An ordinary overcurrent relay trips whenever the current is too big — but it cannot tell which way the current is flowing. On a radial feeder that does not matter. On parallel feeders, ring mains and interconnected networks it matters a great deal: a fault on one feeder can feed current backwards through the healthy feeder, and a non-directional relay would trip the healthy one too. The directional overcurrent relay (ANSI device 67) solves this by measuring not just how big the current is, but which direction it flows. This post explains how.

A double-actuating-quantity relay

The directional relay is a double-actuating-quantity relay: it responds to two quantities at once — the magnitude of the fault current I and the phase angle θ between that current and a reference voltage V_ref. The reference is the system voltage itself (the polarising voltage). It is a reliable benchmark because the system voltage does not reverse its phase during a fault — only the current does.

The torque developed in the relay is:

T = K · V_ref · I · cos(θ − τ)

Here τ is the Maximum Torque Angle (MTA) — the angle at which the relay develops its greatest torque. The relay is built so that its MTA points along the direction of a normal forward fault current.

Figure 5.1: Phasor diagram of a directional relay. Current phasors within ±90° of the maximum torque line produce positive torque and trip; phasors in the opposite half-plane produce negative torque and the relay blocks. (Schematic, not to scale.)

Forward fault: it trips

For a forward fault, the fault current phasor lies close to the maximum torque line: |θ − τ| < 90°, so cos(θ − τ) > 0 and the torque is positive (T > 0). The directional contacts close, in series with the IDMT overcurrent unit, and the relay trips the breaker. The directional element on its own does not decide how fast to trip — it only gives permission; the overcurrent unit decides the time.

Reverse fault: it blocks

For a reverse fault — current flowing backwards through the relay, for example a fault on the parallel feeder — the current phasor reverses by 180°. Then cos(θ + 180° − τ) = −cos(θ − τ), which is negative, so the torque is negative (T < 0). The directional contacts are held open against their backstop, the overcurrent unit is blocked, and the relay refuses to trip even though the current is large. The healthy feeder stays in service while the faulted feeder's own relays clear the fault.

This is the whole point of the directional relay: it does not ask "is the current too big?", it asks "is the current too big and flowing in my direction?" — and it acts only when both answers are yes.

Key points to remember

• Directional overcurrent relay = ANSI 67, a double-actuating-quantity relay (current magnitude + phase angle θ against V_ref).
• Torque: T = K · V_ref · I · cos(θ − τ), where τ is the Maximum Torque Angle.
• Forward fault: |θ − τ| < 90° → T > 0 → trips (directional contacts close in series with the IDMT overcurrent unit).
• Reverse fault: current reverses 180° → T < 0 → blocks (contacts held open against the backstop).
• V_ref is a fixed benchmark because the system voltage does not reverse phase during a fault.

Based on Power System Protection & Switchgear, Paper II, Q5(a), Exam 11 June 2026.