Battery Management Systems and Storage Optimization

Module: Sustainable Tech | Difficulty: Premium

Battery Equivalent Circuit

Thermal Model

Comparison

| Technology | Power Density (W/kg) | Energy Density (Wh/kg) | Cycle Life | |-----------|---------------------|----------------------|------------| | Li-ion | 1000-3000 | 150-250 | 1000-5000 | | Flow battery | 50-100 | 15-30 | 10000+ | | Pumped hydro | 0.5-1.5 | 0.5-1.5 | 50000+ | | Compressed air | 1-2 | 3-6 | 10000+ |

Python Implementation

import numpy as np
from scipy.integrate import solve_ivp

class BatteryManagement:
    def __init__(self, capacity=50, R0=0.01, R1=0.005, C1=5000):
        self.capacity = capacity
        self.R0 = R0
        self.R1, self.C1 = R1, C1

    def dynamics(self, t, state, current):
        soc, v1, temp = state
        dsoc = -current / (self.capacity * 3600)
        dv1 = -v1 / (self.R1 * self.C1) + current / self.C1
        heat = current**2 * (self.R0 + self.R1)
        dtemp = (heat - 0.1 * (temp - 298)) / (1.5 * self.capacity * 3600)
        return [dsoc, dv1, dtemp]

    def simulate(self, current, soc0=1.0, T0=298):
        sol = solve_ivp(self.dynamics, (0, 3600 * self.capacity / abs(current)),
                       [soc0, 0, T0], args=(current,), dense_output=True)
        return sol

Research Insight: Advanced BMS using unscented Kalman filtering achieves 1-2% SOC accuracy.