CORE EQUATIONS
Pₜ = ρ g Q Hₙ ηₜ [W]Qₒ = Cᴅ A √(2 g h) [m³/s]ΔE = P Δt / 3600 [Wh]Hₙ = max(2, Hₛ − K(Qₜ² + 0.55Qₚ²)) [m]
ASSUMPTIONS
Water density is 1,000 kg/m³ and gravitational acceleration is 9.81 m/s². Reservoirs are treated as well-mixed stores with fixed plan areas/capacities. Turbine and pump efficiencies are constant user inputs. Inflow includes a simple base contribution and catchment rainfall.
HONEST SIMPLIFICATIONS
This is an educational, approximate lumped-parameter model, not an operational digital twin. Pipe losses use a quadratic proxy; water hammer, cavitation, detailed turbine curves, electrical frequency control, penstock elasticity, terrain hydrology and forecast uncertainty are omitted. Reservoir and grid balances are simplified; do not use outputs for real plant design or dispatch.
NUMERICAL METHOD
Explicit fixed-step integration at 1/120 s with a wall-clock accumulator. The steady-model curve is an analytical power estimate using the present gate setting, nominal head and quadratic loss coefficient; it is not a future forecast.
Credits: procedural scene and original simulation code; no external 3D assets or audio files.