基于动态规划优化的模糊逻辑控制在热电联供系统中的应用研究

doi:10.11949/0438-1157.20251287

摘要/Abstract

摘要：

针对质子交换膜燃料电池热电联供系统（PEMFC-CHP）的能量管理问题，本文采用动态规划（DP）算法优化系统功率分配，分析了离散点数设置与多目标权重配置的影响，并基于高斯混合模型（GMM）与期望最大化（EM）算法，从离线最优数据中提取规则，构建了数据驱动的模糊控制器（DP-FLC），以实现策略的在线应用。结果表明，选取离散点数N=200可在控制计算复杂度的同时，有效平滑PEMFC输出波动；通过多目标权重优化，系统能将PEMFC的最大功率增量限制在8.32 W，并在能耗与寿命间取得良好平衡；所提出的DP-FLC控制器继承了离线优化的优势，相比传统方法，其可将PEMFC功率波动标准差降低约56.7%，且系统能耗与DP最优解接近，验证了该在线管理策略在提升系统平稳性与能效方面的有效性。

关键词: 燃料电池, 热电联供系统, 动态规划, 整体优化, 动态仿真

Abstract:

For the energy management of proton exchange membrane fuel cell-based combined heat and power system (PEMFC-CHP), this study employs a dynamic programming (DP) algorithm to optimize the system's power distribution. The effects of discretization level settings and multi-objective weight configurations are analyzed. Based on the Gaussian Mixture Model (GMM) and the Expectation-Maximization (EM) algorithm, rules are extracted from offline optimal data to construct a data-driven fuzzy logic controller (DP-FLC), enabling the online application of the strategy. The results demonstrate that selecting a discretization level of N=200 effectively smooths PEMFC output fluctuations while controlling computational complexity. Through multi-objective weight optimization, the system can limit the maximum PEMFC power increment to 8.32 W and achieve a sound balance between energy consumption and system durability. The proposed DP-FLC controller inherits the advantages of offline optimization. Compared to conventional methods, it reduces the standard deviation of PEMFC power fluctuations by approximately 56.7%, and the system's energy consumption remains close to the DP-optimized solution. This verifies the effectiveness of the proposed online management strategy in enhancing system stability and energy efficiency.

Key words: fuel cell, combined heat and power system, dynamic programming, overall optimization, dynamic simulation

中图分类号:

TK 91

宁文婧, 陈黎, 陶文铨. 基于动态规划优化的模糊逻辑控制在热电联供系统中的应用研究[J]. 化工学报, DOI: 10.11949/0438-1157.20251287.

Wenjing NING, Li CHEN, Wenquan TAO. Application research of fuzzy logic control optimized by dynamic programming in combined heat and power system[J]. CIESC Journal, DOI: 10.11949/0438-1157.20251287.

图/表 20

表1 燃料电池寿命衰减参数

Table 1 Parameter of PEMFC lifetime degradation

参数	数值
电堆一次完整启停 (P₁)	0.00196(%/次)
加载功率变化率大于10% P_fc,max 或减载功率变化率大于20% P_fc,max (P₂)	0.0000593(%/次)
输出功率小于5% P_fc,max (P₃)	0.00126(%/h)
输出功率大于90% P_fc,max (P₄)	0.00147(%/h)

表2 c与α（c）之间的关系

Table 2 Relationship between c and α（c）

c	0.5	2	6	10
α(c)	31630	21681	12934	15512

图1 PEMFC-CHP系统图

Fig. 1 Diagram of the PEMFC-CHP system

图2 实验结果验证PEMFC模型

Fig. 2 Validating the PEMFC model with experimental results

图3 六种典型用能模式

Fig. 3 Six typical energy utilization modes

图4 模糊逻辑控制器结构示意图

Fig. 4 Schematic of the FLC

表3 不同离散点数下Ifc与SOC离散步长设置

Table 3 Ifc and SOC step size settings under different discretization levels

离散点数	I_fc离散间隔 (A)	SOC离散间隔
100	2	0.01
200	1	0.005
300	0.67	0.0033

图5 不同离散点数下PEMFC-CHP的功率分配与性能指标对比注:under different discretization levels

Fig. 5 Comparison of power distribution and performance indicators of the PEMFC-CHP system

表4 不同离散点数下PEMFC与锂电池运行特性对比

Table 4 Comparison of PEMFC and lithium-ion battery operating characteristics under different discretization levels

离散点数	P_fc平均值/W	PEMFC变载量最大值（取绝对值）/W	P_fc标准差/W	m_H2/g	P_bat标准差/W
100	472.78	45.17	158.23	94.62	185.14
200	473.32	19.48	123.56	93.91	179.77
300	474.68	15.82	108.49	93.90	183.07

图6 不同离散点数系统仿真时长

Fig. 6 Simulation time of the system under different discretization levels

表5 不同优化目标及权重配置

Table 5 Different optimization objectives and weight configurations

算例	J_soc权重	J_H2权重	J_{fc, loss}权重	J_△P权重	J_{bat, loss}权重
算例一	1	0	0	0	0
算例二	0	1	0	0	0
算例三	0	0	0.5	0	0.5
算例四	0	0	0.5	0.35	0.15
算例五	0.2	0.2	0.3	0.25	0.05

图7 不同优化目标下PEMFC-CHP功率分配与性能指标对比

Fig. 7 Comparison of power distribution and performance indicators of the PEMFC-CHP system under different optimization objectives

表6 不同优化目标下PEMFC与锂电池运行特性对比

Table 6 Comparison of PEMFC and lithium-ion battery operating characteristics under different optimization objectives

算例	P_fc平均值/W	PEMFC变载量最大值（取绝对值）/W	P_fc标准差/W	m_H2/g	P_bat标准差/W
算例一	500.31	998.62	234.43	104.10	179.71
算例二	464.88	45	129.90	92.01	95.73
算例三	490.31	45	203.14	100.27	15.01
算例四	474.59	18.81	95.48	93.74	183.11
算例五	472.96	19.56	127.43	93.90	176.70

表7 不同权重分配

Table 7 Different weight distributions

算例	J_soc权重	J_H2权重	J_{fc, loss}权重	J_△P权重	J_{bat, loss}权重
算例五	0.2	0.2	0.3	0.25	0.05
算例六	0.3	0.3	0.1	0.25	0.05
算例七	0.3	0.2	0.1	0.35	0.05
算例八	0.3	0.15	0.15	0.35	0.05
算例九	0.3	0.15	0.1	0.4	0.05

图8 不同权重配置下PEMFC-CHP功率分配与性能指标对比

Fig. 8 Comparison of power distribution and performance indicators of the PEMFC-CHP system under different weight configurations

表8 不同权重配置下PEMFC与锂电池运行特性对比

Table 8 Comparison of PEMFC and lithium-ion battery operating characteristics under different weight configurations

算例	P_fc平均值/W	PEMFC变载量最大值（取绝对值）/W	P_fc标准差/W	m_H2/g	P_bat标准差/W
算例五	472.96	19.56	127.43	93.90	176.70
算例六	472.93	19.56	128.91	93.93	176.78
算例七	482.08	11.48	110.60	95.66	185.74
算例八	487.42	9.35	124.25	97.17	175.06
算例九	487.43	8.32	124.42	97.17	175.17

图9 DP-FLC控制器

Fig. 9 DP-FLC controller

图10 不同优化方案对比

Fig. 10 Comparison of different optimization schemes

表9 不同优化方案下PEMFC与锂电池运行特性对比

Table 9 Comparison of PEMFC and lithium-ion battery operating characteristics under different optimization schemes

算例	P_fc平均值/W	PEMFC变载量最大值（取绝对值）/W	P_fc标准差/W	m_H2/g	P_bat标准差/W
算例九	487.43	8.32	124.42	97.17	175.17
FLC	474.16	80.55	217.96	98.54	43.58
DP-FLC	491.78	76.44	94.27	100.70	162.63

图11 PEMFC-CHP系统输出特性

Fig. 11 Output characteristics of the PEMFC-CHP system

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