Overvoltage due to chopping of magnetising current

When a breaker interrupts the small magnetising current of an unloaded transformer, the arc is weak. The current may be forced to zero (chopped) at an instantaneous value $i$ before its natural zero. The energy then trapped in the transformer inductance produces a switching overvoltage.

Mechanism

  CB (opens, chops i)
 ---/ ---+-----------+
         |           |
         C          L  (magnetising
     (winding +      |   inductance)
      bushing)       |
 --------+-----------+--- ground

At the chopping instant:

• Current in the magnetising inductance $= i$. Magnetic energy $= \tfrac12 L i^2$.
• Voltage on the stray capacitance $= v$. Electric energy $= \tfrac12 C v^2$.

After the breaker opens, $L$ and $C$ form a closed oscillating circuit. The inductor current cannot change suddenly, so it charges $C$. Energy swings between $L$ and $C$ at $f = 1/(2\pi\sqrt{LC})$, often a few hundred Hz to a few kHz. The peak voltage $V_m$ is reached when all the energy is in $C$:

$$\frac12 CV_m^2 = \frac12 Li^2 + \frac12 Cv^2$$ $$V_m = \sqrt{v^2 + \frac{L}{C}i^2}$$

Effect of the chopping instant

The magnetising current lags the voltage by about $90^\circ$. With $i = I_m\sin\theta$ at the chopping angle $\theta$, the capacitor voltage is $v = V_p\cos\theta$, where $V_p$ is the system peak voltage.

Chopping at the current peak ($\theta = 90^\circ$): $i = I_m$, $v = 0$.

$$V_m = I_m\sqrt{\frac{L}{C}}$$

This is the maximum overvoltage. $\sqrt{L/C}$ is of the order of tens of kΩ, so it can be several times the system voltage.

Interruption at current zero ($\theta = 0$): $i = 0$, so the magnetic energy $\tfrac12Li^2 = 0$. Then

$$V_m = \sqrt{v^2 + 0} = v = V_p$$

No extra energy is released. The voltage across the transformer does not exceed the normal system peak, and it simply decays through losses. The overvoltage is minimum (zero excess) when interruption takes place at the natural current zero.

Example: $L = 5$ H, $C = 0.01\ \mu$F, so $\sqrt{L/C} = 22.36$ kΩ. Chopping at 10 A gives 223.6 kV. Interrupting at current zero gives no overvoltage.

Remedies

• Breakers with low chopping current. Vacuum and SF$_6$ breakers are designed to interrupt near the natural zero.
• Resistance switching across the contacts to damp the oscillation.
• Surge arresters or RC snubbers at the transformer terminals.