PW-D3 · Power flow, faults, protection

Fault types and fault current: how the sequence circuits connect

In D2 the unbalance was split into three balanced circuits: positive, negative and zero sequence. Now the fault current follows directly once those three circuits are connected the way each fault type requires. Switch the fault type with the tabs and check which sequence circuits get connected, and how the sum of the connected impedances sets the fault current.

Switch the fault type and read the connection

Three sequence circuits, Z_1, Z_2 and Z_0, sit between the source E and the fault point (the red mark), and switching the fault type with the tabs changes which circuits light up in gold. A three-phase short passes through the positive sequence only, a ground fault through all three circuits, and a line-to-line short through the positive and negative sequences; around any unused circuit the wire detours underneath. The larger the sum of the connected impedances, the smaller the fault current, and the gold bar below gives that value in pu.

Tap a tab to switch the fault type.

Fault current (prefault voltage E = 1 pu)

I_f ≈ 5.00 pu

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

Three-phase short · a balanced fault

When all three phases short together, the fault itself is balanced, so no negative or zero sequence appears. Only the positive-sequence circuit is used, giving a fault current I_f = E/Z_1; with the figure's values that is 1 ÷ 0.2 = 5.00 pu. Because the current passes through just the one positive-sequence impedance, this is usually the largest fault current, which is why a circuit breaker's interrupting rating is normally set from the three-phase short-circuit current. It is the rarest fault but the most severe.

Ground fault · the zero-sequence path opens

A ground fault, where one phase touches earth, is the most common fault in real power systems. Here all three circuits, positive, negative and zero, are connected in series, giving a fault current I = 3E/(Z_1+Z_2+Z_0); with the figure's values that is 3 ÷ 0.8 = 3.75 pu, smaller than the three-phase short. The flow is governed by the zero-sequence impedance Z_0. Solidly grounding the neutral keeps Z_0 small and the ground-fault current large (if Z_0 is smaller than Z_1, it can even exceed the three-phase short-circuit current); high-resistance grounding makes Z_0 large and the current smaller; and in an ungrounded system Z_0 is effectively infinite, so the ground-fault current is nearly 0 (only a small current flows through the capacitance between the lines and earth). The point from D2, that zero-sequence current needs a return path, shows up here exactly.

Observe3φ: I_f = E / Z₁

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

ChooseLG: I = 3E / (Z₁ + Z₂ + ?)

A ground fault puts all three, zero included, in series.

Fill inLL: I = √3 E / (Z₁ + ?)

A line-to-line short uses only positive and negative.

On your ownZ₀ → ∞ → I_ground = ?

With no return path for the zero sequence, the ground-fault current is 0.

Line-to-line short · the earth stays out

A line-to-line short, where two phases touch each other, does not involve the earth, so no zero sequence appears. The positive- and negative-sequence circuits are connected in parallel at the fault point, but since the negative-sequence circuit has no source, the current passes through Z_1 and then Z_2 in turn. That is why the figure lights two boxes in a row, and the fault current is I = √3 E/(Z_1+Z_2). Because Z_2 is usually close to Z_1, the line-to-line current is about √3/2 ≈ 0.87 of the three-phase short, and in the figure 4.33 pu is likewise 0.87 times 5.00 pu. With the zero sequence left out it is simpler than a ground fault, but large currents flow in two phases, so it too must be cleared quickly.

Back to the first screen

The three sequence circuits stayed the same, yet every change of fault type lit a different set of circuits and changed the fault current, to 5.00, 3.75 and 4.33 pu. The three-phase short passed through the positive sequence alone, so its impedance was the smallest and its current the largest, while the ground fault added the zero sequence in series and its current fell. The positive, negative and zero sequences separated in D2 have become parts wired together according to the switch called fault type. With the fault current in hand, we move on to protection, which detects it and cuts it off.

Fault types and fault current: the fault type sets the connection of the three sequence circuits, and the sum of the connected impedances sets the fault current. A three-phase short passes through the positive sequence only, I = E/Z₁ (usually the largest); a ground fault puts positive, negative and zero in series, I = 3E/(Z₁+Z₂+Z₀); a line-to-line short uses the positive and negative circuits, I = √3 E/(Z₁+Z₂). With no zero-sequence path (grounding), the ground-fault current is 0.

The next step

With the fault current calculated, what remains is how to detect it and cut it off. The last unit of section D (PW-D4) covers protective relaying and circuit breaking. A relay measures current and voltage, judges whether there is a fault, and signals a breaker, which interrupts the arc and separates only the faulted section from the system. The heart of protection is selectivity and time coordination: clearing nearby faults quickly and distant ones later, so that only the section that has to go dark loses power.