State of charge estimation for lithium battery based on grey Kalman filter model

doi:10.23919/JSEE.2025.000125

Abstract

Abstract:

In this paper, a grey Kalman filter model is proposed for lithium battery charge state estimation. Firstly, this paper establishes a recursive relation equation between the front and back terms through the grey model (GM). Secondly, the state space expression is constructed based on the recursive relationship equation. Next, the Kalman filter algorithm is integrated to form a grey Kalman filter model. Finally, the charge state is estimated based on public lithium battery data. In this paper, the state of charge is estimated from three different aspects, including different driving cycles, randomly mixed driving cycles, and the estimation of the state of charge by different temperatures under the same driving cycle conditions. On this basis, the model is applied to a life scenario using the charge state of 20 electric vehicles. The results show that the proposed model has good accuracy.

Key words: grey model (GM), lithium batteries, state of charge, electric vehicle

Zhicun XU, Naiming XIE. State of charge estimation for lithium battery based on grey Kalman filter model[J]. Journal of Systems Engineering and Electronics, 2025, 36(6): 1579-1594.

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k	US06	GKFM	GM	ADGM	NNAR	SVM
44	0.5062	0.504 0	0.5369	0.489 0	0.516 0	0.5523
45	0.4914	0.4989	0.529 0	0.4759	0.5108	0.5577
46	0.4703	0.497 0	0.5213	0.4626	0.5063	0.5653
47	0.4516	0.474 0	0.5137	0.4491	0.5024	0.5747
48	0.4427	0.4722	0.5062	0.4354	0.499 0	0.5858
49	0.4432	0.4659	0.4988	0.4215	0.4961	0.5981
50	0.4364	0.4623	0.4916	0.4074	0.4936	0.6113
51	0.430 0	0.4401	0.4844	0.3931	0.4915	0.6251
52	0.4137	0.4197	0.4773	0.3785	0.4896	0.6389
53	0.4012	0.4236	0.4704	0.3638	0.4881	0.6526
54	0.3856	0.3967	0.4635	0.3487	0.4868	0.6659
55	0.3703	0.3612	0.4567	0.3335	0.4856	0.6784
56	0.3486	0.3547	0.4501	0.318	0.4847	0.6899
57	0.3294	0.3456	0.4435	0.3023	0.4839	0.7005
58	0.3194	0.3432	0.437	0.2864	0.4832	0.7099
59	0.3208	0.3477	0.4307	0.2702	0.4827	0.7182
60	0.313 0	0.3362	0.4244	0.2538	0.4822	0.7253
61	0.3071	0.3418	0.4182	0.2371	0.4818	0.7314
RMSE	—	0.0204	0.0811	0.0353	0.1077	0.2734
MAPE	—	0.0479	0.2074	0.0848	0.2627	0.6791

Model	MAPE	RMSE
GKFM	0.047 9	0.020 4
GM	0.207 4	0.081 1
ADGM	0.084 8	0.035 3
NNAR	0.262 7	0.107 7
SVM	0.679 1	0.273 4

Model	HWFETa		HWFETb		UDDS		LA92
Model	MAPE	RMSE	MAPE	RMSE	MAPE	RMSE	MAPE	RMSE
GKFM	0.030 5	0.014 4	0.027 1	0.014 5	0.046 1	0.000 5	0.038 9	0.020 3
GM	0.194 1	0.077 9	0.194 9	0.078 1	0.188 0	0.076 8	0.183 1	0.074 8
ADGM	0.162 2	0.065 4	0.162 4	0.065 4	0.160 4	0.065 6	0.124 9	0.063 8
NNAR	0.239 5	0.102 6	0.235 3	0.100 8	0.289 7	0.124 7	0.264 7	0.114 9
SVM	0.629 3	0.263 5	0.631 1	0.263 8	0.587 2	0.253 2	0.569 6	0.246 5

EV	Cycle	EV	Cycle	EV	Cycle	EV	Cycle
#1	1566	#6	1504	#11	1498	#16	1559
#2	1580	#7	1518	#12	1515	#17	1404
#3	1498	#8	1509	#13	1846	#18	1549
#4	1532	#9	1455	#14	1474	#19	1469
#5	1532	#10	1322	#15	1261	#20	1499

EV	a	EV	a
#1	−0.0234	#11	−0.024
#2	−0.0231	#12	−0.021
#3	−0.024 0	#13	−0.023
#4	−0.0233	#14	−0.024
#5	−0.0229	#15	−0.022
#6	−0.0245	#16	−0.023
#7	−0.0237	#17	−0.023
#8	−0.024 0	#18	−0.024
#9	−0.0239	#19	−0.024
#10	−0.0228	#20	−0.025