Presets
Playback
Wind, farm and grid
Power in MW, frequency in Hz. Wind power rises with the cube of speed (P = 1/2 rho A v^3 Cp). When generation exceeds demand the frequency rises, and the swing equation sets how fast. The battery pushes back in proportion to the deviation (droop).
Test actions
Model checks
The science
What is modelled
A farm of identical turbines with a lumped rotor, a power-coefficient curve that peaks near a tip-speed ratio of 7, a load-damped single-area grid with inertia constant H, an 11 kV collector cable and a battery whose power follows a droop law with a short response lag.
Equations
- Wind power:
P = 1/2 rho pi R2 v3 Cp(lambda, beta). - Rotor:
J d omega/dt = Taero - Tgen - Tbrake. - Swing equation:
df/dt = f0 (Pgen + Pbat - Pload - Ploss - D (f - f0)) / (2 H Sbase). - Battery:
Pb = clamp(K (f0 - f), ± Pmax),dSOC/dt = -Pb / (3600 Emax). - Cable:
Ploss = 3 I2 RwithI = P / (sqrt(3) V pf).
Checks run in the page
- Wind power against the closed formula.
- The power coefficient never exceeds the Betz limit 16/27.
- Steady frequency against (generation - demand - losses) / D.
- Battery charge against the integral of battery power.
- Cable loss against 3 I2 R.
Honest simplifications
One lumped rotor and one grid area, an empirical Cp curve rather than blade-element theory, a deterministic sinusoidal gust pattern instead of turbulence, no voltage or reactive-power model. Illustrative, not a grid-planning tool.
What to try
- Switch the battery off and press Wind lull: the frequency sags much further and stays low until the wind returns.
- Raise the droop gain: the frequency deviation shrinks but the battery charge swings more.
- Lower the grid inertia and press Demand surge: the frequency changes faster.