Abstract:
In a method for determining a parameter set describing electric parameters of a route section of a magnetic suspension railway, the route section contains a stator section forming a drive section of the magnetic suspension railway and a route cable connecting the stator section to an associated converter device. In the method, the current and voltage values are measured at the electric connecting point between the route cable and the converter device. The parameters of the parameter set are determined using the measurement values, thus forming the parameter set. Accordingly, the current and voltage values are additionally measured at the electrical connecting point between the route cable and the stator section and the current values at the neutral point side of the stator section, if the stator section is electrically connected to the route cable. The additional measurement values are also considered when determining the parameters.

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The invention relates to a method having the features according to the precharacterizing clause of claim  1 . 
     In order to control a magnetic levitation railroad, in particular in order to regulate the thrust force current of a magnetic levitation railroad, it is necessary to know as accurately as possible the electrical parameters of the individual track sections of the magnetic levitation railroad. 
     It is known from the Transrapid track built in Shanghai for a corresponding parameter set to be determined for each track section. In this case, a track section comprises at least one stator section, which forms a drive section of the magnetic levitation railroad, and a track cable, which connects the stator section to an associated converter device. In order to determine the parameter set, the current and voltage values are measured at the electrical connection point between the track cable and the converter device. These measured values are then used to determine the parameters of the parameter set, and therefore to form the parameter set. The already known procedure for determination of the parameters is illustrated in a simplified form in  FIG. 1 . 
       FIG. 1  shows a stator section  10 , one of whose connections  20  is connected via a switch Se to a track cable A and to a further track cable B. The stator section connection  30  of the stator section  10  is connected to the star point via a switch Ss. 
     The track cable A is connected by means of its feed connection  40  via switches Sua and Ska to a converter device URA. The further track cable B is connected by means of its feed connection  50  via switches Sub and Skb to a further converter device URB. 
     Measurements are taken at the feed connection  40  and at the feed connection  50  in order to determine the parameters of the track section, using a converter-related measurement device  60  and a further converter-related measurement device  70 , which, for example, can be connected to an evaluation device  90  via current regulation  80  for the magnetic levitation railroad. During the measurement at the feed connection  40 , the switches Se and Sub are open, and the voltages Ua and the currents Ia are measured for an open track cable end (Skb open) and a closed track cable end (Skb closed). During the measurement at the feed connection  50 , the switches Se and Sua are open and the voltages Ub and the currents Ib are measured for an open track cable end (Ska open) and a closed track cable end (Ska closed). The corresponding measured values are used to determine the electrical parameters of the two track cables A and B. The characteristics of the stator section  10  are then calculated back from current measured values of the currents Ia and Ib and measured values of the voltages Ua and Ub, which are determined with the switch Se closed. Back-calculation such as this is possible since the characteristics of the two track cables A and B are already known, separately from the stator section  10 , at this time. 
     The already known method has the disadvantage that the measurements must be carried out with extreme care in order to prevent damage to the converter devices URA and URB. In the case of the short-circuit measurement, that is to say when the switches Ska or Skb are closed, short-circuit currents with very high harmonic components can flow, which can in some circumstances lead to destruction of the semiconductor valves contained in the converter devices. 
     BRIEF SUMMARY OF THE INVENTION 
     Against the background of a method of the type mentioned initially, the invention is based on the object of specifying a method for parameter determination, in which the risk of damage to the converter devices is avoided, or at least considerably reduced. 
     According to the invention, this object is achieved by a method having the features as claimed in claim  1 . Advantageous refinements of the method according to the invention are specified in dependent claims. 
     The invention accordingly provides that the current and voltage values are measured at the electrical connection point between the track cable and the converter device when the stator section is electrically connected to the track cable, and in addition the current and voltage values are measured at the electrical connection point between the track cable and the stator section, and the current values are measured on the star point side of the stator section, and these additional measured values are likewise taken into account in determination of the parameters. 
     One major advantage of the method according to the invention is that the risk of damage to the converter devices is relatively low; because of the stator section, which is connected in parallel during the measurements, the current harmonic components are shifted to a different frequency, and the natural frequencies of the electrical overall system are distributed considerably better in comparison to a measurement with the stator section disconnected. The short-circuit measurements with switches Ska and Skb closed therefore correspond to electrical states as can occur during normal operation of the magnetic levitation railroad, as a result of which the risk of destruction of the converter devices while the parameters are being determined is relatively low. 
     The parameters can be determined particularly easily and therefore advantageously when the measured values are evaluated with the aid of the four-pole theory. 
     As already mentioned initially, the stator section can be connected via a further track cable to a further converter device: In this case, it is considered to be advantageous for the current and voltage values likewise to be measured at the electrical connection point between the further track cable and the further converter device when the stator section is switched on, and for these measured values to be additionally taken into account in determination of the parameters. 
     One or more of the following parameters are preferably determined for the parameter set: the electrical resistance, the inductance, the capacitance, the electrical resistance per unit length, the inductance per unit length, the susceptance per unit length, the capacitance per unit length and/or the conductance, be this for the track cable, the further track cable and/or the stator section. 
     The current and voltage values are in each case preferably measured on three phases at the electrical connection point between the track cable and the converter device, and the current and voltage values are in each case measured on three phases at the electrical connection point between the track cable and the stator section, and are evaluated on a phase-conductor-specific basis. 
     The current and voltage values are recorded at the electrical connection point between the track cable and the stator section, and the current values are recorded on the star point side of the stator section by means of a mobile measurement device, and are transmitted to a stationary evaluation device, by means of which the parameters are then determined. 
     Alternatively, the current and voltage values can be recorded at the electrical connection point between the track cable and the stator section, and the current values can be recorded on the star point side of the stator section by means of a stationary measurement device, and transmitted to a stationary evaluation device, by means of which the parameters are then determined. 
     After the determination of the parameters, the current and voltage values are measured at least one more time, preferably repeatedly, at the electrical connection point between the track cable and the converter device, the current and voltage values are measured at least one more time, preferably repeatedly, at the electrical connection point between the track cable and the stator section, and the current values are measured at least one more time, preferably repeatedly, on the star point side of the stator section during operation of the magnetic levitation railroad, in order to determine the parameters which result from each of the measured values and to use the respectively up-to-date parameters to update the parameter set. 
     It is considered to be particularly advantageous if the current and voltage values at the electrical connection point between the track cable and the stator section are also used to determine the position of a vehicle on the stator section during operation of the magnetic levitation railroad. In addition the current values on the star point side of the stator section are preferably also used for determination of the position of the vehicle. 
     It is also considered to be advantageous if the measured star point current is considered to be approximately equal to the stator current underneath a vehicle which is located on the stator section, and to set the thrust force current of the magnetic levitation railroad on the basis of this assumption. 
     The invention also relates to an arrangement for determination of a parameter set which describes electrical parameters of a track section of a magnetic levitation railroad, wherein the track section comprises a stator section, which forms a drive section of the magnetic levitation railroad, and a track cable which connects the stator section to an associated converter device, wherein the arrangement has a converter-related measurement device which is connected to the electrical connection point between the track cable and the converter device and measures the current and voltage values at the connection point during its operation, and wherein the arrangement has an evaluation device, which is connected to the converter-related measurement device and uses the measured values from the converter-related measurement device to determine the parameters of the parameter set, and therefore to form the parameter set. 
     For an arrangement such as this, the invention provides that the arrangement additionally has one stator-related measurement device which is connected on the input side to the electrical connection point between the track cable and the stator section and to the star point side of the stator section, and is connected on the output side to the evaluation device, wherein the stator-related measurement device is designed such that, during its operation, it measures the current and voltage values at the connection point between the track cable and the stator section and the current values on the star point side, and transmits these to the evaluation device, wherein the evaluation device is designed such that it additionally takes account of the measured values of the stator-related measurement device in the determination of the parameters and carries out the measurements when the stator section is electrically connected to the track cable. 
     The arrangement preferably has a further converter-related measurement device, which is connected on the input side to the electrical connection point between a further track cable and a further converter device, and is connected on the output side to the evaluation device, and is designed such that, during its operation, it measures the current and voltage values at the connection point between the further track cable and the further converter device, and transmits these to the evaluation device. 
     The stator-related measurement device may be formed by a mobile unit or by a stationary unit. The evaluation device may be a component of a mobile or stationary unit such as this, or may form a separate component. 
     The arrangement is preferably designed such that, after determination of the parameters, it measures the current and voltage values at the electrical connection point between the track cable and the converter device, the current and voltage values at the electrical connection point between the track cable and the stator section, and the current values on the star point side of the stator section during operation of the magnetic levitation railroad, at least once more, and preferably repeatedly, it determines the parameters which result from each of the measured values, and uses the respectively up-to-date parameters to update the parameter set. 
     In addition, the evaluation device may also be designed such that it uses the current and voltage values at the electrical connection point between the track cable and the stator section during operation of the magnetic levitation railroad to determine the position of a vehicle on the stator section. 
     In addition, the current values on the star point side of the stator section can also be used to determine the position of the vehicle. 
     Furthermore, a magnetic levitation railroad having a multiplicity of track sections is considered to be inventive, wherein at least one of the track sections, preferably all of the track sections, is or are each equipped with an individual, local arrangement—as described—in order to determine a parameter set, and wherein the thrust force current of the track section is in each case determined for each track section which is provided with a local arrangement, using its locally determined parameter set. 
     Furthermore, an arrangement and a method for location of a vehicle on a track section of a magnetic levitation railroad are considered to be an autonomous invention, to be precise independently of how the parameters and parameter sets have been determined for the magnetic levitation railroad. 
     Furthermore, an arrangement and a method for adjusting the thrust force current for a vehicle which is located on a track section of a magnetic levitation railroad is regarded as an autonomous invention, in which the star point current of the stator section is regarded as the stator current underneath the vehicle, and is used to adjust the thrust force current. 
     The invention will be explained in more detail in the following text with reference to exemplary embodiments, and in this case, by way of example: 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
         FIG. 1  is an illustration for understanding a method for determining parameters according to the prior art. 
         FIG. 2  shows one exemplary embodiment of an arrangement according to the invention, on the basis of which the method according to the invention will also be explained by way of example, 
         FIG. 3  shows general explanations relating to the four-pole theory, 
         FIG. 4  shows the four-pole theory applied to the arrangement shown in  FIG. 2 , and 
         FIG. 5  shows schematically, the process of finding the position of a vehicle which is located on a stator section of the arrangement as shown in  FIG. 2 . 
     
    
    
     DESCRIPTION OF THE INVENTION 
     For clarity reasons, the same reference symbols are used for identical or comparable components in  FIGS. 1 to 5 . 
       FIG. 2  shows one exemplary embodiment of an arrangement according to the invention. Corresponding to the arrangement shown in  FIG. 1 , this arrangement has a stator section  10 , a track cable A, a further track cable B, a plurality of switches Se, Ss, Sua, Ska, Sub and Skb, a converter device URA, a further converter device URB, a converter-related measurement device  60 , a further converter-related measurement device  70  and current regulation  80  for the magnetic levitation railroad. 
     In addition, in the arrangement shown in  FIG. 2 , a stator-related, mobile or stationary measurement device is provided, is annotated with the reference symbol  100  and is electrically connected on the input side to the connection point  20  between the two track cables A and B and the stator section  10 , and to the star point side  30  of the stator section. On the output side, the stator-related measurement device  100  is connected to an evaluation device  110 . The stator-related measurement device  110  is designed such that, during operation, it measures the current and voltage values Ix, Ux at the connection point  20  between the track cables A, B and the stator section  10 , as well as the star point current values, Is on the star point side  30 , and transmits these to the evaluation device  110 . 
     In the exemplary embodiment shown in  FIG. 2 , the evaluation device  110  is connected only indirectly via the stator-related measurement device  100  to the two converter-related measurement devices  60  and  70 , as a result of which the converter-related measurement results Ia, Ib, Ua, Ub from the converter-related measurement devices  60  and  70  can be passed to the evaluation device  110  only via the stator-related measurement device  100 . Alternatively, the evaluation device  110  can also be connected to one of the two converter-related measurement devices  60  or  70 , and can receive the measurement results from the other measurement devices via them. It is likewise possible to in each case connect the evaluation device  110  to all the measurement devices  60 ,  70  and  100  directly, thus allowing direct transmission of the measurement results. 
     The arrangement shown in  FIG. 2  may be operated, for example, as follows: 
     The converter-related measurement device  60  is used to measure the current Ia flowing into the track cable A, and the voltage Ua applied to the track cable A. The further converter-related measurement device  70  is used to measure the current Ib flowing into the further track cable B, and the voltage Ub applied to the further track cable B. The stator-related measurement device  100  is used to measure the current Ix and the voltage Ux at the electrical connection point  20  between the track cables A, B and the stator section  10 , as well as the current Is on the star point side of the stator section  10 . 
     The evaluation device  110  uses these measurement results to determine the electrical parameters of the two track cables A and B, as well as those of the stator section  10 , using the four-pole theory, as will be explained in detail in the following text. 
     The electrical characteristics of a long track cable or of a long stator section can be represented mathematically using the four-pole theory as follows: 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             I 
                             1 
                           
                         
                       
                       
                         
                           
                             I 
                             2 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               Y 
                               11 
                             
                           
                           
                             
                               Y 
                               21 
                             
                           
                         
                         
                           
                             
                               Y 
                               21 
                             
                           
                           
                             
                               Y 
                               22 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               U 
                               1 
                             
                           
                         
                         
                           
                             
                               U 
                               2 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
               
             
           
         
       
     
     The voltages U 1  and U 2  are, of course, the stimuli, and the currents I 1  and I 2  are the responses thereto. The voltages and currents are complex and may, for example, be represented using the αβ representation, which can be derived from the three-phase system representation (R, S and T). Y ij  are admittances which are dependent on the frequency (s-domain according to Laplace). Schematically, the four-pole theory can be visualized as illustrated in  FIG. 3 . The conductance matrix is referred to as [Y]. The structure of the conductance matrix of a track cable and of a stator section with a length L are in this case identical: 
     The diagonal admittance is given by: 
                     Y   11     =       Y   22     =       Y   D     =     1       Z   w     ⁢     tanh   ⁡     (     γ   ⁢           ⁢   L     )                       Equation   ⁢           ⁢   2               
and the parallel admittance is given by:
 
     
       
         
           
             
               
                 
                   
                     Y 
                     12 
                   
                   = 
                   
                     
                       Y 
                       21 
                     
                     = 
                     
                       
                         Y 
                         C 
                       
                       = 
                       
                         - 
                         
                           1 
                           
                             
                               Z 
                               w 
                             
                             ⁢ 
                             
                               sinh 
                               ⁡ 
                               
                                 ( 
                                 
                                   γ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   L 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
               
             
           
         
       
     
     The conductance matrix of a track cable or of a stator section as shown in equations 2 and 3 is completely symmetrical. 
     Z w  forms the wave impedance, where: 
                     Z   w     =           R   ′     +     sL   ′           G   ′     +     sC   ′                   Equation   ⁢           ⁢   4               
and γ is the propagation constant:
 
γ=√{square root over (( R′+sL′ )( G′+sC′ ))}{square root over (( R′+sL′ )( G′+sC′ ))}.  Equation 5
 
     In this case:
         R′ is the resistance per unit length (Ω/m),   L′ is the inductance per unit length (H/m),   G′ is the susceptance per unit length (Ω −1 /m) and   C′ is the capacitance per unit length (F/m).       

     Important characteristics of the equations 2 and 3 are obtained as follows: 
     
       
         
           
             
               
                 
                   
                     
                       Y 
                       D 
                       2 
                     
                     - 
                     
                       Y 
                       C 
                       2 
                     
                   
                   = 
                   
                     
                       
                         1 
                         
                           Z 
                           w 
                           2 
                         
                       
                       ⇒ 
                       
                         Z 
                         w 
                       
                     
                     = 
                     
                       1 
                       
                         
                           
                             Y 
                             D 
                             2 
                           
                           - 
                           
                             Y 
                             C 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   6 
                 
               
             
             
               
                 
                   
                     
                       Y 
                       D 
                     
                     
                       Y 
                       C 
                     
                   
                   = 
                   
                     
                       
                         - 
                         
                           cosh 
                           ⁡ 
                           
                             ( 
                             
                               γ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               L 
                             
                             ) 
                           
                         
                       
                       ⇒ 
                       γ 
                     
                     = 
                     
                       
                         1 
                         L 
                       
                       ⁢ 
                       
                         
                           a 
                           ⁢ 
                           cosh 
                         
                         ⁡ 
                         
                           ( 
                           
                             - 
                             
                               
                                 Y 
                                 D 
                               
                               
                                 Y 
                                 C 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   7 
                 
               
             
           
         
       
     
     Z w  and γ can be derived from Y D  and Y C . 
     The impedance per unit length is calculated in the following manner:
 
 Z=γ·Z   w   =R′+sL′   Equation 8
 
     The admittance per unit length is calculated as follows: 
     
       
         
           
             
               
                 
                   Y 
                   = 
                   
                     
                       γ 
                       
                         Z 
                         w 
                       
                     
                     = 
                     
                       
                         G 
                         ′ 
                       
                       + 
                       
                         sC 
                         ′ 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   9 
                 
               
             
           
         
       
     
     The following relationships can also be derived from equation 6 and equation 7, using s=jω: 
     The resistance per unit length is the real component of the impedance per unit length:
 
 R′=Re ( Z )
 
     The inductance per unit length is the imaginary component of the impedance per unit length: 
     
       
         
           
             
               
                 
                   
                     L 
                     ′ 
                   
                   = 
                   
                     
                       1 
                       ω 
                     
                     ⁢ 
                     
                       Im 
                       ⁡ 
                       
                         ( 
                         Z 
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   11 
                 
               
             
           
         
       
     
     The susceptance per unit length is the real component of the admittance per unit length:
 
 G′=Re ( Y )  Equation 12
 
     The capacitance per unit length is the imaginary component of the admittance per unit length: 
     
       
         
           
             
               
                 
                   
                     C 
                     ′ 
                   
                   = 
                   
                     
                       1 
                       ω 
                     
                     ⁢ 
                     
                       Im 
                       ⁡ 
                       
                         ( 
                         Y 
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   13 
                 
               
             
           
         
       
     
     If the characteristics of the diagonal and parallel admittances of a track cable or of a stator section are known (as a function of the frequency), then the characteristics of the electrical parameters per unit length R′, L′ G′ and C′ are also known, provided that the length L of the track cable or of the stator section is known, for example because it has been measured in advance. 
     The characteristics of the diagonal and parallel admittances as a function of the frequency can be determined by means of various measurements (e.g. voltage stimuli during commissioning) as a function of the frequency. 
     The purpose of determination of R′, L′, G′ and C′ is to derive models for the two track cables A, B and the stator section  10 . By way of example, the models are used for current regulation of the magnetic levitation railroad. 
     The process of determining parameters during the commissioning of a magnetic levitation railroad (without a vehicle) will be explained in more detail in the following text using the example of the arrangement shown in  FIG. 2 . 
     The four-pole representation, which has been explained in a general form with reference to  FIG. 3 , is in this case applied to the arrangement shown in  FIG. 2 ; this is shown in  FIG. 4 . The switches Se, Ss, Sua, Ska, Sub and Skb are not shown in  FIG. 4 ; the switches Se and Ss are assumed to be switched on. 
     It is also assumed that the stator current Ic on the stator section  10  corresponds to the star point current Is of the stator section  10 ; this approximation applies very accurately at low frequencies up to 350 Hertz. 
     The following four-pole equations are applicable: 
     Track cable A: 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             I 
                             c 
                           
                         
                       
                       
                         
                           
                             I 
                             ax 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               Y 
                               Da 
                             
                           
                           
                             
                               Y 
                               Ca 
                             
                           
                         
                         
                           
                             
                               Y 
                               Ca 
                             
                           
                           
                             
                               Y 
                               
                                 D 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 a 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               U 
                               a 
                             
                           
                         
                         
                           
                             
                               U 
                               x 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   14 
                 
               
             
           
         
       
     
     Track cable B: 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             I 
                             b 
                           
                         
                       
                       
                         
                           
                             I 
                             bx 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               Y 
                               Db 
                             
                           
                           
                             
                               Y 
                               Cb 
                             
                           
                         
                         
                           
                             
                               Y 
                               Cb 
                             
                           
                           
                             
                               Y 
                               Db 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               U 
                               b 
                             
                           
                         
                         
                           
                             
                               U 
                               x 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   15 
                 
               
             
           
         
       
     
     Stator section: 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             I 
                             x 
                           
                         
                       
                       
                         
                           
                             I 
                             c 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               Y 
                               Ds 
                             
                           
                           
                             
                               Y 
                               Cs 
                             
                           
                         
                         
                           
                             
                               Y 
                               Cs 
                             
                           
                           
                             
                               Y 
                               Ds 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               U 
                               
                                 x 
                                 ⁢ 
                                 
                                     
                                 
                               
                             
                           
                         
                         
                           
                             
                               U 
                               c 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   16 
                 
               
             
             
               
                 
                   
                     I 
                     x 
                   
                   = 
                   
                     - 
                     
                       ( 
                       
                         
                           I 
                           ax 
                         
                         + 
                         
                           I 
                           bx 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   17 
                 
               
             
           
         
       
     
     R′, L′, G′ and C′ of the stator section  10  are determined by the evaluation device  110  during the commissioning process (without a vehicle), by means of the feed from the converter device URA and/or from the further converter device URB. When the switches Se and Ss are closed and there is no vehicle on the stator section  10 , then, from equation 16: 
     
       
         
           
             
               
                 
                   
                     I 
                     x 
                   
                   = 
                   
                     
                       
                         
                           Y 
                           Ds 
                         
                         ⁢ 
                         
                           U 
                           x 
                         
                       
                       ⇒ 
                       
                         Y 
                         Ds 
                       
                     
                     = 
                     
                       
                         
                           ( 
                           
                             
                               I 
                               x 
                             
                             
                               U 
                               x 
                             
                           
                           ) 
                         
                         
                           Uc 
                           = 
                           0 
                         
                       
                       = 
                       
                         1 
                         
                           
                             Z 
                             ws 
                           
                           ⁢ 
                           
                             tanh 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   γ 
                                   s 
                                 
                                 ⁢ 
                                 
                                   L 
                                   
                                     s 
                                     ⁢ 
                                     
                                         
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   18 
                 
               
             
             
               
                 
                   
                     I 
                     c 
                   
                   = 
                   
                     
                       
                         
                           Y 
                           Cs 
                         
                         ⁢ 
                         
                           U 
                           x 
                         
                       
                       ⇒ 
                       
                         Y 
                         Cs 
                       
                     
                     = 
                     
                       
                         
                           ( 
                           
                             
                               I 
                               c 
                             
                             
                               U 
                               x 
                             
                           
                           ) 
                         
                         
                           Uc 
                           = 
                           0 
                         
                       
                       = 
                       
                         - 
                         
                           1 
                           
                             
                               Z 
                               ws 
                             
                             ⁢ 
                             
                               sinh 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     γ 
                                     s 
                                   
                                   ⁢ 
                                   
                                     L 
                                     s 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   19 
                 
               
             
           
         
       
     
     According to equations 6 to 13, the values R s ′, L s ′, G s ′ and C s ′ of the stator section can thus be calculated analytically, and unambiguously. 
     The stray resistance of the stator section is calculated as follows:
 
 R   σ   =R′   s   ·L   s   Equation 20
 
     The stray inductance of the stator section is calculated as follows:
 
 L   σ   =L′   s   ·L   s   Equation 21
 
     The stray resistance R σ  and the stray inductance L σ  may be used, for example, for calculation and determination of pole wheel voltage UC during operation of the stator section  10  with a vehicle; this will be explained in more detail further below. 
     The values R′, L′, G′ and C′ of the track cables A and B are determined during the commissioning process (without a vehicle), by way of example as follows: 
     The switches Sub and Ska are opened, and the switch Sua is closed; the feed is provided via the converter device URA:
         1. When the switch Skb is closed (short-circuit measurement), U b =0 and, from equation 1:       

     
       
         
           
             
               
                 
                   
                     I 
                     b 
                   
                   = 
                   
                     
                       
                         
                           Y 
                           Cb 
                         
                         ⁢ 
                         
                           U 
                           x 
                         
                       
                       ⇒ 
                       
                         Y 
                         Cb 
                       
                     
                     = 
                     
                       
                         
                           ( 
                           
                             
                               I 
                               b 
                             
                             
                               U 
                               x 
                             
                           
                           ) 
                         
                         
                           Ub 
                           = 
                           0 
                         
                       
                       = 
                       
                         - 
                         
                           1 
                           
                             
                               Z 
                               
                                 w 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 b 
                               
                             
                             ⁢ 
                             
                               sinh 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     γ 
                                     b 
                                   
                                   ⁢ 
                                   
                                     L 
                                     b 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   22 
                 
               
             
           
         
       
         
         
           
             2. When the switch Skb is open (no-load measurement), I b =0 and, from equation 1: 
           
         
       
    
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           I 
                           b 
                         
                         = 
                           
                         ⁢ 
                         0 
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               
                                 Y 
                                 Db 
                               
                               ⁢ 
                               
                                 U 
                                 b 
                               
                             
                             + 
                             
                               
                                 Y 
                                 Cb 
                               
                               ⁢ 
                               
                                 U 
                                 x 
                               
                             
                           
                           ⇒ 
                           
                             
                               Y 
                               Db 
                             
                             
                               Y 
                               Cb 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           - 
                           
                             
                               ( 
                               
                                 
                                   U 
                                   x 
                                 
                                 
                                   U 
                                   b 
                                 
                               
                               ) 
                             
                             
                               Ib 
                               = 
                               0 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           - 
                           
                             cosh 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   γ 
                                   b 
                                 
                                 ⁢ 
                                 
                                   L 
                                   b 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   23 
                 
               
             
           
         
       
     
     Y Db  is derived from equations 22 and 23, as a result of which, according to equations 6 to 13, the values R b ′, L b ′, G b ′ and C b ′ of the track cable B can be determined analytically and unambiguously, provided that its length L b  is known. 
     The parameters of the track cable A can be determined by a corresponding measurement by the further converter device URB, provided that its length L a  is known. The two track cables A and B are preferably identical. 
     The only variable which cannot be measured directly in equation 14 is the current I ax . However, this can nevertheless be determined because it can be derived from equations 15 and 17:
 
 I   ax =−( I   x   +I   bx )=−( I   x   +Y   Db   ·U   x   +Y   Cb   ·U   b )  Equation 24
 
     The admittances Y Db  and Y Cb  are calculated in advance from equations 22 and 23. Since the currents and the voltages in equation 12 are now known, the components of the conductance matrix [Y a ], specifically Y Da  and Y Ca  can likewise be determined. The values R a ′, L a ′, G a ′ and C a ′ for the track cable A are therefore also obtained from equations 6 to 13. 
     A mathematical model for the two track cables A and B and for the stator section  10  can now be created using the values R′, L′, G′ and C′, and can be used for current regulation for the magnetic levitation railroad. 
     In some circumstances, the configuration of the track cable may be more complicated than is illustrated in  FIGS. 1 and 2 . Nevertheless, the four-pole theory is always valid and applicable. For example, the symmetry according to equation 2 may no longer be satisfied (Y 11 ≠Y 22 ). Equation 3, which states that the parallel conductances are identical, is still valid, however (Y 12 =Y 21 ). In general, the following equations are always valid. 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             I 
                             a 
                           
                         
                       
                       
                         
                           
                             I 
                             ax 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               Y 
                               Daa 
                             
                           
                           
                             
                               Y 
                               Ca 
                             
                           
                         
                         
                           
                             
                               Y 
                               Ca 
                             
                           
                           
                             
                               Y 
                               
                                 Dax 
                                 ⁢ 
                                 
                                     
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               U 
                               a 
                             
                           
                         
                         
                           
                             
                               U 
                               x 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   25 
                 
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             I 
                             b 
                           
                         
                       
                       
                         
                           
                             I 
                             bx 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               Y 
                               Dbb 
                             
                           
                           
                             
                               Y 
                               Cb 
                             
                           
                         
                         
                           
                             
                               Y 
                               Cb 
                             
                           
                           
                             
                               Y 
                               Dbx 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               U 
                               b 
                             
                           
                         
                         
                           
                             
                               U 
                               x 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   26 
                 
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             I 
                             x 
                           
                         
                       
                       
                         
                           
                             I 
                             c 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               Y 
                               Ds 
                             
                           
                           
                             
                               Y 
                               Cs 
                             
                           
                         
                         
                           
                             
                               Y 
                               Cs 
                             
                           
                           
                             
                               Y 
                               Ds 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               U 
                               x 
                             
                           
                         
                         
                           
                             
                               U 
                               
                                 c 
                                 ⁢ 
                                 
                                     
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   27 
                 
               
             
             
               
                 
                   
                     I 
                     x 
                   
                   = 
                   
                     - 
                     
                       ( 
                       
                         
                           I 
                           ax 
                         
                         + 
                         
                           I 
                           bx 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   28 
                 
               
             
           
         
       
     
     The parameters can therefore be determined unambiguously by means of the measured values from the three measurement devices  60 ,  70  and  100 . 
     With a vehicle located on it, the stator section  10  behaves slightly differently than during commissioning without a vehicle. The electrical characteristics of the stator section  10  with a vehicle can be approximated very accurately, using the following model, for frequencies below 350 Hz: 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             U 
                             c 
                           
                         
                       
                       
                         
                           
                             I 
                             c 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             1 
                           
                           
                             
                               - 
                               
                                 ( 
                                 
                                   
                                     R 
                                     σ 
                                   
                                   + 
                                   
                                     sL 
                                     σ 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 sC 
                                 ⁡ 
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                   
                               
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               U 
                               x 
                             
                           
                         
                         
                           
                             
                               I 
                               x 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   29 
                 
               
             
           
         
       
     
     In this case as well, it is approximately true that the stator current I c  corresponds to the star point current I s  of the stator section  10 , approximately (&lt;350 Hz),
 
I c =I s   Equation 30
 
       FIG. 5  shows the stator section  10  with a vehicle F traveling at a speed v, and which vehicle F is currently at a relative position x on the stator section  10 . The vehicle F can be represented electrically as a point voltage Uc. The point voltage corresponds to the pole wheel voltage Uc of the stator section, and cannot be measured directly, however, it can be calculated as follows,
 
 U   c   =U   x −( R   σ   +sL   σ )· I   x   Equation 31
 
     It is assumed that U c  forms a pure sinusoidal voltage; in this case, a harmonic model of the stator section can be derived from equation 31,
 
0 =U   x,harm −( R   σ   +sL   σ )· I   x,harm               U   x,harm =( R   σ   +sL   σ ) I   x,harm   Equation 32

     The stray resistance R σ  and the stray inductance L σ  can then be determined by means of this harmonic model, as is described in the document “Sensorless Control of a 2.4 MW Linear Motor for launching roller-coasters” (EPE 2003-Toulouse (ISBN: 90-75815-07-7), Authors: Andre Veltman, Paul van der Hulst, Marco C. P. Jonker, Jan P. van Gurp). 
     In the case of a complicated track cable configuration, the following relationship can also be derived by means of the equations 25, 26 and 28: 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             I 
                             a 
                           
                         
                       
                       
                         
                           
                             I 
                             b 
                           
                         
                       
                       
                         
                           
                             I 
                             x 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               Y 
                               
                                 D 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 aa 
                               
                             
                           
                           
                             0 
                           
                           
                             
                               Y 
                               Ca 
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               Y 
                               Cb 
                             
                           
                           
                             
                               Y 
                               Dbb 
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 Y 
                                 
                                   Da 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   x 
                                 
                               
                             
                           
                           
                             
                               - 
                               
                                 Y 
                                 Dbx 
                               
                             
                           
                           
                             
                               - 
                               
                                 ( 
                                 
                                   
                                     Y 
                                     Ca 
                                   
                                   + 
                                   
                                     Y 
                                     Cb 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               U 
                               a 
                             
                           
                         
                         
                           
                             
                               U 
                               b 
                             
                           
                         
                         
                           
                             
                               U 
                               x 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   33 
                 
               
             
           
         
       
     
     In equation 33, all the measurable variables (I a , I b , I x , U a , U b  and U x ) are combined in a single equation. The conductance matrix is now a 3×3 matrix (3 equations). The six unknown conductances (Y Daa , Y Dax , Y Ca , Y Dbb , Y DBx  and Y Cb ) can easily be determined since at least six equations are available. The six equations may be created, for example, by measuring the currents and the voltages at two different sampling times, since the currents and the voltages vary over time. 
     Furthermore, measurements at a plurality of sampling times also statistically improve the parameter estimation quality. 
     The problem in equation 36 can also be generalized using the following formulation:
 
I=YU  Equation 34
 
or
 
 e=I−ŶU   Equation 35
 
     In this case, I denotes a current vector, U a voltage vector, e an error vector (vector with the dimension 3×1), Y a real conductance matrix and Ŷ an estimated conductance matrix (matrix with the dimension 3×3). 
     A cost function J can be defined, for example, as follows: 
     
       
         
           
             
               
                 
                   J 
                   = 
                   
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         N 
                       
                       ⁢ 
                       
                         
                           e 
                           T 
                         
                         · 
                         e 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         N 
                       
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               I 
                               - 
                               
                                 
                                   Y 
                                   ^ 
                                 
                                 ⁢ 
                                 U 
                               
                             
                             ) 
                           
                           T 
                         
                         · 
                         
                           ( 
                           
                             I 
                             - 
                             
                               
                                 Y 
                                 ^ 
                               
                               ⁢ 
                               U 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   36 
                 
               
             
           
         
       
     
     This formulation is a known problem representation (according to Gauβ), where N denotes the number of measurements at a plurality of sampling times. There are a large number of methods for solving the equation 36, for example by minimizing J. 
     The position x of the vehicle F as shown in  FIG. 5  can moreover likewise be determined, to be precise using: 
                   x   =       1     j   ⁢           ⁢   ω   ⁢           ⁢     C   s   ′         ⁢       Ix   +   Is     Ux               Equation   ⁢           ⁢   37               
where Cs′ denotes the capacitance per unit length of the stator section  10 . The equation 37 can be used during operation of the magnetic levitation railroad, when the two switches Se and Ss are closed.
 
     When the two switches Se and Ss are open, the position x can be determined via the pole wheel angle Φ of the voltage Uc by measuring the phase angle of the voltage Ux; this is because Ux and Uc have the same phase angle and are accordingly collinear: 
     
       
         
           
             Uc 
             = 
             
               
                 ( 
                 
                   l 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     x 
                     Ls 
                   
                 
                 ) 
               
               ⁢ 
               Ux 
             
           
         
       
     
     In this case, the phase angle of Ux is therefore measured, the pole wheel angle Φ of the voltage Uc is determined using the phase angle of Ux, and the location of the vehicle calculated using the pole wheel angle Φ. 
     LIST OF REFERENCE SYMBOLS  
     
         
           10  Stator section 
           20  Connection 
           30  Star point 
           40  Feed connection 
           50  Feed connection 
           60  Converter-related measurement device 
           70  converter-related measurement device 
           80  Current regulation 
           90  Evaluation device 
           100  Stator-related measurement device 
           110  Evaluation device 
         A, B Track cable 
         Se Switch 
         Ss Switch 
         Sua Switch 
         Ska Switch 
         Sub Switch 
         Skb Switch 
         URA Converter device 
         URB Further converter device