CN102930077A - Error-resistant excitation system parameter identification method based on improved target function - Google Patents

Abstract

The invention discloses a parameter identification method of an anti-difference excitation system based on an improved objective function in the technical field of excitation system parameter identification in a power system. The technical solution is: firstly, use the Matlab/Simulink toolbox to build the variable parameter transfer function model of the excitation system to be identified; secondly, use the improved objective function with tolerance ability as the objective function of the excitation system parameter identification; finally, based on The transfer function model of the excitation system to be identified in Matlab/Simulink uses the genetic algorithm to identify the parameters of the excitation system. The invention uses an improved objective function with strong error resistance as the objective function of excitation system parameter identification, and combines the genetic algorithm GA suitable for nonlinear systems to identify the parameters of the excitation system. The simulation results show that the method for identifying the parameters of the excitation system with tolerance to tolerance proposed by the present invention has strong tolerance to tolerance.

Description

A Parameter Identification Method of Robust Excitation System Based on Improved Objective Function

technical field

The invention belongs to the technical field of excitation system parameter identification in electric power systems, and in particular relates to an identification method for anti-difference excitation system parameters based on an improved objective function.

Background technique

The excitation system of a large generator plays a vital role in maintaining the normal operation level of the system and ensuring the safety and stability of the system. Improving the accuracy of the excitation system parameters to obtain an accurate simulation of the power grid, so as to ensure the safe and stable operation of the power grid, is an urgent problem to be solved. The parameters provided by the manufacturer are usually under the condition of off-line test, each component is tested separately to obtain the parameters of the component, and they are combined to obtain the integrated system model parameters; the parameters are directly used for the stability of the power system Calculation simulation, the results obtained may be different from the actual situation. Therefore, it has become a research trend to identify the parameters of the excitation system based on field measured data, and the identified parameters are more in line with the actual situation.

The emergence of the GPS-based phasor measurement unit PMU provides a new and powerful platform for the online identification of power system parameters. Most of the PMU data of the phasor measurement unit comes from the calculation of the measurement data. The current and voltage are all from the measurement, including errors caused by current transformers, voltage transformers, digital sampling, FFT, filtering and other links, which will be inevitable. The PMU data of the phasor measurement unit has errors, and is affected by random disturbances during the entire process of data processing and transmission, and there will also be bad data in the PMU data of the phasor measurement unit. These measurement errors (subtle errors) and bad data (gross errors) will have a certain impact on parameter identification. The measurement error cannot be changed artificially, and it is very difficult to eliminate all kinds of bad data from the massive data of the phasor measurement unit PMU. Therefore, the most effective method is to use a parameter identification method with robustness.

The excitation system parameter identification generally uses the sum of squares of the error between the measured excitation voltage and the excitation voltage calculated by the excitation model as the objective function. large, which seriously distorts the identification results.

Contents of the invention

Aiming at the problems in the tolerance and identification results of the calculation method of the objective function described in the background technology, a parameter identification method of the tolerance-resistant excitation system based on the improved objective function is proposed.

A method for identifying parameters of a robust excitation system based on an improved objective function, characterized in that it specifically includes the following steps:

Step 1: Use the Matlab/Simulink toolbox to build a variable parameter transfer function model of the excitation system to be identified, and use the terminal voltage and current phasors measured by the phasor measurement unit PMU as well as the excitation current as the input data of the model;

Step 2: Use the improved objective function with robustness as the objective function for parameter identification of the excitation system;

Step 3: Based on the transfer function model of the excitation system to be identified in Matlab/Simulink, use the genetic algorithm to identify the parameters of the excitation system.

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

$\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; fdm</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; fdc</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

The robustness criterion function ρ(·) is:

$\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; |</span>}_{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&Delta;\&sigma;</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;\&sigma;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; |</span>}_{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; \&Delta;\&sigma;</span>}}$

Among them, α represents the set of parameters to be identified; N is the total number of sampling points, t _k is the sampling time; E _fdm (t _k ) is the PMU measured excitation voltage value at the t _kth time, E _fdc (t _k , α) is the The excitation voltage value calculated and output by the transfer function model of the excitation system to be identified at time t k; e ₍ t _k ) is the error between the calculated output excitation voltage value and the measured excitation voltage value at time t _k ; Δσ is used to balance the Positive real numbers for difference and validity.

In step 3, the described transfer function model of the excitation system to be identified based on Matlab/Simulink utilizes the genetic algorithm to identify the parameter process of the excitation system specifically includes the following steps:

Step 301: using the Matlab/Simulink toolbox to build a variable parameter transfer function model of the excitation system to be identified, using the actual measured terminal voltage and current phasor and excitation current of the PMU as the input data of the model;

Step 302: Add the upper and lower limit constraints of the unidentified parameters of the unidentified excitation system as a penalty item to the fitness function; and the expression of this penalty item is:

$\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; Max</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; Min</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>$

表示第i个待辨识参数的下限；N表示具有上下限约束的参数个数，M是正比例系数。Among them, α _i represents the ith parameter to be identified, Indicates the upper limit of the i-th parameter to be identified,

Indicates the lower limit of the i-th parameter to be identified; N indicates the number of parameters with upper and lower limit constraints, and M is a proportional coefficient.

Step 303: determine the optimal number of individuals n and the maximum genetic algebra g of the genetic algorithm;

Step 304: Encoding the parameter variables to be identified with real numbers to form chromosomes;

Step 305: Determine the range of the parameter variables to be identified according to the upper and lower limit constraints of the parameters to be identified, and randomly generate the first-generation population by using the inter-cell generation method;

Step 306: For each individual in the current group, convert the individual code into the parameter of the excitation system and put it into the transfer function model, and obtain the calculated output value of the excitation voltage through simulation; and calculate the objective function of the individual according to the measured excitation voltage value of the PMU Value J(α) and fitness function value Ffitness; the calculation formula of fitness function value is:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; fitness</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; P</span>}}$

Among them, C is the proportional amplification factor, and D is a constant item set to prevent the denominator from being zero; C can be 1000, and D can be 0.0001.

Step 307: Check whether the objective function value is less than the set value or whether the GA has reached the maximum genetic algebra; if not, continue; otherwise, end.

Step 308: Generate a new generation of population by using the random uniform selection method, the arithmetic crossover method Heuristic and the adaptive mutation method Adaptive feasible; and return to step 6 to continue.

The invention proposes an improved objective function with strong error tolerance as the objective function of excitation system parameter identification, and combines the genetic algorithm GA which is widely used in engineering and is suitable for nonlinear systems to identify the parameters of the excitation system. A large number of simulations show that the excitation system parameter identification method with tolerance ability proposed by the present invention has strong tolerance ability and is very effective; this has certain engineering application for online identification of excitation system parameters based on PMU measured data value.

Description of drawings

Fig. 1 is a basic principle diagram of a method for identifying parameters of a robust excitation system based on an improved objective function provided by the present invention;

Fig. 2 is a genetic algorithm GA flowchart of a method for identifying parameters of a robust excitation system based on an improved objective function provided by the present invention;

Fig. 3 is a schematic diagram of the BPA-FV model without over-excitation restriction and under-excitation restriction provided by the embodiment of the present invention;

Fig. 4 is a schematic diagram of the measured excitation voltage curve obtained by the PSCAD simulation provided by the embodiment of the present invention, including Gaussian noise with a standard deviation of 0.05 and three bad data randomly appearing.

Detailed ways

The preferred embodiments will be described in detail below in conjunction with the accompanying drawings. It should be emphasized that the following description is only exemplary and not intended to limit the scope of the invention and its application.

为实测的发电机机端电压和电流相量；E_fdm为考虑量测误差后的实际励磁系统输出的实测励磁电压；ω(t)为量测误差；E_fdc为传递函数模型计算输出的励磁电压。Fig. 1 is a basic schematic diagram of a parameter identification method for a robust excitation system based on an improved objective function provided by the present invention. In Fig. 1, the input of the actual excitation system and its transfer function model

is the measured generator terminal voltage and current phasor; E _fdm is the measured excitation voltage output by the actual excitation system after considering the measurement error; ω(t) is the measurement error; E _fdc is the excitation output calculated by the transfer function model Voltage.

The process of excitation system parameter identification can be briefly described as: find a set of optimal parameters α, so that the excitation voltage E _fdm curve output by the actual excitation system and the excitation voltage E _fdc curve output by the transfer function model can fit best, and also Even if the objective function with the error of the two as a function is the smallest, the mathematical expression is:

$\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; fdm</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; fdc</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, N is the total number of sampling points, t _k is the sampling time, E _fdm is the measured excitation voltage output by the actual excitation system after considering the measurement error, and E _fdc is the excitation voltage calculated by the transfer function model.

Here, the objective function formula (1) is called a conventional objective function. This conventional objective function is not resistant to errors, and is greatly affected by measurement errors and bad data to a certain extent, which seriously distorts the identification results.

The present invention adopts an improved objective function with robustness, the form is as follows:

$\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

(2)

$<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; fdm</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; fdc</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

The robustness criterion function ρ(·) is:

$\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; |</span>}_{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&Delta;\&sigma;</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;\&sigma;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; |</span>}_{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; \&Delta;\&sigma;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Among them, Δσ is a positive real number used to balance robustness and effectiveness. Only by selecting an appropriate value of Δσ can we ensure a strong tolerance to errors, and at the same time ensure the validity of the identification results when the measurement error is small.

The robustness criterion function formula (3) shows that when the PMU measurement error is small, the improved objective function formula (2) is the conventional objective function formula (1), and the two are equivalent; When there is a large measurement error or bad data, ρ(e) is a constant, and its contribution to the objective function is fixed at (Δσ) ² , that is, the robustness criterion function limits its influence on the objective function by a fixed value. Therefore, for large measurement errors or bad data, the improved objective function weakens its influence on the objective function by setting a value, which has stronger tolerance to errors than the conventional objective function.

The excitation system is a nonlinear system, which contains various limiting links, exciter saturation and other nonlinear links. The traditional frequency domain method and time domain method can only identify the parameters of the linear system, and cannot take into account the role of nonlinear links. , while the genetic algorithm GA overcomes the problem that the parameters of the nonlinear link cannot be identified, and can identify the parameters of each link needed at one time. Therefore, the present invention uses the GA algorithm to identify the parameters of the excitation system.

Fig. 2 is a flow chart of a genetic algorithm GA of a method for identifying parameters of a robust excitation system based on an improved objective function provided by the present invention. In Figure 2, it specifically includes the following steps:

Step 201: use the Matlab/Simulink toolbox to build a variable parameter transfer function model of the excitation system to be identified, and use the machine terminal voltage and current phasor and excitation current measured by the PMU as the input data of the model;

Step 202: Add the upper and lower limit constraints of the unidentified parameters of the unidentified excitation system as a penalty item to the fitness function; and the expression of this penalty item is:

$\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; Max</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; Min</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>$

表示第i个待辨识参数的上限，

表示第i个待辨识参数的下限；N表示具有上下限约束的参数个数，M是正比例系数。Among them, α _i represents the i-th parameter to be identified,

Indicates the upper limit of the i-th parameter to be identified,

Indicates the lower limit of the i-th parameter to be identified; N indicates the number of parameters with upper and lower limit constraints, and M is a proportional coefficient.

Step 203: determine the optimal number of individuals n and the maximum genetic algebra g of the genetic algorithm;

Step 204: Encoding the parameter variables to be identified with real numbers to form chromosomes;

Step 205: Determine the range of the parameter variables to be identified according to the upper and lower limit constraints of the parameters to be identified, and randomly generate the first-generation population by using the inter-cell generation method;

Step 206: For each individual in the current group, convert the individual code into the parameter of the excitation system and put it into the transfer function model, and obtain the calculated output value of the excitation voltage through simulation; and calculate the objective function of the individual according to the excitation voltage value measured by the PMU value and fitness function value Ffitness;

The objective function is: J(α) of the improved objective function formula (2)

The fitness function is: $f_{\mathrm{fitness}}=\frac{C}{\mathrm{D.}+J\left(\mathrm{\&alpha;}\right)+P}$

Among them, C is the proportional amplification factor, and D is a constant item set to prevent the denominator from being zero; C can be 1000, and D can be 0.0001.

Step 207: Check whether the objective function value is less than the set value or whether the GA reaches the maximum genetic algebra; if not, continue; otherwise, end;

Step 208: Generate a new generation of population by using the random uniform selection method, the arithmetic crossover method Heuristic and the adaptive mutation method Adaptive feasible; and return to step 206 to continue.

Example:

为发电机的机端电压和电流相量，输出E_fd为发电机的励磁电压，I_fd为发电机的励磁电流，V_REF为参考电压。Fig. 3 is a schematic diagram of a BPA-FV model provided by an embodiment of the present invention without over-excitation limitation and under-excitation limitation. Excitation system input

Is the terminal voltage and current phasor of the generator, the output E _fd is the excitation voltage of the generator, I _fd is the excitation current of the generator, and V _REF is the reference voltage.

The simulation data comes from the IEEE-3M9BUS system, and the excitation model is the BPA-FV model. The machine terminal voltage and current, excitation voltage and excitation current are simulated. The data sampling period is 10ms, and the data of 3s in total are used as the actual measurement data of the PMU. The setting values of the parameters of the FV model are shown in Table 1:

Table 1 Simulation parameter values of FV model

parameter Rc Xc Tr T1 T2 K Kv T3 T4 set 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 set value 500 0.02 7.33 -6.23 0 1 0.08 7.33 -6.60

A BPA-FV model with variable parameters is built in Matlab's Simulink. The machine terminal voltage and current and excitation current are used as the model input, and the excitation voltage calculated by the model is used as the output. The GA algorithm is used to identify the excitation parameters.

Considering the overall identification of the excitation system using the GA algorithm, the identification results are not ideal due to the large number of parameters. In order to illustrate the problem, the present invention only identifies the parameter that has the greatest influence on the FV model—the magnification factor Ka. By superimposing Gaussian noise and bad data with different standard deviations in the measured excitation voltage data, the improved objective function formula is investigated with the identification effect of Ka (2) Comparing with the conventional objective function formula (1), it also illustrates the effectiveness of the present invention.

The optimization range of the parameters in the GA algorithm is [0.5*α _set , 1.5*α _set ], and α _set is the set value of the parameter; the optimal number of individuals is set to 120, and the genetic algebra is set to 25. In view of the simulation data of the present invention, the Δσ=0.1 in the tolerance criterion function formula (3) of the improved objective function formula (2) can ensure that there is not only a strong tolerance ability, but also when the measurement error is not large Validity of identification results.

The Gaussian noise with different standard deviations is superimposed on the measured excitation voltage data, and the conventional objective function and the improved objective function are respectively used as the objective functions of the excitation system parameter identification, and the parameter Ka is optimized by using the GA algorithm. The identification results under different noise conditions are shown in Table 2:

Table 2 Identification results of two objective functions under different noises

It can be seen from Table 2:

1) When the measurement noise is not large, the identification results and objective function values of the two objective functions are approximately the same, and the accuracy of the identification results is very high (the results of GA multiple optimizations will be different, but the difference is very small).

2) With the increase of measurement noise, the identification result of the improved objective function is better than that of the conventional objective function, because the improved objective function can weaken the influence of relatively large error data on the objective function, making the accuracy of the identification result has seen an increase. But when the measurement noise is too large, the identification results of the two objective functions become worse.

Fig. 4 is a schematic diagram of a measured excitation voltage curve obtained by PSCAD simulation provided by an embodiment of the present invention, including Gaussian noise with a standard deviation of 0.05 and three bad data randomly appearing. Here, it is assumed that the bad data is random sampling data that deviates from the true value by about 25%. The identification results of the two objective functions with different numbers of bad data are shown in Table 3.

Table 3 Identification results of two objective functions under different numbers of bad data

It can be seen from the results that with the increase of the number of bad data, the identification result of the conventional objective function deteriorates rapidly, while the error of the identification result of the improved objective function is relatively small, and is not greatly affected by bad data; this shows that The improved objective function can limit the error caused by bad data and weaken the impact of bad data on the objective function, which is equivalent to eliminating bad data and has a strong ability to resist errors.

The simulation results show that when there is little measurement noise in the PMU data, the identification result of the improved objective function is better than that of the conventional objective function; and when there is a certain amount of bad data in the PMU data, the identification result of the improved objective function It is obviously better than the conventional objective function, can limit the adverse effects of bad data, and has a strong ability to resist errors. Therefore, the identification method of the excitation system parameters with tolerance capability proposed by the present invention is effective and has certain engineering application value.

The above is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed in the present invention can easily think of changes or Replacement should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the protection scope of the claims.

Claims (3)

1. the anti-differential excition magnetic system parameter identification method based on the modified objective function is characterized in that, specifically may further comprise the steps:

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

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

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

2. a kind of anti-differential excition magnetic system parameter identification method based on the modified objective function according to claim 1 is characterized in that in the described step 2, described mathematical form with modified objective function of robustness is:

$\min J\left(\mathrm{\&alpha;}\right)\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&rho;}\left(e\left(t_k\right)\right)$

$=\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&rho;}(E_{\mathrm{fdm}}\left(t_k\right)-E_{\mathrm{fdc}}(t_k,\mathrm{\&alpha;}))$

Anti-poor criterion function ρ () is:

$\mathrm{\&rho;}\left(e\left(t_k\right)\right)=e^2\left(t_k\right){|}_{\left|e\left(t_k\right)\right|\&le;\mathrm{\&Delta;\&sigma;}}+{\left(\mathrm{\&Delta;\&sigma;}\right)}^2{|}_{\left|e\left(t_k\right)\right|>\mathrm{\&Delta;\&sigma;}}$

Wherein, α represents parameter sets to be identified; N is total number of sample points, t _kBe 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 of the anti-poor property of balance and validity.

3. a kind of anti-differential excition magnetic system parameter identification method based on the modified objective function according to claim 1, it is characterized in that, in the described step 3, utilize the parametric procedure of Identification of Genetic Algorithm excitation system specifically to may further comprise the steps based on the transfer function model of the excitation system to be identified of Matlab/Simulink:

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

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

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

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 the direct proportion coefficient;

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

Step 304: treat the 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 the 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:

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

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

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

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

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