Real power/frequency control in interconnected system

In an interconnected system all generators run at one common frequency. Frequency stays constant only while total generation = total load + losses. Real power/frequency control (load-frequency control, LFC) keeps this balance.

What happens on a load change

1. Inertial response (first seconds): when load rises by $\Delta P_L$, the deficit is supplied from the kinetic energy of all rotors. From the swing equation $\frac{2H}{\omega_s}\frac{d^2\delta}{dt^2} = P_m - P_e$, they slow down and frequency falls.
2. Primary control (governor): each speed governor senses $\Delta f$ and opens the turbine valve/gate. With speed regulation (droop) $R$:

$$\Delta P_{m,i} = -\frac{\Delta f}{R_i},\qquad \Delta f_{ss} = \frac{-\Delta P_L}{\sum_i \dfrac{1}{R_i} + D}$$

The load change is shared by all units of all areas, in inverse proportion to their droop. A steady-state frequency error remains, and tie-line flows change from schedule. 3. Secondary control (AGC): each area computes its Area Control Error

$$ACE_i = \Delta P_{tie,i} + B_i\,\Delta f$$

An integral controller changes the speed-changer set points until $ACE_i = 0$. Frequency returns to nominal and each area again supplies its own load, with tie flows back at schedule. 4. Tertiary control: economic dispatch sets the new outputs at minimum cost.

 dPL -> [Power system] -> df
           ^               |
           |  dPm          v
      [Turbine] <- [Governor 1/R] <- df
           ^
     speed changer <- integral(ACE)

Example: in a two-area system, if area 1 load increases, at first both areas raise generation and power flows from area 2 to area 1 over the tie-line; AGC in area 1 then raises its own generation so the tie-line flow returns to schedule.