CN102904519B - Robust excitation system parameter identification method based on exponential-type target function - Google Patents

Abstract

The invention discloses a robust excitation system parameter identification method based on an exponential-type target function in the technical field of excitation system parameter identification in a power system. The technical scheme comprises the steps of: firstly, determining a mathematical description form of the excitation system parameter identification; secondly, taking the exponential-type target function with robust capability as a target function of the excitation system parameter identification; and finally, identifying the parameter of the excitation system by utilizing a genetic algorithm (GA). The invention provides the exponential-type target function with very high robust capability to serve as the target function of the excitation system parameter identification; and the parameter of the excitation system is identified by combining the GA which is widely applied in engineering and is suitable for a nonlinear system. A large amount of simulation shows that the excitation system parameter identification method with the robust capability has very high robust capability, and has an engineering application value for online identification of the parameter of the excitation system on the basis of measured data of a power management unit (PMU).

Description

A kind of robust Excitation System Parameter Identification of Synchronous method based on exponential type target function

Technical field

The invention belongs to the Excitation System Parameter Identification of Synchronous technical field in electric power system, particularly relate to a kind of robust Excitation System Parameter Identification of Synchronous method based on exponential type target function.

Background technology

Electric power system model and parameter are the every calculating of power department and the foundation determining operational mode, and the accuracy of model and parameter is related to the safe and stable operation of electrical network; And generator excited system plays vital effect for maintenance system normal operating level and guarantee system safety stability.Therefore, improve the accuracy of parameters of excitation system, to obtain the accurate analog of electrical network, thus ensureing 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 obtaining this element, they are combined and obtains integrated system model parameter, this parameter is directly used in the stability Calculation emulation of electric power system, acquired results can have difference with actual conditions.Therefore, the parameter identification carrying out excitation system based on field measurement data becomes research tendency, and the parameter that identification obtains just more tallies with the actual situation.

Based on the appearance of the phasor measurement unit PMU of global position system GPS, the on-line identification for parameters of electric power system provides a new strong platform.Mostly the data of phasor measurement unit PMU are to derive from the calculating to measurement data, electric current, voltage etc. all carry out measurement, containing the error that the links such as current transformer, voltage transformer, digital sample, FFT, filtering bring, error is there is by inevitably making phasor measurement unit PMU data, and by the impact of random perturbation in the whole process transmitting procedure of data, also can there is various types of bad data in phasor measurement unit PMU 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 reject from the mass data of phasor measurement unit PMU various types of bad data need expend time in and be difficult to guarantee whole rejecting, therefore, most effective method uses the parameter identification method with robustness.

Excitation System Parameter Identification of Synchronous is generally to survey the error sum of squares of the exciting voltage that exciting voltage and master pattern calculate for target function, the target function of this routine does not have robustness, impact to a certain extent by error in measurement and bad data is very large, makes identification result serious distortion.

Summary of the invention

For computational methods Problems existing in robustness and identification result of the target function described in background technology, propose a kind of robust Excitation System Parameter Identification of Synchronous method based on exponential type target function.

Based on a robust Excitation System Parameter Identification of Synchronous method for exponential type target function, it is characterized in that, described method specifically comprises the following steps:

Step 1: the mathematical description form determining Excitation System Parameter Identification of Synchronous;

Step 2: utilize the exponential type target function with robustness as the target function of Excitation System Parameter Identification of Synchronous;

Step 3: the parameter utilizing Genetic Algorithms identification excitation system.

In step 1, the mathematical description form of described Excitation System Parameter Identification of Synchronous is:

$\underset{\mathrm{\α}}{\min }J\left(\mathrm{\α}\right)=J\left(e(t,\mathrm{\α})\right|e(t,\mathrm{\α})=E_{\mathrm{fdm}}\left(t\right)-E_{\mathrm{fdc}}(t,x\left(t\right),y\left(t\right),\mathrm{\α}))$

$s.t.\frac{\mathrm{dx}}{\mathrm{dt}}=f(t,x\left(t\right),y\left(t\right),\mathrm{\α})$

$\hat{z}\left(t\right)=z(t,x\left(t\right),y\left(t\right),\mathrm{\α})$

s(a)≤s _Max

a∈[a _min,α _max]

Wherein, t represents the time; F () represents the state equation of excitation system; X (t) represents the state variable of excitation system; Y (t) represents the algebraic variable of excitation system; Z () represents the algebraic equation of excitation system; A represents parameter sets to be identified; a _minrepresent the lower limit of parameter to be identified; a _maxrepresent the upper limit of parameter to be identified; S (a) represents the nonlinear element of excitation system, as amplitude limit link.S (a)≤s _maxrepresent the inequality constraints of nonlinear element.E (t) represents the exciting voltage E of actual excitation system _fdmthe exciting voltage E exported is calculated with standard excitation model to be identified _fdcerror; E _fdmfor the exciting voltage that actual excitation system exports, E _fdcfor standard excitation model to be identified calculates the exciting voltage exported; First and second constraintss represent with the linear element of the excitation model of differential-algebraic equation formal description, and the 3rd constraints represents that the nonlinear element of excitation model is as amplitude limit link, and the 4th constraints represents the bound constraint that parameter to be identified meets.

In step 2, the described mathematical form with the exponential type target function of robustness is:

$\max J\left(\mathrm{\α}\right)=\frac{1}{T}{\∫}_0^T{e}^{-{[E_{\mathrm{fdm}}\left(t\right)-E_{\mathrm{fdc}}(t,\mathrm{\α})]}^2}\mathrm{dt}$

Consider the discontinuity of measurement amount and convert the form of minimizing to and be:

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

Wherein, T is the time window of metric data, and N is total number of sample points, t _kfor sampling instant, E _fdmfor the exciting voltage that actual excitation system exports, E _fdcfor standard excitation model to be identified calculates the exciting voltage exported.

Using the target function of this exponential type target function as Excitation System Parameter Identification of Synchronous.When there is larger error in measurement or bad data in PMU data, exponential type target function can the impact of automatic Compression bad data, also the weight being just equivalent to the error making bad data cause adaptively reduces significantly, thus the impact of bad data on target function is diminished significantly, be equivalent to automatic rejection and fall bad data, thus also just without the need to carrying out the data processing before identification, there is very strong robustness.

Certainly, every exponential type target function using maximum form is transformed to minimum value and the form of non-negative as the target function of Excitation System Parameter Identification of Synchronous, and can have same robustness.

In step 3, the selection of each process of described Genetic Algorithms comprises:

1) employing of encoding has and easily restrains under Big mutation rate rate, the comparatively effective real coding of process function optimization problem.

2) initialization population: adopt Small section method, first the span of each parameter to be optimized is divided into the total several minizone of colony, an initial individuals is generated randomly respectively again in each minizone, this ensure that the range that initial population distributes at Feasible Solution Region to a certain extent, and amount of calculation is also little simultaneously.

3) the choosing of target function: using exponential type target function as the target function of parameter identification.

4) selection strategy: adopt random uniform system of selection.

5) crossover and mutation: cross method selects arithmetic crossover method Heuristic, variation method selects TSP question method Adaptive feasible.

The invention has the beneficial effects as follows, propose a kind of target function of exponential type target function as Excitation System Parameter Identification of Synchronous with very strong robustness, and on incorporation engineering, the Genetic Algorithms being suitable for non linear system of extensive use carries out identification to the parameter of excitation system.A large amount of emulation shows, the excitation parameter discrimination method with robustness that the present invention proposes has very strong robustness, and for the parameter based on PMU measured data on-line identification excitation system, has engineer applied and be worth.

Accompanying drawing explanation

Fig. 1 is the general principle figure of a kind of robust Excitation System Parameter Identification of Synchronous method based on exponential type target function provided by the invention;

Fig. 2 is that the embodiment of the present invention encouraged restriction and low BPA FV model schematic of encouraging restriction at not containing of providing;

Fig. 3 is that PSCAD emulation that the embodiment of the present invention provides obtains and superposes standard deviation is exciting voltage curve synoptic diagram after the normally distributed error of 0.05;

Fig. 4 is schematic diagram when there is indivedual bad data in the emulation exciting voltage curve that provides of the embodiment of the present invention;

Fig. 5 is schematic diagram when there is continuous bad data in the emulation exciting voltage curve that provides of the embodiment of the present invention.

Embodiment

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

Fig. 1 is the general principle figure of a kind of robust Excitation System Parameter Identification of Synchronous method based on exponential type target function provided by the invention.In Fig. 1, the input of actual excitation system and standard excitation model for set end voltage and the electric current of generator; E _fdmfor considering the exciting voltage that the actual excitation system after error in measurement exports; ω (t) is error in measurement; E _fdcfor standard excitation model calculates the exciting voltage exported.

The process of Excitation System Parameter Identification of Synchronous can be sketched and be: the parameter a finding one group of optimum, makes the exciting voltage E that actual excitation system exports _fdmcurve and standard excitation model calculate the exciting voltage E exported _fdccurve best, even if be also function with both errors, target function is minimum, and mathematical description is:

J＝J(e(t,α))→min

The standard excitation model represented using transfer function is as model to be identified, need in simulation software, build this master pattern, and the master pattern represented with transfer function in frequency domain is converted in time domain with the master pattern that differential-algebraic equation represents by the present invention, do not need to build master pattern in simulation software, only by Program differential-algebraic equation, thus the calculating output exciting voltage of master pattern need be obtained.

The standard excitation model of the consideration nonlinear element described with differential-algebraic equation is:

$\left\{\begin{array}{c}\frac{\mathrm{dx}}{\mathrm{dt}}=f(t,x\left(t\right),y\left(t\right),\mathrm{\α})\\ \hat{z}\left(t\right)=z(t,x\left(t\right),y\left(t\right),\mathrm{\α})\\ s\left(\mathrm{\α}\right)\≤s_{\mathrm{Max}}\end{array}\right.$

Wherein, x (t), y (t), a represent state variable, algebraic variable and parameter to be identified respectively; S (α)≤s _maxrepresent that the nonlinear element of excitation system is as amplitude limit link.

Therefore, also just excitation parameter identification problem can be described as following mathematical problem:

In the input of known actual excitation system with exciting voltage E _fdm, solve the minimum problems of following Prescribed Properties, mathematical form is:

$\underset{\mathrm{\α}}{\min }J\left(\mathrm{\α}\right)=J\left(e(t,\mathrm{\α})\right|e(t,\mathrm{\α})=E_{\mathrm{fdm}}\left(t\right)-E_{\mathrm{fdc}}(t,x\left(t\right),y\left(t\right),\mathrm{\α}))$

$s.t.\frac{\mathrm{dx}}{\mathrm{dt}}=f(t,x\left(t\right),y\left(t\right),\mathrm{\α})$

$\hat{z}\left(t\right)=z(t,x\left(t\right),y\left(t\right),\mathrm{\α})---\left(1\right)$

s(a)≤s _Max

a∈[α _min,α _max]

Wherein, a ∈ [a _min, a _max] represent that the bound of parameter to be identified retrains.

The target function of Excitation System Parameter Identification of Synchronous is generally the integrated square of error, and mathematical form is:

$\max J\left(\mathrm{\α}\right)=\frac{1}{T}{\∫}_0^{T}e{(t,\mathrm{\α})}^2\mathrm{dt}$

$=\frac{1}{T}{\∫}_0^T{[E_{\mathrm{fdm}}\left(t\right)-E_{\mathrm{fdc}}(t,\mathrm{\α})]}^2\mathrm{dt}$

Consider the discontinuity of measurement amount, time domain continuous print target function discretization is obtained

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

Wherein, T is the time window of metric data, and N is total number of sample points, t _kfor sampling instant.

At this, target function type (2) is called conventional target function.When conventional target function is equivalent to think that PMU data do not exist error in measurement and bad data, the weight of the error in each moment is identical, but when there is bad data, the weight of the error that bad data causes will become large, thus the impact of target function is also just become large, this directly has influence on the accuracy of parameter identification result.

The present invention adopts a kind of exponential type target function with robustness, and form is as follows:

$\max J\left(\mathrm{\α}\right)=\frac{1}{T}{\∫}_0^T{e}^{-{[E_{\mathrm{fdm}}\left(t\right)-E_{\mathrm{fdc}}(t,\mathrm{\α})]}^2}\mathrm{dt}---\left(3\right)$

Consider the discontinuity of measurement amount and convert the form of minimizing to and be:

$\min J\left(\mathrm{\α}\right)=1-\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{e}^{-{[E_{\mathrm{fdm}}\left(t_k\right)-E_{\mathrm{fdc}}(t_k,\mathrm{\α})]}^2}---\left(4\right)$

Exponential type target function type (4), compared with conventional target function type (2), has obvious advantage:

1) when there is not relatively large survey error and bad data in measured data, two target functions are approximately equivalents.Because when error is less, by exponential type target function in Taylor expansion at zero point, after ignoring higher order term, be conventional target function.Namely

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

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

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

2) when there is larger error in measurement or bad data, exponential type target function can the impact of automatic Compression bad data, also the weight being just equivalent to the error making bad data cause adaptively reduces significantly, thus the impact of bad data on target function is diminished significantly, be equivalent to automatic rejection and fallen bad data, thus also just without the need to carrying out the data processing before identification.And conventional target function does not have this advantage.

Formula (4) is the one distortion of the minimum value form of formula (3), and the inverse of formula (3) also can be used as target function, and but, this target function does not have when error is less and the feature of conventional target function approximately equivalent.Certainly, everyly formula (3) is deformed into minimum value and the form of non-negative as the target function of Excitation System Parameter Identification of Synchronous, and can have same robustness.

Excitation system is a non linear system, containing the nonlinear element such as various amplitude limit link, exciter be saturated, traditional frequency domain method and time domain method all can only carry out the parameter identification of linear system, the effect of nonlinear element cannot be taken into account, and Genetic Algorithms overcomes the problem cannot carrying out parameter identification to nonlinear element, and disposable identification can obtain the parameter of required links.Therefore, the present invention adopts the parameter of GA algorithm to excitation system to be optimized.

The selection of each process of Genetic Algorithms comprises:

1) employing of encoding has and easily restrains under Big mutation rate rate, the comparatively effective real coding of process function optimization problem.

2) initialization population: adopt Small section method, first the span of each parameter to be optimized is divided into the total several minizone of colony, an initial individuals is generated randomly respectively again in each minizone, this ensure that the range that initial population distributes at Feasible Solution Region to a certain extent, and amount of calculation is also little simultaneously.

3) the choosing of target function: using exponential type target function type (4) as the target function of parameter identification.

4) selection strategy: adopt random uniform system of selection.

5) crossover and mutation: cross method selects arithmetic crossover method Heuristic, variation method selects TSP question method Adaptive feasible.

The optimized individual number of Genetic Algorithms is set to 120, and genetic algebra is set to 25.

Embodiment:

Fig. 2 is that the embodiment of the present invention encouraged restriction and low BPA FV model schematic of encouraging restriction at not containing of providing.Excitation system inputs for set end voltage and the electric current of generator, export E _fdfor the exciting voltage of generator, I _fdfor the exciting current of generator, V _rEFfor reference voltage.

The description form of the differential-algebraic equation of FV model is:

$T_A\frac{{\mathrm{dE}}_{\mathrm{fd}}}{\mathrm{dt}}=-E_{\mathrm{fd}}+K_A(U_R-U_F)$

$T_F\frac{d{U}_F}{\mathrm{dt}}=-U_F+K_F(-E_{\mathrm{fd}}+K_A(U_R-U_F))/T_A$

$T_4=\frac{d{U}_R}{\mathrm{dt}}=-U_R+U_S+T_3\frac{d{U}_S}{\mathrm{dt}}$

$T_2=\frac{d{U}_S}{\mathrm{dt}}=-K_V{U}_S+K(V_{\mathrm{ERR}}+T_1\frac{d{V}_{\mathrm{ERR}}}{\mathrm{dt}})$

$T_R\frac{d{V}_{\mathrm{CR}}}{\mathrm{dt}}=-V_{\mathrm{CR}}+V_C$

V _ERR=V _REF-V _CR

$V_C=|{\stackrel{\·}{V}}_t+(R_C+j{X}_C){\stackrel{\·}{I}}_t|$

Above five differential equations represent amplifying element, Parallel Adjustment link, the second level and first order cascade compensation link and measurement links respectively; Two algebraic equation representative voltage comparing elements and reactive power compensation link.

The inequality constraints of nonlinear element is interior amplitude limit and the constraint of exciting voltage bound of amplifying element.

In PSCAD, build one machine infinity bus system, and build BPA FV self-shunt excitation system model as actual excitation system model; FV model only adopts one-level cascade compensation, does not adopt Parallel Adjustment, and ignore the low effect of encouraging restriction, excessively encouraging restriction and PSS, the set point of each parameter is as table 1.

The set point of each parameter of table 1 FV model

Parameter	Rc	Xc	Tr	T1	T2	K	Kv	T3	T4
										Set point	0	0	0.02	1	10	1	1	0.02	0.02
Parameter	Ka	Ta	Vamax	Vamin	Kf	Tf	Kc	Vrmax	Vrmin
										Set point	100	0.023	9.44	-8.02	0	1	0.099	9.44	-8.46

Apply external disturbance to this system, emulation obtains set end voltage and machine end electric current, exciting voltage and exciting current, and as measured data, data sampling period is 10ms, gets the data of 5s altogether.Respectively using exponential type target function type (4) and conventional target function type (2) as the target function of Excitation System Parameter Identification of Synchronous, GA algorithm is utilized to carry out optimizing to parameters of excitation system.In GA algorithm, the Search Range of parameter is [0.5*a _set, 1.5*a _set], a _setfor the set point of parameter.

Identification parameter-multiplication factor Ka that self-shunt excitation system is had the greatest impact below, by the bad data that the normally distributed error and different proportion that superpose various criterion difference in actual measurement exciting voltage data are respectively dissimilar, illustrate that exponential type target function type (4) has very strong robustness compared to conventional target function type (2) with the identification effect of Ka.

Fig. 3 is that PSCAD emulation that the embodiment of the present invention provides obtains and superposes standard deviation is exciting voltage curve synoptic diagram after the normally distributed error of 0.05.In actual measurement exciting voltage data, superpose that average is 0, the normally distributed error of various criterion difference, utilize GA algorithm to parameter Ka optimizing.Identification result under different error condition is as table 2:

Identification result under the different normally distributed error of table 2

From identification result:

1) in measured data without error in measurement time, the identification result of two kinds of target functions and target function value are all the same, and the error of identification result very little (result of GA many optimizing can difference to some extent, but difference is very little).

2), when error in measurement is little, the identification result difference of exponential type target function and conventional target function is little, and this is consistent with theory analysis; But the identification result of exponential type target function is better than conventional target function, because exponential type target function can the relatively large data of compressed error, the precision of identification result is increased.

3) along with the increasing of error in measurement, the identification result of two kinds of target functions is all deteriorated.

Fig. 4 is schematic diagram when there is indivedual bad data in the emulation exciting voltage curve that provides of the embodiment of the present invention.GA optimizing result in discontinuous indivedual bad data situation as following table 3, bad data to be measuring value be 0 data.

Identification result in a table 3 other bad data situation

Can as apparent from result, along with the increase of bad data number, the identification result of conventional target function worsens rapidly, and the error of the identification result of exponential type target function is no more than 0.1%, accuracy is very high, shows that exponential type target function can the error that causes of the indivedual bad data of automatic Compression, makes target function by the impact of bad data, be equivalent to weed out bad data, there is very strong robustness.

Fig. 5 is schematic diagram when there is continuous bad data in the emulation exciting voltage curve that provides of the embodiment of the present invention.GA optimizing result in the continuous bad data situation of different number as table 4, bad data to be measuring value be 0 data.

Identification result in the continuous bad data situation of table 4

Can as apparent from result, along with the increase of continuous bad data number, the identification result of conventional target function is in rapid deterioration, and the identification result of exponential type target function is not equally also by the impact of bad data, the accuracy of identification result is still very high, show that exponential type target function also has very strong robustness to the bad data of this kind, be equivalent to automatic rejection and fallen bad data.To count to that 100(accounts for sum 20% of the continuous bad data of further increasing), the error of identification result is still in 0.1%.

Exponential type target function has extremely strong compressed capability for the bad data that deviation true value is very large, almost can eliminate its error caused, and makes target function not by the impact of bad data; But when bad data deviation true value is relatively little, exponential type target function can reduce the compressed capability of bad data, and bad data also can have an impact to target function, and the precision of identification result also decreases.But as a whole, no matter, the identification result of exponential type target function is all better than conventional target function, has very strong robustness if there is error in measurement or bad data in PMU data.Therefore, the Excitation System Parameter Identification of Synchronous method with robustness that the present invention proposes is effective, has potential engineer applied and is worth.

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

Claims (3)

1., based on a robust Excitation System Parameter Identification of Synchronous method for exponential type target function, it is characterized in that, described method specifically comprises the following steps:

Step 1: the mathematical description form determining Excitation System Parameter Identification of Synchronous;

Step 2: utilize the exponential type target function with robustness as the target function of Excitation System Parameter Identification of Synchronous;

The described mathematical form with the exponential type target function of robustness is:

$\max J\left(\mathrm{\α}\right)=\frac{1}{T}{\∫}_0^T{e}^{-[E_{\mathrm{fdm}}\left(t\right)-E_{\mathrm{fdc}}(t,\mathrm{\α}){]}^2}\mathrm{dt}$

Consider the discontinuity of measurement amount and convert the form of minimizing to and be:

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

Wherein, T is the time window of metric data, and N is total number of sample points, and t represents the time, and α represents parameter sets to be identified, t _kfor sampling instant, E _fdmfor the exciting voltage that actual excitation system exports, E _fdcfor standard excitation model to be identified calculates the exciting voltage exported;

Step 3: the parameter utilizing Genetic Algorithms identification excitation system.

2. a kind of robust Excitation System Parameter Identification of Synchronous method based on exponential type target function according to claim 1, it is characterized in that, in described step 1, the mathematical description form of Excitation System Parameter Identification of Synchronous is:

$\underset{\mathrm{\α}}{\min }J\left(\mathrm{\α}\right)=J\left(e\left(t\right)\right|e\left(t\right)=E_{\mathrm{fdm}}\left(t\right)-E_{\mathrm{fdc}}(t,x\left(t\right),y\left(t\right),\mathrm{\α}))$

$s.t.\frac{\mathrm{dx}}{\mathrm{dt}}=f(t,x\left(t\right),t\left(t\right)\mathrm{\α})$

$\hat{z}\left(t\right)=z(t,x\left(t\right),y\left(t\right),\mathrm{\α})$

s(α)≤s _Max

α∈[α _min,α _max]

Wherein, t represents the time; F (i) represents the state equation of excitation system; X (t) represents the state variable of excitation system; Y (t) represents the algebraic variable of excitation system; Z () represents the algebraic equation of excitation system; α represents parameter sets to be identified; α _minrepresent the lower limit of parameter to be identified; α _maxrepresent the upper limit of parameter to be identified; S (α) represents the nonlinear element of excitation system, as amplitude limit link; S (α)≤s _maxrepresent the inequality constraints of nonlinear element; E (t) represents the exciting voltage E of actual excitation system _fdmthe exciting voltage E exported is calculated with standard excitation model to be identified _fdcerror; E _fdmfor the exciting voltage that actual excitation system exports; E _fdcfor standard excitation model to be identified calculates the exciting voltage exported; First and second constraintss represent with the linear element of the excitation model of differential-algebraic equation formal description, and the 3rd constraints represents that the nonlinear element of excitation model is as amplitude limit link, and the 4th constraints represents the bound constraint that parameter to be identified meets.

3. a kind of robust Excitation System Parameter Identification of Synchronous method based on exponential type target function according to claim 1, it is characterized in that, in described step 3, the selection of each process of described Genetic Algorithms comprises:

1) coding adopts real coding;

2) adopt Small section method initialization population, the span of each parameter to be optimized is divided into the total several minizone of colony, then generate an initial individuals randomly respectively in each minizone, thus ensure that the range that initial population distributes at Feasible Solution Region;

3) using exponential type target function as the target function of parameter identification;

4) selection strategy adopts random uniform system of selection;

5) crossover and mutation: cross method selects arithmetic crossover method Heuristic, variation method selects TSP question method Adaptive feasible.