CN102930077B - Error-resistant excitation system parameter identification method based on improved target function - Google Patents

Abstract

The invention discloses an error-resistant excitation system parameter identification method based on an improved target function, and belongs to the technical field of excitation system parameter identification in a power system. According to the technical scheme, the method comprises the following steps of: building a variable parameter transmission function model of an excitation system to be identified by using a Matlab/Simulink tool case; taking the improved target function with the error resistance as a target function for excitation system parameter identification; and identifying parameters of the excitation system by a genetic algorithm according to the transmission function model of the excitation system to be identified based on Matlab/Simulink. By the error-resistant excitation system parameter identification method, the improved target function with relatively high error resistance is used as the target function for excitation system parameter identification, so that the parameters of the excitation system can be identified by the genetic algorithm (GA) of a nonlinear system. A simulation result shows that the error-resistant excitation system parameter identification method is relatively high in error resistance.

Description

A kind of robust Excitation System Parameter Identification of Synchronous method based on modified objective function

Technical field

The invention belongs to the Excitation System Parameter Identification of Synchronous technical field in electric system, relate in particular to a kind of robust Excitation System Parameter Identification of Synchronous method based on modified objective function.

Background technology

The excitation system of high-rating generator plays vital effect for the normal operation level of the system that maintains with guaranteeing security of system stability.Improving the accuracy of parameters of excitation system, to obtain the accurate simulation of electrical network, thereby guarantee power network safety operation, is problem demanding prompt solution.And the parameter that manufacturing firm provides is normally under the condition of off-line testing, respectively each element is tested to the parameter that obtains this element, they are combined and obtain integrated system model parameter; This parameter is directly used in to the stability Calculation emulation of electric system, acquired results can have difference with actual conditions.Therefore, the parameter identification that carries out excitation system based on field measurement data has become research tendency, and the parameter that identification obtains just more tallies with the actual situation.

The appearance of the phasor measurement unit PMU based on global position system GPS, for the on-line identification of parameters of electric power system provides a new strong platform.Mostly phasor measurement unit PMU data are to derive from the calculating to measurement data, electric current, voltage etc. are all from measurement, contain the error that the links such as current transformer, voltage transformer (VT), digital sample, FFT, filtering bring, to inevitably make phasor measurement unit PMU data have error, and in the whole processing transmitting procedure of data, be subject to the impact of random perturbation, in phasor measurement unit PMU data, also can have bad data.These errors in measurement (carefully poor) and bad data (rough error) can produce certain impact to parameter identification.Error in measurement cannot people for a change, and from the mass data of phasor measurement unit PMU, to reject various bad datas be very difficult.Therefore, effective method is to use the parameter identification method with robustness.

It is objective function that Excitation System Parameter Identification of Synchronous generally be take the error sum of squares of the field voltage that actual measurement field voltage and excitation model calculate, the objective function of this routine does not have robustness, be subject to a certain extent the impact of error in measurement and bad data very large, make identification result serious distortion.

Summary of the invention

For the computing method of the objective function described in background technology, in the problem existing aspect robustness and identification result, a kind of robust Excitation System Parameter Identification of Synchronous method based on modified objective function has been proposed.

A robust Excitation System Parameter Identification of Synchronous method based on modified objective function, is characterized in that, specifically comprises the following steps:

Step 1: utilize Matlab/Simulink tool box to build the transfer function model of the variable element of excitation system to be identified, the set end voltage of the phasor measurement unit PMU of usining actual measurement and electric current phasor and exciting current are as the input data of this model;

Step 2: will there is the objective function of the modified objective function of robustness as Excitation System Parameter Identification of Synchronous;

Step 3: the transfer function model of the excitation system to be identified based on Matlab/Simulink, utilizes the parameter of Identification of Genetic Algorithm excitation system.

In step 2, the mathematical form of the described modified objective function with robustness is:

$\min J\left(\mathrm{\α}\right)\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\ρ}\left(e\left(t_k\right)\right)$

$=\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\ρ}(E_{\mathrm{fdm}}\left(t_k\right)-E_{\mathrm{fdc}}(t_k,\mathrm{\α}))$

Robust criterion function ρ () is:

$\mathrm{\ρ}\left(e\left(t_k\right)\right)=e^2\left(t_k\right){|}_{\left|e\left(t_k\right)\right|\≤\mathrm{\Δ\σ}}+{\left(\mathrm{\Δ\σ}\right)}^2{|}_{\left|e\left(t_k\right)\right|>\mathrm{\Δ\σ}}$

Wherein, α represents parameter sets to be identified; N is total number of sample points, t _kfor sampling instant; E _fdm(t _k) be t _kpMU actual measurement field voltage value constantly, E _fdc(t _k, α) be t _kthe transfer function model of excitation system to be identified constantly calculates the field voltage value of output; e(t _k) be t _kthe field voltage value of calculating output constantly and the error of actual measurement field voltage value; Δ σ is the arithmetic number for balance robust and validity.

In step 3, the transfer function model of the described excitation system to be identified based on Matlab/Simulink utilizes the parametric procedure of Identification of Genetic Algorithm excitation system specifically to comprise the following steps:

Step 301: utilize Matlab/Simulink tool box to build the transfer function model of the variable element of excitation system to be identified, the set end voltage of the PMU of usining actual measurement and electric current phasor, exciting current are as the input data of this model;

Step 302: the bound constraint condition of the parameter to be identified of excitation system to be identified is added in fitness function as penalty term; And the expression formula of this penalty term is:

$P=M\underset{i=1}{\overset{N}{\mathrm{\Σ}}}({\left[\max \right\{0,{\mathrm{\α}}_i-{\mathrm{\α}}_i^{\mathrm{Max}}\left\}\right]}^2+{\left[\max \right\{0,{\mathrm{\α}}_i^{\mathrm{Min}}-{\mathrm{\α}}_i\left\}\right]}^2)$

Wherein, α _irepresent i parameter to be identified, the upper limit that represents i parameter to be identified, the lower limit that represents i parameter to be identified; N represents to have the number of parameters of bound constraint, and M is direct proportion coefficient.

Step 303: the optimized individual of determining genetic algorithm is counted n and maximum genetic algebra g;

Step 304: treat identified parameters variable and carry out real coding, form chromosome;

Step 305: determine the scope of parametric variable to be identified according to the bound constraint condition of parameter to be identified, adopt Small section method to generate at random first generation population;

Step 306: each individuality to when pre-group, become the parameter of excitation system to be updated in transfer function model individual code conversion, emulation obtains the calculating output valve of field voltage; And according to PMU actual measurement field voltage value, calculate its individual target function value J (α) and fitness function value Ffitness; The computing formula of fitness function value is:

$F_{\mathrm{fitness}}=\frac{C}{D+J\left(\mathrm{\α}\right)+P}$

Wherein, C is rate mu-factor, and D prevents that denominator from being zero constant term arranging; C is desirable 1000, and D gets 0.0001.

Step 307: check whether target function value is less than setting value or whether GA reaches maximum genetic algebra; If not, continue; Otherwise, finish.

Step 308: adopt random system of selection uniformly, arithmetic cross method Heuristic and self-adaptation variation method Adaptive feasible, generate population of new generation; And get back to step 6 and continue.

The present invention proposes a kind ofly have the modified objective function of stronger robustness as the objective function of Excitation System Parameter Identification of Synchronous, and on incorporation engineering, the Genetic Algorithms that is suitable for nonlinear system of widespread use carries out identification to the parameter of excitation system.A large amount of emulation show, the Excitation System Parameter Identification of Synchronous method with robustness that the present invention proposes has stronger robustness, is highly effective; This has certain engineering using value for the parameter based on PMU measured data on-line identification excitation system.

Accompanying drawing explanation

Fig. 1 is the ultimate principle figure of a kind of robust Excitation System Parameter Identification of Synchronous method based on modified objective function provided by the invention;

Fig. 2 is the Genetic Algorithms process flow diagram of a kind of robust Excitation System Parameter Identification of Synchronous method based on modified objective function provided by the invention;

Fig. 3 is that the embodiment of the present invention is provided at not containing of providing by restriction and low BPA-FV model schematic diagram of encouraging restriction;

Fig. 4 is the Gaussian noise that is 0.05 containing standard deviation that obtains of PSCAD emulation that the embodiment of the present invention provides and the actual measurement field voltage curve synoptic diagram that occurs at random 3 bad datas.

Embodiment

Below in conjunction with accompanying drawing, preferred embodiment is elaborated.Should be emphasized that following explanation is only exemplary, rather than in order to limit the scope of the invention and to apply.

Fig. 1 is the ultimate principle figure of a kind of robust Excitation System Parameter Identification of Synchronous method based on modified objective function provided by the invention.In Fig. 1, the input of actual excitation system and its transfer function model generator terminal voltage and electric current phasor for actual measurement; E _fdmfor considering the actual measurement field voltage of the actual excitation system output after error in measurement; ω (t) is error in measurement; E _fdcfor transfer function model calculates the field voltage of output.

The process of Excitation System Parameter Identification of Synchronous can be sketched and be: find the parameter alpha of one group of optimum, make the field voltage E of actual excitation system output _fdmcurve and transfer function model calculate the field voltage E of output _fdccurve best, even if it is minimum also to take the objective function that both error is function, mathematic(al) representation is:

$\min J\left(\mathrm{\α}\right)=\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{[E_{\mathrm{fdm}}\left(t_k\right)-E_{\mathrm{fdc}}(t_k,\mathrm{\α})]}^2---\left(1\right)$

Wherein, N is total number of sample points, t _kfor sampling instant, E _fdmfor considering the actual measurement field voltage of the actual excitation system output after error in measurement, E _fdcfor transfer function model calculates the field voltage of output.

At this, target function type (1) is called to conventional objective function.The objective function of this routine does not have robustness, is subject to a certain extent the impact of error in measurement and bad data very large, makes identification result serious distortion.

The present invention adopts a kind of modified objective function with robustness, and form is as follows:

$\min J\left(\mathrm{\α}\right)\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\ρ}\left(e\left(t_k\right)\right)$

（2）

$=\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\ρ}(E_{\mathrm{fdm}}\left(t_k\right)-E_{\mathrm{fdc}}(t_k,\mathrm{\α}))$

Robust criterion function ρ () is:

$\mathrm{\ρ}\left(e\left(t_k\right)\right)=e^2\left(t_k\right){|}_{\left|e\left(t_k\right)\right|\≤\mathrm{\Δ\σ}}+{\left(\mathrm{\Δ\σ}\right)}^2{|}_{\left|e\left(t_k\right)\right|>\mathrm{\Δ\σ}}---\left(3\right)$

Wherein, Δ σ is the arithmetic number for balance robust and validity.Choose suitable Δ σ value, guarantee has stronger robust, when error in measurement is little, guarantees the validity of identification result simultaneously.

Robust criterion function formula (3) shows, when PMU error in measurement hour, this modified target function type (2) is conventional target function type (1), both are of equal value; And while there is larger error in measurement or bad data in PMU data, ρ (e) is a constant, its contribution to objective function is fixed on (Δ σ) ², robust criterion function limits its impact on objective function by definite value.Therefore, to larger error in measurement or bad data, modified objective function slackens its impact on objective function by definite value, compared to conventional objective function, has stronger robustness.

Excitation system is a nonlinear system, contain the nonlinear elements such as various amplitude limit links, exciter are saturated, traditional frequency domain method and time domain method all can only carry out the parameter identification of linear system, cannot take into account the effect of nonlinear element, and Genetic Algorithms overcome and cannot carry out to nonlinear element the problem of parameter identification, and can disposable identification obtain the parameter of needed links.Therefore, the present invention adopts GA algorithm to carry out identification to the parameter of excitation system.

Fig. 2 is the Genetic Algorithms process flow diagram of a kind of robust Excitation System Parameter Identification of Synchronous method based on modified objective function provided by the invention.In Fig. 2, specifically comprise the following steps:

Step 201: utilize Matlab/Simulink tool box to build the transfer function model of the variable element of excitation system to be identified, the set end voltage of the PMU of usining actual measurement and electric current phasor, exciting current are as the input data of this model;

Step 202: the bound constraint condition of the parameter to be identified of excitation system to be identified is added in fitness function as penalty term; And the expression formula of this penalty term is:

$P=M\underset{i=1}{\overset{N}{\mathrm{\Σ}}}({\left[\max \right\{0,{\mathrm{\α}}_i-{\mathrm{\α}}_i^{\mathrm{Max}}\left\}\right]}^2+{\left[\max \right\{0,{\mathrm{\α}}_i^{\mathrm{Min}}-{\mathrm{\α}}_i\left\}\right]}^2)$

Wherein, α _irepresent i parameter to be identified, the upper limit that represents i parameter to be identified, the lower limit that represents i parameter to be identified; N represents to have the number of parameters of bound constraint, and M is direct proportion coefficient.

Step 203: the optimized individual of determining genetic algorithm is counted n and maximum genetic algebra g;

Step 204: treat identified parameters variable and carry out real coding, form chromosome;

Step 205: determine the scope of parametric variable to be identified according to the bound constraint condition of parameter to be identified, adopt Small section method to generate at random first generation population;

Step 206: each individuality to when pre-group, become the parameter of excitation system to be updated in transfer function model individual code conversion, emulation obtains the calculating output valve of field voltage; And according to PMU actual measurement field voltage value, calculate its individual target function value and fitness function value Ffitness;

Objective function is: the J (α) of modified target function type (2)

Fitness function is: $F_{\mathrm{fitness}}=\frac{C}{D+J\left(\mathrm{\α}\right)+P}$

Wherein, C is rate mu-factor, and D prevents that denominator from being zero constant term arranging; C is desirable 1000, and D gets 0.0001.

Step 207: check whether target function value is less than setting value or whether GA reaches maximum genetic algebra; If not, continue; Otherwise, finish;

Step 208: adopt random system of selection uniformly, arithmetic cross method Heuristic and self-adaptation variation method Adaptive feasible, generate population of new generation; And get back to step 206 and continue.

Embodiment:

Fig. 3 is that the embodiment of the present invention is provided at not containing of providing by restriction and low BPA-FV model schematic diagram of encouraging restriction.Excitation system input for set end voltage and the electric current phasor of generator, output E _fdfor the field voltage of generator, I _fdfor the exciting current of generator, V _rEFfor reference voltage.

Emulated data is from IEEE-3M9BUS system, and excitation model is BPA-FV model, and emulation obtains set end voltage electric current, field voltage and exciting current, and the data sampling cycle is 10ms, is total to the data of 3s, as PMU measured data.The setting value of each parameter of FV model is as table 1:

The simulation parameter value of table 1 FV model

Parameter	Rc	Xc	Tr	T1	T2	K	Kv	T3	T4
										Setting value	0	0	0.02	1.2	8.57	1	1	0.025	0.025
Parameter	Ka	Ta	Vamax	Vamin	Kf	Tf	Kc	Vrmax	Vrmin
										Setting value	500	0.02	7.33	-6.23	0	1	0.08	7.33	-6.60

In the Simulink of Matlab, build the BPA-FV model of variable element, using set end voltage electric current, exciting current as mode input, the field voltage that the model of usining calculates, as output, utilizes GA algorithm to carry out identification to excitation parameter.

Consider and utilize GA algorithm to carry out whole identification to excitation system, because parameter is more, identification result is undesirable.In order to describe the problem, parameter-enlargement factor Ka that the present invention's identification has the greatest impact to FV model, by superpose in actual measurement field voltage the data poor Gaussian noise of various criterion and bad data, the robustness of investigating modified target function type (2) and conventional target function type (1) with the identification effect of Ka illustrates validity of the present invention simultaneously.

In GA algorithm, the Search Range of parameter is [0.5* α _set, 1.5* α _set], α _setsetting value for parameter; Optimized individual number is set to 120, and genetic algebra is set to 25.In view of emulated data of the present invention, Δ σ=0.1 in the robust criterion function formula (3) of modified target function type (2), can guarantee existing stronger robustness, can guarantee again the validity of identification result when error in measurement is little.

The poor Gaussian noise of various criterion that superposes in actual measurement field voltage data, take respectively the objective function that conventional objective function and modified objective function be Excitation System Parameter Identification of Synchronous, utilizes GA algorithm to parameter K a optimizing.Identification result under different noise situations is as table 2:

The identification result of two kinds of objective functions under the different noises of table 2

As seen from Table 2:

1), when measurement noise is little, the identification result of two kinds of objective functions and target function value are approximate the same, and the precision of identification result very high (result of many optimizing of GA is difference to some extent, but difference is very little).

2) along with the increasing of measurement noise, the identification result of modified objective function is better than conventional objective function, because modified objective function can slacken the impact of the relatively large data of error on objective function, the precision of identification result is increased.But when measurement noise is too large, the identification result of two kinds of objective functions is variation all.

Fig. 4 is the Gaussian noise that is 0.05 containing standard deviation that obtains of PSCAD emulation that the embodiment of the present invention provides and the actual measurement field voltage curve synoptic diagram that occurs at random 3 bad datas.This supposition bad data for random that occur, depart from the sampled data of true value 25% left and right.The identification result that contains two kinds of objective functions in different bad data number situations is as shown in table 3.

The identification result of two kinds of objective functions under the different bad data numbers of table 3

From result, can obviously find out, along with the increase of bad data number, the identification result of conventional objective function worsens rapidly, and the error of the identification result of modified objective function is relatively very little, is subject to the impact of bad data also little; This shows that modified objective function can limit the error that bad data causes, slackens the impact of bad data on objective function, also is just equivalent to weed out bad data, has stronger robustness.

Simulation result shows, when PMU data exist little measurement noise, the identification result of modified objective function is better than conventional objective function; And while there is the bad data of some in PMU data, the identification result of modified objective function is obviously better than conventional objective function, can limit the harmful effect of bad data, has stronger robustness.Therefore, the Excitation System Parameter Identification of Synchronous method with robustness that the present invention proposes is effective, has certain engineering using value.

The above; be only the present invention's embodiment preferably, but protection scope of the present invention is not limited to this, is anyly familiar with in technical scope that those skilled in the art disclose in the present invention; the variation that can expect easily or replacement, within all should being encompassed in protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claim.

Claims (2)

1. the robust Excitation System Parameter Identification of Synchronous method based on modified objective function, is characterized in that, specifically comprises the following steps:

Step 1: utilize Matlab/Simulink tool box to build the transfer function model of the variable element of excitation system to be identified, the set end voltage of the phasor measurement unit PMU of usining actual measurement and electric current phasor and exciting current are as the input data of this model;

Step 2: will there is the objective function of the modified objective function of robustness as Excitation System Parameter Identification of Synchronous;

The mathematical form of modified objective function is:

$\begin{array}{c}\min J\left(\mathrm{\α}\right)=\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\ρ}\left(e\left(t_k\right)\right)\\ =\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\ρ}(E_{\mathrm{fdm}}\left(t_k\right)-E_{\mathrm{fdc}}(t_k,\mathrm{\α}))\end{array}$

Robust criterion function ρ () is:

$\mathrm{\ρ}\left(e\left(t_k\right)\right)=e^2\left(t_k\right){|}_{\left|e\left(t_k\right)\right|\≤\mathrm{\Δ\σ}}+{\left(\mathrm{\Δ\σ}\right)}^2{|}_{\left|e\left(t_k\right)\right|>\mathrm{\Δ\σ}}$

Wherein, α represents parameter sets to be identified; N is total number of sample points, t _kfor sampling instant; E _fdm(t _k) be t _kpMU actual measurement field voltage value constantly, E _fdc(t _k, α) be t _kthe transfer function model of excitation system to be identified constantly calculates the field voltage value of output; e(t _k) be t _kthe field voltage value of calculating output constantly and the error of actual measurement field voltage value; Δ σ is the arithmetic number for balance robust and validity;

Step 3: the transfer function model of the excitation system to be identified based on Matlab/Simulink, utilizes the parameter of Identification of Genetic Algorithm excitation system.

2. a kind of robust Excitation System Parameter Identification of Synchronous method based on modified objective function according to claim 1, it is characterized in that, in described step 3, the transfer function model of the excitation system to be identified based on Matlab/Simulink utilizes the parametric procedure of Identification of Genetic Algorithm excitation system specifically to comprise the following steps:

Step 301: utilize Matlab/Simulink tool box to build the transfer function model of the variable element of excitation system to be identified, the set end voltage of the PMU of usining actual measurement and electric current phasor, exciting current are as the input data of this model;

Step 302: the bound constraint condition of the parameter to be identified of excitation system to be identified is added in fitness function as penalty term; And the expression formula of this penalty term is:

$P=M\underset{i=1}{\overset{N}{\mathrm{\Σ}}}({\left[\max \right\{0,{\mathrm{\α}}_i-{\mathrm{\α}}_i^{\mathrm{Max}}\left\}\right]}^2+{\left[\max \right\{0,{\mathrm{\α}}_i^{\mathrm{Min}}-{\mathrm{\α}}_i\left\}\right]}^2)$

Wherein, α _irepresent i parameter to be identified, the upper limit that represents i parameter to be identified, the lower limit that represents i parameter to be identified; N represents to have the number of parameters of bound, and M is direct proportion coefficient;

Step 303: the optimized individual of determining genetic algorithm is counted n and maximum genetic algebra g;

Step 304: treat identified parameters variable and carry out real coding, form chromosome;

Step 305: determine the scope of parametric variable to be identified according to the bound constraint condition of parameter to be identified, adopt Small section method to generate at random first generation population;

Step 306: each individuality to when pre-group, become the parameter of excitation system to be updated in transfer function model individual code conversion, emulation obtains the calculating output valve of field voltage; And according to PMU actual measurement field voltage value, calculate its individual target function value J (α) and fitness function value Ffitness; The computing formula of fitness function value is:

$\mathrm{Ffitness}=\frac{C}{D+J\left(\mathrm{\α}\right)+P}$

Wherein, C is rate mu-factor, and D prevents that denominator from being zero constant term arranging; C is desirable 1000, and D gets 0.0001;

Step 307: check whether target function value is less than setting value or whether GA reaches maximum genetic algebra; If not, continue; Otherwise, finish;

Step 308: adopt random system of selection uniformly, arithmetic cross method Heuristic and self-adaptation variation method Adaptive feasible, generate population of new generation; And get back to step 306 and continue.