Energy Storage Technologies

Module: Sustainable Tech | Difficulty: Intermediate

Overview

Learn about battery technologies, pumped hydro, and emerging storage solutions for grid-scale applications.

Learning Objectives

• Understand the core scientific principles underlying this sustainable technology.
• Apply quantitative methods to analyze system performance and efficiency.
• Implement Python-based models for simulation and optimization.
• Evaluate environmental impact using sustainability metrics.
• Design solutions that integrate renewable energy and resource conservation.

System Architecture

Electrochemical Storage Fundamentals

where is the number of electrons and .

import numpy as np

class LithiumIonBattery:
    def __init__(self, capacity_ah, voltage_nominal, internal_resistance):
        self.capacity = capacity_ah
        self.voltage = voltage_nominal
        self.resistance = internal_resistance
        self.soc = 1.0

    def discharge(self, current_a, dt_hours):
        energy_delivered = current_a * self.voltage * dt_hours
        capacity_used = current_a * dt_hours
        self.soc = max(0, self.soc - capacity_used / self.capacity)
        terminal_voltage = self.voltage - current_a * self.resistance
        return energy_delivered, terminal_voltage

battery = LithiumIonBattery(200, 3.6, 0.01)
energy, voltage = battery.discharge(50, 1)
print(f"Delivered: {energy:.1f} Wh, SOC: {battery.soc:.1%}")

Pumped Hydro Energy Storage

Round-trip efficiency: .

Flow Battery Technology

Vanadium redox flow batteries decouple energy and power capacity. Energy scales linearly with electrolyte volume:

where is the vanadium concentration and is the electrolyte volume in each tank. Power is determined by the cell stack area and current density:

def flow_battery_sizing(energy_kwh, power_kw, electrolyte_cost_per_l=85):
    faraday = 96485
    v_cell = 1.26
    c_v = 1500  # mol/m^3
    n_cells = 40
    electrolyte_vol_m3 = energy_kwh * 3600 / (2 * v_cell * faraday * c_v)
    electrolyte_vol_l = electrolyte_vol_m3 * 1000
    stack_area = power_kw * 1000 / (n_cells * v_cell * 500)
    cost = electrolyte_vol_l * electrolyte_cost_per_l
    return electrolyte_vol_l, stack_area, cost

vol, area, cost = flow_battery_sizing(100, 25)
print(f"Electrolyte: {vol:.0f} L, Stack area: {area:.2f} m2, Cost: ${cost:,.0f}")

Compressed Air Energy Storage

Adiabatic CAES (A-CAES) stores heat of compression for later use, achieving round-trip efficiencies of . Diabatic systems require natural gas during expansion.

Thermal Energy Storage

Phase change materials (PCM) store latent heat during melting:

where is the specific latent heat of fusion. Sensible heat storage:

Comparison Matrix

Hands-On Exercise

import numpy as np

def size_battery_system(daily_load_kwh, autonomy_hours, dod=0.8, voltage=48):
    required_capacity_kwh = daily_load_kwh * (autonomy_hours / 24)
    required_capacity_ah = (required_capacity_kwh * 1000) / (dod * voltage)
    num_parallel = int(np.ceil(required_capacity_ah / 200))
    series_cells = voltage // 3.6
    total_cells = series_cells * num_parallel
    print(f"Required: {required_capacity_kwh:.0f} kWh, {total_cells} cells")
    return required_capacity_kwh, total_cells

size_battery_system(daily_load_kwh=15, autonomy_hours=48)

Key Takeaways

1. Li-ion batteries offer high energy density but limited cycle life at deep discharge.
2. Pumped hydro remains the largest form of grid-scale energy storage.
3. Flow batteries decouple energy and power for long-duration storage.
4. Proper sizing requires analyzing load profiles, not just peak demand.
5. Round-trip efficiency is a critical comparison metric.

Review Questions

1. Derive the relationship between SOH and cycle count for Li-ion cells.
2. Compare energy density and power density of batteries vs. flywheels.
3. What geological requirements exist for CAES?
4. Design a 4-hour duration storage system for a 10 MW solar farm.
5. How does temperature affect internal resistance and capacity?

References and Further Reading

• Dunn, B. et al. (2011). Electrical Energy Storage for the Grid.
• Ribeiro, P. F. et al. (2001). Energy Storage Systems.
• Luo, X. et al. (2015). Overview of Current Development in Electrical Energy Storage.
• Bloom, H. et al. (2022). Handbook of Battery Materials.