---
title: "Function of excitation system and its transfer function"
subject: "Power Plant Equipment"
chapter: 3
key: "semester_7/power_plant_equipment:excitation-function-tf"
source: https://www.bctengineer.com/q/semester_7/power_plant_equipment/excitation-function-tf
site: BCT Engineering
---

# Function of excitation system and its transfer function

Power Plant Equipment · Chapter 3: Var/Voltage Control in Hydrogenerating Systems

- Asked in: 2074 Asoj, 2+6 marks; 2072 Chaitra, 6 marks (asked 2 times)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/power_plant_equipment/excitation-function-tf
- Whole chapter: https://www.bctengineer.com/md/semester_7/power_plant_equipment/chapter-3

## Question

What is the function of excitation system in generating station? Derive the transfer function of an excitation system with stabilizing transformer.

## Short answer

The excitation system supplies DC field current, regulates terminal voltage, controls reactive power, and improves stability. With stabilizing transformer, Vt/Vref = K_AK_EK_G(1+sTF) / [(1+sTA)(1+sTE)(1+sTG)(1+sTF) + sKF K_AK_E(1+sTG) + K_AK_EK_G(1+sTF)].

## Answer

#### Function of excitation system

The **excitation system** supplies and controls the DC field current of a synchronous generator. Its functions are:

- Supply DC current to the rotor field winding to produce the main flux.
- Keep the terminal voltage constant as load changes (automatic voltage regulation).
- Control the reactive power (VAr) output and share it correctly among parallel generators.
- Improve transient and steady-state stability by fast field forcing during faults.
- Provide protective limits (over/under-excitation limiters, V/Hz limiter).

#### Transfer function with stabilizing transformer

The system has four blocks: amplifier, exciter, generator field and a **stabilizing transformer** that feeds back the rate of change of exciter voltage to damp oscillations.

```text
Vref +  e   +   +-----------+    +---------+  Efd
 --->(Σ)-->(Σ)-->| Amplifier |--->| Exciter |--+--+
      ^-    ^-   +-----------+    +---------+  |  |
      |     |     +---------------+            |  |
      |     +-----| Stab. transf. |<-----------+  |
      |           +---------------+               |
      |   Vt      +-----------+                   |
      +-----------| Generator |<------------------+
                  +-----------+
```

**1. Amplifier:** $\dfrac{V_R(s)}{V_e(s)} = \dfrac{K_A}{1+sT_A}$

**2. Exciter** (field $R_e$, $L_e$; $E_{fd} = K i_e$): from $v_R = R_e i_e + L_e \frac{di_e}{dt}$,

$$
\frac{E_{fd}(s)}{V_R(s)} = \frac{K/R_e}{1+s(L_e/R_e)} = \frac{K_E}{1+sT_E}
$$

**3. Generator field** (open circuit): $\dfrac{V_t(s)}{E_{fd}(s)} = \dfrac{K_G}{1+sT_G}$

**4. Stabilizing transformer:** primary ($R_1$, $L_1$) is across the exciter output; secondary (mutual inductance $M$) is practically open-circuited by the high-impedance amplifier input.

$$
\begin{aligned}
E_{fd} &= R_1 i_1 + L_1 \frac{di_1}{dt} \;\Rightarrow\; I_1(s) = \frac{E_{fd}(s)}{R_1(1+sT_F)} \\
V_F &= M\frac{di_1}{dt} \;\Rightarrow\; \frac{V_F(s)}{E_{fd}(s)} = \frac{sK_F}{1+sT_F}
\end{aligned}
$$

where $K_F = M/R_1$ and $T_F = L_1/R_1$.

**5. Closed loop.** Let $G_1 = \dfrac{K_A K_E}{(1+sT_A)(1+sT_E)}$, $H_F = \dfrac{sK_F}{1+sT_F}$, $G_2 = \dfrac{K_G}{1+sT_G}$. The minor loop gives $\dfrac{G_1}{1+G_1H_F}$; with unity voltage feedback:

$$
\frac{V_t(s)}{V_{ref}(s)} = \frac{G_1G_2}{1+G_1H_F+G_1G_2}
$$

Substituting and clearing fractions:

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

The $sK_F$ term adds damping, so a high loop gain (small steady-state error) can be used without oscillation.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which is NOT a function of the excitation system?
   A. Supplying DC to the rotor field
   B. Keeping terminal voltage constant
   C. Controlling reactive power and its sharing
   D. Controlling turbine steam flow
   Answer: D. Turbine flow is controlled by the governor, not the excitation system. (Key point: Function of excitation)

2. Why is fast field forcing during faults useful?
   A. It improves transient stability
   B. It reduces VAr
   C. It lowers the frequency
   D. It saves fuel
   Answer: A. Rapid field forcing helps keep the machine in step during faults. (Key point: Field forcing)

3. The exciter transfer function Efd/VR is:
   A. K_E/(1 + sT_E) with T_E = L_e/R_e
   B. K_E s/(1 + sT_E)
   C. K_E/(1 + sR_e)
   D. K_E L_e/R_e
   Answer: A. vR = Re ie + Le die/dt and Efd = K ie give a first-order lag. (Key point: Exciter transfer function)

4. What does the sK_F term in the closed-loop denominator do?
   A. Adds damping, allowing high loop gain without oscillation
   B. Raises steady-state error
   C. Removes the generator lag
   D. Makes the system unstable
   Answer: A. The rate feedback term damps oscillations so a high gain with low steady-state error is usable. (Key point: Effect of stabilizer term)

## Related in Power Plant Equipment

- [Excitation system with stabilizing transformer: transfer function](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aexcitation-stabilizing-transformer-model) — Power Plant Equipment, chapter 3, asked 13×

## Related in other subjects

- [DC supply system in a generating station](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Adc-supply-system) — Power Plant Design, chapter 4