Patent Publication Number: US-9407162-B2

Title: Method for designing power controller, power controller, and power control device

Description:
TECHNICAL FIELD 
     The present invention relates to a power control device which is used for a power supply device which supplies alternating power to a load device, and relates to a power controller and a method for designing the power controller. 
     BACKGROUND ART 
     Recent years have seen widespread use of so-called distribution-type power supply devices such as photovoltaic power generating devices, fuel cells, storage batteries etc. These power supply devices are capable of converting direct current power to alternating current power through power control devices having an inverter, and supplying power as current sources interconnected with commercial use systems. 
     In addition, some of these power supply devices have independent operation functions for operating as a voltage source similarly to an Uninterruptible Power Supply (UPS). The power supply devices having such independent operation function is capable of supplying power independently from any commercial use system even when power supplied from the commercial use system stops due to a blackout or an accident. 
     CITATION LIST 
     Patent Literature 
     
         
         [PTL 1] 
       
    
     Japanese Unexamined Patent Application Publication No. 2006-146525 
     Non Patent Literature 
     
         
         [NPL 1] 
       
    
     “State-space solutions to standard H2 and H∞control problems”, written by Doyle, John C. and Glover, Keith and Khargonekar, Pramod P. and Francis, and Bruce A., IEEE Transactions on Automatic Control, 1989, vol. 34, No. 8, p. 831-847 
     SUMMARY OF INVENTION 
     Technical Problem 
     In general, an UPS or a distribution-type power supply device is connected to a distribution system that is small compared to a commercial use system and has small impedances of a distribution line and loads connected thereto in an office, a commercial use establishment, an apartment house, a detached house, etc. Here, a distribution system means a system composed of distribution lines in a house such as a detached house and an apartment house or an establishment such as a commercial use establishment etc., and does not mean a distribution network from a distribution point of a so-called power company to power consumers. 
     For this reason, when a power supply device connected to such a distribution system operates as a voltage source, there is a possibility that a distortion in voltage waveform of an output from the power supply device or a decrease in voltage occurs due to a change in the impedances of devices connected to the power supply device, and the connected devices may not accurately operate. 
     The present invention was made to solve the above-described problems, and has an object to provide a method for designing a power controller which stably operates as a voltage source even when it is impossible to precisely identify the impedances of the distribution line and loads connected to the power supply device. 
     Solution to Problem 
     In order to solve the above-described problems, a power controller designing method according to an aspect of the present invention is for designing a power controller which receives, as an input, a difference between a voltage reference value and an output voltage value output from a control target including an inverter, and outputs, to the control target, a control output for conforming the output voltage value to the voltage reference value, and the power controller designing method includes: setting a weighting function based on an amount of change in impedance of the control target; and determining, for the power controller, a transfer function composed of a transfer function of an internal model obtainable by performing Laplace transform on the voltage reference value and a transfer function of a partial controller, the transfer function of the partial controller being for outputting the control output after receiving, as an input, an output of the transfer function for the internal model, wherein the determining includes determining the transfer function of the partial controller using an H∞control theory and determining, for the power controller, the transfer function of the partial controller by calculating a product of the transfer function of the partial controller and the transfer function of the internal model, so as to reduce (i) a first amount of control obtainable by multiplying the control output and the weighting function and (ii) a second amount of control that is an output of the transfer function of the internal model. 
     These general and specific aspects may be implemented in the form of a system, a method, an integrated circuit, a computer program, or a recording medium, or any combination of systems, methods, integrated circuits, computer programs, or recording media. 
     Advantageous Effects of Invention 
     The power controller designed using the power controller designing method according to the present invention is capable of outputting a voltage with small distortion and stably operating the load device even when it is impossible to accurately identify the impedances of a distribution line and a load. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a diagram illustrating a control block of a conventional power control device. 
         FIG. 2  is a diagram illustrating an entire system configuration of a power supply device including a power control device according to an embodiment. 
         FIG. 3  is a block diagram illustrating a functional structure of the power control device according to the embodiment. 
         FIG. 4  is a block diagram illustrating a functional structure of a power controller according to the embodiment. 
         FIG. 5  is a diagram illustrating an example of the waveform of a current which is consumed by load devices. 
         FIG. 6  is a block diagram illustrating a structure of a model of a power control device which is used when a power controller is designed as an H∞controller. 
         FIG. 7  is a block diagram of targets which are controlled by the power control device according to the embodiment. 
         FIG. 8  is a diagram illustrating an example of valid power which is consumed by the load devices and invalid power. 
         FIG. 9  is a flowchart of a method for designing the power controller according to the embodiment. 
         FIG. 10  is a Bode diagram of a weighting function W T  (s) according to the embodiment. 
         FIG. 11  is examples of control target model parameters at the time when the power controller for the power control device according to the embodiment is designed. 
         FIG. 12  is a block diagram obtained by performing equivalent conversion on the block diagram illustrated in  FIG. 6 , using a generalized plant G (s). 
         FIG. 13  is a Gain diagram of the power controller according to the embodiment. 
         FIG. 14  is a diagram illustrating a result of simulation of output by the power control device including the power controller according to the embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     (Underlying Knowledge Forming Basis of the Present) Disclosure 
     When a power supply device connected to a distribution system smaller than a commercial use system operates as a voltage source, a distortion occurs in the voltage waveform of an output from the power supply device and a voltage decreases due to changes in the impedances of devices connected to the power supply device. The distortion in the voltage waveform and decrease in the voltage may cause a problem that any of the devices connected to the power supply device may not operate normally. 
     In view of the problem, Patent Literature 1 discloses a technique for controlling an inverter device illustrated in  FIG. 1 . A voltage change compensating block  1501  illustrated in the diagram feeds back a current value obtainable from a current sensor  7  to a controller which controls a voltage source  1 . In this way, the voltage change compensating block  1501  compensates a voltage by the amount of change in voltage due to the impedances of a distribution line and load devices connected to the inverter device. According to the control technique, it is possible to calculate the amount of decrease in voltage based on the impedances and current values of the distribution line and load devices, and prevent the voltage from decreasing by adding the calculated amount of decrease to a voltage instruction value based on the load voltage detection. 
     In this control technique, there is a need to set impedance values for the distribution line and loads in a control block. For this reason, there is a need to accurately calculate the impedances of the distribution line and loads at the time of designing the controller. However, it is difficult to know in advance the impedance of the distribution line of a system to which the power supply device is connected, and to identify loads to be connected to the power supply device. For this reason, it is impossible to set accurate impedance values to the control block, and thus cannot completely compensate a decreased voltage. 
     In addition, Patent Literature 1 describes that a change and an error in impedance can be corrected using a feedback method. However, based on the internal model principle, the use of only the feedback method is insufficient for such correction. In other words, in order that the power supply device outputs a voltage of a sine wave, the control block needs to have a transfer function including a term of (S 2 +ω 2 ) in the denominator obtained by performing Laplace transform on a sine wave so that trackability is compensated. 
     Furthermore, with the mere feedback structure as in Patent Literature 1, it is impossible to ensure robust stability to a modeling error (an unconceivable change or error in impedance) and a disturbance. Accordingly, when a rectifier load or the like is connected to the power supply device, a voltage waveform with a superimposed distortion due to a harmonic current is to be generated. 
     In this way, when an output voltage of the power supply device has a voltage decrease and a harmonic distortion, the load device may not operate normally. In addition, the voltage decrease and harmonic distortion in the output voltage of the power supply device may cause an overheat and a breakdown of the load device. 
     The present invention was made to solve problems like this, and can be implemented as a power controller for a power supply device providing robust stability and trackability even when it is impossible to accurately identify impedances of the distribution line and the load which are connected. 
     In order to solve the above-described problems, a power controller designing method according to an aspect of the present invention is for designing a power controller which receives, as an input, a difference between a voltage reference value and an output voltage value output from a control target including an inverter, and outputs, to the control target, a control output for conforming the output voltage value to the voltage reference value, and the power controller designing method includes: setting a weighting function based on an amount of change in impedance of the control target; and determining, for the power controller, a transfer function composed of a transfer function of an internal model obtainable by performing Laplace transform on the voltage reference value and a transfer function of a partial controller, the transfer function of the partial controller being for outputting the control output after receiving, as an input, an output of the transfer function for the internal model, wherein the determining includes determining the transfer function of the partial controller using an H∞control theory and determining, for the power controller, the transfer function of the partial controller by calculating a product of the transfer function of the partial controller and the transfer function of the internal model, so as to reduce (i) a first amount of control obtainable by multiplying the control output and the weighting function and (ii) a second amount of control that is an output of the transfer function of the internal model. 
     According to the power controller designing method, it is possible to provide the power controller capable of ensuring robust stability and increasing load trackability to impedance changes and outputting a voltage with little distortion even when it is impossible to identify the impedances of the distribution line and the load. In other words, the power supply device using the power controller is capable of stably operating the load device. 
     In addition, the voltage reference value may be represented as a sin function, and the transfer function of the internal model may be obtainable by performing Laplace transform on the sin function. 
     In this way, with the term of (S 2 +ω 2 ) in the denominator, the transfer function of the internal model has an increased output voltage trackability based on the internal model principle. 
     In addition, the control target may include at least one of a filter, a distribution line, or a load device connected to an output of the inverter. 
     In addition, in the setting, the weighting function may be set based on the amount of change, the amount of change being a difference between a minimum impedance conceivable for the control target and a maximum impedance conceivable for the control target. 
     Furthermore, the control target may include a filter, a distribution line, and a load device which are connected to an output of the inverter, and in the setting, when impedances of the filter and the distribution line which are connected to the output of the inverter are determined to be nominal models, the weighting function may be set based on the amount of change, the amount of change being a difference between a combined impedance of the nominal models and a maximum combined impedance of the filter, the distribution line, and the load device which are connected to the output of the inverter. 
     In addition, a power controller according to an aspect of the present invention includes: a matrix storage unit configured to store a coefficient matrix for representing, as a state space, a transfer function for the power controller determined using the power controller designing method; a state storage unit for storing a vector representing an internal state in the state space; and an operating unit configured to calculate the control output based on a difference between the voltage reference value and the output voltage value, the vector representing the internal state stored in the state storage unit, and the coefficient matrix. 
     With the power controller, it is possible to ensure robust stability and increase load trackability to impedance changes and outputting a voltage with little distortion even when it is impossible to identify the impedances of the distribution line and the load. In other words, the power supply device using the power controller is capable of stably operating the load device. 
     In addition, the power controller may have gain frequency characteristics including: a gain shown in an upward convex in a graph in a frequency band of the voltage reference value; and a gain at or below 0 decibel in a frequency band in which impedances of the distribution line and the load device connected to the power controller change. 
     In addition, the power controller may have gain frequency characteristics that a gain is at or below 0 decibel and is shown as a downward convex in a resonant frequency band of an LC filter included in the control target. 
     Furthermore, a power control apparatus according to an aspect of the present invention includes: the power controller; and an inverter which is controlled by the control output by the power controller. 
     According to the power controlling device, it is possible to ensure robust stability and increase load trackability to impedance changes and outputting a voltage with little distortion even when it is impossible to identify the impedances of the distribution line and the load, and thus to cause the load device to operate stably. 
     In addition, the present invention may be implemented as a program, and/or a computer-readable recording media having the program recorded thereon. 
     Hereinafter, an embodiment is described with reference to the drawings. 
     Each of the exemplary embodiments described below shows a general or specific example. The numerical values, elements, the arrangement and connection of the elements, steps, the processing order of the steps etc. shown in the following exemplary embodiment are mere examples, and therefore do not limit the present invention. Therefore, among the elements in the following exemplary embodiment, elements not recited in any one of the independent claims which define the most generic concept are described as arbitrary elements. 
     [Description of Embodiment] 
       FIG. 2  is a diagram illustrating an entire system configuration of a power supply device including a power control device according to an embodiment. 
     As shown in  FIG. 2 , the power supply device  101  according to this embodiment includes: a storage battery  105  as a direct current power source and a power control device  102 . 
     The storage battery  105  is a secondary battery. The storage battery  105  is a lithium ion battery, a lead battery, a redox flow battery, or the like, as a non-limiting example. 
     The power control device  102  converts direct current power output from the storage battery  105  to alternating current power. The power control device  102  is connected to a distribution switchboard/power switchboard  107 , and the distribution switchboard/power switchboard  107  is further connected to a load device  108 . The alternating current power output by the power control device  102  is supplied to the load device  108  via the distribution switchboard/power switchboard  107 . 
     Next, the power control device  102  is described in detail. 
     The power control device  102  is composed of the power controller  103  and the inverter  104 . 
     The power controller  103  controls the inverter  104  by outputting a control output u, based on an output voltage value and an output current value of the power supply device  101  which are detected by the voltage/current sensor  106 . For example, the power controller  103  controls the inverter  104  by the control output u using a pulse width modulation. 
     The inverter  104  converts the direct current power from the storage battery  105  to alternating current power based on the control output u from the power controller  103 , and outputs the alternating current power. 
     The voltage value and current value of the power supply device  101  change depending on the kind and number of load devices  108  which are connected thereto. For this reason, the power controller  103  controls the inverter  104  so that an expected voltage waveform is output from the power supply device  101  while measuring the output voltage and output current from the power supply device  101 . 
     Next, the functional structure of the power control device  102  is described in detail with reference to  FIG. 3 . 
       FIG. 3  is a block diagram illustrating the functional structure of the power control device  102 . 
     As shown in  FIG. 3 , the power control device  102  includes: the power controller  103 ; the inverter  104  connected to the storage battery  105 ; and the filter  201 . 
     The inverter  104  outputs power to the distribution system via the filter  201 , based on the control output u of the power controller  103 . At this time, the inverter  104  operates such that a momentary voltage at the time of output to the distribution system matches (conforms to) a voltage reference value which is given as an instruction from the power controller  103 . The inverter  104  includes four switching elements which are formed by full bride connection and each of which includes diodes connected in parallel in a reversed direction. Here, the inverter  104  is not limited to be the inverter configured in this way. In other words, the inverter  104  may be configured differently. 
     When power is output from the inverter  104 , the power changes a voltage of a direct current line through which the inverter  104  and the storage battery  105  are connected. The power output from the inverter  104  takes a value that may be positive or negative. 
     A case where the power output from the inverter  104  is a positive value indicates that the inverter  104  discharges power to a distribution line. In this case, the voltage value of the direct current line decreases, and thus the storage battery  105  discharges power to compensate power corresponding to the decrease. 
     In addition, a case where the power to be output from the inverter  104  has a negative value indicates that power is charged from the distribution line to the inverter  104 . In this case, the voltage value of the direct current line increases, and thus the storage battery  105  charges power to compensate power corresponding to the increase. 
     The filter  201  is mounted between the inverter  104  and the distribution line, and has a function for removing harmonic components of a voltage to be output from the inverter  104 . The filter  201  is normally composed of a reactor and a capacitor, and has properties of inductance, capacitance, etc. In addition, the filter  201  may have a structure having a resistor. 
     When a difference between a voltage reference value Vref and an output voltage V is input, the power controller  103  calculates a control output u, and outputs the control output u to the inverter  104 . In other words, the power controller  103  has a feedback loop for obtaining an output of the inverter  104  through the filter  201 . 
     More specifically, a signal e to be input to the power controller  103  is described according to Expression (1) below. 
     [Math. 1]
 
 e =voltage reference value Vref−output voltage value V  Expression (1)
 
     With the feedback loop, an output voltage value to be output from the inverter  104  through the filter  201  is controlled to follow a voltage reference value. 
     Next, with reference to  FIG. 4 , a structure of the power controller  103  is described in detail. 
       FIG. 4  is a block diagram illustrating the functional structure of the power controller  103 . 
     As shown in  FIG. 4 , the power controller  103  includes: an operating unit  301 ; a matrix storage unit  302 ; and a state storage unit  303 . 
     The matrix storage unit  302  stores a coefficient matrix for representing, as a state space, a transfer function determined according to a method of designing the power controller  103  according to this embodiment. The matrix storage unit  302  is, specifically, a Random Access Memory (RAM), a Read Only Memory (ROM), a Static Random Access Memory (SRAM), or the like. It is to be noted that a method for determining a coefficient matrix is described later. 
     The state storage unit  303  is a storage unit for storing a vector indicating an internal state in a state space. The state storage unit  303  is, specifically, a RAM or the like. It is to be noted that a specific example of a vector indicating an internal state is described later. 
     The operating unit  301  calculates a control output u, based on (i) a signal e which is a difference between a control target value (a voltage reference value) input to the power controller  103  and an output voltage value output by the inverter  104  through the filter  201 , (ii) a vector x representing an internal state stored in the state storage unit  303 , and a coefficient matrix stored in the matrix storage unit  302 . 
     More specifically, the operating unit  301  multiplies a first coefficient matrix A K  stored in the matrix storage unit  302  and a vector x [n] representing an internal state in a certain point of time n (n is an integer). 
     Next, the operating unit  301  multiplies a second coefficient matrix B K  stored in the matrix storage unit  302  and a signal e [n] obtained by the power controller  103  in a certain point of time n. 
     Next, the operating unit  301  calculates a vector x [n+1] indicating an internal state in a point of time next to n (that is, n+1 point of time), by adding these two multiplication results. In other words, the vector x [n+1] indicating the internal state is represented according to Expression (2) below. 
     [Math. 2]
 
 x[n+ 1]= Ax[n]+Be[n]   Expression (2)
 
     Next, the operating unit  301  calculates a control output u [n] at an n point of time, by multiplying a third coefficient matrix C K  stored in the matrix storage unit  302  and a vector x [n] representing an internal state at the n point of time. In other words, the control output u [n] is represented according to Expression (3) below. 
     [Math. 3]
 
 u[n]=Cx[n]   Expression (3)
 
     It is to be noted that coefficient matrices A K , B K , and C K  are calculated as shown in Non-patent Literature 1. 
     Next,  FIG. 5  illustrates waveforms of a voltage and a current at the time when a rectifier load or a pure resistor load is connected as a load device  108  to a stand-alone outlet of a photovoltaic power generating device on the market. 
       FIG. 5  is a current waveform at the time when a rectifier load or the like is connected as the load device  108 . 
     As shown in  FIG. 5 , the current waveform becomes non-linear according to changes in the load, which produces distortion in the voltage waveform. 
     It is concerned that the distortion in the voltage waveform places various kinds of influence on the load device. For example, when the load device  108  is a device such as a washing machine having an induction motor load, the distortion in the voltage waveform causes a change in the number of turns or overheat. In addition, when the load device  108  is a device having a rectifier load such as a television receiver, the distortion in the voltage waveform causes a flicker in a video or a malfunction of a device. In addition, when the load device  108  is a fluorescent lamp, a distortion in the voltage waveform may cause a burnout in a ballast or a burnout in a capacitor. For this reason, the power controller  103  in the inverter  104  in the power supply device  101  is desired to have a robust stability. Here, the robust stability means that it is possible to output a voltage waveform having a small distortion when it is unclear that the inverter  104  does not have impedances of the distribution line and the load, or even when the impedances change. 
     In view of this, a description is given of a method for designing the power controller  103  which is robust to a change in impedance and is capable of increasing trackability to a voltage reference value Vref provided as a sine wave. More specifically, an H∞controller is used as a model for the power controller  103 . The H∞controller constitutes the related art to the present invention capable of balancing a target trackability and robustness. The following description explains a method for determining various kinds of parameters that are necessary at the time when the H∞controller is mounted, as a method for designing the power controller  103 . 
       FIG. 6  is a block diagram illustrating a structure of a model of a power control device  102  which is used when the power controller  103  is designed as the H∞controller. 
     Here, K (s) denotes a transfer function of the power controller  103  included in the power control device  102  illustrated in  FIG. 3 . More specifically, the K (s) corresponds to a model representing a dynamic characteristic of the power controller  103 . The K (s) is composed of a transfer function M (s) of an internal model  501  and a transfer function K′ (s) of a partial controller  502 . The K (s) is designed by appropriately determining parameters included in a transfer function P (s) of a control target  503  and a weighting function  504  W T  (s). 
     First, the internal model  501  is described. 
     According to an internal model principle, in a servo problem in which an output of a control target is caused to track a target value, an open loop transfer function composed of a controller and a control target needs to have the same polarity with a target generator. 
     In this embodiment, the target value is a sine wave (sin function) of 60 Hz or 50 Hz which is a voltage reference value Vref (in the following descriptions in this embodiment, the frequency of the voltage reference value is assumed to be 60 Hz). Accordingly, the open loop transfer function needs to include a denominator having a term of S 2 +ω 2  which is a Laplace transform of the sin function. The transfer function M (s) of the internal model  501  is a transfer function indulging a denominator having a term of S 2 +ω 2 , and is represented as, for example, Expression (4) below. 
     [Math. 4]
 
 M ( s )= k 1/( s   2 +ω 2 )  Expression (4)
 
     Here, ω is an angular frequency which is given as 2*n*frequency. 
     Here, k1 is a coefficient which is set at the time of design, and s is a variable in Laplace transform. It is to be noted that Expression (4) has a form obtained by performing constant multiplication on Laplace-transformed sin function. Likewise, an expression having a form obtained by performing constant multiplication on Laplace-transformed cos function is also possible. In other words, M (s) may be a transfer function obtained by multiplying a term of s with a denomination of Expression (4). 
     The transfer function K′ (s) of the partial controller  502  is a communication function which is derived according to the H∞control theory to be described later. The method for determining a transfer function of the partial controller  502  is described in detail later. 
     P (s) is a transfer function of the control target  503 . 
       FIG. 7  is a block diagram representing details of the transfer function P (s) of the control target  503 . The transfer function P (s) of the control target  503  is composed of an inverter block  601 , a filter block  602 , and a load device block  603 . 
     The inverter block  601  is a transfer function representing a dynamic characteristic of the inverter  104  in  FIG. 3 . 
     The filter block  602  is a transfer function representing a dynamic characteristic of the filter  201  in  FIG. 3 . 
     The load device block  603  is a transfer function representing an impedance of the load device  108  in  FIG. 2 . 
     The inverter block  601  and the filter block  602  are respectively represented as, for example, a first and second order lag systems in Expressions (5) and (6). 
     [Math. 5]
 
 P   INV ( s )=1/( T   INV   *s+ 1)  Expression (5)
 
[Math. 6]
 
 P   filter ( s )=1/( L*C*s   2 +1)  Expression (6)
 
     Here, T INV  denotes a time constant of the inverter  104 , L denotes an inductance component of the filter  201 , and C denotes a conductance component of the filter  201 . 
     Next, a description is given of a method for representing the load device  108  as the load device block  603  according to a transfer function representation. 
       FIG. 8  illustrates examples of valid power P and invalid power Q at the time when the load device  108  is actually operated. In the diagram, the valid power P reaches a maximum value when P is 280 [W], and Q is 310 [Var]. Expression (7) represents a relationship between P and an output voltage V and a resistance R, and Expression (8) represents a relationship between Q and an inductive reactance X. 
     [Math. 7]
 
 P =V 2   /R   Expression (7)
 
[Math. 8]
 
 Q =V 2   /X   Expression (8)
 
     When the output voltage V is set to 101 [V], and the value of Q is substituted, R and X are calculated respectively as 36.43 and 32.91. In addition, when 2*n*60 Hz is substituted as an angular frequency ω in Expression (9) which is the relational expression of R, X, and an impedance Z, a result of the impedance Z=36.43+0.0873 s is obtained. 
     [Math. 9]
 
 Z=R+s*X /ω)  Expression (9)
 
     In addition, in  FIG. 6 , w denotes a disturbance, and an input of the power controller  103  which becomes a model as the H∞controller is denoted as e. Here, e is an error between a voltage reference value Vref and an output voltage V which is represented as a sum of an output of the control target  503  and a disturbance w. When the error e is input to the power controller  103 , the power controller  103  outputs a control output u, and thereby realizes a feedback structure to a target value input. 
     In addition, in  FIG. 6 , an input y with respect to a transfer function K′ (s) of the partial controller  502  which is the H∞controller is defined as the amount of control Ze (a second amount of control). 
     Likewise, in  FIG. 6 , a value obtained by multiplying a weighting function  504  W T  (s) with a control output u is defined as the amount of control Z T  (a first amount of control). 
     The weighting function  504  is represented as a transfer function W T  (s). By providing the characteristic of the weighting function  504  W T  (s) in a frequency area, it is possible to change the characteristic of the power controller  103 . More specifically, by designing the weighting function  504  W T  (s) to have a large gain in a frequency area in which the amount of control is desired to be small, it is possible to provide a desirable characteristic to the power controller  103 . It is to be noted that the amounts of control Z T  and Ze, and the weighting function  504  W T  (s) are described later in detail. 
     Next, the method for designing the partial controller that is the H∞controller is described with reference to  FIG. 9 . 
       FIG. 9  is a flowchart of a method for designing the power controller  103  according to this embodiment. 
     As described above, the power controller  103  is modeled as a product of a transfer function M (s) of the internal model  501  for a voltage reference value and a transfer function K′ (s) of the partial controller  502  that is the H∞controller. 
     Here, the H∞control theory is a control theory for configuring a control system for suppressing influences of a disturbance signal and a modeling error. More specifically, a transfer function is evaluated by a scalar value called an H∞norm which becomes an indicator for control. By determining a transfer function that makes the H∞norm smaller than a desired value, a target performance is achieved. 
     More specifically, a designing procedure taken here is to reduce the H∞norm of the transfer function from the disturbance signal is input to an evaluation result is output, for a general-purpose target control model called a generalized plant. By assuming an uncertain part of the control target as a modeling error and designing the transfer function from the input to the output of the disturbance signal to have a small H∞norm, the resulting control system becomes a control system which suppresses the influences of the uncertainty of the model and the disturbances. 
     Here, a characteristic which is valid and stable to an error from an assumed control target model (which is an ideal model without any change and error, and is hereinafter referred to as a nominal model) is referred to as robustness. When a control system is designed, a control target model is required. However, it is difficult to obtain a precise control target model in many cases, and some error is inevitably occurs between a prepared model and an actual control target. The robust control is a control system designing method for designing a control system that is robust in terms of maintaining stability to such error. With the robustness, the H∞control has an advantage of eliminating the need to prepare a precise control target model. 
     In the earlier described designing of the H∞controller, specifications of the amounts of control Z T  and Ze are determined in advance based on the control model illustrated in  FIG. 6 . The specifications of the amounts of control Z T  and Ze are, for example, threshold values corresponding to upper limits for the amounts of control Z T  and Ze. In addition, the threshold values corresponding to upper limits and lower limits may be determined as specifications. 
     In general, both of the amounts of control Z T  and Ze are preferably close to 0. However, in the case of actually determining a gain for the H∞controller, it is difficult to completely reduce the amounts of control Z T  and Ze to 0. Accordingly, there is a need to determine a smaller threshold value for the amount of control that should be preferentially made smaller according to the specifications of the power controller  103  that are determined by characteristics of the power supply device  101  that is the target system. 
     For example, in the case where assumed noise includes many high-frequency band components, a threshold value for the amount of control Z is preferentially made smaller in the high-frequency band. In the opposite case where assumed noise includes many low-frequency band components, a threshold value for the amount of control Z is preferentially made smaller in the low-frequency band. 
     First, the weighting function  504  W T  (s) is set based on the specifications (S 801  in  FIG. 9 ). 
     The weighting function  504  W T  (s) has an effect of suppressing influences on the modeling error. For this reason, by appropriately setting the weighting function  504  W T  (s), it is possible to increase the robustness of the power controller  103 . More specifically, it is possible to realize robust control performances to a change in impedance that depends on the kind of the load device  108  connected to the distribution line, or that is caused by activation/stoppage or the like of the load device  108 . 
     Here, the method for designing the weighting function  504  W T  (s) is described in detail. Now, loads having three kinds of impedances are assumed as examples of loads connected to the distribution line, as represented by Expressions (10) to (12) below. It is to be noted that the method for calculating negative impedances is performed using actually measured values, as illustrated with reference to  FIG. 8 . 
     [Math. 10]
 
 Z 1= R 1  Expression (10)
 
[Math. 11]
 
 Z 2= R 2+ L 2* s   Expression (11)
 
[Math. 12]
 
 Z 3= R 3+ L 3* s   Expression (12)
 
     Here, Z 1  is a pure resistor load such as a table lamp (lighting equipment). The inverter distribution lines Z 2  and Z 3  are, for example, rectifier loads such as a television receiver and an air conditioner. 
     The weighting function  504  W T  (s) is set to suppress the influence of the modeling error of the control target. As described above, the control target is represented by a product of the inverter block  601 , the filter block  602 , and the load device block  603  which are structural elements illustrated in  FIG. 7 . 
     Here, as an example, assuming that the inverter block  601  and the filter block  602  do not have any modeling error, changes in impedance caused by activation/stoppage or the like of the loads represented by Expressions (10) to (12) are handled as modeling errors. 
     First, a control target P (s) in  FIG. 7  is assumed to be a control target nominal model at the time when only a load Z 1  is connected. In other words, P (s) is represented as Expression (13). 
     [Math. 13]
 
 P ( s )= P   INV ( s )* P   filter ( s )* Z 1  Expression (13)
 
     In addition, a combined impedance Za when all of the loads in Expression (10) to (12) are connected is represented as in Expression (14) below, and thus is provided as the weighting function  504  W T  (s) according to Expression (15). 
     [Math. 14]
 
 Za= 1(1/ Z 1+1/ Z 2+1/ Z 3)  Expression (14)
 
[Math. 15]
 
 WT ( s )= P   INV ( s )* P   filter ( s )*( Za−Z 1)  Expression (15)
 
     Expression (15) represents a variation in impedance from the nominal model with a combination of loads Z 1 , Z 2 , and Z 3  when the load in an ideal nominal model without any change and error is assumed to be Z 1 . In other words, by setting the weighting function  504  W T  (s) in this way, it is possible to design the power controller  103  with a robust stability in a conceivable impedance change range. 
       FIG. 10  illustrates the Bode diagram of the weighting function  504  W T  (s) set in this way. 
     As illustrated in  FIG. 10 , the gain of the weighting function  504  W T  (s) increases (takes a largest value) around a frequency of 1000 Hz. This is because an LC filter is included in a transfer function of the weighting function  504  W T  (s), and a resonance frequency of an LC filter is 1000 Hz in this embodiment. 
     In other words, with these characteristics of the weighting function  504 , the partial controller  502  derived according to the H∞control theory is to have a characteristic of having a low gain in the resonance frequency of the LC filter included in the control target. In this way, it is possible to prevent the partial controller  502  from operating unstably at the resonance frequency of the LC filter. 
     In addition,  FIG. 10  illustrates the gain of the weighting function  504  W T  (s) is set to be high at a low frequency area. This means that the impedance changes significantly at the low frequency area. In this way, it is possible to increase the robustness of the partial controller  502  at the low frequency area. 
       FIG. 11  illustrates examples of various kinds of parameters and transfer functions illustrated in this embodiment. 
     Although the impedance of only the load device  108  is described as the target in this embodiment, the impedance of the distribution line may further be considered. In this embodiment, a conceivable impedance change range is set for each of three loads represented by Expressions (10) to (12). However, without being limited thereto, an impedance range may be determined for another load device which may be connected, or for the load device  108  which should perform motion compensation. In this way, it is possible to compensate the robustness of the power controller  103  within the change range. 
     Lastly, based on a generalized plant, the method for solving the H∞control problem is applied to derive a transfer function K′ (s) of the partial controller  502 , and calculate the power controller  103  together with the internal model  501  described above (S 802  in  FIG. 9 ). 
     For example, a model illustrated in  FIG. 6  can be represented as in  FIG. 12  by performing equivalent transform using the generalized plant G (s). At this time, it is possible to calculate K′ (s) in suboptimal solution by solving the H∞control problem represented by Expression (16) below so as to reduce the H∞norm from a disturbance w to the amounts of control Z T  and Ze at or below a predetermined value. 
     [Math. 16]
 
∥ G ( s ) K ′( s )∥ ∞ &lt;1  Expression (16)
 
     Here, ∥G∥ ∞  is defined by Expression (17). 
     
       
         
           
             
               
                 
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     Here, in Expression (17), σ(•) denotes a largest singular value. 
     The method for solving the H∞control problem described in detail in Non-patent Literature 1, and thus details thereof are not described here. 
     Based on the transfer function K′ (s) of the partial controller  502  calculated in this way and a transfer function M (s) of the internal model  501 , a model of the power controller  103  is calculated. 
     After the weighting function  504  is defined according to the characteristics of the control target system as described above, a transfer function K (s) of the power controller  103  calculated based on the partial controller  502  which is the earlier described H∞controller and the internal model  501  are calculated as a transfer function for continuous time duration. The transfer function K (s) calculated in this way is transformed into a transfer function in discrete time by 50 [μ sec] at a sampling cycle Ts, and is then transformed into state spatial representations as represented as Expressions (2) and (3). 
     In Expression (2), x [n] is an internal state represented as an N-dimensional column vector in Step n. In addition, e [n] is a feedback input to be input to the power controller  103  in Step n. More specifically, e [n] is an input representing an error between a voltage reference value and an output value by the power supply device  101 . 
     In Expression (3), u [n] is an output by the power controller  103  in Step u [n]. In addition, A K , B K , and C K  are coefficient matrices in a state space equation. More specifically, A K , B K , and C K  are values calculated as shown in the above Non-patent Literature 1 or the like. 
       FIG. 13  illustrates a Gain diagram of the power controller  103  which is the H∞controller designed using the designing method according to this embodiment. The Gain diagram is a diagram in which the horizontal axis represents logarithm frequency and the vertical axis represents the amount of logarithm [dB] of an amplitude ratio (gain) between input and output. 
     As shown in  FIG. 13 , the power controller  103  has a high gain in a frequency (60 Hz in this embodiment) of a voltage reference value. In other words, the gain frequency characteristics of the power controller  103  shows an upward convex in the frequency band of the voltage reference value such that the gain of the power controller  103  takes the local maximum value at the frequency of the voltage reference value. Here, the local maximum value means a locally maximum value in the frequency band of the voltage reference value. In this way, it is possible to represent a high trackability performance to an instruction value (voltage reference value) which is one of characteristics of the power controller  103 . 
     In addition, the power controller  103  has a robustness to a load change when gains other than 60 Hz are suppressed. More specifically, as a characteristic, a gain is at or below 0 in a frequency band in which the impedances of the distribution line connected to the output of the power controller  103  and the load device  108  change. 
     In addition, the gain frequency characteristic of the power controller  103  shows a downward convex around 1000 Hz such that the gain of the power controller  103  takes a local minimum value at a resonant frequency of the LC filter. Here, the local minimum value means a locally minimum value at a frequency band of 1000 Hz. In addition, the gain around 1000 Hz of the power controller  103  is at or below 0. In this way, reducing the gain around 1000 Hz provides an advantageous effect of suppressing resonance of the LC filter. 
     Next,  FIG. 14  illustrates a simulation result for output by the power controlling device having the power controller  103  designed as in this embodiment. In the diagram, the upper, middle, and lower graphs respectively represent temporal changes in voltage, current, and the distortion rate of output voltage. In  FIG. 14 , as for the already described three kinds of loads Z 1 , Z 2 , and Z 3 , only the load Z 1  is ON from 0 to 0.05 second, all of the loads are ON from 0.05 to 0.15 second, and only the loads Z 1  and Z 2  are ON from 0.15 to 0.25 second. 
     In  FIG. 14 , the voltage approximately tracks an instruction value while the current value and the current waveform significantly change depending on how the loads are combined. More specifically, the voltage changes within approximately 10% or slightly above even when the distortion rate and current described in  FIG. 5  changes most significantly. In other words,  FIG. 14  indicates that the power controller  103  has a high robustness to a load change. 
     In this embodiment, the storage battery  105  is used as a direct current power source. In addition to this, various kinds of power sources such as a photovoltaic power generating device and a wind power generating device are also conceivable. In addition, the direct current power source does not need to be present inside the power supply device  101 , and may be connected through a direct current bus line from outside. 
     As clear from the descriptions above, the power controller according to this embodiment is designed based on the H∞control theory with reference to the load change range, and has an internal model for a voltage reference value which is desired to be tracked based on the internal model principle. The power control device using the power controller has an increased load trackability even when it is impossible to accurately identify the impedances of the distribution line and load to be connected. Thus, the power control device is capable of outputting a stable voltage that is robust to load changes and thus has little distortion. In other words, the use of the method for designing a power controller according to the present invention makes it possible to realize the power control device capable of operating load devices stably. 
     Although the present invention has been described based on the above embodiment, the present invention is not limited to the above embodiment as a matter of course. The following cases are also included in the present invention. 
     (1) Each of the device can be implemented specifically as a computer system including a microprocessor, a ROM, a RAM, a hard disk unit, a display unit, a keyboard, a mouse, and so on. A computer program is stored in the RAM or hard disk unit. Each of the devices achieves its functions through the microprocessor&#39;s operations according to the computer program. Here, in order to achieve predetermined functions, the computer program is configured by combining plural instruction codes indicating instructions for the computer. 
     (2) A part or all of the structural elements of the device may be configured with a single system-LSI (Large-Scale Integration). The system-LSI is a super-multi-function LSI manufactured by integrating structural units on a single chip, and is specifically a computer system configured to include a microprocessor, a ROM, a RAM, and so on. A computer program is stored in the ROM. The system-LSI achieves its function through the microprocessor&#39;s loading the computer program from the ROM to the RAM and performing operations etc. according to the computer program. 
     (3) A part or all of the elements constituting the devices may be configured as an IC card which can be attached to and detached from the respective devices or as a stand-alone module. The IC card or the module is a computer system configured from a microprocessor, a ROM, a RAM, and so on. The IC card or the module may include the above-described super-multifunctional LSI. The IC card or the module achieves its functions through the microprocessor&#39;s operations according to the computer program. The IC card or the module may also be tamper-resistant. 
     (4) The present invention may be realized as the above-described methods. In addition, any of the methods may be implemented as computer programs for executing the above-described method, using a computer, and may also be implemented as digital signals including the computer programs. 
     Furthermore, the present invention may also be implemented as computer programs or digital signals recorded on computer-readable recording media such as a flexible disc, a hard disk, a CD-ROM, an MO, a DVD, a DVD-ROM, a DVD-RAM, a BD (Blu-ray Disc), and a semiconductor memory. Furthermore, the present invention may also be implemented as the digital signals recorded on these recording media. 
     Furthermore, the present invention may also be implemented as the aforementioned computer programs or digital signals transmitted via a telecommunication line, a wireless or wired communication line, a network represented by the Internet, a data broadcast, and so on. 
     The present invention may also be implemented as a computer system including a microprocessor and a memory, in which the memory stores the aforementioned computer program and the microprocessor operates according to the computer program. 
     Furthermore, it is also possible to execute another independent computer system by transmitting the programs or the digital signals recorded on the aforementioned recording media, or by transmitting the programs or digital signals via the aforementioned network and the like. 
     (5) The embodiments and variations thereof may be arbitrarily combined. 
     When the present invention is implemented as software, the functional elements of the present invention can naturally be executed by the program(s) being executed using hardware resources of the computer such as a CPU, a memory, an input and output circuit, etc. In other words, the functions of the various kinds of processing units are realized by means of the CPU reading (extracting) processing target data from the memory or the input and output circuit and performing operations, temporarily storing (outputting) the operation results into the memory or the input and output circuit, and the like. 
     Furthermore, when the present invention is implemented as hardware, the present invention may be implemented as a single-chip semiconductor circuit, as a single circuit board on which a plurality of semiconductor chips are mounted, as a single device having an enclosure in which all of the elements are housed, or by means of linking operations by a plurality of devices connected through a transmission path. For example, the present invention may be realized using a server-client system by providing the storage unit in the embodiment to a server device and providing the processing units in the embodiment to a client device which wirelessly communicates with the server device. 
     It is to be noted that the present invention is not limited to the embodiments and variations thereof. The present invention includes various kinds of modifications that would be conceived by any person skilled in the art and made to the embodiments and variations thereof and other embodiments that would be configured by any person skilled in the art by combining the structural elements in different embodiments and variations thereof, without deviating from the scope of the present invention. 
     INDUSTRIAL APPLICABILITY 
     The present invention is applicable as methods for designing power controllers, and power controllers designed according to the present invention, and power control devices including the power controllers are applicable to controllers for inverters which convert direct-current power to alternating-current power and output the alternating-current power. 
     REFERENCE SIGNS LIST 
     
         
           101  Power supply device 
           102  Power control device 
           103  Power controller 
           104  Inverter 
           105  Storage battery 
           106  Voltage/current sensor 
           107  Distribution switchboard/Power switchboard 
           108  Load device 
           201  Filter 
           301  Operating unit 
           302  Matrix storage unit 
           303  State storage unit 
           501  Internal model (transfer function of an internal model) 
           502  Partial controller (transfer function of a partial controller) 
           503  Control target 
           504  weighting function 
           601  Inverter block 
           602  Filter block 
           603  Load device block 
           1501  Voltage change compensating block