The impedance relay is the simplest member of the distance relay family. Instead of comparing a current against a fixed setting, it measures the impedance of the line as seen from the relay — voltage divided by current — and trips when that impedance falls below a set value. This post derives its operating condition, shows why its R–X characteristic is a circle centred on the origin, and explains its three disadvantages.

Operating principle and trip condition

The relay has two opposing torques. The operating torque comes from the current transformer and the fault current: T_op = K₁I². The restraining torque comes from the potential transformer and the voltage: T_res = K₂V². Neglecting the small spring restraint, the relay trips when the operating torque wins:

K₁I² ≥ K₂V²   ⇒   (V/I)² ≤ K₁/K₂   ⇒   Z = √(R² + X²) ≤ Z_set

In words: the relay trips whenever the measured impedance Z = V/I is less than the setting Z_set. A close fault gives a small impedance and trips; a distant fault or normal load gives a large impedance and does not.

Figure 6.1: Impedance relay R–X characteristic — a circle of radius Z_set centred at the origin. Impedances inside the circle trip the relay; impedances outside it block. (Schematic, not to scale.)

Why the characteristic is a circle at the origin

The trip condition depends only on the magnitude of the impedance, Z = √(R² + X²), and not at all on the phase angle θ of the fault. Plotted on the R–X plane, the set of points with |Z| = Z_set is a circle of radius Z_set — and because the condition does not involve any angle, the circle is centred exactly at the origin. Everything inside the circle is the trip zone (Z < Z_set); everything outside is the block zone.

That is both the strength and the weakness of the relay. It is beautifully simple — one setting, Z_set, covers faults in every direction — but it is also blind: it cannot tell a forward fault from a reverse fault, and it cannot tell a fault from a heavy load or a power swing if the impedance happens to fall inside its circle.

Disadvantages

1. Non-directional. The circle is centred on the origin, so it covers faults behind the relay just as well as faults in front of it. The relay will trip for reverse faults unless it is supervised by a separate directional element. On its own it cannot be used where direction matters.

2. High sensitivity to arc resistance. A fault arc adds a resistance R_arc in series with the line, so the relay measures Z_measured = Z_line + R_arc. The extra resistance pushes the measured impedance to the right on the R–X plane — possibly outside the circle — so the relay under-reaches: it sees the fault as further away than it really is, and may fail to trip for a fault inside its zone.

3. Susceptible to power swings. During a synchronous power swing, the system impedance as seen by the relay swings around the R–X plane, and the large circular area around the origin is easily entered by the swinging impedance. The relay can then trip falsely on a swing that is not a fault at all.

Key points to remember

• Trip condition: K₁I² ≥ K₂V² ⇒ Z = V/I = √(R² + X²) ≤ Z_set.
• R–X characteristic is a circle of radius Z_set centred at the origin, because the relay is independent of the phase angle θ.
• Inside the circle = trip zone; outside = block zone.
• Disadvantages: (1) non-directional — trips for reverse faults unless supervised; (2) arc resistance R_arc causes under-reach (Z_measured = Z_line + R_arc); (3) prone to false tripping during power swings.

Based on Power System Protection & Switchgear, Paper II, Q6(a), Exam 11 June 2026.