PSO-based speed and power allocation strategy collaborative optimization method for hydrogen fuel cell ships

参数	数值	参数	数值
船长/ m	163	船宽/ m	25
最大功率/kW	30 000	排水量/t	20 000
吃水/m	4.9	最大速度/kn	20.6
设计速度/kn	18.5	航程/n mile	约93
燃料电池功率/kW	28 800	锂电池容量/(kW·h)	15 120

Table 2. Meteorological information clustering center
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Table 2. Meteorological information clustering center
气象信息类型编号风速/(m·s⁻¹) 风向/(°) 流速/(m·s⁻¹) 流向/(°) 浪高/m
1 8.3 222.6 0.20 268.1 0.7
2 6.6 216.5 0 0 0
3 7.7 222.9 0.10 203.8 0.5
4 10.5 241.5 0 0 0
5 8.9 226.6 0.15 230.9 0.9

Table 3. Wind resistance coefficient of different types of ships
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Table 3. Wind resistance coefficient of different types of ships
船型 $ {C_{{\text{wind}}}} $
平底船 1.2
V形底船 0.9
散货船 1.2
集装箱船 1.0

Table 4. Approximate calculation parameters of ship wind area

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Table 4. Approximate calculation parameters of ship wind area

船舶类型	$ {M_{{\text{ship}}}} $	横向受风面积$ {A_x} $		纵向受风面积$ {A_y} $
船舶类型	$ {M_{{\text{ship}}}} $	$ \alpha\mathrm{_w} $	$ \beta\mathrm{_w} $	$ \alpha\mathrm{_w} $	$ \beta\mathrm{_w} $
滚装船	DWT	1.029	0.435	1.453	0.464
客船	GT	0.947	0.426	0.059	0.680

Table 5. Pseudo code of speed - power allocation collaborative optimization algorithm

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Table 5. Pseudo code of speed - power allocation collaborative optimization algorithm

	输入：航线分段信息(航向$ \psi $，航段航程$ {X_S} $，气象类型$ \mathcal{N} $)输出：每个航段的航速$ V(t) $和燃料电池输出功率$ {P_{{\text{fc}}}}(t) $
1	for$ i = 1\;\;{\text{to}}\;N $ (N为航段总数)
	输入：$ {\psi _i} $，航段i的速度初值$ {V_{{\text{ini-}} i}} $，航段i的锂电池荷电状态初值$ SO{C_{{\text{ini-}} i}} $，航段所处位置的气象类型$ {\mathcal{N}_i} $　输出：粒子全局最优值$ {G_{{\text{best-}}i}} $，航段i的速度末端值$ {V_{{\text{end-}}i}} $，航段i的锂电池荷电状态末端值$ SO{C_{{\text{end-}}i}} $
2	#初始化$ {J_P} $个粒子的位置#$ \left\{ {({a_j},{P_{{\text{fc-}}j}})\|j = 1,2,3, \cdot \cdot \cdot ,{J_P}} \right\} $
3	#计算$ {J_P} $个粒子的适应度，即氢耗总质量$ {m_{{{\text{H}}_{\text{2}}}}} $#
4	$ \left\{ {{m_{{{\text{H}}_{\text{2}}}}}_j\|j = 1,2,3, \cdot \cdot \cdot ,{J_P}} \right\} $，设置为每个粒子j的个体最优值$ {P_{{\text{best}}}}_j $
5	$ {G_{{\text{best}}}} = \min \left( {{P_{{\text{best}}}}_j} \right) $
6	for$ {m_{{\text{it}}}} = 1\;\;{\text{to}}\;{M_{{\text{it}}}} $ (mit为粒子的迭代更新次数；$ {M_{{\text{it}}}} $为粒子的迭代总次数)
7	#更新$ {J_P} $个粒子的位置#　　$ \left\{ {({a_{j,{m_{{\text{it}}}}}},{P_{{\text{fc, }}j,{m_{{\text{it}}}}}})\|j = 1,2,3, \cdot \cdot \cdot ,{J_P}} \right\} $
8	#计算第$ {m_{{\text{it}}}} $次迭代更新后，每个粒子j的适应度值#　　$ \left\{ {{m_{{{\text{H}}_{\text{2}}}}}_{j,,{m_{{\text{it}}}}}\|j = 1,2,3, \cdot \cdot \cdot ,{J_P}} \right\} $
9	if$ {m_{{{\text{H}}_{\text{2}}}}}_j < {P_{{\text{best}}}}_j $
10	$ {P_{{\text{best}}}}_j = {m_{{{\text{H}}_{\text{2}}}}} $
11	if$ {P_{{\text{best}}}}_j < {G_{{\text{best}}}} $
12	$ {G_{{\text{best}}}} = {P_{{\text{best}}}}_j $
13	end for
14	Print $ {G_{{\text{best-}}i}} $，$ {a_i} $，$ {P_{{\text{fc-}}i}} $，$ SO{C_{{\text{end-}}i}} $，$ {V_{{\text{end-}}i}} $
15	end for
16	return 每一航段的$ V(t) $和$ {P_{{\text{fc}}}}(t) $

Table 6. Results of route segmentation

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Table 6. Results of route segmentation

航段	航向/(°)	航程/m	气象信息类型
1	186	44.96	4
2	154	1 846.34	4
3	149	4 648.52	4
4	100	3 151.41	4
5	185	8 536.32	1
6	187	14 289.90	1
7	187	14 592.27	4
8	191	13 235.15	4
9	192	20 345.08	5
10	195	6 760.40	5
11	191	32 221.05	1
12	190	9 729.71	3
13	193	18 727.02	3
14	191	10 983.18	2
15	196	3 913.65	2
16	239	6 390.01	2
17	230	2 155.75	2

Table 7. Comparison of total hydrogen consumption results for three methods

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Table 7. Comparison of total hydrogen consumption results for three methods

方法	方法	航行时间	氢耗总质量/t	优化效果/%
功率分配优化	原始航速数据	6 h 40 min	6.903 8	0
航速−功率分配协同优化	分段航速优化^[6]	6 h 57 min	6.772 7	1.90
航速−功率分配协同优化	传承−链接优化	6 h 58 min	6.638 0	3.85

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Ning WANG, Zhiqiang LI. PSO-based speed and power allocation strategy collaborative optimization method for hydrogen fuel cell ships[J]. Chinese Journal of Ship Research, 2025, 20(3): 211

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