﻿ 船舶中压直流电力系统配电网络重构技术研究
 舰船科学技术  2020, Vol. 42 Issue (1): 116-122 PDF

Research on the network reconfiguration of power distribution in the medium voltage dc power system on ships
LIU Sheng, WANG Tian-qi, ZHANG Lan-yong
Automation School of Harbin Engineering University, Harbin 150000, China
Abstract: The network reconfiguration of power syetem is a question with muti-objective optimization.The topology model of the network of power distribution in the medium voltage propulsion power system on ships was established, to analyze the circuitry current and power distribution under the different circuit fault by designing improved point-voltage method used to calculate the power flow in the network of power distribution. The fault reconfiguration model of the network of power distribution was established according to restore load,stability and switching frequency. The PSO (particles swarm optimization) algorithm was improved by designing "directional variation method" combined with self-adaption algorithm and hybridization pool algorithm, to speed up the optimizing and enhance the searching ability of PSO. The improved PSO algorithm was used to solve the fault reconfiguration mo-del of the network of power distribution. The test results show that the proposed algorithm can provide more comprehensive restoration strategy faster, possessing better optimizing cap-ability.
Key words: the medium voltage DC propulsion power system on ships     network reconfigu-ration     point-voltage method     particles swarm optimization algorithm
0 引言

1 拓扑建模 1.1 网络故障的提取

 $\begin{split} &{{{M}}_1} = {{M}} \cdot {\rm{diag}}(X) \text{，} \\ & \left[ {{{\dot Y}_y}} \right] = \left[ {{{{M}}_1}} \right]\left[ {\dot Y} \right]{\left[ {{{{M}}_1}} \right]^{\rm T}}\text{。} \\ \end{split}$ (1)

1.2 配电网络中各设备的数学模型

 图 1 换流器等效电路图 Fig. 1 Converter equivalent circuit diagram

 $\begin{split} &{P_{\rm{d}}} = {U_d}{I_d} \text{，} \\ & {P_1} = A + B{I_{\rm{c}}} + C{I_c}^2 \text{，} \\ & A = \frac{{6.62{S_N}}}{{600{S_B}}} \text{，} \\ &B = \frac{{1.8V_N^{\rm{d}}}}{{{\rm{600V}}_{\rm{B}}^{\rm{d}}}}\text{，} \\ & C = \frac{{3.0{{(V_N^d)}^2}{S_B}}}{{600{{(V_B^d)}^2}{S_N}}}\text{，} \\ &{P_C} = {P_{\rm{d}}} + {P_1} \text{，} \\ & {U_S} = \frac{{\cos {\sigma _c}M}}{{\sqrt 2 }}{U_{\rm{d}}}\text{，} \\ & {I_{\rm{s}}} = \frac{{\sqrt 2 {I_d}}}{{M\cos {\sigma _{\rm{c}}}}} \text{。} \end{split}$ (2)

 图 2 DC/DC变换器等效电路图 Fig. 2 DC/DC converter equivalent circuit diagram

 $\begin{split} &{I_{\rm{i}}} = \frac{{{U_i}{K_e}^2}}{{N{R_E}}} - \frac{{{U_j}{K_e}}}{{{R_E}}} = ({y_{ij}} + {y_{i0}}){U_i} - {y_{ij}}{U_j}\text{，} \\ & {I_{\rm{i}}} = \frac{{{U_i}{K_e}^2}}{{N{R_E}}} - \frac{{{U_j}{K_e}}}{{{R_E}}} = ({y_{ij}} + {y_{i0}}){U_i} - {y_{ij}}{U_j}\text{，} \\ &{y_{ij}} = \frac{{{K_e}}}{{{R_e}}}\text{，} \\ & {y_{i0}} = \frac{{K_e^2 - {K_e}N}}{{N{R_E}}}\text{，} \\ &{y_{j0}} = \frac{{N - {K_e}}}{{{R_E}}}\text{。} \end{split}$ (3)

 图 3 T型电动机等效电路图 Fig. 3 T-motor equivalent circuit diagram
 $\begin{split} &\frac{{{{\left| {{u_1}} \right|}^2}}}{{{{\left| {{r_1} + \frac{{{r_2}}}{s} + j({x_1} + {x_2})} \right|}^2}}} \cdot \frac{{1 - s}}{s}{r_2} = {p_2}\text{，} \\ & {z_{eq}} = \frac{{({r_m} + j \cdot {x_m})}}{{\left[ {{r_1} + \frac{{{r_2}}}{s} + j \cdot ({x_1} + {x_2})} \right]}} \text{。} \\ \end{split}$ (4)

2 MVDC配电网络潮流计算

 $\begin{array}{l} \left[ {{{\dot U}_b}} \right] = {\left[ {M_1} \right]^{\rm T}}\left[ {\dot U} \right]\text{，} \\ \left[ {{I_b}} \right] = \left[ {\dot Y} \right]\left[ {{{\dot U}_b}} \right]\text{。} \\ \end{array}$ (5)

 ${\left[ {\dot U} \right]^{(k + 1)}} = \left[ {{{\dot Y}_y}} \right] - 1\left[ {{{\dot s}_i}/\dot u_i^{(k)}} \right]\text{。}$ (6)

 $\dot u_i^{(k + 1)} = \frac{1}{{{y_{ij}}}} \cdot \left[ {\dot i_i^{(k)} - \sum\limits_{j = 0}^{i - 1} {{y_{ij}}} \cdot \dot u_j^{(k + 1)} - \sum\limits_{j = i + 1}^{n - 1} {{y_{ij}}} \cdot \dot u_j^{(k)}} \right]\text{。}$ (7)

 图 4 船舶中压直流综合电力推进系统配电网络简图 Fig. 4 Schematic diagram of the distribution network of a ship's medium-voltage DC integrated electric propulsion system

3 配电网络的稳定性分析

 \begin{aligned} {L_{pm}} = x{v_k}^2 - 4{z^2}Q_m' \text{，} \\ {L_{qm}} = rv_k^2 - 4{z^2}{P_m}' \text{。} \end{aligned} (8)

 ${\rm{a}}{s^2} + bs + c = 0\text{。}$ (9)

 \begin{aligned} &a = {p_1}{{\rm{r}}_{\rm{1}}}^2 + {\left| {{{\rm{u}}_1}} \right|^2}{r_2}\text{，}\\ &{{b}} = {p_2}({x_1}^2 + 2{x_1}{x_2} + {x_2}^2 + 2{r_1}{r_2}) - {\left| {{u_1}} \right|^2}{r_2}\text{，}\\ &{{c}} = {p_2}{r_2}^2\text{。} \end{aligned} (10)

4 配电网络重构数学模型

 $\max {L_{j1}} = \sum\limits_{i = 1}^k {{x_i}} {L_{j1i}}\text{；}$ (11)

 ${\rm{max}}({L_{j1}} + {L_{j2}}) = \sum\limits_{i = 1}^k {{x_i}} {L_{j1i}} + \sum\limits_{p = 1}^m {{x_p}} {L_{j2p}}\text{。}$ (12)

 ${\rm{max}}({L_{j1}} + {L_{j2}} + {L_{j3}}) = \sum\limits_{i = 1}^k {{x_i}} {L_{j1i}} + \sum\limits_{p = 1}^m {{x_p}} {L_{j2p}} + \sum\limits_{h = 1}^n {{x_h}} {L_{j3h}}\text{。}$ (13)

 ${\rm {Min}}({f_2}) = \Delta X\text{，}$ (14)

 ${\rm{Max}}({f_3}) = {\rm {Min}}(S)\text{，}$ (15)

 ${{f}} = {w_1}\max ({l_{j1}} + {l_{j2}} + {l_{j3}}) + {{{w}}_{\rm{2}}}{\rm {Min}}({f_2}) + {w_3}{\rm {Max}}({f_3})\text{。}$ (16)

 $\begin{array}{l} \alpha \sum {P \leqslant {P_{\max }}} \text{，} \\ {I_b} \leqslant {I_b}_{\max }\text{。} \\ \end{array}$ (17)

5 改进粒子群算法

 $\begin{array}{l} \!{v_{i,j}}(t + 1) \!= \!w{v_{i,j}}(t)\! +\! {c_1}{r_1}\left[ {{p_{i,j}}\! -\! {x_{i,j}}(t)} \right] + {c_2}{r_2}\left[ {{p_{g,j}} - {x_{i,j}}(t)} \right]\text{，}\\ \!{x_{i,j}}(t + 1) = {x_{i,j}}(t) + {v_{i,j}}(t + 1),j = 1,2, \cdots ,d \text{。} \end{array}$ (18)

 $\left( { - \infty ,0.5} \right) \to 0,[0.5,1.5) \to 1,[1.5, + \infty ) \to 2\text{。}$

1）为平衡PSO算法的全局搜索能力，采用非线性的动态惯性权重系数公式，其表达式如下：

 $w = \left\{ \begin{array}{l} {w_{\min }} - \frac{{({w_{\max }} - {w_{\min }}) * (f - {f_{\min }})}}{{({f_{avg}} - {f_{\min }})}},f \leqslant {f_{avg}}\text{；} \\ {w_{\max }},f > {f_{avg}}\text{。} \\ \end{array} \right.$ (19)

2）在每次迭代过程中，当所有粒子的个体最优解都已确定后，将这些个体记录下来，并令其每一位按照一定概率重新生成新的坐标，然后计算其适应度，并按照结果更新粒子个体极值和全局最优值。这样可使得寻优过程中，增加“优等粒子”的多样性，避免粒子的“早熟”现象。

3）借鉴遗传算法中的杂交概念，在每次迭代中，根据杂交概率选取指定数量的粒子放入杂交池内，池中的随机粒子可两两杂交，产生同样数目的子代粒子，后用子代粒子代替父代粒子。子代粒子位置由父代粒子位置进行算数交叉得到[15]

 ${\rm{child}}(x) = p \cdot paren{t_1}(x) + (1 - p) \cdot paren{t_2}(x)\text{，}$ (20)

 ${\rm{child}}(v) = \frac{{paren{t_1}(v) + paren{t_2}(v)}}{{\left| {paren{t_1}(v) + {\rm{paren}}{t_2}(v)} \right|}}\left| {paren{t_1}(v)} \right|\text{，}$ (21)

1）初始化种群中各微粒的位置和速度；

2）计算出每个微粒的适应度，将当前各微粒的位置和适应度函数值存储在各微粒的pbest中，将所有pbest中适应值最优的个体和适应值存储在gbest中；

3）更新粒子的速度和位移；

4）采用非线性的动态惯性权重系数公式更新权重w

5）对每个微粒，将其当前适应值与pbest进行比较，如更优，则将该值更新pbest，然后更新gbest

6）使pbest中的微粒每一位按一定概率重新生成新的坐标，计算新微粒的适应度值，然后更新pbestgbest

7）根据杂交概率选取一定数量的粒子放入杂交池内，池内粒子随机两两杂交，产生同样数目的子代粒子；

8）若满足迭代停止条件，则输出最终结果；若不满足，则返回步骤3继续运行算法。

6 算例分析

 图 5 仿真结果1 Fig. 5 Simulation results 1

 图 9 仿真结果5 Fig. 9 Simulation results 5

 图 6 仿真结果2 Fig. 6 Simulation results 2

 图 7 仿真结果3 Fig. 7 Simulation results 3

 图 8 仿真结果4 Fig. 8 Simulation results 4

7 结　语

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