Battery State Estimation, Degradation Modeling, and Lifecycle Management

Module: Sustainable Tech | Difficulty: Premium

Equivalent Circuit Model

State of Health

The capacity fade model:

Comparison

| Chemistry | Energy Density (Wh/kg) | Cycle Life | Cost ($/kWh) | |-----------|----------------------|------------|---------------| | LFP | 90-160 | 3000-5000 | 100-130 | | NMC | 150-250 | 1000-2000 | 120-160 | | NCA | 200-300 | 800-1500 | 130-170 | | Solid-state | 300-500 | 5000+ | 200-400 |

Python Implementation

import numpy as np
from scipy.integrate import odeint

class BatteryStateEstimator:
    def __init__(self, capacity=50, R0=0.01, R_RC=0.005, C_RC=5000):
        self.capacity = capacity
        self.R0 = R0
        self.R_RC = R_RC
        self.C_RC = C_RC

    def ocv_curve(self, soc):
        return 3.0 + 1.2 * soc - 0.5 * soc**2 + 0.3 * soc**3

    def state_equations(self, state, t, current):
        soc, v_rc = state
        dsoc_dt = -current / (self.capacity * 3600)
        dvrc_dt = current / self.C_RC - v_rc / (self.R_RC * self.C_RC)
        return [dsoc_dt, dvrc_dt]

    def predict_degradation(self, cycles, temperature=298):
        alpha, beta, Ea, R = 0.002, 0.01, 20000, 8.314
        return np.exp(-alpha * np.sqrt(cycles) - beta * (Ea/R) * (1/temperature - 1/298))

Research Insight: Digital twin models for EV batteries can predict remaining useful life within 5% error, enabling optimized second-life deployment.