以等效電路模型與DEKF架構於E-bike鋰電池SOC估測與比較

Abstract

本論文針對電輔自行車(E-bike)於實際騎乘工況下之鋰電池電量估測問題。對電輔自行車之鋰離子電池模組，建立基於等效電路模型與雙擴展卡爾曼濾波器(Dual Extended Kalman Filter, DEKF)估測架構。藉由狀態擴展卡爾曼濾波器即時估算SOC與極化電壓，並結合參數擴展卡爾曼濾波器更新模型參數，以降低因工況變動或量測雜訊所致的模型不確定性。 在實驗測試方面，首先進行階梯放電與恆流放電兩種基準測試。在兩種完整放電情境下，SOC估測之平均絕對誤差與均方根誤差均於1%以內，且端電壓殘差維持在毫伏等級，評估模型在全電量區間誤差表現。 為進一步評估模型在真實動態負載下的表現，本研究測試Eco節能、Trekking日常巡航與Boost強力助力三種助力模式，於電量區段進行定速與不定速之片段騎乘實測，並比較State-EKF與DEKF兩種方法。結果顯示三種模式下SOC估測RMSE均能維持一致的誤差範圍內，端電壓殘差約佔標稱電壓的0.03%至0.09%。參數分析方面，R0之Mean在三模式間接近，但R0之Rate隨Eco到Boost呈上升趨勢，R1與R2之Mean與Rate亦為相同的上升趨勢。動態負載指標方面皆為Boost最大、Eco最小。跨模式能耗比較中，Boost單位距離能耗約3.48 Wh/km，高於Eco之2.09 Wh/km，反映高助力將顯著縮短續航。綜合實驗結果，本研究之二階等效電路模型結合DEKF可在E-bike高動態騎乘環境中維持穩定且低誤差之SOC估測表現，並可作為輕型電動載具於動態工況下電量估測設計之參考。

This thesis addresses the problem of state-of-charge (SOC) estimation for the lithium-ion battery pack of an electric-assist bicycle (E-bike) under real riding conditions. An estimation framework is developed that combines an equivalent circuit model (ECM) with a dual extended Kalman filter (DEKF). The state EKF is used to estimate SOC and polarization voltages in real time, while a parameter EKF updates the model parameters online to reduce model uncertainty caused by operating-condition changes and measurement noise. For experimental validation, step-current pulse (step-discharge) tests and constant-current discharge tests are first carried out as baseline experiments. Under these two full-discharge scenarios, the mean absolute error (MAE) and root-mean-square error (RMSE) of SOC estimation both remain within 1%, and the terminal-voltage residual stays in the millivolt range, confirming good accuracy over the entire SOC range. To further examine performance under realistic dynamic loads, three assist modes—Eco, Trekking, and high-power Boost—are tested using constant-speed and variable-speed riding segments within selected SOC windows, and two estimation schemes, a State-EKF and the proposed DEKF with online parameter updating, are compared. The results show that the SOC estimation accuracy remains within a consistent error range across the three modes, and the terminal-voltage residual corresponds to only about 0.03%–0.09% of the nominal pack voltage. Parameter analysis indicates that the mean value of R0 is similar among the three modes, whereas the update activity of R0(Rate) increases from Eco to Boost; both the Mean and Rate of R1 and R2 exhibit the same increasing trend. Regarding dynamic load indicators, both reach their maximum in Boost mode and their minimum in Eco mode. In cross-mode energy analysis, Boost consumes about 3.48 Wh/km, higher than Eco at 2.09 Wh/km, indicating that stronger assist significantly shortens the riding range. Overall, the experiments demonstrate that the proposed second-order ECM combined with DEKF maintains stable and low-error SOC estimation performance for E-bike batteries under highly dynamic riding conditions, and it can serve as a reference for SOC estimation and BMS design in light electric vehicles.