                           
                             
                               
                                 i 
                                 _ 
                               
                               2 
                             
                           
                         
                         
                           
                             
                               
                                 i 
                                 _ 
                               
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   41 
                   ) 
                 
               
             
           
         
       
     
     In this equation, {dot over (w)} 1 , {dot over (w)} 2 , {dot over (w)} 3  denote the time derivative of the energies and thus a power in each case, and u d0  denotes the internal DC voltage of the converter; ī 1  to ī 3  and ū 1  and ū 3  are the DC variables in the branches of the converter. If equation (41) is simplified by assuming an operating point ū 1 =ū 2 =ū 3 =ū dAP , then the relationship (41) is simplified to equation (42) below: 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               w 
                               . 
                             
                             1 
                           
                         
                       
                       
                         
                           
                             
                               w 
                               . 
                             
                             2 
                           
                         
                       
                       
                         
                           
                             
                               w 
                               . 
                             
                             3 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       u 
                       
                         d 
                         AP 
                       
                     
                     · 
                     
                       ( 
                       
                         
                           
                             
                               
                                 i 
                                 _ 
                               
                               1 
                             
                           
                         
                         
                           
                             
                               
                                 i 
                                 _ 
                               
                               2 
                             
                           
                         
                         
                           
                             
                               
                                 i 
                                 _ 
                               
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   42 
                   ) 
                 
               
             
           
         
       
     
     After an αβ transformation and permissible omission of the zero phase sequence system, the following then results with regard to horizontal balancing 
                     (             w   .     α                 w   .     β           )     =         (             u     d     A   ⁢           ⁢   P         /   2         0           0           u     d     A   ⁢           ⁢   P         /   2           )       ︸     A     b   ⁢           ⁢   Bal           ·     (           i     Kr   α                 i     Kr   β             )               (   43   )               
in which {dot over (w)} α , {dot over (w)} β  and i Krα , i Krβ  indicate αβ-transformed powers or circulating currents.
 
     If the vertical balancing at the operating point U MMCAP  of the converter  1  is designated by U MMCAP =U N , where u N  denotes the power supply system voltage, then this gives rise to the following in complex notation: 
                     (             w   .     11                 w   .     22                 w   .     33           )     =     Re   ⁢     {       (             u   _     1         0       0           0           u   _     2         0           0       0           u   _     3           )     ·     (             i   _     1   *                 i   _     2   *                 i   _     3   *           )       }               (   44   )               
in which {dot over (w)} 11 , {dot over (w)} 22  and {dot over (w)} 33  denotes the time derivative of the energy on the power supply system side in the three phases, u N1  to u N3  denote the phase voltages, and i 1 * to i 3 * denote complex conjugate power supply system currents. After conversion and transformation whilst resorting to the negative phase sequence system in the circulating current, the following then arises
 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               w 
                               . 
                             
                             
                               d 
                               
                                 - 
                                 1 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               w 
                               . 
                             
                             
                               q 
                               
                                 - 
                                 1 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   - 
                                   
                                     1 
                                     2 
                                   
                                 
                                 ⁢ 
                                 
                                   u 
                                   N 
                                 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 
                                   - 
                                   
                                     1 
                                     2 
                                   
                                 
                                 ⁢ 
                                 
                                   u 
                                   N 
                                 
                               
                             
                           
                         
                         ) 
                       
                       
                         ︸ 
                         
                           
                             A 
                             v 
                           
                           ⁢ 
                           Bal 
                         
                       
                     
                     · 
                     
                       ( 
                       
                         
                           
                             
                               i 
                               
                                 Kr 
                                 
                                   d 
                                   
                                     - 
                                     1 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               i 
                               
                                 Kr 
                                 
                                   q 
                                   
                                     - 
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   45 
                   ) 
                 
               
             
           
         
       
     
     For modeling the converter  1 , the known system model is taken as a basis—here in the dq system:
 
 {dot over (x)}=A   dq   x+B   dq   u, x   dq =( i   N     d      i   N     q      i   d    i   Kr     d      i   Kr     q   )  (46)
 
     If an extension to the αβ and the negative phase sequence system of the circulating current is effected here, then the new state vector reads as follows:
 
 x =( i   N     d      i   N     q      i   d    i   Kr     d      i   Kr     q      i   Kr     α      i   Kr     β      i   Kr     d-1      i   Kr     q-1   )  (47)
 
     The following then holds true for the system matrix: 
                     A   =     (           A   dq         0       0       0       0           0         -       R   Kr       L   Kr             0       0       0           0       0         -       R   Kr       L   Kr             0       0           0       0       0         -       R   Kr       L   Kr             ω           0       0       0         -   ω           -       R   Kr       L   Kr               )       ,           (   48   )               
wherein the signs of ω are opposite to those in A dq . The variables R Kr  and L Kr  are evident from  FIG. 1 .
 
     The following is furthermore summarized: 
     
       
         
           
             
               
                 
                   
                     
                       A 
                       αβ 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               - 
                               
                                 
                                   R 
                                   Kr 
                                 
                                 
                                   L 
                                   Kr 
                                 
                               
                             
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             
                               - 
                               
                                 
                                   R 
                                   Kr 
                                 
                                 
                                   L 
                                   Kr 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                   , 
                   
                     
                       A 
                       
                         dq 
                         
                           - 
                           1 
                         
                       
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               - 
                               
                                 
                                   R 
                                   Kr 
                                 
                                 
                                   L 
                                   Kr 
                                 
                               
                             
                           
                           
                             ω 
                           
                         
                         
                           
                             
                               - 
                               ω 
                             
                           
                           
                             
                               - 
                               
                                 
                                   R 
                                   Kr 
                                 
                                 
                                   L 
                                   Kr 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   49 
                   ) 
                 
               
             
           
         
       
     
     If the following holds true for
 
 u =( u   p     d      u   p     q      u   d    u   n     d      u   n     q   ),  (50)
 
then the following holds true for
 
                     B   dq     =     (           -     1     L   L             0       0         1     L   L           0           0         -     1     L   L             0       0         1     L   L               0       0         -     1     L   d   ′             0       0             -     1     2   ⁢           ⁢     L   Kr               0       0         -     1     2   ⁢           ⁢     L   Kr               0           0         -     1     2   ⁢           ⁢     L   Kr               0       0         -     1     2   ⁢           ⁢     L   Kr                 )             (   51   )               
where R L =1/2 R Kr +R σ , L L =1/2 L Kr +L σ , R′ d =2/3 R Kr +R r  and L′ d =2/3 L Kr +L d  (cf.  FIG. 1 ). The other frequency ranges of the circulating current are linked to one another via the same input variables. This linkage can be expressed by the inverse transformation T dq   −1 (t). The following thus holds true for
 
     
       
         
           
             
               
                 B 
                 ⁡ 
                 
                   ( 
                   t 
                   ) 
                 
               
               = 
               
                 ( 
                 
                   
                     
                       
                           
                       
                     
                     
                       
                         B 
                         dq 
                       
                     
                     
                       
                           
                       
                     
                   
                   
                     
                       
                         
                           
                             T 
                             dq 
                             
                               - 
                               1 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           B 
                           Kr 
                         
                       
                     
                     
                       0 
                     
                     
                       
                         
                           
                             T 
                             dq 
                             
                               - 
                               1 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           B 
                           Kr 
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             T 
                             dq 
                             
                               - 
                               2 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           B 
                           Kr 
                         
                       
                     
                     
                       0 
                     
                     
                       
                         
                           
                             T 
                             dq 
                             
                               - 
                               2 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           B 
                           Kr 
                         
                       
                     
                   
                 
                 ) 
               
             
             , 
             where 
           
         
       
       
         
           
             
               B 
               Kr 
             
             = 
             
               ( 
               
                 
                   
                     
                       - 
                       
                         1 
                         
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             L 
                             Kr 
                           
                         
                       
                     
                   
                   
                     0 
                   
                 
                 
                   
                     0 
                   
                   
                     
                       - 
                       
                         1 
                         
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             L 
                             Kr 
                           
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     The system model A,B(t) is therefore a time-variant system. Since T dq (t) is repeated periodically, this is referred to as a periodically time-variant system, or PLTV system (periodic linear time-variant system). If a matrix A w  is defined in accordance with the following equation (53) 
                           ⁢       A   w     =     (           2       
                   
                   
                   
                       
                   
                   
                   
                   
                       )               (   53   )               
it is possible to describe the system matrix A p2TV  for such a system and the input matrix B PLTV 
 
                         A   _     PLTV     =     (           A   dq         0       0       0       0       0           0         A   αβ         0       0       0       0           0       0         A     dq     -   1             0       0       0           0         A   hBal         0       0       0       0           0       0         A   vBal         0       0       0             A   w         0       0       0       0       0         )       ,     
     ⁢         B   PLTV     ⁡     (   t   )       =     (           B   ⁡     (   t   )               0           0           0           0           0         )                               
and also the state variable x PLTV  and the input variable u PLTV  with
 
     
       
         
           
             
               
                 
                   
                     
                       x 
                       PLTV 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             x 
                           
                         
                         
                           
                             
                               x 
                               αβ 
                             
                           
                         
                         
                           
                             
                               x 
                               
                                 dq 
                                 
                                   - 
                                   1 
                                 
                               
                             
                           
                         
                         
                           
                             
                               w 
                               αβ 
                             
                           
                         
                         
                           
                             
                               w 
                               
                                 dq 
                                 
                                   - 
                                   1 
                                 
                               
                             
                           
                         
                         
                           
                             w 
                           
                         
                       
                       ) 
                     
                   
                   , 
                   
                     
                       u 
                       PLTV 
                     
                     = 
                     u 
                   
                 
               
               
                 
                   ( 
                   55 
                   ) 
                 
               
             
           
         
       
     
     Methods are known for designing optimal controllers for PLTV systems. Recourse is had thereto here in order to make possible a common controller design for the entire converter control including energy control and balancing. The designed controller replaces the function of all controllers which previously fulfilled the corresponding tasks. Detailed descriptions of one method are found in Bittanti, S.; Colaneri, P.; De Nicolao, G.: “The Periodic Riccati Equation”: In: Bittanti, S. (ed.); Laub, A. J. (ed.); Willems, J. C. (ed.): The Riccati Equation. Berlin: 1991 and Gorges, Daniel; Izák Michal; Liu Steven “Optimal Control of Systems with Resource Constraints”. In: Proceedings of the 46 th  IEEE Conference on Decision and Control, 2007, pages 1070-1075. 
     As an alternative to the control of the energy of the positive-side  2 P and of the negative-side  2 N three-phase voltage source, it is also possible to control the deviation between these sources Δw by means of a positive phase sequence system in the circulating current—to be precise as pure circulating active current. The matrix A w  then reads as follows: 
     
       
         
           
             
               
                 
                   
                     A 
                     w 
                   
                   ⁡ 
                   
                     ( 
                     
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           
                             
                               - 
                               
                                 u 
                                 N 
                               
                             
                             s 
                           
                         
                         
                           0 
                         
                       
                       
                         
                           
                             - 
                             
                               u 
                               
                                 N 
                                 p 
                               
                             
                           
                         
                         
                           
                             - 
                             
                               u 
                               
                                 N 
                                 q 
                               
                             
                           
                         
                         
                           
                             u 
                             
                               d 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               0 
                             
                           
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   56 
                   ) 
                 
               
             
           
         
       
     
     In the modeling of the converter  1  from equation (54), A PLTV  is always constant and B PLTV  (t) is periodically time-variant. If sampling is effected 512 times per power supply system period, p=512 holds true. Furthermore, 
                 t   k     =     k   ·       2   ⁢   π       ω   ·   p           ,         
then holds true for the sampling instants. The continuous periodically time-variant system A k , B k  and its continuous weighting matrices Q, N, R can be discretized in a known manner, such that the time-discrete optimization problem is subsequently obtained from equation (5.17):
 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         min 
                         
                           u 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             0 
                           
                           ∞ 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       x 
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       u 
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                             T 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     Q 
                                     k 
                                   
                                 
                                 
                                   
                                     N 
                                     k 
                                   
                                 
                               
                               
                                 
                                   
                                     N 
                                     k 
                                     T 
                                   
                                 
                                 
                                   
                                     R 
                                     k 
                                   
                                 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     x 
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     u 
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     NB 
                     ⁢ 
                     
                       : 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       { 
                       
                         
                           
                             
                               
                                 x 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                               = 
                               
                                 
                                   
                                     Φ 
                                     k 
                                   
                                   ⁢ 
                                   
                                     x 
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                                 + 
                                 
                                   ⁢ 
                                   
                                     u 
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     x 
                                     ⁡ 
                                     
                                       ( 
                                       0 
                                       ) 
                                     
                                   
                                   = 
                                   
                                     ⁢ 
                                     
                                       ( 
                                       0 
                                       ) 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     … 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       
                                         x 
                                         N 
                                         T 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         0 
                                         ) 
                                       
                                     
                                   
                                 
                                 ) 
                               
                               T 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   57 
                   ) 
                 
               
             
           
         
       
     
     In the known method for controller design discussed above, so-called lifting is carried out, which in principle represents a further transformation, in which the p-periodic PLTV system is converted into an LTI system (linear time-invariant system). In this case, the state equation is solved over one period, that is to say p discretization steps: 
     
       
         
           
             
               
                 
                   
                     
                       x 
                       ⁡ 
                       
                         ( 
                         
                           k 
                           + 
                           1 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         
                           
                             Φ 
                             ^ 
                           
                           k 
                         
                         ⁢ 
                         
                           x 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                       + 
                       
                         
                           
                             Γ 
                             ^ 
                           
                           k 
                         
                         ⁢ 
                         
                           
                             u 
                             ^ 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           
                             x 
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 + 
                                 2 
                               
                               ) 
                             
                           
                           = 
                             
                           ⁢ 
                           
                             
                               
                                 
                                   Φ 
                                   ^ 
                                 
                                 
                                   k 
                                   + 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 x 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 
                                   Γ 
                                   ^ 
                                 
                                 
                                   k 
                                   + 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   u 
                                   ^ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                           ⁢ 
                           
                             
                               
                                 
                                   Φ 
                                   ^ 
                                 
                                 
                                   k 
                                   + 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   Φ 
                                   ^ 
                                 
                                 k 
                               
                               ⁢ 
                               
                                 x 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 
                                   Φ 
                                   ^ 
                                 
                                 
                                   k 
                                   + 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   Γ 
                                   ^ 
                                 
                                 k 
                               
                               ⁢ 
                               
                                 
                                   u 
                                   ^ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 
                                   Γ 
                                   ^ 
                                 
                                 
                                   k 
                                   + 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   u 
                                   ^ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   ⋮ 
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           
                             x 
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 + 
                                 p 
                               
                               ) 
                             
                           
                           = 
                             
                           ⁢ 
                           
                             
                               
                                 Ψ 
                                 
                                   
                                     k 
                                     + 
                                     p 
                                   
                                   , 
                                   k 
                                 
                               
                               ⁢ 
                               
                                 x 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 Ψ 
                                 
                                   
                                     k 
                                     + 
                                     p 
                                   
                                   , 
                                   
                                     k 
                                     + 
                                     1 
                                   
                                 
                               
                               ⁢ 
                               
                                 
                                   Γ 
                                   ^ 
                                 
                                 k 
                               
                               ⁢ 
                               
                                 
                                   u 
                                   ^ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                             + 
                           
                         
                       
                     
                     
                       
                         
                             
                           ⁢ 
                           
                             
                               
                                 Ψ 
                                 
                                   
                                     k 
                                     + 
                                     p 
                                   
                                   , 
                                   
                                     k 
                                     + 
                                     2 
                                   
                                 
                               
                               ⁢ 
                               
                                 
                                   Γ 
                                   ^ 
                                 
                                 
                                   k 
                                   + 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   u 
                                   ^ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             + 
                             … 
                             + 
                             
                               
                                 
                                   Γ 
                                   ^ 
                                 
                                 
                                   k 
                                   + 
                                   p 
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   u 
                                   ^ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     + 
                                     p 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                             
                           ⁢ 
                           
                             
                               where 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 Ψ 
                                 
                                   
                                     k 
                                     + 
                                     p 
                                   
                                   , 
                                   k 
                                 
                               
                             
                             = 
                             
                               
                                 
                                   Φ 
                                   ^ 
                                 
                                 
                                   k 
                                   + 
                                   p 
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   Φ 
                                   ^ 
                                 
                                 
                                   k 
                                   + 
                                   p 
                                   - 
                                   2 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               … 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   Φ 
                                   ^ 
                                 
                                 k 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                           ⁢ 
                           
                             
                               
                                 
                                   Ψ 
                                   
                                     
                                       k 
                                       + 
                                       p 
                                     
                                     , 
                                     k 
                                   
                                 
                                 
                                   ︸ 
                                   
                                     Ψ 
                                     k 
                                   
                                 
                               
                               ⁢ 
                               
                                 x 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                             + 
                           
                         
                       
                     
                     
                       
                         
                             
                           ⁢ 
                           
                             
                               
                                 ( 
                                 
                                   
                                     Ψ 
                                     
                                       
                                         k 
                                         + 
                                         p 
                                       
                                       , 
                                       
                                         k 
                                         + 
                                         1 
                                       
                                     
                                   
                                   ⁢ 
                                   
                                     
                                       Γ 
                                       ^ 
                                     
                                     k 
                                   
                                   ⁢ 
                                   
                                     Ψ 
                                     
                                       
                                         k 
                                         + 
                                         p 
                                       
                                       , 
                                       
                                         k 
                                         + 
                                         2 
                                       
                                     
                                   
                                   ⁢ 
                                   
                                     
                                       Γ 
                                       ^ 
                                     
                                     
                                       k 
                                       + 
                                       1 
                                     
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   … 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     
                                       Γ 
                                       ^ 
                                     
                                     
                                       k 
                                       + 
                                       p 
                                       - 
                                       1 
                                     
                                   
                                 
                                 ) 
                               
                               
                                 ︸ 
                                 
                                   
                                     Γ 
                                     ^ 
                                   
                                   k 
                                 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     
                                       
                                         u 
                                         ^ 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         u 
                                         ^ 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         
                                           k 
                                           + 
                                           1 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     ⋮ 
                                   
                                 
                                 
                                   
                                     
                                       
                                         u 
                                         ^ 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         
                                           k 
                                           + 
                                           p 
                                           - 
                                           1 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     It is then possible to use known optimal controller design methods for LTI systems. The result is a p-periodic controller. The control unit  16  therefore has periodically time-variant gains. The implementation can take place, for example, by periodic changeover of the controller matrices of K 1  . . . K 512 . 
     If the arrangement according to the invention uses an input structure as illustrated in  FIG. 8  with a control unit  16  as periodic controller between the transformation component  21 ′ or the conditioning unit  21 A′ and the adding unit  15 , then it is also possible to use a periodic feedforward control unit  50  with a transfer response N(k)
 
 N ( k )= N   v   2   +K   k   ·N   x   (59)
 
wherein N v  denotes the transfer property of the feedforward control unit  14  and N x  denotes the transfer property of the mapping unit  14 ′ and K k  denotes the control response of the control unit  16  in accordance with  FIG. 4 .
 
     An observer which takes account of disturbances, harmonics, measurement and actuating dead times is made possible according to the invention. By means of such an observer, a control structure embodied as state control, for example, can provide undelayed estimated measurement values and, with the aid of the determined disturbances and harmonics, indirectly compensate for these. The overall control thus acquires the ability to compensate for different harmonics and disturbances in the positive and negative phase sequence and αβ system, without the response to desired value changes being adversely influenced. 
     As a result of accelerated control and fast disturbance variable compensation, the intermediate circuit energy control and the balancing of the energies of the upper and lower three-phase voltage sources can be improved such that in comparison with known solutions, either a smaller number of submodules per branch or a lower capacitor capacitance suffices to control the same power supply system fault situations. A smaller number of modules or a lower capacitor capacitance is manifested in lower converter costs. 
     The possibility for harmonic compensation furthermore affords the advantage that economic utilization of the converter is achieved since acquiring this ability means that power supply system filters of active or passive type can be obviated. 
     Better control of power supply system fault situations means a shorter failure time or lower failure probability, which may be an advantage from an economic standpoint for power supply system operators.