﻿ 基于改进人工蜂群算法的配电网重构方法
 计算机系统应用  2020, Vol. 29 Issue (10): 211-216 PDF

1. 国家电网 国网安徽省电力有限公司, 合肥 230061;
2. 国家电网 国网安徽省电力有限公司 电力科学研究院, 合肥 230601

Reconstruction Method of Distribution Network Based on Improved Artificial Colony Algorithm
ZHAO Yong-Sheng1, ZHAO Ai-Hua2
1. State Grid Anhui Electric Power Co. Ltd., State Grid, Hefei 230061, China;
2. Electric Power Research Institute, State Grid Anhui Electric Power Co. Ltd., State Grid, Hefei 230601, China
Foundation item: National Key Research and Development Program of China (2016YFB0901100)
Abstract: In order to improve the economy of distribution network operation and the reliability of power supply, the system average outage frequency and the system average outage duration are selected to represent the power supply reliability of the distribution network in this study, and the active power loss factor is considered at the same time, a multi-objective reconstruction model of distribution network is established, which takes the power supply reliability index into account. This study introduces quantum theory and Metropolis criterion into artificial swarm algorithm, and the optimal solution of multi-objective reconstruction model is determined by fuzzy satisfaction decision method, a multi-objective reconstruction model optimization method for distribution network based on improved artificial swarm algorithm is proposed. The distribution network reconstruction example simulation system established, and the feasibility and superiority of the reconstruction model and solution method are verified by comparison with other intelligent methods.
Key words: distribution network reconstruction     reliability     artificial swarm algorithm     quantum theory

1 计及可靠性指标的配电网重构模型

1.1 目标函数

 ${P_L} = \sum\limits_{i = 1}^L {{k_i}} {R_i}\frac{{P_i^2 + Q_i^2}}{{U_i^2}}\;\;\;$ (1)

 $SAIFI = \frac{{{\text{用户总停电次数}}}}{{{\text{总用户数}}}}{\rm{ = }}\frac{{\displaystyle \sum {{\lambda _i}{N_i}} }}{{\displaystyle \sum {{N_i}} }}$ (2)
 $SAIDI = \frac{{{\text{用户停电持续时间总和}}}}{{{\text{总用户数}}}}{\rm{ = }}\frac{{\displaystyle \sum {{T_i}{N_i}} }}{{\displaystyle \sum {{N_i}} }}$ (3)

 $F = ({f_1},{f_2},{f_3}) = \min({P_L},SAIFI,SAIDI)$ (4)
1.2 约束条件

 ${P_{{\rm{G}}i}} - {U_i}\sum\limits_{j \in i} {{U_j}\left( {{G_{ij}}\cos {\delta _{ij}} + {B_{ij}}\sin {\delta _{ij}}} \right)} - {P_{{{L}}i}} = 0$ (5)
 ${Q_{{\rm{G}}i}} - {U_i}\sum\limits_{j \in i} {{U_j}({G_{ij}}\sin{\delta _{ij}} - {B_{ij}}\cos{\delta _{ij}})} - {Q_{{{L}}i}} = 0$ (6)

 $U_i^{\min } \le {U_i} \le U_i^{\max }$ (7)
 ${I_l} \le I_l^{\max }$ (8)
 ${g_k} \in {G_k}$ (9)

2 配电网重构模型优化算法 2.1 改进后的人工蜂群算法

 ${v_k} = \left[ {\begin{array}{*{20}{c}} {{\alpha _{k1}}}&{{\alpha _{k2}}}&\cdots&{{\alpha _{kl}}} \\ {{\beta _{k1}}}&{{\beta _{k2}}}&\cdots&{{\beta _{kl}}} \end{array}} \right]$ (10)

 $v_{ki}^{t + 1} = {\rm{abs}}(U(\theta _{ki}^{t + 1})v_{ki}^t)$ (11)
 $U(\theta _{ki}^{t{\rm{ + 1}}}) = \left[ {\begin{array}{*{20}{c}} {\cos \theta _{ki}^{t{\rm{ + 1}}}}&{ - \sin \theta _{ki}^{t{\rm{ + 1}}}} \\ {\sin \theta _{ki}^{t{\rm{ + 1}}}}&{\cos \theta _{ki}^{t{\rm{ + 1}}}} \end{array}} \right]$ (12)

$\theta _{ki}^{t{\rm{ + 1}}}=0$ , 则vki通过非门进行更新:

 $v_{ki}^{t + 1} = \overline N v_{ki}^t = \left[ {\begin{array}{*{20}{c}} 0&1 \\ 1&0 \end{array}} \right]v_{ki}^t$ (13)

 $x_{kd}^{t + 1} = \left\{ \begin{array}{l} 1,\;\;\eta _{kd}^{t + 1} > {(a_{kd}^{t + 1})^{\rm{2}}} \\ {\rm{0,}}\;\;\eta _{kd}^{t + 1} \le {(a_{kd}^{t + 1})^{\rm{2}}} \\ \end{array} \right.$ (14)

 $\theta _{id}^{t + 1} = {e_1}(p_{id}^t - x_{id}^t) + {e_2}(p_{gd}^t - x_{id}^t)$ (15)
 $v_{id}^{t + 1} = \left\{ \begin{array}{l} \overline N v_{id}^t,\;\;{\text{若}}\theta _{id}^{t + 1}{\rm{ = 0}}{\text{且}}\gamma _{id}^{t + 1} < {c_1}\\ {\rm{abs}}[U(\theta _{id}^{t + 1})v_{id}^t],\;\;{\text{其他}} \end{array} \right.$ (16)

 $\theta _{jd}^{t + 1} = {e_3}\left( {p_{id}^t - x_{jd}^t} \right) + {e_4}\left( {p_{jd}^t - x_{jd}^t} \right) + {e_5}\left( {p_{gd}^t - x_{jd}^t} \right)$ (17)
 $v_{jd}^{t + 1} = \left\{ \begin{array}{l} \overline N v_{jd}^t,\;\;{\text{若}}\theta _{jd}^{t + 1}{\rm{ = 0}}{\text{且}}\gamma _{jd}^{t + 1} < {c_{\rm{2}}}\\ {\rm{abs}}[U(\theta _{jd}^{t + 1})v_{jd}^t],\;\;{\text{其他}} \end{array} \right.$ (18)

 ${Q_{i + 1}} = \left\{ {\begin{array}{l} {1\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;fit({x_{i + 1}}) < fit({x_i})} \\ {\min [1,1 - Z] > K\;\;fit({x_{i + 1}}) \ge fit({x_i})} \end{array}} \right.$ (19)
 $Z = \exp (\left( {fit({x_{i + 1}}) - fit({x_i})} \right)/fit({x_i}))$ (20)
 ${x_{i + 1}} = \alpha \times {x_i}$ (21)

2.2 改进蜂群算法性能检验

 $\begin{array}{l} f\left( {x,y} \right) = \left\{ {\displaystyle \sum\limits_{i = 1}^5 {i\cos \left[ {\left( {i + 1} \right)x + i} \right]} } \right\}\left\{ {\displaystyle \sum\limits_{i = 1}^5 {i\cos \left[ {\left( {i + 1} \right)y + i} \right]} } \right\} \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;+0.5\left[ {{{\left( {x + 1.425\;13} \right)}^2} + {{\left( {y + 0.800\;32} \right)}^2}} \right] \end{array}$ (22)

2.3 配电网重构模型的优化求解

 ${\mu _j} = \left\{ \begin{array}{l} 1,\;\;\;{f_j} \le f_j^{\min } \\ \dfrac{{f_j^{\max } - {f_j}}}{{f_j^{\max } - f_j^{\min }}},\;\;\;f_j^{\min } \le {f_j} \le f_j^{\max } \\ 0,\;\;\;{f_j} \ge f_j^{\max } \\ \end{array} \right.$ (23)

 图 1 不同个体数量下优化结果

 $U = \sum\limits_{j = 1}^J {{\mu _j}}$ (24)

 图 2 本文求解基本流程图

3 配电网重构实例分析 3.1 系统实例分析

 图 3 IEEE-33节点系统图

3.2 配电网重构结果对比分析

 图 4 不同方法获得的Pareto最优解前沿

 图 5 优化过程收敛曲线图

4 结论与展望

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