Differential Relay

In power system protection a differential relay is the usual unit scheme for protecting transformers and generators from faults inside a defined zone.
Differential relays trip when the difference between two or more similar currents or voltages exceeds a set value. They stay stable for a fault outside that zone. An over current relay trips when the current through it exceeds a set value. The principle of differential relay is the comparison of those similar quantities, not a single threshold.

Definition of Differential Relay

A differential relay operates when the difference between two or more similar electrical quantities exceeds a set value. In the scheme, two currents arrive from two parts of an electrical power circuit and meet at a junction where the relay coil is connected. By Kirchhoff Current Law the current in that coil is the phasor sum of the two incoming currents. Ratio and polarity are chosen so that sum is zero in normal load. No current then flows in the coil. An internal fault breaks that balance, a residual current flows in the coil, and the relay operates.

In a current differential scheme, two sets of current transformer sit on either side of the protected equipment. Their ratios and polarity are chosen so the secondary currents match in magnitude under through current.
Those secondary currents are wired to oppose each other. A nonzero difference feeds the operate coil. When that difference exceeds the setting, the relay trips the circuit breakers and isolates the equipment. An attracted armature type instantaneously relay has little intentional time delay. It still needs matching CTs and restraint or a stabilizing resistor so CT saturation on an external fault does not trip it.

Types of Differential Relay

There are two main types of differential relay, grouped by how the comparison is made.

1. Current Balance Differential Relay
2. Voltage Balance Differential Relay

In a current differential relay two current transformers sit on either side of the equipment to be protected. The CT secondaries are connected in series so they carry secondary current in the same circulating-current sense.

The operating coil of the relaying element is connected across the CT secondary circuit. Under normal load the protected equipment (either power transformer or alternator) carries through current. If the secondary current of CT₁ is I₁ and that of CT₂ is I₂, the current in the relay coil is I₁-I₂. Ratio and polarity are chosen so I₁ = I₂, so no current flows in the coil. An external fault still passes through both CT primaries, so the secondaries stay balanced and the relay does not trip. An internal earth fault, as shown, makes the two secondary currents unequal. The relay then isolates the faulty transformer or alternator from the system.
This type of relay scheme has practical limits

1. Pilot cable impedance from each CT secondary to a remote relay panel may not match.
2. Pilot-cable capacitance can operate the relay on a large through fault outside the equipment.
3. CT magnetizing curves never match exactly, so some spill current can flow in the relay even in normal load.

Percentage Differential Relay

This form responds to the differential current as a fraction of the current through the protected section. Restraint coils sit with the operate coil and produce torque opposite to the operate torque. Under load and through-fault current the restraint torque is larger, so the relay stays open. On an internal fault the operate force exceeds the bias and the relay trips. Bias is set by the number of turns on the restraint coils. If I₁ is the secondary current of CT₁ and I₂ is the secondary current of CT₂, current through the operate coil is I₁ – I₂ and current through the restraint coil is (I₁ + I₂)/2. In load and through-fault conditions the restraint torque from (I₁+ I₂)/2 exceeds the operate torque from I₁– I₂. On an internal fault that relationship reverses. Bias setting is the ratio of (I₁– I₂) to (I₁+ I₂)/2.

A larger through current in the restraint coils therefore raises the operate current needed to trip. The relay is called a percentage relay because that operate current is expressed as a percentage of through current.

CT Ratio and Connection for Differential Relay

A common electromechanical rule is that CTs on a star winding are connected in delta and CTs on a delta winding are connected in star. That pairing removes zero-sequence current from the relay circuit and also corrects the 30 degree winding shift. Numerical relays often use wye CTs on both sides and do the same compensation in software.
If the CTs are connected in star, the CT ratio is written I_n/1 or 5 A
CTs connected in delta use a secondary of about I_n/0.5775 or 5×0.5775 A, where 0.5775 approximates 1/√3 so the delta connection still delivers 1 A or 5 A to the relay.

Voltage Balance Differential Relay

In this arrangement the current transformers sit on either side of the equipment so that the EMFs induced in the two secondaries oppose each other. The CT secondaries are connected in series with opposite polarity. The differential relay coil sits in that series loop, as shown. In normal load and on a through fault the two secondary EMFs are equal and opposite, so no current flows in the relay coil. An internal fault unbalances those EMFs. Current then flows in the coil and the relay trips the circuit breaker.

A voltage balance differential relay has limits. Multi-tap CTs are needed to balance each pair. The scheme suits relatively short cables; on a longer run, pilot-wire capacitance disturbs the comparison. Charging current on a long pilot can operate the relay even when the CTs themselves match.
The Translay system is a later voltage-balance feeder scheme. It compares voltages induced in the relay secondary windings, not the line CT secondary voltages, and it includes compensation for pilot capacitance.

Here, two sets of current transformers sit at either end of the feeder. Each CT secondary feeds the primary of a double-winding induction relay. The secondary circuit of each relay is connected in series through pilot wires to form a closed loop. The induced voltage in one relay secondary opposes that in the other. A compensating device offsets pilot-wire capacitance current and residual mismatch between the two current transformers.

Under load and through-fault conditions the current at the two ends of the feeder is the same, so the CT secondary currents are equal. Those equal currents induce the same EMF in each relay primary, and therefore the same EMF in each relay secondary. The secondaries are connected in opposition, so no current flows in the pilot loop and neither relay produces operate torque.

If a fault occurs on the feeder between the current transformers, the current leaving one end differs from the current entering the other. The CT secondary currents are then unequal, the induced secondary voltages no longer cancel, current circulates in the pilot loop, and both relays produce torque.

Because the secondary current direction is opposite in the two relays, torque in one relay tends to close the trip contacts while torque in the other tends to hold them open. Which end operates depends on the position and type of fault in the feeder zone. The faulty section is isolated when at least one element of either relay closes.

In a Translay scheme a closed copper ring sits on the centre limb of the primary core of the relay. Those rings offset pilot capacitance currents. Capacitance currents lead the voltage on the pilot by 90^o and, when they flow in the low-inductance operate winding, produce flux that also leads the pilot voltage by 90^o. The pilot voltage is the voltage induced in the relay secondary coils, so it lags by a large angle behind the flux in the field-magnet air gap. The copper rings are adjusted so that angle is about 90^o. The fluxes acting on the disc are then in phase and produce no torque.