01 · Wind energy capturedPₐ = ½ ρ A v³ Cₚ(λ, β), A = πR², λ = ωR/v
02 · Rotor accelerationJ dω/dt = Tₐ − Tgen − Tbrake
03 · Three-phase cable lossP_loss = 3 I²R, I = P/(√3 V pf)
04 · Grid frequencydf/dt = ΔP · f₀ / (2 H Sbase)
05 · Battery droop and energyPb = clamp(Kb(f₀−f), ±Pmax); dSOC/dt = −Pb/(3600Emax)
What this means. Wind power rises approximately with the cube of wind speed. The rotor converts part of that power into shaft torque. The grid swing equation links a supply-demand imbalance to a change in frequency; battery droop responds when frequency moves away from 50 Hz.
Assumptions and honest simplifications.
- One representative rotor state stands in for identical online turbines. Wake effects are omitted.
- The smooth Cₚ envelope is an approximate teaching model, not a measured turbine performance curve.
- The collector cable is a lumped 11 kV, three-phase resistance. Reactive power and voltage control are not solved.
- Grid inertia and load damping are fixed equivalent parameters. This is a single-bus model.
- Battery energy is integrated ideally; conversion losses, temperature and degradation are omitted.
- Events and wind variation are deterministic so experiments can be repeated.
All displayed power and frequency values are approximate educational estimates, not operational grid data.