Investigation of RUL prediction of lithium-ion battery equivalent cycle battery pack
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摘要: 電動汽車以零污染、零排放等優點成為新能源汽車中最具有發展潛力的對象，鋰離子電池作為其動力來源，科學準確地預測其剩余使用壽命是決定電動汽車性能的重要因素。本文研究等效循環電池組在等效循環工況、不同循環次數時，鋰離子電池電壓隨著放電時間的變化曲線。通過分析不同循環次數下導函數在等效特征點處的斜率變化規律，建立鋰離子電池等效循環工況下的壽命退化曲線。選取NASA等效循環電池組和自測JZ等效循環電池組，將放電初期和放電后期曲線與特定斜率直線交點作為等效循環壽命預測的等效特征點，根據這兩組特征點分別建立退化模型Mini和Mlat。最后選取等效循環電池組內的其他電池進行鋰離子電池等效循環壽命預測的驗證。通過鋰離子電池測試數據集驗證其預測精度較高，穩定性較好，具有較強的應用價值。Abstract: The depletion and environmental pollution associated with traditional fossil energy sources has generated great interest in the development of new energy. Among the kinds of new-energy batteries, lithium-ion batteries have the advantages of small size, high energy density, a long life cycle, zero emissions, and no pollution. These batteries are widely used in many industries and fields, including vehicles. Currently, assessments of the health status of lithium-ion batteries have become a hot research topic. The lithium-ion battery has complex electrochemical characteristics and its capacity tends to degrade with cyclic charges and discharges. When its capacity degrades to the failure threshold (usually 70%–80% of rated capacity), the life of lithium ion battery is considered to have reached an end. Therefore, investigations to better predict the remaining useful life of a lithium-ion battery can help to improve system reliability and prevent accidents. Battery-system health evaluations have important research and application value. In this study, the voltage change curves of the lithium-ion battery were investigated with discharge time under equivalent cycle conditions and different cycle times. By analyzing the slope change rule of the derivative function at an equivalent characteristic point for different cycle times, the life degradation curves of the lithium-ion battery under equivalent cycle conditions were established. Using the NASA and self-test JZ equivalent cycle batteries, the intersection point of the specific-slope straight line and curve at early and late stages of discharge was taken as the equivalent feature points for predicting the equivalent cycle life. Based on these two groups of feature points, Mini and Mlat degradation models were established, respectively. To verify this method, other batteries in the equivalent-cycle battery pack were tested. The results of the test data set validate the prediction accuracy and stability, which has strong application value.
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圖 1 B6電池等壓降放電時間?電壓曲線圖
Figure 1. Curves of discharge time and voltage of B6 battery with constant voltage drop
圖 2 B6電池數據處理后等壓降放電時間?電壓曲線圖
Figure 2. Curves of discharge time and voltage of B6 battery with constant voltage drop based on data processing
圖 4 使用B6放電數據建立退化曲線。（a）放電前期數據；（b）放電后期數據
Figure 4. Degradation curves using the B6 discharge data: (a) pre-discharge data; (b) after discharge
圖 5 驗證B6電池濾波后時間一階導函數曲線圖
Figure 5. Validation of the derivative function curves after B6 battery filtering
表 1 驗證退化模型Mini和Mlat壽命預測表（B6）
Table 1. Verification of life predictions with degradation models Mini and Mlat（B6）
Model number Nver e Npre ΔN δ/% Model number Nver e Npre ΔN δ/% Mini 40 0.816 44 4 2.85 Mlat 40 0.465 41 1 0.71 85 0.790 92 7 5.00 85 0.440 61 24 17.10 115 0.782 108 ?7 ?5.00 115 0.405 95 20 14.30 
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表 2 驗證退化模型Mini和Mlat壽命預測表（B5）
Table 2. Verification of the life predictions with degradation models Mini and Mlat（B5）
Model number Nver e Npre ΔN δ/% Model number Nver e Npre ΔN δ/% Mini 40 0.815 45 5 3.33 Mlat 40 0.4525 49 9 6.00 65 0.798 73 8 5.33 65 0.4111 88 23 8.00 95 0.785 102 7 4.67 95 0.3966 105 10 6.67
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表 3 驗證退化模型Mini和Mlat壽命預測表（B7）
Table 3. Verification of the life predictions with degradation models Mini and Mlat（B7）
Model number Nver e Npre ΔN δ/% Model number Nver e Npre ΔN δ/% Mini 21 0.825 30 9 5.81 Mlat 21 0.445 56 35 22.60 60 0.799 73 13 8.38 60 0.4338 66 6 3.87 101 0.780 111 10 6.45 101 0.415 85 ?16 ?10.32 141 0.770 130 ?11 ?7.09 141 0.362 146 5 3.22
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表 4 驗證退化模型Mini和Mlat壽命預測表（JZ-1）
Table 4. Verification of the life predictions with degradation models Mini and Mlat（JZ-1）
Model number Nver e Npre ΔN δ/% Model number Nver e Npre ΔN δ/% Mini 80 0.855 70 ?10 ?2.86 Mlat 80 0.315 61 ?19 ?5.43 190 0.810 194 4 1.14 190 0.285 202 12 3.43 250 0.790 267 17 4.86 250 0.280 236 14 4.00
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表 5 驗證退化模型Mini和Mlat壽命預測表（JZ-2，JZ-3）
Table 5. Verification of the life predictions with degradation models Mini and Mlat（JZ-2，JZ-3）
Model number Battery model Nver e Npre ΔN δ/% Model number Battery model Nver e Npre ΔN δ/% Mini JZ-2 75 0.850 81 6 1.71 Mlat JZ-2 75 0.320 45 ?30 ?8.57 150 0.820 161 11 3.14 150 0.310 80 ?70 ?20.00 300 0.785 286 ?14 ?4.00 300 0.290 175 ?125 ?35.7 JZ-3 75 0.856 68 ?7 2.00 JZ-3 75 0.330 18 ?57 ?11.4 150 0.821 149 ?1 ?0.28 150 0.320 45 ?105 ?21.00 300 0.775 328 28 8.00 300 0.280 236 ?64 ?12.80 380 0.780 307 ?73 ?20.80 380 0.285 204 ?176 ?35.20
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