﻿ 基于NSGA-II优化的船舶串联式混合动力系统能量管理策略
 舰船科学技术  2022, Vol. 44 Issue (14): 113-118    DOI: 10.3404/j.issn.1672-7649.2022.14.024 PDF

1. 上海交通大学 动力装置与自动化研究所，上海 200240;
2. 上海交通大学 海洋工程国家重点实验室，上海 200240

Energy management strategy of marine series hybrid system based on NSGA-II optimization
MIAO Dong-xiao1,2, CHEN Li1,2, WANG Xin-ran1,2
1. Institute of Power Plant and Automation, Shanghai Jiaotong University, Shanghai 200240, China;
2. State Key Laboratory of Ocean Engineering, Shanghai Jiaotong University, Shanghai 200240, China
Abstract: Taking the energy management strategy of the ship series hybrid system as the research object, the mathematical model of hybrid system is established and the real-time energy management strategy based on logic rules is adopted. To reduce fuel consumption and carbon emissions, a multi-objective optimization algorithm based on NSGA-II is proposed to optimize logic thresholds in the logic rules. The simulation results of the cycle condition of an inland transport ship show that compared with the traditional power system, the hybrid system with optimized energy management strategy saves 11.09% fuel and reduces carbon emissions by 4.32%; compared with experience-based logic rules, the optimized energy management strategy saves fuel by 1.18% and reduces carbon emissions by 4.32%.
Key words: hybrid system     energy management strategy     multi-objective optimization
0 引　言

1 船舶串联式混合动力系统描述 1.1 串联式混合动力系统架构

 图 1 船舶动力系统架构 Fig. 1 Architecture of ship power system
1.2 动力系统建模

 图 2 动力系统建模信号流图 Fig. 2 Signal flow diagram for dynamic system modeling

1.2.1 柴油发电机模型

 ${P_G} = \eta {P_D} ,$ (1)
 ${P_D} = {T_D}{\omega _D}。$ (2)

 图 3 柴油机脉谱图 Fig. 3 Map of diesel engine
1.2.2 动力电池模型

 ${V_{oc}}{I_{bat}}{{ - }}I_{bat}^2{R_{bat}} = {P_{bat}}，$ (3)
 ${I_{bat}} = \frac{{{V_{oc}}}}{{2{R_{bat}}}} - \sqrt {{{\left(\frac{{{V_{oc}}}}{{2{R_{bat}}}}\right)}^2} - \frac{{{P_{bat}}}}{{{R_{bat}}}}} 。$ (4)

 $SOC = SO{C_0} - \int {\frac{{{I_{bat}}{\rm{d}}t}}{{{Q_{bat}}}}}，$ (5)

 ${P_{bat\_\max }} = ({V_{oc}} - {I_{\max }}{R_{bat}}) \cdot {I_{\max }} 。$ (6)

 图 4 电池参数曲线 Fig. 4 Battery parameter curves
1.2.3 驱动电机模型

 ${P_m}{\text{ = }}\frac{{{T_m} \cdot {\omega _m}}}{{{\eta _m}}}。$ (7)

 图 5 电机效率脉谱图 Fig. 5 Map of motor efficiency
1.2.4 船舶阻力模型

 $T - {F_R} = ma 。$ (8)

 图 6 航行阻力 Fig. 6 Sailing resistance
1.2.5 螺旋桨模型

 $T = {K_T}{n^2}{D^4}\rho ，$ (9)
 $Q = {n^2}{D^5}\rho {K_Q} ，$ (10)
 ${K_T} = {K_{T1}}{\left(\frac{V}{{nD}}\right)^2} + {K_{T2}}\left(\frac{V}{{nD}}\right) + {K_{T3}}，$ (11)
 ${K_Q} = {K_{Q1}}{\left(\frac{V}{{nD}}\right)^2} + {K_{Q2}}\left(\frac{V}{{nD}}\right) + {K_{Q3}}。$ (12)

2 基于NSGA-II优化的能量管理逻辑门限规则 2.1 基于逻辑门限规则的能量管理策略

 图 7 能量管理策略框图 Fig. 7 Diagram of energy management strategy

2.2 优化问题描述

2.2.1 优化目标

 $M = \int {({g_{t1}} + {g_{t2}}){\rm{d}}t} 。$ (13)

 $G = ({E_{d1}} + {E_{d2}}){G_{fuel}} + {E_{bat}}{G_{ele}} 。$ (14)

 $\min \{ {f_1},{f_2}\} 。$ (15)
2.2.2 优化变量

 \begin{aligned}[b] & 250 \leqslant {P_1} \leqslant 300，\\ & 120 \leqslant {P_2} \leqslant 160，\\ & 65 \leqslant SO{C_{up}} \leqslant 75，\\ & 25 \leqslant SO{C_{low}} \leqslant 35。\\ \end{aligned} (16)
2.2.3 NSGA-II优化算法

NSGA是一种基于帕累托(Pareto)最优解的遗传算法，它与普通的遗传算法的主要区别在于增加了非支配排序步骤，对个体进行分层排序。2002年，Deb等[15]提出带精英策略的非支配排序遗传算法(NSGA-II)，采用快速非支配排序算法，降低复杂度，同时引入精英策略，有利于保证父代的满意解进入下一代。

 图 8 NSGA-II算法流程图 Fig. 8 Flow chart of NSGA-II algorithm
3 结果分析 3.1 NSGA-II优化结果

 图 9 工况曲线 Fig. 9 Speed curve

NSGA-II优化算法的种群个数为20，迭代次数为60，优化结果如图10所示。20个点代表Pareto最优解，并选择其中一个点的优化结果作进一步对比分析。该点的优化变量取值分别为： ${P_1} = 298.81\;{\rm{kW}}$ ${P_2} = 159.69\;{\rm{kW}}$ ${S OC_{{\rm{up}}}} = 65.02$ %， ${S OC_{{\rm{low}}}} = 33.45$ %.

 图 10 NSGA-II优化结果 Fig. 10 Optimization results of NSGA-II
3.2 仿真结果分析与对比

 图 11 仿真结果 Fig. 11 Simulation results

4 结　语

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