﻿ 配电网在风险状态下的重构优化方法
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 应用科技  2020, Vol. 47 Issue (4): 100-105  DOI: 10.11991/yykj.202001016 0

### 引用本文

SUN Xuri, LI Yanzhen. Optimized reconfiguration method of distribution network in risk state[J]. Applied Science and Technology, 2020, 47(4): 100-105. DOI: 10.11991/yykj.202001016.

### 文章历史

Optimized reconfiguration method of distribution network in risk state
SUN Xuri, LI Yanzhen
Qingdao Power Supply Company, State Grid Shandong Power Corporation, Qingdao, 266000, China
Abstract: In order to achieve the purpose of multi-objective optimization of the distribution network reconstruction, a random weight method is used to construct the objective function. And in order to meet different reconstruction goals of the distribution network in different operating states, the weight of each indicator in the objective function will be dynamically adjusted according to the operating state of the power grid. An improved BPSO algorithm is proposed to increase speed in solving the binary particle swarm optimization algorithm. The improved algorithm can quickly transfer the equipment at risk to the end of the power supply line, thereby improving the stability of the system. Finally, the IEEE 33-node system is used as an example for simulation verification. By comparing the improved BPSO algorithm with three existing algorithms, it is verified that the improved algorithm has the advantages of short calculation time, small network loss, and high maximum power supply capacity.
Keywords: self-healing control    distribution network reconfiguration    binary particle swarm optimization    topology adjustment    load shedding    network loss    load balance    maximum power supply capacity

1 配电网重构数学模型 1.1 问题目标函数

 $\min F = {w_{\rm{1}}}{f_1} + {w_{\rm{2}}}{f_2} + {w_{\rm{3}}}{f_3} + {w_{\rm{4}}}{f_4}$ (1)

 $\min {f_1} = \sum\limits_{i = 1}^n {\frac{{{P_i}^2 + {Q_i}^2}}{{{U_i}^2}}{s_i}{r_i}}$

 $\min {f_2} = \mathop {\max }\limits_{i \in n} \left( {\frac{{{I_i}}}{{{I_{{N_i}}}}}} \right) - \mathop {\min }\limits_{i \in n} \left( {\frac{{{I_i}}}{{{I_{{N_i}}}}}} \right)$

 $\min {f_3} = \sum\limits_{i = 1}^N {\left| {{x_i} - {x_{i_0}}} \right|}$

 $\max {f_4} = - \left( {\sum\limits_{i = 1}^N {{S_i}} + \sum\limits_{j \in D} {k{S_j}} } \right)$

1.2 约束条件

 $\left\{ \begin{array}{l} {P_i} = {P_{L_i}} + {V_i} \displaystyle\sum\limits_{j = 1}^{N_b} {{V_j}\left( {{G_{ij}}\cos {\delta _{ij}} + {B_{ij}}\sin {\delta _{ij}}} \right)} \\ {Q_i} = {Q_{L_i}} + {V_i}\displaystyle\sum\limits_{j = 1}^{N_b} {{V_j}\left( {{G_{ij}}\sin {\delta _{ij}} - {B_{ij}}\cos {\delta _{ij}}} \right)} \\ \end{array} \right.$

 $\left\{ {\begin{array}{*{20}{l}} {{V_{i,\min }} \leqslant {V_i} \leqslant {V_{i,\max }}} \\ {{I_i} \leqslant {I_{i,\max }}} \\ {{S_{G,\min }} \leqslant {S_G} \leqslant {S_{G,\max }}} \end{array} } \right.$

 $t \in T$

2 配电网重构控制模型选择

3 改进型BPSO算法 3.1 BPSO算法原理

BPSO算法是粒子群优化(particle swarm optimization，PSO)算法在离散问题中的应用。BPSO算法将粒子的位置信息用二进制变量“0-1”表示，粒子的速度大小用来表示粒子位置为“1”的概率，且粒子速度越大，粒子位置为“1”的概率越大；粒子速度越小粒子位置为“1”的概率越小[17-19]。BPSO算法中粒子的速度和位置信息迭代过程为

 $O_{iv}^{h + 1} = \alpha O_{iv}^h + a{}_1{r_1}(p_{iv}^h - X_{iv}^h) + {a_2}{r_2}(g_v^h - X_{iv}^h)$
 $\left\{ \begin{array}{l} S(X_{iv}^{h + 1}) = {1 / {1 + {{\rm{e}}^{ - O_{iv}^{h + 1}}}}} \\ X_{iv}^{h + 1} = 1,\quad \quad {{r}} < {\rm{Sig}}(X_{iv}^{h + 1}) \\ X_{iv}^{h + 1} = 0,\quad \quad {{r}} > {\rm{Sig}}(X_{iv}^{h + 1}) \end{array} \right.$
 ${\rm{Sig}}(X) = \left\{ \begin{array}{l} 0.99,\quad \quad \quad \quad \quad X > 5 \\ \dfrac{1}{{1 + {{\rm{e}}^{ - X}}}},\quad \quad - 5 < X < 5 \\ - 0.99,\quad \quad \quad \quad X < - 5 \end{array} \right.$

3.2 改进型BPSO算法

BPSO算法虽然具有精确度高、收敛性好的优点，但是求解的速度普遍较慢，当应用在系统对求解速度要求比较高的异常或警戒状态时，效果不好。为此，本文提出改进BPSO算法，该方法根据系统运行特点和规则进行求解，不仅能快速找到问题可行解，还保留了传统BPSO算法精确度高的优点，适用于系统处于风险状态的情况。

1)采用动态规划法找到高风险设备所在的最短供电线路及其下游负荷；

2)若高风险设备处在供电路径的上游，则通过控制联络开关及分段开关的通断状态，将其转移至供电路径末端或直接退出运行；

3)将原高风险设备的下游负荷转移至剩余容量大的可行供电路径或直接退出运行。

1)当节点j1的设备处于异常状态时，节点j2设备退出运行，节点j3(或j4)设备投入运行。将j1设备转移至供电路径末端，将由j1供电的下游负荷转移到由节点j3(或j4)供电。此调整策略不仅提高系统的安全性，还有提高负载的均衡性、保证辐射状网络结构的特点。拓扑调整结果如图3(b)所示。

2)当节点j1的设备处于警戒状态时，系统处于故障和事故的临界处，节点j1设备需退出运行以提高系统安全性。将节点j3(或j4)设备投入运行，使节点j2的负荷由电源G1(或G2)经过节点j3(或j4)供电。拓扑调整结果如图3(c)所示。

4 算例分析

5 结论

1)本文建立的数学模型，综合考虑了配电网重构的各项优化指标，包括网络损耗、负荷均衡性、开关操作次数、最大供电能力等，达到了多目标优化的目的。

2)重构之后配电网的有功损耗降低，节点最低电压有了很大提升，说明配电网重构可以达到优化系统运行的目的。

3)相比于其他3种算法，改进型BPSO算法的有功损耗最小、最大供电能力最高、计算速度最快，适用于系统处于风险状态的情况，满足系统安全经济运行的要求。

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