Presets
Playback
Plant, demand and weather
Turbine power is P = rho g Q H_net eta with H_net reduced by pipe loss K Q squared. Pumping lifts water back up at 88 % of the static head and costs rho g Q H / eta electrical power. The battery covers the difference between generation, pumping and the settlement demand.
Model checks
The science
What is modelled
An upper reservoir feeds a turbine through a penstock into a lower reservoir; a pump can lift water back. Catchment rainfall and a base stream add inflow. A small battery balances generation, pumping and the settlement demand, and any imbalance appears as grid import or export. Reservoir volumes are tracked exactly and overflow is spilled.
Equations
- Turbine power:
Pt = ρ g Qt Hn ηt,Hn = Hlevel - K (Qt² + 0.55 Qp²). - Pump electrical power:
Pp = ρ g Qp Hp / ηp. - Volume balance:
dVup/dt = Qin + Qp - Qt - Qrunoff. - Outlet reference:
Q = Cd A √(2 g h).
Checks run in the page
- Turbine and pump power against rho g Q H.
- Water conservation over an hour.
- Single-step reservoir balance.
- Torricelli outlet flow and battery arithmetic.
Honest simplifications
Constant efficiencies, a quadratic pipe loss, no water-hammer, no turbine curve, a head that varies only linearly with the upper level and no electrical network model. It teaches the energy and water bookkeeping of pumped storage, not plant design.
What to try
- Press Pump at night to refill the upper reservoir while demand is low.
- Press Peak demand and see how long the stored water lasts.
- Press Storm refill and watch rain fill both reservoirs until water is spilled.