基於雙指數模型與Levenberg-Marquardt演算法優化之電動機車鋰電池在不同溫度下放電電壓建模

Discharge Voltage Modeling of Electric Motorcycle Lithium-Ion Batteries at Different Temperatures by Employing a Double-Exponential Model Optimized Using the Levenberg–Marquardt Algorithm

鋰電池在電動機車及能源儲存系統中具有關鍵地位，其放電特性深受環境溫度影響。一般的鋰電池端電壓建模方法，例如差分方程式模型，雖能描述放電趨勢，卻難以準確捕捉極端溫度下的非線性行為，導致模擬誤差顯著。本研究以市售動力型32700規格組成之電動機車磷酸鋰鐵電池組為研究對象，於恆定放電電流（16.93 A）下，分別在25°C、0°C與−20°C三種環境溫度進行放電實驗，每兩分鐘量測一次端電壓，建立雙指數數學模型，以描述快速與緩慢兩種時間尺度之電壓衰減。為了提升模型精度，本研究採用Levenberg-Marquardt（LM）非線性最小平方法進行參數辨識，使模型輸出與實測數據之間的平方誤差最小化。結果顯示，所提出模型在三種溫度下皆能有效擬合放電曲線，均方根誤差（RMSE）均顯著低於差分方程式模型，平均改善幅度超過95%。研究證明，結合雙指數模型與LM演算法的建模方法，不僅能精確模擬鋰電池在不同溫度條件下的放電電壓變化，亦具備實際應用價值，將可作為電池管理系統（BMS）在狀態估測與低溫啟動策略設計之重要依據。

Lithium-ion batteries are critical components of electric motorcycles and energy storage systems, and their discharge characteristics are strongly influenced by ambient temperature. Conventional voltage modeling approaches, such as difference equation models, can capture general discharge trends but often fail to accurately describe nonlinear discharge behavior under extreme temperature conditions, resulting in substantial simulation errors. This study investigated a commercial lithium iron phosphate（LiFePO4）battery pack composed of 32700-type cells and designed for electric motorcycles. Constant-current discharge tests（16.93 A）were conducted at three ambient temperatures（25, 0, and−20°C）, with terminal voltage recorded every 2 min. A double-exponential model was developed to characterize both fast and slow decay processes in the voltage response. Model parameter optimization was conducted using the Levenberg–Marquardt algorithm, thereby minimizing the sum of squared deviations between model outputs and experimental data. The results indicated that the proposed model effectively fit discharge curves across all tested temperatures, with its average root mean square error being >95% lower than that of the difference equation model. Overall, the proposed model enables precise simulation of the discharge behavior of lithium-ion batteries under varying temperatures; thus, it can be used in battery management systems to estimate state of charge and optimize low-temperature operation strategies.