Functional block diagram of excitation control

The excitation system is the set of equipment (exciter, regulator, control and protection) that supplies the DC field current to a synchronous generator and controls it to hold terminal voltage and reactive power at the set values.

Functional block diagram

          +-----------+  +---------+  +-----------+
Vref ->(Σ)| Regulator |->| Exciter |->| Generator |-> Vt
       ^ ^|(amplifier)|  |         |  | + system  |
       | |+-----------+  +----+----+  +-----+-----+
       | |  +------------+    |             |
       | +--| Stabilizer |<---+             |
       |    +------------+                  |
       |    +--------------------------+    |
       +----| Voltage transducer and   |<---+
            | load compensator         |
            +--------------------------+
 Limiters/protection act on the regulator;
 PSS (optional) adds a signal at the summing point

Role of each block

Transfer functions

$$G_R = \frac{K_R}{1+sT_R},\quad G_A = \frac{K_A}{1+sT_A},\quad G_E = \frac{K_E}{1+sT_E},\quad G_G = \frac{K_G}{1+sT_G},\quad H_F = \frac{sK_F}{1+sT_F}$$

($G_R$: sensor, $G_A$: amplifier, $G_E$: exciter, $G_G$: generator, $H_F$: stabilizer.)

The exciter TF comes from its field circuit: $v_R = R_e i_e + L_e\,di_e/dt$ and $E_{fd} = Ki_e$, so $E_{fd}/V_R = K_E/(1+sT_E)$ with $T_E = L_e/R_e$. The stabilizing transformer gives $V_F = M\,di_1/dt$ with $i_1 = E_{fd}/(R_1+sL_1)$, hence $H_F = sK_F/(1+sT_F)$, $K_F = M/R_1$.

Minor (stabilizing) loop around amplifier and exciter:

$$G_1(s) = \frac{G_AG_E}{1+G_AG_EH_F}$$

Complete closed loop (sensor in feedback path):

$$\frac{V_t(s)}{V_{ref}(s)} = \frac{G_AG_EG_G}{1+G_AG_EH_F+G_AG_EG_GG_R}$$

With unity sensor ($K_R=1$, $T_R \approx 0$):

$$\frac{V_t}{V_{ref}} = \frac{K_AK_EK_G(1+sT_F)}{(1+sT_A)(1+sT_E)(1+sT_G)(1+sT_F)+sK_FK_AK_E(1+sT_G)+K_AK_EK_G(1+sT_F)}$$

Steady-state ($s\to 0$): $\dfrac{V_t}{V_{ref}} = \dfrac{K}{1+K}$, with $K = K_AK_EK_G$, so the steady error is $\dfrac{1}{1+K}$ and falls as the loop gain rises.