Grid-Scale Long-Duration Storage, Hydropower Engineering & Power Markets
Pumped-Storage Hydro Reservoir MWh & Grid Arbitrage Formula
Calculate Pumped-Storage Hydropower (PSH) Upper-Reservoir Gravitational Potential Energy (MWh = 2.725 * Mm³ * Head_m), Generated MWh Delivered, AC-to-AC Round-Trip Efficiency, and Full-Cycle Duck-Curve Arbitrage Margin ($).
Use the exact 2.725 MWh/(Mm³·m) gravitational identity to value pumped-hydro grid storage!
Closed-loop Pumped-Storage Hydropower (PSH) provides over 90% of global long-duration grid storage! Converting freshwater density ρ = 1,000 kg/m³ and standard gravity g = 9.81 m/s² across active reservoir volume V (million m³, 10^6 m³) and net hydraulic head H (m) into megawatt-hours (1 MWh = 3.6 × 10^9 J) simplifies WITHOUT approximation to Gravitational Hydraulic Energy E_hyd (MWh) = (9.81 / 3.6) * V_Mm3 * H_m = 2.725 * V_Mm3 * H_m! Pumping water uphill at pump-motor efficiency η_pump consumes E_pump = E_hyd / η_pump MWh from the midday grid, whereas generating through the Francis turbine-generator at η_gen delivers E_gen = E_hyd * η_gen MWh during the evening peak—yielding Round-Trip Efficiency η_RT = η_pump * η_gen!
Verify on a 360-Meter Head Closed-Loop PSH Plant—Active_Upper_Volume = 4.00 million m³ (B2), Mean_Net_Head = 360.0 m (B3 -> Stored Hydraulic Potential = 2.725 * 4 * 360 = 3,924.00 MWh in E2), Pump_Mode_Efficiency = 0.90 (consuming 3,924 / 0.90 = 4,360 MWh to fill, B4), Turbine_Gen_Efficiency = 0.88 (delivering 3,924 * 0.88 = 3,453.12 MWh to the evening grid in E3, at η_RT = 0.7920 or 79.20% in E4, B5), Midday_Solar_Pump_Price = $25.00/MWh (B6), and Evening_Peak_Price = $100.00/MWh (B7): Net Full-Cycle Arbitrage Profit is 3,453.12*100 - 4,360*25 = $236,312.00 (E5)!
| Pumped-Storage Hydro Metric (4.0 Mm³, 360 m Head, η_p=90%, η_g=88%, $25->$100/MWh) | Formula | Verified Output |
|---|---|---|
| Stored Hydraulic Energy (MWh) | 2.725 * Volume_Mm3 * Net_Head_m | 3,924.00 MWh |
| Evening Grid Delivered (MWh) | Stored_Hydraulic_MWh * η_gen | 3,453.12 MWh (vs 4,360 MWh Pumped) |
| AC Round-Trip Efficiency η_RT | η_pump * η_gen | 0.7920 (79.20%) |
| Full-Cycle Arbitrage Margin ($) | E_gen * P_peak - (E_hyd / η_pump) * P_pump | $236,312.00 ($388,912 @ -$10 Solar) |
Pumped-Hydro Full-Cycle Grid Arbitrage Formula
Validate Volume > 0, Head > 0, Pump and Generator efficiencies in (0, 1], and Peak_Price > 0 while explicitly ALLOWING negative midday charging prices (solar curtailment)! In shared energy-trading models in Arte Sheets, test negative wholesale LMPs before accepting dispatch-threshold formula suggestions.
=LET(vl_m, B2, hd_m, B3, ep_m, B4, eg_n, B5, pr_c, B6, pr_d, B7, IF(OR(vl_m <= 0, hd_m <= 0, ep_m <= 0, ep_m > 1, eg_n <= 0, eg_n > 1, pr_d <= 0), "Invalid Pumped-Hydro Input", LET(eh_y, 2.725 * vl_m * hd_m, ep_u, eh_y / ep_m, eg_d, eh_y * eg_n, ROUND(eg_d * pr_d - ep_u * pr_c, 2))))Negative Midday Solar Curtailment Price Check (Set Charging LMP = -$10.00/MWh)
When spring solar oversupply drives midday wholesale prices negative (B6 = -10 $/MWh), the grid PAYS the plant $43,600 to pump uphill AND $345,312 to generate at dusk—lifting Full-Cycle Arbitrage Profit E5 to $388,912.00!
=IF(ISTEXT(E5), E5, ROUND(B4 * B5, 4))Try the example
Use the original values or change them to test your understanding.