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Grid Energy Storage (BESS) & Electrochemistry

Battery Coulombic, Voltaic & Round-Trip RTE Formula

Decompose Grid Battery Storage Round-Trip Energy Efficiency RTE = eta_Coulombic * eta_Voltaic from Charge/Discharge Amp-Hours and Mean Voltages, and quantify Dissipated Cycle Energy Loss.

Never mistake 99% Coulombic Amp-Hour efficiency for Round-Trip Watt-Hour efficiency!

Battery cell datasheets frequently highlight near-unity Coulombic (Faradaic) Efficiency eta_C = Q_discharge_Ah / Q_charge_Ah (99%+ in LiFePO4, 93%–96% in Vanadium Redox Flow Batteries due to membrane ion crossover and shunt currents). Yet utility BESS arbitrage revenue depends on Watt-Hour Round-Trip Energy Efficiency RTE = E_discharge_Wh / E_charge_Wh! Because charging requires an overpotential ABOVE equilibrium open-circuit voltage while discharging sags BELOW open-circuit voltage, Voltaic Efficiency eta_V = V_discharge_avg / V_charge_avg multiplies Coulombic Efficiency directly: RTE = eta_C * eta_V, dissipating E_loss = Q_chg * V_chg - Q_dis * V_dis as waste heat requiring HVAC cooling!

Verify on a Storage Module Cycle—Charge_Input Q_chg = 200.0 Ah (B2), Discharge_Output Q_dis = 190.0 Ah (B3 -> Coulombic Efficiency eta_C = 190 / 200 = 0.9500 in E2), Mean_Charge_Voltage V_chg = 3.50 V (B4 -> 700.0 Wh input), and Mean_Discharge_Voltage V_dis = 3.15 V (B5 -> 598.5 Wh output -> Voltaic Efficiency eta_V = 3.15 / 3.50 = 0.9000 in E3): Exact Round-Trip Efficiency RTE is 0.9500 * 0.9000 = 0.8550 (85.50% in E4), with 700.0 - 598.5 = 101.50 Wh lost per cycle (E5)!

BESS Cycle Efficiency Metric (200Ah @ 3.50V Charge -> 190Ah @ 3.15V Discharge)FormulaVerified Output
Coulombic Efficiency eta_CQ_discharge_Ah / Q_charge_Ah0.9500 (95.00% Faradaic)
Voltaic Efficiency eta_VV_discharge_avg / V_charge_avg0.9000 (90.00% Overpotential)
Round-Trip Energy Efficiency RTEeta_C * eta_V = E_dis_Wh / E_chg_Wh0.8550 (85.50%; 0.9453 LFP C/5)
Cycle Energy Dissipated (Wh)Q_chg * V_chg - Q_dis * V_dis101.50 Wh HVAC Thermal Load

Exact Multiplicative BESS Round-Trip Efficiency (RTE) Formula

Validate 0 < Q_dis <= Q_chg and 0 < V_dis <= V_chg (steady-state isothermal cycle cannot output more charge or higher average voltage than input)!

=LET(q_ch, B2, q_ds, B3, v_ch, B4, v_ds, B5, IF(OR(q_ch <= 0, q_ds <= 0, q_ds > q_ch, v_ch <= 0, v_ds <= 0, v_ds > v_ch), "Invalid Cycle Telemetry", LET(et_c, q_ds / q_ch, et_v, v_ds / v_ch, ROUND(et_c * et_v, 4))))

Low-Rate LFP Benchmark Check (99.5% Coulombic x 95.0% Voltaic)

Test slow C/5 LFP cycling (Q_dis = 199 Ah, V_chg = 3.40 V, V_dis = 3.23 V): RTE rises to 0.9453 (94.53%)!

=IF(ISTEXT(E4), E4, ROUND(B2 * B4 - B3 * B5, 2))

Try the example

Use the original values or change them to test your understanding.

Further reading