﻿ 基于改进混沌优化算法的船舶综合负荷模型参数辨识
 舰船科学技术  2017, Vol. 39 Issue (3): 74-77 PDF

Parameter identification of ship integrative load model based on improved chaos optimization algorithm
TANG Zhuo-zhen, GU Qu-fei, NI Wei, XU Liang
Nantong Shipping College, Nantong 226010, China
Abstract: On-line parameter identification is the main method of power system load modeling, and the optimization algorithm is mainly used in the identification method. Firstly, the flow of the chaos optimization algorithm is improved, the function of the automatic reduction of the parameter search scope is added, and the steps of the generation of a chaotic sequence are reduced. The optimization results of the test function show that the improved algorithm can greatly improve the search speed based on the guaranteed precision. Then, the improved algorithm is applied to the parameter identification of ship integrative load model. The simulation results show that the algorithm is fast and accurate. Through the analysis of the simulation results, it is pointed out that, for the load model parameter identification, the reasonable reduction of the parameter optimization range is helpful to improve the accuracy of the algorithm.
Key words: ship load modeling     parameter identification     chaos optimization algorithm
0 引　言

1 SILM 模型及参数辨识方法

SILM 模型的结构如图 1 所示。该综合负荷模型由等值静态负荷（包括无功补偿）和等值电动机（动态负荷）并联组成。静态负荷一般只考虑恒阻抗负荷，且方程采用指数形式，因为指数形式参数较少，利于参数辨识[3]

 图 1 SILM 模型结构 Fig. 1 The Structure of SILM

 ${P_S} = {P_{S0}}{(\frac{{{U_L}}}{{{U_{L0}}}})^{{p_v}}},\quad {Q_S} = {Q_{S0}}{(\frac{{{U_L}}}{{{U_{L0}}}})^{{q_v}}},$ (1)

 $T'\frac{{{\rm{d}}E'}}{{{\rm{d}}t}} = - E' + C{U_L}\cos \delta \text{，}$ (2)
 $\frac{{{\rm{d}}\delta }}{{{\rm{d}}t}} = - \frac{{C{U_L}}}{{T'E'}}\sin \delta + ({\omega _r} - 1)\text{，}$ (3)
 $M\frac{{{\rm{d}}{\omega _r}}}{{{\rm{d}}t}} = - \frac{{{U_L}E'}}{{X'}}\sin \delta - {T_m}\text{。}$ (4)

 ${P_d} = - \frac{{{U_L}E'}}{{X'}}\sin \delta ,\quad {Q_d} = \frac{{{U_L}({U_L} - E'\cos \delta )}}{{X'}}\text{。}$ (5)

 ${P_D} = \frac{{{P^2} + {Q^2}}}{{U_S^2}}{R_D}, {Q_D} = \frac{{{P^2} + {Q^2}}}{{U_S^2}}{X_D}\text{，}$ (6)

 $P \! \! = \! \! {P_S} \! + \! {P_d} \! + \! {P_D} \! \!=\! \! {P_{S0}}{(\frac{{{U_L}}}{{{U_{L0}}}})^{{p_v}}}\! \! -\! \! \frac{{{U_L}E'}}{{X'}}\sin \delta \! +\! \! \frac{{{P^2}\! \! +\! \! {Q^2}}}{{U_S^2}}{R_D}\text{，}\! \!$ (7)
 $\begin{split}Q = {Q_S} + {Q_d} + {Q_D} = {Q_{S0}}{(\displaystyle\frac{{{U_L}}}{{{U_{L0}}}})^{{q_v}}} + \\[5pt]\quad \:\displaystyle\frac{{{U_L}({U_L} - E'\cos \delta )}}{{X'}} + \frac{{{P^2} + {Q^2}}}{{U_S^2}}{X_D}\text{。}\end{split}$ (8)

$\theta = \{ {X_s},{P_{MP}},{K_L},{X_D}\}$ ，设实际测量到的负荷动态响应数据有N 点，实测有功和无功分别为PQ，根据式（7）和式（8）计算得到的有功和无功分别为PC QC 。则参数辨识所使用的目标函数可定义为：

 $\min E \! = \! \! \sum\limits_{K = 1}^N {[{{(P(K) \! - \! {P_C}(K,\theta ))}^2} + } {(P(K) - {P_C}(K,\theta ))^2}]\text{。}$ (9)

2 混沌优化算法及其改进

 ${{ x}_{n + 1}} = u{{ x}_n}(1 - {x_n}) n = 0,1,2, \cdots \text{。}$ (10)

 ${X_i}(k) = {c_i} + {d_i}{x_i}(k)$ (11)

 ${X_i}(k') = X_i^ * + {\alpha _i}({x_i}(k') - 0.5)\text{。}$ (12)

 ${X_i}(k') = {c_i} + {d_i}{x_i}(k)\text{。}$ (13)

 $F_1 = 100{(x_1^2 - {x_2})^2} + {(1 - {x_1})^2}, {x_i} \in [ - 2.048,2.048]\text{，}$ (14)
 $\begin{split}\\[1pt]F_2 =& [1+(x_1+x_2+1)^2(19-14x_1+3x_1^2-14x_26 +\\[2pt]& x_1x_2+3x_2^2]{\cdot}[30+(2x_1-3x_2)^2(18-32x_1 + \\[2pt]& 12x_1^2+48x_2-36x_1x_2+27x_2^2], x_i \in [-2,2]\text{，}\end{split}$ (15)
 $F_3 = x_1^2 + x_2^2 + x_3^2, {x_i} \in [ - 5.12,5.12]\text{，}$ (16)
 $F_4 = 0.5 + \frac{{{{\sin }^2}\sqrt {x_1^2 + x_2^2} - 0.5}}{{{{[1.0 + 0.001(x_1^2 + x_2^2)]}^2}}}, {x_i} \in [ - 5,5]\text{，}$ (17)
 $\begin{split}\\F_5 =& |4 - 2.1x_1^2 +\! x_1^4/3| + {x_1}{x_2} + (4x_2^2 - 4)x_2^2, \\[2pt]& {x_i} \in [ - 5,5]\text{。}\end{split}$ (18)

3 仿真算例

1）两参数（PMP KL ）优化结果

2）三参数（PMP KL XD ）优化结果

3）四参数（PMP XS KL XD ）优化结果

4 结　语

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