Storage Dispatch Scheduling
Linear Programming · Temporal Arbitrage
Battery energy storage systems can capture €30–€80 per MWh in price arbitrage by charging during off-peak hours and discharging during peaks, generating €2–€8M annually for a 100MW/400MWh installation. Every day, a storage operator must decide the charge/discharge schedule across 24 hours to maximize revenue from price spreads. This is a linear program with state-of-charge dynamics — solvable exactly — where round-trip efficiency losses and depth-of-discharge limits constrain the temporal arbitrage strategy.
Where This Decision Fits
Energy systems planning chain — the highlighted step is what this page optimizes
The Problem
Maximizing revenue from temporal price arbitrage
Consider a 100 MW / 400 MWh battery energy storage system (BESS) connected to a wholesale electricity market. The battery has a 90% round-trip efficiency (η = 0.9, meaning √0.9 ≈ 0.949 one-way efficiency for charge and discharge). Prices vary from €25 to €120 per MWh across the 24-hour day, driven by demand patterns, renewable generation, and grid congestion.
The operator must decide, for each hour t ∈ {1, …, 24}, how much power to charge (buy from grid) or discharge (sell to grid), subject to power rating limits, energy capacity constraints, and state-of-charge (SoC) dynamics. The objective is to maximize daily revenue from buying low and selling high — pure temporal arbitrage.
Because the SoC dynamics are linear and all constraints are linear inequalities, this is a Linear Program (LP) solvable to global optimality in polynomial time. With integer on/off constraints (e.g., minimum run times), it becomes a Mixed-Integer Program (MIP).
subject to
SoCt = SoCt-1 + ηc · ct − dt / ηd // state-of-charge dynamics
SoCmin ≤ SoCt ≤ SoCmax // depth-of-discharge limits
0 ≤ ct ≤ Pmax // charge power limit
0 ≤ dt ≤ Pmax // discharge power limit
SoC0 = SoCinit // initial state of charge
Where pt is the electricity price at hour t, ct and dt are charge and discharge power, ηc and ηd are one-way efficiencies, and Pmax is the power rating (100 MW).
Try It Yourself
Optimize a 24-hour battery dispatch schedule
Storage Dispatch Optimizer
100 MW · 400 MWh · 90% Eff.Ready. Click “Solve & Compare All Algorithms” to run.
| Algorithm | Revenue (€) | Cycles | Time |
|---|---|---|---|
| Click Solve & Compare All Algorithms | |||
The Algorithms
Three approaches to storage dispatch optimization
Linear Program (LP)
O(n³) | Guarantees global optimumFormulate the 24-hour dispatch as a linear program with 48 decision variables (charge and discharge power per hour) and 120+ constraints (SoC dynamics, capacity bounds, power limits). Solved exactly using the simplex or interior-point method. The LP finds the provably optimal schedule that maximizes revenue subject to all physical and operational constraints. For the continuous relaxation (no integer variables), this is the gold standard.
Greedy Threshold
O(n) | Simple price-based ruleCompute the median price across the 24-hour window. Charge at maximum rate whenever the price is below the median (buy cheap), and discharge at maximum rate whenever the price is above the median (sell expensive). Respects SoC limits but makes no look-ahead decisions — each hour is decided independently based on the threshold. Fast and intuitive but misses opportunities where partial charge/discharge or shifting timing would improve revenue.
Peak Shaving
O(n log n) | Flatten load profileTarget a flat average-price load profile. Sort hours by price, then charge during the cheapest hours and discharge during the most expensive hours, aiming to equalize the effective price across all hours. This approach prioritizes grid stability over pure profit — it captures most of the arbitrage value while producing smoother charge/discharge transitions. Often used in utility-scale deployments where grid services revenue supplements arbitrage.
Real-World Complexity
Why production storage dispatch goes beyond a simple LP
Beyond the Basic Model
- Degradation costs — Every charge/discharge cycle degrades the battery; deep cycles cost more than shallow ones, requiring lifecycle-aware optimization
- Stochastic prices — Day-ahead prices are forecasts with uncertainty; robust or stochastic programming hedges against price prediction errors
- Ancillary services — Frequency regulation, spinning reserve, and voltage support create co-optimization opportunities beyond pure energy arbitrage
- Ramp rate limits — Power electronics impose limits on how quickly charge/discharge can change between hours
- Temperature effects — Battery efficiency and capacity vary with ambient temperature, especially in extreme climates
- Multi-day planning — Weekly or seasonal patterns require look-ahead beyond 24 hours, coupling daily dispatch decisions
- Market participation rules — Minimum bid sizes, settlement periods (5-min vs hourly), and market-specific constraints shape feasible strategies
Key References
Foundational works in energy storage optimization
- (2018). “Modeling of lithium-ion battery degradation for cell life assessment.” IEEE Transactions on Smart Grid, 9(2), 1131–1140.
- (2018). “Energy storage arbitrage under day-ahead and real-time price uncertainty.” IEEE Transactions on Power Systems, 33(1), 84–93.
- (2009). “Estimating the value of electricity storage in PJM.” Energy Policy, 37(12), 5166–5175.
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