Method for determining control parameters of a voltage regulator of a synchronous machine

Abstract

A synchronous machine (12) comprises a stator (22) having a stator winding (18) and a rotor (24) having a rotor winding (26), the stator winding (18) being connected to a power grid (16) together with stator terminals (20), and the rotor winding (26) being rotatably mounted in the stator (22), wherein a voltage regulator (14) of the synchronous machine (12) is adapted to output an excitation signal (u) to adjust a current in the rotor winding (26) for controlling the synchronous machine (12). A method for determining a control parameter (54) of a voltage regulator (14) comprises: receiving a first time series of values ​​of an excitation signal (u) and a second time series of measured values ​​of a terminal voltage (y) at stator terminals (20), wherein the first time series and the second time series are acquired within a time interval; determining coefficients (52) of a system transfer function (G(s)) of a synchronous machine (12), wherein the system transfer function (G(sj)) is a rational function, wherein the coefficients (52) of the system transfer function (G(s)) are recursively determined by performing a regression analysis using instrumental variables based on the first time series as a system input and the second time series as a system output; and determining the control parameter (54) of the voltage regulator (14) based on the coefficients (52) of the system transfer function (G(s)) by comparing a closed-loop transfer function formed by a controller transfer function (C(s)) and the system transfer function (G(s)) of the voltage regulator (14) with a desired closed-loop transfer function.

Description

Technical Field

[0001] The present invention relates to the field of synchronous machines, and in particular to a method, a computer program and a computer-readable medium for determining control parameters of a voltage regulator of a synchronous machine, and a synchronous machine having such a voltage regulator. Background Art

[0002] An automatic voltage regulator regulates the amplitude of the three-phase AC voltage at the terminals of a synchronous generator, whose exciter winding may be energized by an exciter machine, and typically comprises a PID controller. The control parameters of the PID controller may need to be adjusted during commissioning of the synchronous generator.

[0003] To simplify the commissioning procedure of synchronous generators, auto-tuning methods have been developed to automatically determine the control parameters based on data and high-level specifications. The available procedure proceeds roughly in three steps. First, the system is excited and the terminal voltages are recorded along with the excitation signal (e.g., the exciter voltage). Second, a transfer function model of the small signal behavior of the system around a given operating point is identified using the recorded data. Third, the transfer function model is used to calculate the parameters of the regulator.

[0004] Unfortunately, currently available methods may have problems identifying the transfer function model in the second step. For example, the least squares method may result in biased control parameter estimates, so that the model quality may be affected. It is also known to use particle swarm optimization. However, particle swarm optimization methods may result in inaccurate parameter estimates, may require the solution of a large number of initial value problems, and require expert knowledge to tune the parameters of the algorithm, such as the number of particles, parameters in the sample update rule.

[0005] Available methods for calculating the control parameters in the third step may also be problematic. The methods for calculating the control parameters may be very restrictive with respect to the achievable controller performance, or may again result in a tedious and time consuming trial and error method.

[0006] WO 2009 / 097 605 A1 describes a digital excitation control system in which a transfer function model is determined using the least squares method and control parameters are derived therefrom using zero-pole cancellation. Summary of the invention

[0007] The object of the present invention is to determine the control parameters of an automatic voltage regulator for a synchronous machine in an easy to use and automatic manner.

[0008] This object is achieved by the subject-matter of the independent claims. Further exemplary embodiments are evident from the dependent claims and the following description.

[0009] One aspect of the invention relates to a method for determining control parameters of a voltage regulator of a synchronous machine. With this method, control parameters of an automatic voltage regulator can be automatically calculated. The voltage regulator can be used to adjust the amplitude of the three-phase AC terminal voltage of the synchronous generator at a desired level.

[0010] The synchronous machine may comprise a stator with a stator winding and a rotor with a rotor winding, the stator winding being connected to the grid together with the stator terminals and the rotor winding being rotatably mounted in the stator. The (automatic) voltage regulator may be adapted to output an excitation signal to adjust the current in the rotor winding for controlling the synchronous machine such that the terminal voltage in the stator terminals is controlled. For example, the excitation signal may be a voltage signal applied to the rotor winding itself or to an excitation system coupled to the rotor.

[0011] With the voltage regulator, the terminal voltage in the stator terminals can be adjusted and / or controlled. Other control targets of the voltage regulator can be the reactive power and / or the power factor of the synchronous machine.

[0012] The method may be automatically performed by a controller, which may be a part of a voltage regulator. The control parameter may be a parameter of another controller and / or a control part of the voltage regulator.

[0013] Using this method, the control parameters can be determined in three steps.

[0014] According to an embodiment of the invention, the method comprises: in a first step, receiving a first time series of values ​​of an excitation signal and a second time series of measured values ​​of a terminal voltage, wherein the first time series and the second time series are acquired within a time interval. First, a synchronous machine such as a generator may be excited (possibly by an exciter system). For example, the synchronous machine may be excited at a fixed operating point and the terminal voltages as well as the excitation signal may be recorded. The first time series and the second time series may comprise values ​​acquired at consecutive time instants and / or equidistant time instants.

[0015] According to an embodiment of the present invention, the method comprises: in a second step, determining coefficients of a system transfer function of the synchronous machine, wherein the system transfer function is a rational function, wherein the coefficients of the system transfer function are recursively determined by regression analysis using instrumental variables. In the regression analysis, the first time series can be regarded as a system input and the second time series can be regarded as a system output.

[0016] The system transfer function and other transfer functions mentioned below may be provided in a Laplace transform system.It may be that the first time series and the second time series are Laplace transformed before being input into the regression analysis.

[0017] For example, a reduced instrumental variable method may be used.By means of the instrumental variable method, a continuous time transfer function may be identified.The system transfer function may be determined for the small signal behavior of the system around a given operating point using the recorded data from the first step.

[0018] The instrumental variable method may not lead to biased parameter estimates like the (recursive) least squares method. Furthermore, it may not require the expertise to manually tune the algorithm. Moreover, the instrumental variable method may require only the solution of a few initial value problems to find the coefficients of the system transfer function. For example, fewer than 25 initial value problems may have to be solved before the algorithm terminates.

[0019] According to an embodiment of the invention, the method comprises: in a third step, determining a control parameter of the voltage regulator according to coefficients of the system transfer function by comparing a closed-loop transfer function formed by a controller transfer function of the voltage regulator and the system transfer function with a desired closed-loop transfer function.

[0020] The controller transfer function may be a transfer function of a controller of a voltage regulator for which the control coefficients are determined. Thus, the controller transfer function may depend on controller parameters. From the controller transfer function and the system transfer function, an open-loop transfer function may be determined, for example, by multiplying the two transfer functions. From the open-loop transfer function, a closed-loop transfer function may be determined. Finally, it may be assumed that the closed-loop transfer function is equal to an expected closed-loop transfer function with known coefficients, such as a transfer function of a first-order system or a second-order system. For example, the expected coefficients of the expected transfer function may be an expected settling time and / or an expected overshoot. Thus, the control parameters may be calculated from the expected coefficients of the expected closed-loop transfer function and the coefficients of the system transfer function.

[0021] According to an embodiment of the present invention, in a regression analysis using instrumental variables, the coefficients of the system transfer function are recursively determined in the following manner: an actual step excitation signal is calculated by filtering a previous step excitation signal using the denominator of the system transfer function having the actual step coefficient; and an actual step terminal voltage is calculated by filtering a previous step terminal voltage using the denominator of the system transfer function having the actual step coefficient.

[0022] As already mentioned, all these functions and signals can be evaluated in the Laplace domain. In particular, the higher-order derivatives of the excitation signal and the terminal voltage can be determined by multiplying by the corresponding exponentiation of the Laplace variables. For the excitation signal, all derivatives of the denominator up to the n-1 order can be determined, and / or for the terminal voltage, all derivatives of the numerator of the system transfer function up to the mth order can be determined.

[0023] According to an embodiment of the present invention, in the regression analysis using instrumental variables, the coefficients of the system transfer function are recursively determined by: calculating the actual step response by filtering the first time series of measured values ​​of the excitation signal using the system transfer function with the actual step coefficients; and determining the next step coefficient by minimizing the difference between the n-th order derivative of the actual step terminal voltage and the product of the coefficient vector and the instrumental variable vector. As mentioned before, n is the order of the denominator of the system transfer function.

[0024] The coefficient vector may be formed from the next step coefficients. Note that there are n+m-1 such coefficients, ie, m represents the numerator and n-1 represents the denominator.

[0025] The instrumental variable vector is formed by the n-1 derivatives of the actual step response and the m derivatives of the actual step excitation signal.

[0026] According to an embodiment of the present invention, the method further comprises: forming an initial step excitation signal by filtering a first time series of measured values ​​of the excitation signal using a high pass filter; and / or forming an initial step terminal voltage by filtering a second time series of measured values ​​of the terminal voltage using a high pass filter. The filtering can be performed in the Laplace domain by multiplying by a filter factor. The filter factor can be a cutoff frequency divided by a fraction of the cutoff frequency plus a Laplace variable exponentiated. The filter factor can be exponentiated by n+1.

[0027] According to an embodiment of the present invention, the method also includes: determining the initial step coefficient of the system transfer function by minimizing the product of the nth-order derivative of the initial step terminal voltage and the coefficient vector and the regression vector, wherein the coefficient vector is formed by the initial step coefficients, and the regression vector is formed by n-1 derivatives of the initial step terminal voltage and m derivatives of the initial step excitation signal.

[0028] The initial step signal can be determined by Laplace transforming the corresponding time series. The derivatives of these signals can be determined by multiplying by the corresponding exponentiated Laplace variables. In addition, as described above, a filter factor can be multiplied.

[0029] In a third step, the control parameter calculation may be based on a pole-zero cancellation procedure, wherein the poles and / or zeros of the resulting closed-loop transfer function are matched to the poles and / or zeros of the desired closed-loop transfer function. Specifically, a pole cancellation procedure that implements a desired settling time and / or overshoot may be applied. In a variant, a desired steady-state error may also be used as the desired parameter.

[0030] Thus, there may be no need for mapping of closed-loop poles to time-domain behavior and / or there may be no need for tuning of objective functions and algorithms. The commissioning engineer can directly interpret the desired settings implemented in the closed loop (i.e., settling time, overshoot, and possible steady-state error) and avoid any tedious and time-consuming indirect parameter tuning.

[0031] According to an embodiment of the present invention, the desired closed-loop transfer function is a second-order transfer function, for example, a second-order transfer function with a desired settling time and / or a desired overshoot. In this way, the performance of the closed loop is not necessarily limited to a first-order system.

[0032] According to an embodiment of the present invention, the desired closed-loop transfer function is a first-order transfer function, for example, a first-order transfer function with a desired settling time. In addition, as mentioned before, the first-order transfer function can also be used to determine the control parameters. In general, higher-order transfer functions are also possible.

[0033] According to an embodiment of the invention, the controller transfer function is a transfer function of a PID controller. The PID controller may include a proportional controller part, an integral control part and a differential controller part. The control parameter may be a factor of these parts, or the factor of these parts may depend on the control parameter. It may be that the control parameter sets the factor of the proportional controller part, the integral control part and the differential controller part.

[0034] According to an embodiment of the present invention, the desired steady state error is set by comparing the closed loop transfer function with the controller transfer function.For controllers that do not automatically force the steady state error to zero, the maximum magnitude of the error can also be used as a setting for a fixed control parameter.

[0035] According to an embodiment of the present invention, the controller transfer function is a transfer function of a lead-lag controller. Such a transfer function may include at least two factors, wherein each factor has a pole and a zero. For one factor, the pole may be located at a higher position as a zero, while for another factor, the pole may be located at a lower position as a zero.

[0036] Furthermore, the lead-lag controller need not automatically adjust the steady-state error to zero. Thus, the lead-lag controller may have at least four control parameters that may be determined such that a desired settling time, a desired overshoot, and a desired steady-state error are achieved.

[0037] According to an embodiment of the present invention, the method further comprises: generating a voltage to be applied to the rotor winding by generating a first time sequence of values ​​of the excitation signal and applying the first time sequence to the synchronous machine; and measuring a second time sequence of the terminal voltage. For example, the first time sequence may have a special form, such as a specific step function or a random signal. The first time sequence may also be determined during normal operation of the synchronous machine system, i.e., the first time sequence is generated by a voltage regulator having another set of control parameters.

[0038] According to an embodiment of the invention, the control parameters are determined during commissioning of the synchronous machine. The method may be performed once when the synchronous machine is installed. Afterwards, the once determined control parameters may be used during operation of the synchronous machine.

[0039] According to an embodiment of the present invention, the control parameter is periodically determined during the continuous operation of the synchronous machine. In this case, the first time series and the second time series can be determined at regular intervals, and the control parameter can be determined therefrom. In other words, the determined control parameter can change over time. Note that in this case, two time series can be determined during the operation of the synchronous machine system.

[0040] Generally speaking, a three-step procedure may be applied during commissioning of a voltage regulator to determine controller parameters once and / or periodically to update control parameters while a synchronous machine system is operating.

[0041] Another aspect of the invention relates to a method for controlling a synchronous machine. The method can be used not only for setting and / or determining control parameters, but also for using the control parameters during operation of the synchronous machine.

[0042] The method for controlling a synchronous machine may include: determining control parameters as described above and below, applying the determined control parameters to a voltage regulator of the synchronous machine, specifically, to a controller of the voltage regulator; and controlling the synchronous machine using the voltage regulator. Specifically, the synchronous machine may be controlled by adjusting the terminal voltage using the voltage regulator.

[0043] Another aspect of the invention relates to a computer program for determining a control parameter of a voltage regulator, which computer program, when executed on a processor, is adapted to perform the method as described above and below.

[0044] Another aspect of the invention relates to a computer readable medium for determining control parameters of a voltage regulator having such a computer program stored therein. The computer readable medium may be a floppy disk, a hard disk, a USB (Universal Serial Bus) storage device, a RAM (Random Access Memory), a ROM (Read Only Memory), an EPROM (Erasable Programmable Read Only Memory) or a flash memory. The computer readable medium may also be a data communication network, for example the Internet, which allows downloading program code. In general, the computer readable medium may be a non-transitory medium or a transient medium.

[0045] Another aspect of the invention relates to a controller for a voltage regulator of a synchronous machine, the controller being adapted to perform the method described above and below. The controller may comprise a processor and a memory in which a computer program is stored. However, the method may also be implemented partially or completely in hardware.

[0046] Another aspect of the invention relates to a synchronous machine system, the synchronous machine system comprising a synchronous machine having a stator and a rotor, the stator having a stator winding connected to a power grid via a terminal, the rotor having a rotor winding rotatably mounted in the stator; and a voltage regulator, the voltage regulator supplies voltage to the rotor winding. The voltage regulator may include an electrical converter, which may be supplied with electrical power from the power grid and is suitable for generating a voltage for the rotor winding. The voltage regulator may also be powered by a permanent magnet generator (PMG) and / or a battery. Further, the voltage regulator may include a controller for controlling the converter and for performing the methods described above and below.

[0047] It has to be understood that features of the method described above and below may be features of the synchronous machine system, the controller, the computer program and / or the computer readable medium described above and below.

[0048] These and other aspects of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The subject matter of the invention is explained in more detail in the following text with reference to exemplary embodiments illustrated in the drawings.

[0050] Figure 1 A synchronous machine system according to an embodiment of the invention is schematically shown.

[0051] Figure 2 shows a Figure 1 A graph of the response function of a system.

[0052] Figure 3 Schematically shows a controller according to an embodiment of the present invention. Figure 1A block diagram of the various parts of the system.

[0053] Figure 4 A flow chart of a method for determining a control parameter of a voltage regulator according to an embodiment of the present invention is shown.

[0054] The reference numerals used in the drawings and their meanings are listed in summary form in the reference numeral list. In principle, identical parts are provided with the same reference numerals in the drawings. DETAILED DESCRIPTION

[0055] Figure 1 A synchronous machine system 10 is shown with a synchronous machine 12 and a voltage regulator 14. The synchronous machine 12, such as a synchronous generator and / or a synchronous motor, is connected to a power grid 16 via its stator windings 18 and in particular stator terminals 20. The stator windings are mounted to a stator 22 of the synchronous machine 12, a rotor 24 of the synchronous machine 12 is rotatably mounted in the stator 20 and carries rotor windings 26, which are powered by the voltage regulator 14.

[0056] like Figure 1 As shown, the rotor winding 26 may be powered by an exciter system 28 that includes an exciter winding 30 that rotates with the rotor 24 and is powered by a static voltage regulator winding 32 that is electrically connected to the voltage regulator 14. The voltage from the voltage regulator 14 induces a voltage in the exciter winding 30 that is rectified using an exciter rectifier 34 and supplied to the rotor winding 26.

[0057] The voltage regulator 14 comprises a converter 36 which is powered via a transformer 38 connected to the grid 16. The converter 36 is controlled by a controller 40 which measures the terminal voltage y and the terminal current i in the terminals 20 of the synchronous machine 12.

[0058] For example, the synchronous generator 12 can contribute to the electrical power in the grid 16 by converting mechanical energy into electrical energy. The mechanical energy can be powered by a steam turbine, a gas turbine, or a hydro turbine. The turbine can power the rotor 24 of the synchronous generator 12, which maintains a magnetic field generated by a current flowing through a rotor winding 26 such as a wire coil attached to the rotor 24. The magnetic field on the rotor 24 relative to the stator winding 18 such as a wire coil mounted on the stator 22 induces a voltage in the stator winding 18. Typically, the three stator windings 18 are mounted on the stator 22 in a geometric manner so that under steady-state conditions, the induced voltage y measured at the terminals 20 of the stator windings 18 produces three sinusoidal waveforms with the same amplitude and frequency, which are phase-shifted by 120 degrees. The frequency and amplitude of the terminal voltage y are mainly affected by the angular velocity of the rotor 24 and the intensity of the exciter current, respectively.

[0059] Stable operation of the grid 16 may require that the amplitude of the (typically three-phase) terminal voltage y of the synchronous generator 12 is almost constant and deviates only slightly from a given desired value. However, the terminal voltage y of the grid-connected generator 12 may depend non-locally on all other entities present in the grid 16, such as electrical loads, renewable power sources, other generators, and may deviate significantly from its desired waveform. Therefore, it may be necessary to adjust the amplitude and frequency of the terminal voltage y to the desired value by appropriately adjusting the exciter current and the rotor speed, respectively. Typically, the current in the rotor winding 26 is provided by an exciter system 28, which can be regarded as a second generator 30, 32. Since the winding 30 of the exciter system 28 can be connected to the rotor winding 26 of the synchronous generator 12 via a rectifier 34, the amplitude of the terminal voltage y of the synchronous generator 12 can be adjusted by manipulating the exciter current of the exciter system 28.

[0060] The (automatic) voltage regulator (AVR) 14 is used to regulate the actual amplitude of the terminal voltage y(t) of the synchronous machine 12. Generally speaking, its output is either directly connected to the rotor winding 26 of the synchronous machine 12 or to the winding 32 of the exciter system 28. The output signal u of the voltage regulator 14 is avr (t) can be determined based on the error e(t)=r(t)-y(t) between the expected amplitude of the terminal voltage r(t) and the measured amplitude of the terminal voltage y(t).

[0061] For example, in the case of a PID controller, the output signal may consist of three terms:

[0062]

[0063] The output of the voltage regulator 14 may be formed by a linear combination of the error, the integral of the error, and the derivative of the error. The constant coefficient k of the linear combination is p , k i and k d The control parameters may be referred to as controller parameters or controller gains. The control parameters affect the performance of the closed loop formed by the dynamic system including the voltage regulator 14 and the synchronous machine 12 which may include an exciter system 28.

[0064] Figure 2 shows that under the control of the controller 40, the initial expected value r i To the final expected value r f The terminal voltage y during a step (which is usually called a step response) m (t) is a graph of examples of actual amplitudes.

[0065] Furthermore, Figure 2The performance index of the step response is shown. In general, it may be desirable for the closed loop to react quickly to changes in the reference signal so that the actual amplitude of the terminal voltage y(t) approaches the new desired value r as quickly as possible. f The rise time T associated with the step response r , stabilization time T s and overshoot OS can be used as controller performance indicators. For example, the rise time T r It can mean that the amplitude of the terminal voltage y(t) needs to be increased from the initial expected value r i and the final expected value r f The time interval between the 10% to 90% increase of the reference step. s It can be the time interval from the reference step to the time when y(t) remains within ±2% of r(t). Overshoot OS can be the time interval from the reference step to the time when y(t) remains within ±2% of r(t). f The maximum excess y(t) and / or may be stated in %, such as

[0066] Terminal voltage y(t) with stabilization time T s The curve form of the overshoot OS is a typical form of a second-order system. In the following, it is assumed that the closed loop consisting of the controller 40 and the synchronous machine 12 is used to set the control parameters of the controller 30 to achieve the stabilization time T s and overshoot for a second-order system for a specific value of OS.

[0067] Figure 3 A block diagram with controller components 42 , 44 , 44 , 48 of the controller 40 and a block 50 illustrating components of the system 10 such as the synchronous machine 12 and the actuator system 28 reacting to an actuator signal u(t) of the controller 40 is shown. Figure 4 A flow chart of a method that may be performed by the controller portions 42, 44, 44, 48 is shown.

[0068] In step S10, the system including the synchronous machine 12 and the optional exciter system 28 is excited within a specific time interval [0, T], and a signal (excitation signal u ) can be recorded within a certain sampling time h. c ) (such as the voltage applied to the winding 32 or 26 and the terminal voltage y m of magnitude).

[0069] For example, the excitation signal u may be generated by the signal generator 42 and / or may be a step signal or a pseudo-random binary signal. The signal generator 42 may generate the voltage to be applied to the rotor winding by generating a first time series of values ​​of the excitation signal u and applying them to the synchronous machine 12 .

[0070] However, the excitation signal uc It may also be generated by the controller 48 , ie, during operation of the synchronous machine 12 .

[0071] The terminal voltage y can be measured m To determine the second time series.

[0072] Then, a first time series of values ​​of the excitation signal u and a second time series of measured values ​​of the terminal voltage y may be received in the system identification block 40 .

[0073] In step S12, the system identifier 44 determines coefficients 52 of the system transfer function G(s) of the system indicated by box 50. The system transfer function G(s) is a rational function in the Laplace variable s.

[0074]

[0075] Generally speaking, the coefficient b of the system transfer function G(s) 0 , …, b m b 0 , …, b m , a 1 , …, a n ( Figure 3 and Figure 4 52) is determined recursively by performing a regression analysis using instrumental variables based on the first time series as system input and the second time series as system output, as explained below.

[0076] Depending on the specific application, the model structure (n,m) (i.e., the order of the numerator m and the order of the denominator n) may vary. In a typical application, the winding 26 of the synchronous machine 12 is excited by the exciter system 28, and when the synchronous machine 12 is disconnected from the grid 16, the small signal behavior of the terminal voltage y is of interest, and the structure can be fixed to (2,1). By increasing the order of the denominator, the dynamics of the sensor can also be taken into account to obtain a better fitting model. Similarly, (n,m) can be adapted to different situations, for example, when the winding 26 of the synchronous machine 12 is energized by a static exciter system.

[0077] Reduced Instrumental Variable Method

[0078] The reduced instrumental variable (SRIV) approach can be used to calculate the coefficients of the system transfer function G(s)52(b 0 , …, b m , a 1 , …, a n ) to model the small signal behavior of a system 50 including the synchronous machine 12 and possibly the exciter system 28.

[0079] The basis for calculation is the data set

[0080] (u,y)

[0081] Where u and y are discrete time signals mapped from discrete intervals {1, 2, ..., T} to real numbers. Here, y is the amplitude of the measured terminal voltage and u is the voltage of the windings 26, 32 of the synchronous machine 12 or the exciter system 28. The constant h is the sampling time of the recorded signal. The data can be collected by referencing a step excitation system or by applying a pseudo-random binary signal to the field winding voltage.

[0082] We then refer to the coefficient 52 via the coefficient vector,

[0083] θ=(a 1 , …, a n , b 0 , …, b m ) T

[0084] And use u c and c to denote the continuous-time signals obtained from the zero-order hold interpolation of signals u and y, respectively. The parameters θ are calculated in an iterative manner.

[0085] Initial parameter calculation

[0086] Note that all the following signals have been Laplace transformed. Initially, the signal u c and c Filtering is performed using a filter with a cutoff frequency of λ = 10 / (2πh):

[0087]

[0088] Specifically, for i∈{1,…,n},j∈{0,…,m}, where y f =y c and u f =u c , calculates the following filter response:

[0089]

[0090] The initial step excitation signal u can be formed by filtering the first time series of measured values ​​of the excitation signal u using a high-pass filter f , and / or the initial step terminal voltage y may be formed by filtering the second time series of measured values ​​of the terminal voltage y using a high pass filter f .

[0091] if Yes f The derivative of y fis the function of G(s) on u f The response is, then for all t = ∈ [0, h (T-1)], the following equation is satisfied:

[0092]

[0093] Use the regression vector:

[0094]

[0095] It can be concluded that Initial parameter estimates are obtained by using At sampling time t i =(i-1)h total The objective function is obtained by minimizing the deviation of , where i∈{1,…,T}.

[0096]

[0097] Generally speaking, the initial step coefficient θ of the system transfer function G(s) 0 The initial step terminal voltage y f The nth-order derivative and coefficient vector θ 0 With the regression vector It is obtained by minimizing the product of , where the coefficient vector is formed by the initial step coefficients, and the regression vector is formed by the derivative of the initial step terminal voltage y and the initial step excitation signal u.

[0098] Initial step coefficient θ 0 It can be calculated explicitly by the following equation:

[0099]

[0100] Parameter Update

[0101] During the parameter update process, the initialization process is essentially repeated and the coefficients θ are determined recursively. However, there are two significant differences. First, the filter for computing the higher-order derivatives is given by the denominator of the system transfer function:

[0102]

[0103] here,

[0104]

[0105] is the coefficient 52 in the actual iteration k. Now, the filter response is calculated by the following equation:

[0106]

[0107] Actual step excitation signal uf By using a step factor θ k The denominator A of the system transfer function G(s) is the previous step excitation signal u f Similarly, the actual step terminal voltage y f By using a step size coefficient θ k The denominator A of the previous step terminal voltage y f Filtering is performed to calculate.

[0108] The second difference stems from the use of instrumental variables when computing the coefficient updates. For this purpose, the system transfer function G(s) is used to compute the noise-free response:

[0109]

[0110] The actual step response x is obtained by using a linear function with actual step coefficient θ k The system transfer function G(s) is the measured value u of the excitation signal c The first time series is filtered to calculate .

[0111] Then, the derivative of x i∈{1,…,n-1} is calculated by the following equation:

[0112]

[0113] And the instrumental variable vector:

[0114]

[0115] is defined.

[0116] The actual step terminal voltage y f The nth order derivative and coefficient vector θ k and the instrumental variable vector ζ T The next step coefficient θ is determined by minimizing the difference between the products k+1 The instrumental variable vector ζ T The actual step response x and the actual step excitation signal u f The derivative of is formed.

[0117] Specifically, the next step coefficient θ k+1 It can be calculated as follows:

[0118]

[0119] The iteration can be repeated until |θ k+1 -θ k |Sufficiently small and / or smaller as a threshold, for example, less than 0.01, or the number of iterations exceeds a certain number, such as 10.

[0120] Note that the method is freely tunable, i.e., given a data set (u,y), there are essentially no parameters that affect the computational results.

[0121] Moreover, for all i∈{1,...,n}, the filter response This is done by solving an initial value problem in one go. Similar comments apply to and Therefore, it is applicable to and Thus, to compute the filter response, two initial value problems may have to be solved in the initial parameter calculation, and three initial value problems may have to be solved in each coefficient update iteration. For example, a fourth-order Runge-Kutta scheme with a fixed step size may be used to solve the initial value problems.

[0122] Calculation of control parameters

[0123] In step S14 , the parameter computer 46 uses the coefficients 52 of the model G(s) and other specifications 56 to determine control parameters 54 .

[0124] In general, there are a variety of methods to design the controller 48 through the controller transfer function C(s). The following assumes that the system transfer model function has a structure where n=2 and m=1, and has the following form:

[0125]

[0126] There may be cases where the identified transfer function G(s) has two complex conjugate poles and it is not possible to express G(s) using two real poles. In this case, we express G(s) by Modify the coefficient a of the denominator polynomial G(s) 1 , so that the modified transfer function It can be represented using two real poles.

[0127] Specifically, as explained below, the closed-loop transfer function formed by the controller transfer function C(s) of the controller 48 and the system transfer function G(s) is compared to a desired closed-loop transfer function, such as Figure 2 As shown, controller parameters 54 are determined.

[0128] Two embodiments of the control parameter calculation for two different controllers 48 are described below. The first controller is a so-called series / cascade PID controller. The second controller is a double lead-lag controller.

[0129] PID controller parameter calculation

[0130] Specification 56 for calculating the PID controller parameters is the desired settling time T s and expected overshoot OS (see Figure 2 ).

[0131] The transfer function of the PID controller 48 is given by the following equation:

[0132]

[0133] Note that the control parameter T a , T b and K b The factor k which can be used to set the proportional controller part, the integral control part and the differential controller part as described above p , k i and k d .

[0134] Control parameter 54(T a , T b and K b ) is determined such that the open loop transfer function, which is the product of the controller transfer function C(s) and the system transfer function G(s), yields:

[0135]

[0136] where α∈]0,1[ is a parameter to be determined in the second step. Specifically, the control parameter 54 is given by the following equation:

[0137] T a =T 1 , T b =T 2 (1-α), and K b =(1-α) / α.

[0138] According to the open-loop transfer function, the closed-loop transfer function follows:

[0139]

[0140] The closed-loop transfer function is similar to the second-order transfer function (see Figure 2 ), where the standard form of the second-order transfer function can be given by the following equation

[0141]

[0142] Among them, heuristic

[0143]

[0144] The damping coefficient and stabilization time T sBy comparing the coefficients of the closed-loop second-order transfer function and the standard form of the second-order transfer function, the parameters can be obtained

[0145]

[0146] and

[0147]

[0148] Damping coefficient It can be derived from the overshoot specification OS. For OS>0, the damping coefficient follows:

[0149]

[0150] And for OS>0, Note that the parameter α is limited to the interval ]0,1[. However, if the desired stabilization time T s If the expected settling time T is too long, α may become greater than 1. In this case, the expected settling time T can be simply reduced to s , so that α∈]0,1[.

[0151] Lead-Lag Controller Parameter Calculation

[0152] The specification 56 for calculating the control parameter 54 of the lead-lag controller 48 is the desired settling time T s , expected overshoot OS and expected steady-state error e ss .

[0153] The controller transfer function C(s) of the controller 48 is given by the following equation:

[0154]

[0155] The numerator time constant of the controller is set as follows:

[0156] T c1 =T 1 ,T c2 =T 2

[0157] So that the open loop transfer function is:

[0158]

[0159] Let T B1 =T and T B2 =cT, then the closed loop follows:

[0160]

[0161] Select gain K R, so that the desired steady-state error e is implemented in the closed loop ss ,Right now

[0162]

[0163] You can choose the remaining parameters T B1 and T B2 (or equivalently c and T) to implement the desired settling time and overshoot in the transfer function:

[0164]

[0165] This transfer function is very close to the actual closed-loop transfer function. In the first step, the damping coefficient It is derived from the overshoot specification, just like a PID controller in a PID controller. By comparing the coefficients to the standard form of the second order transfer function:

[0166]

[0167] It turns out that:

[0168]

[0169] By solving the equation for c, we can conclude that:

[0170]

[0171] If c may result in complex numbers, the gain K can be increased R to ensure that c is a real number. The time constant T is determined by the stable time heuristic:

[0172]

[0173] It follows that:

[0174]

[0175] as well as

[0176] T B1 =cT B2 .

[0177] Synchronous machine control

[0178] The three-step procedure for steps S10, S12, S14 may be applied during commissioning of the voltage regulator 14 to determine the controller parameters 54 and / or to periodically update the controller parameters 54 while the system 10 is operating. In this case, the data in step S10 may be obtained by measuring the desired signals u, y while the system 10 is operating.

[0179] After steps S10 , S12 , S14 , the control parameters 54 may be applied to the controller 48 of the voltage regulator 14 .

[0180] In step S16, the controller 48 may then adjust the terminal voltage y towards a reference signal r(t) which may be time dependent. The controller 48 may receive a reference signal r(t) and may control the terminal voltage y towards this reference signal r(t). m The magnitude of (t).

[0181] Although the invention has been described and illustrated in detail in the drawings and the foregoing description, such description and illustration are to be considered illustrative or exemplary rather than restrictive; the invention is not limited to the disclosed embodiments. Other variations of the disclosed embodiments may be understood and implemented by those skilled in the art in practicing the claimed invention by studying the drawings, the disclosure and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude the plural. A single processor or controller or other unit may perform the functions of several items recited in a claim. The fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be interpreted as limiting the scope.

[0182] Reference numerals list

[0183] 10 Synchronous machine system

[0184] 12 Synchronous machine

[0185] 14 Voltage Regulator

[0186] 16 Power Grid

[0187] 18 Stator winding

[0188] 20 Stator terminal

[0189] 22 Stator

[0190] 24 Rotor

[0191] 26 Rotor winding

[0192] 28 Exciter System

[0193] 30 Exciter winding

[0194] 32 Voltage regulator winding

[0195] 34 Exciter Rectifier

[0196] 36 Converter

[0197] 38 Transformer

[0198] 40 Controller

[0199] 42 Signal Generator

[0200] 44 System Identification

[0201] 46 Parameter calculation

[0202] 48 Voltage Controller

[0203] 50 represents the frame of the system

[0204] t time

[0205] The amplitude of the voltage at the y and y(t) terminals

[0206] T r Rise time

[0207] T s Stabilization time

[0208] OS Overshoot

[0209] G(s) system transfer function

[0210] 52 System transfer model coefficients

[0211] C(s) controller transfer function

[0212] 54 Control parameters

[0213] u, u(t) excitation signal

[0214] r(t) reference signal

[0215] 56 Specifications

Claims

1. A method for determining a control parameter (54) of a voltage regulator (14) of a synchronous machine (12), the synchronous machine (12) comprising a stator (22) having a stator winding (18) and a rotor (24) having a rotor winding (26), the stator winding (18) being connected to a power grid (16) together with stator terminals (20), and the rotor winding (26) being rotatably mounted in the stator (22), wherein the voltage regulator (14) is adapted to output an excitation signal (u) to adjust a current in the rotor winding (26) for controlling the synchronous machine (12); The method comprises: Receiving a first time series of values ​​of the excitation signal (u) and a second time series of measured values ​​of the terminal voltage (y) in the stator terminal (20), wherein the first time series and the second time series are acquired within a time interval; determining coefficients (52) of a system transfer function (G(s)) of the synchronous machine (12), wherein the system transfer function (G(s)) is a rational function, wherein the coefficients (52) of the system transfer function (G(s)) are recursively determined by performing a regression analysis using instrumental variables based on the first time series as a system input and the second time series as a system output; The control parameters (54) for the voltage regulator (14) are determined from the coefficients (52) of the system transfer function (G(s)) by comparing a closed-loop transfer function formed by a controller transfer function (C(s)) of the voltage regulator (14) and the system transfer function (G(s)) with a desired closed-loop transfer function.

2. The method according to claim 1, Wherein, in the regression analysis using instrumental variables, the coefficients (52) of the system transfer function (G(s)) are recursively determined in the following manner: calculating an actual step excitation signal (u) by filtering a previous step excitation signal (u) by the denominator of said system transfer function (G(s)) having an actual step coefficient; calculating an actual step terminal voltage (y) by filtering a previous step terminal voltage (y) using the denominator of the system transfer function (G(s)) having the actual step coefficient; calculating an actual step response by filtering said first time series of measured values ​​of said excitation signal (u) using said system transfer function (G(s)) having said actual step coefficient; and By making the nth derivative of the actual step terminal voltage (y) and the coefficient vector θ k The next step coefficient is determined by minimizing the difference between the product of and the instrumental variable vector, where n is the order of the denominator of the system transfer function (G(s)), and where the coefficient vector θ k is formed by the next step coefficient, and the instrumental variable vector is formed by the derivative of the actual step response and the derivative of the actual step excitation signal (u).

3. The method according to any one of the preceding claims, further comprising: forming an initial step excitation signal (u) by filtering said first time series of measured values ​​of said excitation signal (u) using a high pass filter; The initial step terminal voltage (y) is formed by filtering the second time series of measured values ​​of the terminal voltage (y) using the high pass filter.

4. The method according to claim 1 or 2, further comprising: The initial step coefficient of the system transfer function (G(s)) is determined by minimizing the product of the nth-order derivative of the initial step terminal voltage (y) and the coefficient vector θ0 and a regression vector, wherein the coefficient vector θ0 is formed by the initial step coefficients, and the regression vector is formed by the derivative of the initial step terminal voltage (y) and the derivative of the initial step excitation signal (u).

5. The method according to claim 1 or 2, wherein the closed loop transfer function is determined by the product of the controller transfer function and the system transfer function (G(s)); and / or The desired closed-loop transfer function is a function with a desired settling time (T s ) and / or the second order transfer function of the desired overshoot (OS).

6. The method according to claim 1 or 2, wherein the controller transfer function (C(s)) is the transfer function of the PID controller; The control parameters (54) set factors for a proportional controller part, an integral control part and a derivative controller part.

7. The method according to claim 1 or 2, Wherein the desired steady-state error is set by comparing the closed-loop transfer function and the controller transfer function (C(s)).

8. The method according to claim 1 or 2, The controller transfer function (C(s)) is the transfer function of the lead-lag controller.

9. The method according to claim 1 or 2, further comprising: generating a voltage to be applied to the rotor winding (26) by generating the first time series of values ​​of the excitation signal (u) and applying the first time series to the synchronous machine; The second time series of the terminal voltage (y) is measured.

10. The method according to claim 1 or 2, wherein the control parameter (54) is determined during commissioning of the synchronous machine (12); and / or The control parameter (54) is determined periodically during continuous operation of the synchronous machine (12).

11. A method for controlling a synchronous machine (12), the method comprising: Determining a control parameter (54) according to the method of any one of claims 1 to 10; applying the determined control parameters (54) to the voltage regulator (14) of the synchronous machine (12); The synchronous machine (12) is controlled by means of the voltage regulator (14).

12. A computer program product comprising a computer program for determining a control parameter (54) of a voltage regulator (14), the computer program being adapted to perform the method according to any one of claims 1 to 11 when being executed on a processor.

13. A computer-readable medium for determining a control parameter (54) of a voltage regulator (14), wherein a computer program product according to claim 12 is stored.

14. A controller (40) of a voltage regulator (14) of a synchronous machine (12), the controller being adapted to perform the method according to any one of claims 1 to 11.

15. A synchronous machine system (10), comprising: A synchronous machine (12) having a stator (22) having a stator winding (18) connected to a power grid (16) via terminals (20) and a rotor (24) having a rotor winding (26) rotatably mounted in the stator (22); and a voltage regulator (14) for supplying voltage to the rotor winding (26); wherein the voltage regulator (14) comprises an electrical converter (36) adapted to generate the voltage for the rotor winding (26); The voltage regulator comprises a controller (40) for controlling the electrical converter (36) and for performing the method according to any one of claims 1 to 11.

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