Battery Storage Sizing for Solar Curtailment Recovery in Saudi Arabia

Battery storage can absorb solar generation that exceeds an export limit, but the energy returned to the grid depends on more than the battery's nominal megawatt-hour rating. This paper derives a transparent sizing relation for an AC-coupled photovoltaic plant with surplus-only charging and a subsequent delivery window. The method separates charging-power availability, usable internal energy and discharge opportunity, while enforcing equal initial and final stored energy. An illustrative 100 MW sinusoidal source, a 70 MW export limit and a twelve-hour production period produce 120.22 MWh of otherwise curtailed energy. At 85% round-trip efficiency, a 30 MW battery with 120 MWh of usable internal energy returns 102.18 MWh to the grid and removes the modeled curtailment; 18.03 MWh is lost in conversion. Raising power to 40 MW adds no recovery in this case. A 20 MW battery with 160 MWh usable energy returns only 80.00 MWh within a four-hour delivery window, while a 30 MW battery with 80 MWh returns 73.76 MWh. Independent chronological optimization agrees with the principal analytical results within 0.001 MWh at one-minute resolution. Profile, efficiency and delivery-window sensitivities expose changes in the binding constraint. The contribution is an auditable screening method for early engineering decisions relevant to Saudi solar development. Results are declared scenarios, not measurements, annual-yield forecasts or commercially optimal battery specifications.