Parameter-estimation analyses of reliability models for the core components of a vanadium-redox-flow battery

doi:10.19799/j.cnki.2095-4239.2024.1209

Abstract

Abstract:

Reliability design is an important aspect of the development of vanadium-battery stacks, and it plays a decisive role in the safety and economy of energy-storage systems. Taking the liquid-flow frame and bipolar plate as the research objects, this study establishes reliability models for the core components of vanadium batteries based on the lognormal distribution and on two-parameter and three-parameter Weibull-distribution models. Parameter-estimation in this study is based on the maximum-likelihood estimation method and the GM (1,1) method. The K-S test and the root-mean-square error (RMSE) were adopted as evaluation indicators for exploring the influence of the distribution model and the parameter-estimation method on the reliability of the predictions. The results show that the minimum goodness-of-fit for the liquid-flow-frame reliability model is 0.89, indicating that the reliability models obtained using the two-parameter-estimation methods all pass the goodness-of-fit test. Further, the minimum RMSE of the reliability model is 0.22, which indicates that the two-parameter distribution model based on the GM (1,1) method is the most suitable reliability model for the liquid-flow frame. The minimum goodness-of-fit of the bipolar plate reliability model is 0.03, which indicates that the maximum-likelihood estimation method is not suitable for estimating the parameters of the three-parameter Weibull-distribution. Further, the minimum RMSE of the reliability model is 0.16, which indicates that the two-parameter distribution model based on the GM (1,1) method is the most accurate reliability model for the bipolar plate. These research results have theoretical guiding significance for the reliability design and optimization of vanadium-battery core components and systems.

Key words: vanadium battery, reliability, probability distribution model, K-S test, RMSE

CLC Number:

TB 114.3

Hang XU, Xiaohu SHI, Longhai YU, Yanzhao SUN, You WANG. Parameter-estimation analyses of reliability models for the core components of a vanadium-redox-flow battery[J]. Energy Storage Science and Technology, 2025, 14(6): 2524-2531.

Figures/Tables 9

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试样序号	失效概率P	液流框	双极板
试样序号	失效概率P	拉伸强度/MPa
1	0.05	43.00	15.79
2	0.10	44.38	15.80
3	0.15	45.12	15.95
4	0.20	45.42	16.01
5	0.25	45.88	16.25
6	0.30	45.95	16.42
7	0.35	46.12	16.82
8	0.40	46.50	16.86
9	0.45	46.82	16.90
10	0.50	47.10	16.97
11	0.55	47.35	17.05
12	0.60	47.59	17.08
13	0.65	47.82	17.20
14	0.70	48.31	17.26
15	0.75	49.46	17.38
16	0.80	49.58	17.41
17	0.85	49.84	18.10
18	0.90	50.01	18.11
19	0.95	50.10	18.35

钒电池部件	参数估计方法	对数正态分布	二参数Weibull分布	三参数Weibull分布
液流框	MLE	0.98	0.93	0.95
液流框	GM	0.98	0.89	0.99

双极板	MLE	0.84	0.72	0.03
双极板	GM	0.84	0.79	0.78

钒电池部件	参数估计方法	对数正态分布		二参数Weibull分布		三参数Weibull分布
钒电池部件	参数估计方法	μ	σ	β	λ	β	λ	γ
液流框	MLE	3.85	0.04	27.41	48.04	4.08	7.60	40.23
液流框	GM	3.85	0.04	28.38	48.03	7.33	14.64	33.36

双极板	MLE	2.83	0.05	23.84	17.29	—	—	—
双极板	GM	2.83	0.05	25.68	17.28	2.78	2.40	14.81

钒电池部件	参数估计方法	对数正态分布		二参数Weibull分布		三参数Weibull分布
钒电池部件	参数估计方法	μ	σ	β	λ	β	λ	γ
液流框	MLE	[3.83,3.88]	[0.03,0.06]	[15.06,39.74]	[26.44,69.64]	[4.03,4.13]	[6.74,8.47]	[38.59,41.88]
液流框	GM	[3.83,3.88]	[0.03,0.06]	[15.62,41.15]	[26.43,69.62]	[6.92,7.73]	[8.06,21.22]	[27.18,39.53]

双极板	MLE	[2.81,2.85]	[0.03,0.06]	[13.12,34.56]	[9.52,25.09]	—	—	—
双极板	GM	[2.81,2.85]	[0.03,0.06]	[14.13,37.22]	[9.51,25.05]	[2.39,3.17]	[1.32,3.48]	[13.84,15.77]

钒电池部件	参数估计方法	对数正态分布		二参数Weibull分布		三参数Weibull分布
钒电池部件	参数估计方法	μ	σ	β	λ	β	λ	γ
液流框	MLE	0.05	0.030	24.68	43.20	0.10	1.73	3.29
液流框	GM	0.05	0.030	25.52	43.19	0.81	13.16	12.35

双极板	MLE	0.04	0.030	21.44	15.57	—	—	—
双极板	GM	0.04	0.030	23.09	15.54	0.78	2.16	1.93