# Impedance Relay: Operating Principle, Torque Equation, Characteristics The impedance relay works corresponding to the ratio of voltage V and current I of the circuit to be protected.

To measure the ratio of voltage and current, two elements are used in the impedance relay. One produces torque proportional to the voltage and the second produces torque proportional to the current.

The torque produced by the current element is balanced with the torque produced by the voltage element.

Therefore, the torque produced by the current element is operating torque or pickup torque which is said to be positive torque. And the torque produced by the voltage element is restraining torque or reset torque which is said to be negative torque.

This relay is also known as a voltage restrained overcurrent relay.

The basic operating principle of impedance relay is shown in the figure below.

The current element is energized by the current through CT. And the voltage element is energized by voltage through PT.

Section AB is the area of interest or the transmission line to be protected.

The ratio of voltage V and L under normal conditions is denoted as ZL which is the impedance of a line. Under normal conditions, the ratio measured by the impedance relay is lower than ZL. Hence, the relay remains inoperative under normal conditions.

When the fault occurs (in protected area AB), the voltage drops, and the current increases. Therefore, the ratio V/I reduces drastically.

So, the relay operates when the impedance decreases below the predefined value.

## Torque Equation

The torque produced by the current element is proportional to the square of current I2. And it is said to be positive torque.

Also, the torque produced by the voltage is proportional to the square of voltage V2. And it is said to be negative torque.

Let control spring effect produces a constant torque of -K3.

Therefore, the torque equation is; Where, K1, K2 are constants and V, I is RMS values.

At the balance point, when the relay is on the verge of operating, the net torque is zero.

Hence,  Now, divide both sides by    Generally, the spring effect is neglected as its effect is dominant at low current that generally do not occur in practice. So, we can take ; ## Operating Characteristics

From the torque equation, the impedance relay is on the edge of operating at a given constant value of the impedance (ratio V/I).

For a particular fault position, the ratio V/I is constant. The impedance changes with changes in fault position.

If the fault is near the relay, the impedance will be low. And as the fault position moves far away from the relay, the impedance becomes higher and higher.

Therefore, the impedance relay can be installed and adjusted for a particular section and it is inoperative beyond that section.

The operating characteristics of the impedance relay are shown in the figure below.

For the lower values of current, the spring effect is dominating and the curve shows a noticeable bend.

But for all practical purposes, the dotted line that represents a constant value of Z is considered an operating characteristic.

The impedance Z which is a predetermined set value is given by the below equation. The relay will pick up for any combination of V and I represented by any point above the line in the positive torque region.

The slop of characteristics can be changed by changing adjustments of a relay and the relay will operate to all the values of impedance less than any desired upper limit.

## Operating Characteristics on R-X Diagram

The operating characteristics of an impedance relay can be more easily represented by a diagram known as the R-X plane or R-X diagram.

The diagram having resistance (R) on X-axis and reactance (X) on Y-axis. The impedance Z can be expressed as;   To represent a circuit mathematically, the equation is; Where x and y are vertical and horizontal coordinates and r is the radius of a circle.

Similarly, the above equation makes a circle with R and X being vertical and horizontal coordinates and the magnitude of an impedance is the radius of a circle.

The center of circle is at point where R and X axis intersects each other.  The numerical values of ratio V and I determine the length of radius vector Z while the phase angle ф between V and I determine the exact position of the vector Z.

If a current I is in phase with voltage V, vector Z lies along R-axis. If I lag vector V, vector X is negative. And if I lead vector V, X is positive.

The operation of an impedance relay is independent of phase angle ф. Therefore, the operating characteristic is a circle having a radius equal to the magnitude of impedance Z (predetermine value).

Hence, the entire circuit is an operating region of a relay. It means, that at any value of Z less than the radius of a circle, the relay operates. So, the entire portion inside the circle is a positive torque region (or operating region of a relay).

Similarly, the exterior of the circle is the negative torque region (or nonoperative region) of a relay.

For example, Z is the predefined value of relay. And the fault impedance is Zf. In this condition;

The relay operates when, And relay remains inoperative when, The operating characteristics of the impedance relay on the R-X plane are shown in the figure below.