﻿ 基于改进遗传算法的同步发电机参数辨识

# 基于改进遗传算法的同步发电机参数辨识Parameter Identification of Synchronous Generator Based on Improved Genetic Algorithm

Abstract: A genetic algorithm for the identification of synchronous generator parameters is proposed in the case of system minor disturbance. In view of the randomness of the operation of roulette, the selection method is improved, and the problem of local optimum is avoided effectively. In order to solve the differential equation, the improved Euler method is selected, and the objective function is built according to the application of least square principle, then the improved genetic algorithm and particle swarm optimization (PSO) used for the identification of synchronous generator parameters are identified which based on PMU measured data. The identification results which compare the ad-vantages and disadvantages of two kinds of algorithm show that the improved genetic algorithm has higher identification accuracy.

1. 引言

2. 同步发电机的数学模型

1) 忽略定子磁暂态过程；

2) 计及转子d轴、q轴的暂态过程及次暂态过程。

d轴模型

$\left\{\begin{array}{l}{{T}^{\prime }}_{\text{d}0}\cdot \frac{\text{d}{{E}^{\prime }}_{\text{q}}}{\text{d}t}={E}_{f}-{{E}^{\prime }}_{\text{q}}-\frac{{x}_{\text{d}}-{{x}^{\prime }}_{\text{d}}}{{{x}^{\prime }}_{\text{d}}-{{x}^{″}}_{\text{d}}}\left({{E}^{\prime }}_{\text{q}}-{{E}^{″}}_{\text{q}}\right)\hfill \\ {{T}^{″}}_{\text{d}0}\cdot \frac{\text{d}{{E}^{″}}_{\text{q}}}{\text{d}t}={{E}^{\prime }}_{\text{q}}-{{E}^{″}}_{\text{q}}-\left({{x}^{\prime }}_{\text{d}}-{{x}^{″}}_{\text{d}}\right){i}_{\text{d}}+{{T}^{″}}_{\text{d}0}\cdot \frac{\text{d}{{E}^{\prime }}_{\text{q}}}{\text{d}t}\hfill \\ \begin{array}{l}{u}_{\text{q}}={{E}^{″}}_{\text{q}}-{{x}^{″}}_{\text{d}}{i}_{\text{d}}\\ {E}_{f}=k\cdot {u}_{f\text{d}}\end{array}\hfill \end{array}$ (1)

q轴模型

$\left\{\begin{array}{l}{{T}^{\prime }}_{\text{q}0}\cdot \frac{\text{d}{{E}^{\prime }}_{\text{d}}}{\text{d}t}=-{{E}^{\prime }}_{\text{d}}-\frac{{x}_{\text{q}}-{{x}^{\prime }}_{\text{q}}}{{{x}^{\prime }}_{\text{q}}-{{x}^{″}}_{\text{q}}}\left({{E}^{\prime }}_{\text{d}}-{{E}^{″}}_{\text{d}}\right)\hfill \\ {{T}^{″}}_{\text{q}0}\cdot \frac{\text{d}{{E}^{″}}_{\text{d}}}{\text{d}t}={{E}^{\prime }}_{\text{d}}-{{E}^{″}}_{\text{d}}+\left({{x}^{\prime }}_{\text{q}}-{{x}^{″}}_{\text{q}}\right){i}_{\text{q}}+{{T}^{″}}_{\text{q}0}\cdot \frac{\text{d}{{E}^{\prime }}_{d}}{\text{d}t}\hfill \\ {u}_{\text{d}}={{E}^{″}}_{\text{d}}+{{x}^{″}}_{\text{q}}{i}_{\text{q}}\hfill \end{array}$ (2)

3. 发电机参数辨识

${x}_{\text{q}}={U}_{\text{d}}/{I}_{\text{q}}$ (3)

${x}_{\text{d}}={x}_{\text{q}}$ (4)

3.1. 目标函数

${J}_{\text{d}}=\underset{t=1}{\overset{n}{\sum }}{\left({i}_{\text{dc}}-{i}_{\text{dm}}\right)}^{2}$ (5)

${J}_{\text{q}}=\underset{t=1}{\overset{n}{\sum }}{\left({i}_{\text{qc}}-{i}_{\text{qm}}\right)}^{2}$ (6)

3.2. 微分方程的求解

${\stackrel{¯}{y}}_{n+1}={y}_{n}+hf\left({x}_{n},{y}_{n}\right)$ (7)

${y}_{n+1}={y}_{n}+\frac{h}{2}\left[f\left({x}_{n},{y}_{n}\right)+f\left({x}_{n+1},{\stackrel{¯}{y}}_{n+1}\right)\right]$ (8)

4. 优化算法

Figure 1. Synchronous generator parameter identification

Figure 2. Improved Euler method

5. 算例分析验证

Figure 3. AGA flow-process diagram

Figure 4. Waveform of PMU measured data

Figure 5. Current fitting curve of direct axis-PSO

Figure 6. The current fitting curve of direct axis-AGA

Figure 7. Current fitting curve of quadrature axis-PSO

Figure 8. Current fitting curve of quadrature axis-AGA

Table 1. Comparison of identification result-direct axis

Table 2. Comparison of identification results-quadrature axis

6. 结论

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