Frequency is the energy balance of the spinning machines. The gas turbines store kinetic energy Ek = sum H S (3 x 5 s x 110 MVA = 1650 MWs). Any mismatch ΔP = Psupply - Pload speeds them up or slows them down: dEk/dt = ΔP, f = f0 sqrt(Ek/Ek,nom), so for small deviations df/dt = f0 ΔP / (2 Ek) (the swing equation). Wind turbines, solar inverters and the battery inverter add no inertia unless the battery is told to imitate it.
Primary control. Each governor changes its output by ΔP = -(Δf/f0) Pn/R with droop R = 4 % and a 4 s turbine lag, and the load itself falls about 1.5 % per 1 % frequency drop. After a step ΔP the frequency settles at Δf = -ΔP / (sum Pn/(R f0) + D). Secondary control (AGC) integrates the error and moves the set-point to bring f back to 50 Hz.
Wind. Per turbine P = 1/2 rho A Cp v3 η (rotor 96 m, Cp = 0.45, below the Betz limit 16/27 = 0.593), clipped at 3 MW from 11.7 m/s, zero below 3 m/s and above 25 m/s (storm shutdown, restart below 22 m/s). The farm output is smoothed over the 50 machines and reduced 8 % for wake losses. Solar. Sun elevation from declination and latitude 50 N; clear-sky irradiance G = 1098 sin(a) exp(-0.057/sin a); clouds G(1 - 0.75 c3.4); cell temperature Tc = Ta + (45-20)/800 G; P = Pstc (G/1000)(1 - 0.0035 (Tc - 25)) 0.97 0.90.
Battery and curtailment. State of charge changes by -P/ηd when discharging and -P ηc when charging with ηc = ηd = sqrt(0.90). When renewables exceed demand minus the minimum stable gas output (3 x 30 MW) and the battery cannot absorb the rest, the surplus must be curtailed or the frequency rises; wind and solar also reduce output above 50.2 Hz (grid-code over-frequency response).
Simplifications. A single bus (no network limits), aggregated renewable fleets, no unit-commitment costs, a simple gas heat-rate model; frequency physics runs in real seconds while weather, battery energy and daily demand run on the compressed day clock. Numbers are typical, not from a real utility.