Need for excitation and improving dynamic response

Need of excitation system

A synchronous generator needs DC field current to build up its flux. The excitation system supplies this current and controls it so that:

• terminal voltage stays constant from no load to full load;
• reactive power is shared properly among parallel machines;
• the field is "forced" quickly during faults to keep the machine in step (better transient stability);
• field current stays inside the machine's capability limits.

Basic loop and its limitation

Vref    +--------+  +--------+ Efd +--------+  Vt
 -->(Σ)->|  K_A   |->|  K_E   |---->|  K_G   |--+-->
    ^-   |1+sT_A  |  |1+sT_E  |     |1+sT_G  |  |
    |    +--------+  +--------+     +--------+  |
    +-------------------------------------------+

With loop gain $K = K_AK_EK_G$, the steady-state error for a step in $V_{ref}$ is

$$e_{ss} = \frac{1}{1+K}$$

Raising $K$ lowers the error but, with three lags in the loop, the response becomes oscillatory and finally unstable. The exciter time constant $T_E$ (about 0.5 to 1 s for a DC exciter) is the main cause of slow response.

Methods to improve the dynamic response

1. Rate (derivative) feedback via a stabilizing transformer. Feed back $H_F = \dfrac{sK_F}{1+sT_F}$ from $E_{fd}$ to the amplifier input. The closed loop becomes

$$\frac{V_t}{V_{ref}} = \frac{G_AG_EG_G}{1+G_AG_EH_F+G_AG_EG_G}$$

The extra term $G_AG_EH_F$ contains $s$, so it adds damping only during transients; at steady state ($s\to0$) it vanishes and the low error is kept. Hence high gain and good damping are obtained together.

2. Reducing the effective exciter time constant by feedback. Put a proportional feedback $K_f$ around the exciter:

$$\begin{aligned} \frac{E_{fd}}{V_R} &= \frac{\dfrac{K_E}{1+sT_E}}{1+\dfrac{K_EK_f}{1+sT_E}} = \frac{K_E}{1+K_EK_f+sT_E} \\ &= \frac{K_E/(1+K_EK_f)}{1+s\,\dfrac{T_E}{1+K_EK_f}} \end{aligned}$$

The time constant falls from $T_E$ to $T_E/(1+K_EK_f)$: the exciter responds $(1+K_EK_f)$ times faster. The lost gain is made up in the amplifier.

3. Fast exciters. Replace rotating DC exciters by static (thyristor) or brushless high-initial-response exciters with small time constants and high ceiling voltage (2 to 3 times rated), so field current rises quickly.

4. Power system stabilizer (PSS). Adds a signal from rotor speed or electrical power through lead–lag blocks, giving positive damping to low-frequency rotor oscillations that a fast AVR may otherwise make worse.

5. Lead compensation in the regulator to cancel the largest lag.

Together these give a fast rise, small overshoot and small steady-state error.