Power dispatch
Generation, demand & battery · MW
WindDemandBattery
Grid frequency
50.00 Hz
Operating time
00:00
Wind state
BREEZY
Gust front approachingWind output is rising.
T+ 000.0 s
Frequency
50.00Hz
Nominal target 50.00 Hz
Wind output
—MW
3 turbine array
Battery power
0.00MW
Idle · droop control
Battery charge
76%
Reserve target 25%
Demand
—MW
Flexible demand online
Power balance
—MW
Stable window 100%
LIVE
Grid frequency response
Measured signal & analytic projection · Hz
Live frequencyAnalytic projection
The science · model, assumptions & equations
1 · Wind turbine power
A = πr²
Pwind = min(Prated, ½ ρ A Cp v³) × N
ρ is air density (kg/m³), A is swept area (m²), Cp is a dimensionless power coefficient, v is wind speed (m/s), and N is the number of turbines. The result is converted from watts to megawatts.
2 · Grid frequency response
Pimbalance = Pwind + Pbattery − Pload
df/dt = f₀ Pimbalance / (2 H Sbase) − D(f − f₀)
Frequency f is in hertz; power is in megawatts; H is an approximate inertia constant in seconds; D is a damping coefficient in s⁻¹. A single-bus first-order model is used to make the response understandable.
3 · Battery energy
dSOC/dt = −Pbattery / Ecapacity × 100 / 3600
Positive battery power means discharge. Negative power means charging. The controller applies a simple frequency-droop rule and respects minimum and maximum state-of-charge limits.
Solver & assumptions
State updates use a fixed 1/120-second semi-implicit Euler step with an accumulator. The dashed analytic curve assumes today's net power imbalance stays constant; it is an approximate short-horizon reference, not a second simulation. Wind density is fixed, turbines are aggregated, and the battery uses an idealised energy balance. Weather and demand changes are scripted educational events.
What this model leaves out
- No AC power-flow, voltage, reactive power or transmission-line constraints.
- No blade pitch, wake interaction, generator transients or cell-level battery effects.
- Demand response is a simplified temporary load reduction.
Use: educational exploration only; not for operating a real electricity network.