AVR control of bus voltage

An Automatic Voltage Regulator (AVR) holds the generator terminal (bus) voltage at a set value by automatically adjusting the field excitation, which changes the generator's internal emf and hence its reactive power output.

Equivalent circuit of the synchronous generator

Neglecting armature resistance, the generator is an emf $E_f$ behind synchronous reactance $X_s$:

      jXs       Ia
  +--[~~~~]----->----+---- Vt (bus)
  |                  |
 (Ef)               Load
  |                  |
  +------------------+

$$V_t = E_f - jX_sI_a$$

Taking $V_t$ as reference and $I_a = I_p - jI_q$ (active and reactive components):

$$E_f = V_t + X_sI_q + jX_sI_p$$

For small $\delta$, $|E_f| \approx V_t + X_sI_q$, so

$$V_t \approx |E_f| - X_sI_q = |E_f| - \frac{X_sQ}{V_t}$$

Principle:

• Terminal voltage falls when reactive load $Q$ (lagging current $I_q$) increases, because of the drop $X_sI_q$.
• To keep $V_t$ constant, $|E_f|$ must be raised. Since $E_f = 4.44fN\Phi$ and $\Phi$ depends on field current $I_f$, this is done by increasing $I_f$.
• Active load mainly changes the angle $\delta$, not $|V_t|$ (term $jX_sI_p$ is at 90°), so voltage control is essentially reactive-power control.

AVR loop

Vref -->(+)--> Amplifier --> Exciter --> Gen field
         ^-                                  |
         |                                   v
       Rectifier <-- PT <-------- Terminal voltage Vt
       & filter
       (+ stabilising feedback)

1. Sensing: a potential transformer measures $V_t$; it is rectified and filtered.
2. Comparison: the measured value is compared with $V_{ref}$; error $e = V_{ref} - |V_t|$.
3. Amplification: the error is amplified (amplifier gain $K_A$, time constant $T_A$).
4. Exciter: the amplified signal changes the exciter output voltage, hence field voltage and field current $I_f$.
5. Generator: $E_f$ changes, Q output changes, and $V_t$ is driven back to $V_{ref}$.
6. A stabilising (rate) feedback loop damps oscillations and improves response.

Operation

• Load Q rises → $V_t$ falls → positive error → more $I_f$ → higher $E_f$ → generator supplies more Q → $V_t$ restored.
• Load Q falls (or line charging high) → $V_t$ rises → negative error → less $I_f$ → generator absorbs Q → $V_t$ restored.

The AVR acts within the generator capability limits (field heating limit for Q supply, under-excitation/stability limit for Q absorption). Being fast (time constants of the order of a second or less), it also improves transient stability by raising excitation during faults.