Let us continue green posts. Today we’ll talk about how much the voltage on the equipment may differ from the voltage on the surge arrester (SA). To do this, consider a lighting wave coming from the overhead line (OHL) to switchgear. After passing the SA site, the wave decreases its magnitude to the level of the SA’s residual voltage (Usa), but not changes its steepness (A).

A series of wave reflections occurs in the area between SA and the equipment (say, a transformer T). As a result, the voltage on the equipment (Ut) differs from the voltage on the arrester (Usa). The voltage on the equipment (Ut) is the sum of:
➡️ upcoming wave (Usa+);
➡️ reflected wave (Usa-).

Since the inductance of the equipment at a high frequency does not allow current to pass through, the equipment’s installation point is considered an “idling point”. Therefore, according to the rules of reflection, the reflected wave (Usa-) turns out to be equal in magnitude and sign to the upcoming wave (Usa+). Following this rule, it turns out that the voltage on the equipment (Ut) cannot exceed the value (Usa+)+(Usa-)=2Usa.

The specific voltage on the equipment (Ut) depends on the ratio of two parameters:
✅ duration of the upcoming wave front (tsa=Usa/A);
✅ the doubled travel time (tt) of the wave between the SA and the equipment, determined by dividing the distance between them (l) by the wave speed (300m/µs).

1️⃣ Calm wave:
The voltage (Ut) is proportional to travel time (tt), that is, the length (l). It means, there is a reason to have as short length (l) as possible.

2️⃣ Steep wave:
The voltage (Ut) equals to 2Usa, regardless of the length (l). However, the rate of voltage rise is finite, which is favourable for the coil insulation of the equipment.

3️⃣ Wave of zero front:
The voltage (Ut) is always 2Usa, regardless of the length (l). The rate of voltage rise is infinitely high, which is harmful to the coil insulation of the equipment. Such waves with a steep front arise due to a back flashover from OHL’s grounded part (crossarm) to phase wire, which is typical for lightning strike to poorly grounded tower close to the switchgear. It means, there is a reason to have towers well grounded.

Cases 1️⃣-2️⃣-3️⃣ are well-known. Case 4️⃣ is more interesting.

4️⃣ Capacitance is taken into account:
It turns out that this fundamentally changes the voltage – it increases from 2Usa to 2.43Usa, regardless of the capacitance value. Why is that?

The fact is that when a steep wave (Usa+) comes to the capacitance, it turns out that we have an infinite change in voltage. The capacitance does not tolerate this, and a significant current pulse occurs in the capacitance. In essence, this means that the equipment does not behave like an “idle end”, but like a “short circuit”. Therefore, in the first moments, the reflected wave (Usa-) has a sign that is opposite to the sign (Usa+). Which subsequently causes the described effects.

It can be seen that a kind of “resonance” is developing in the case 4️⃣. However, if attenuation is taken into account, then attention should be focused only on the first maximum of the voltage on the equipment (Ut). It can be mathematically shown why it is always 2.43, almost regardless of the type of equipment (its capacitance).

In other words, it does not really matter whether we are talking about “small” equipment (an open circuit breaker, or an instrument transformer with a capacitance of about 500 pF), or a “large” power transformer (capacitance up to 4000 pF or even more). Increasing the capacitance will make the peak wider but don’t change the peak value, and it will remain as 2.43.

Taking into account the inductance in the arrester circuit (so-called “leads” of surge arrester) will further increase the voltage difference between the equipment (Ut) and the arrester (Usa). But inductance is a different story.

Today, I only wanted to talk about capacitance, because it can increase voltage, although it has always been thought that capacitance decreases a danger to equipment (it slows down the processes, makes a steep front more calm).