V2G Frequency Regulation: Grid Swing-Equation Response (2D)

Grid & Disturbance

Generation loss 300 MW

Grid inertia M 6.0

Load damping D 1.0

V2G Fleet Response

Fleet droop gain k 120 MW/Hz

Fleet power cap 200 MW

Response delay τ 1.5 s

Live Readout

Frequency nadir

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Time to nadir

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Steady-state Δf

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Initial RoCoF

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V2G power now

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Grid frequency

50.00 Hz

How it works

The 3D version tracks individual car batteries during a peak-shaving event. This companion zooms out to what V2G fleets are actually valuable for on the grid — primary frequency response — using the standard linearized swing equation plus a first-order-lag droop controller for the aggregated EV fleet, integrated with RK4:

M·dΔf/dt = ΔP(t) + P_v2g − D·Δf
τ·dP_v2g/dt = clamp(−k·Δf, 0, P_max) − P_v2g
ΔP(t) = −P_loss for t ≥ 0 (a generator trips off-line)

M is grid inertia (a weaker, more renewables-heavy grid has lower M and swings faster and deeper), D is the grid's natural load damping, k is how aggressively the fleet discharges per Hz of frequency droop, P_max is the fleet's total available discharge power, and τ is the communication/response lag before the fleet reacts. Push k and P_max up and the frequency nadir shallows and recovers faster — exactly the ancillary service V2G fleets are paid for in real grids.

Grid frequency deviation Δf(t) V2G fleet power P_v2g(t)