PW-D3 · Power flow, faults, protection

Fault types and fault current: how the sequence circuits connect

In D2 we split unbalance into three balanced circuits — positive, negative and zero sequence. Now, connecting these three differently for each fault type gives the fault current at once. Switch the fault type with tabs and see which sequence circuits connect how, and how their combined impedance sets the fault current.

Switch the fault type and read the connection

Three sequence circuits Z_1, Z_2, Z_0 are shown. Switch the fault type with tabs and the connection changes. A three-phase short uses positive only, a single line-to-ground puts all three in series, a line-to-line joins positive and negative. The larger the sum of connected impedance, the smaller the fault current. The gold bar is that current.

Tap to switch the fault type.

Fault current (prefault E = 1 pu)

I_f ≈ 5.00 pu

Positive only. I_f = E/Z_1. Usually the largest fault current.

Three-phase short · a balanced fault

When all three phases short at once, the fault itself is balanced, so no negative or zero sequence appears. Only the positive-sequence circuit acts and the fault current is I_f = E/Z_1. With just the single positive-sequence impedance, it is usually the largest fault current, so a breaker’s interrupting rating is normally set by this three-phase current. It is the rarest but most severe fault.

Line-to-ground · the zero path opens

A single line touching ground is the most common fault in real systems. Connecting the positive-, negative- and zero-sequence circuits in series gives the fault current I = 3E/(Z_1+Z_2+Z_0). Here the zero-sequence impedance Z_0 governs the flow. A solidly grounded neutral makes Z_0 small and the ground-fault current large; high-resistance or ungrounded systems make Z_0 large and the current small — ungrounded, Z_0 is effectively infinite and the ground-fault current is nearly zero. The fact from D2, that zero-sequence current needs a return path, acts here exactly.

Observe3φ: I_f = E / Z₁

A three-phase short uses one impedance, the positive sequence.

ChooseLG: I = 3E / (Z₁ + Z₂ + ?)

A line-to-ground fault adds zero, three in series.

Fill inLL: I = √3 E / (Z₁ + ?)

A line-to-line fault uses just positive and negative.

On your ownZ₀ → ∞ → I_ground = ?

With no zero-sequence path, the ground current is zero.

Line-to-line · earth stays out

When two phases short to each other, earth is not involved, so no zero sequence appears. Only the positive- and negative-sequence circuits connect in series and the fault current is I = √3 E/(Z_1+Z_2). Since Z_2 is usually close to Z_1, the line-to-line current is about √3/2 ≈ 0.87 times the three-phase one. With zero sequence absent it is simpler than a ground fault, but a large current flows in the two phases and must still be cleared quickly.

Back to the first screen

They were the same three sequence circuits, yet each fault type changed the connection and the fault current with it. The three-phase short, with just the positive sequence, had the smallest impedance and the largest current; the line-to-ground fault added zero in series and the current fell. The positive, negative and zero we split out in D2 became, here, parts wired in series according to the switch of fault type. With the fault current in hand, we now move to the protection that senses and clears it.

The fault types and fault current — the fault type sets the connection of the three sequence circuits, and their combined impedance sets the fault current. Three-phase short: positive only, I = E/Z₁ (usually largest). Line-to-ground: positive, negative, zero in series, I = 3E/(Z₁+Z₂+Z₀). Line-to-line: positive and negative, I = √3 E/(Z₁+Z₂). With no zero-sequence path (grounding), the ground-fault current is zero.

The next step

Having computed the fault current, it remains to sense and clear it. The last unit of section D (PW-D4) is protective relaying and breaking. A relay measures current and voltage to judge a fault and signals the breaker, and the breaker interrupts the arc to remove only the faulted section from the system. Clearing near faults fast and far faults slow, so that only the necessary section is de-energized — selectivity and time coordination — is the heart of protection.