This module focuses on solving numerical problems related to power system protection, a crucial area for the GATE Electrical Engineering exam. We will cover fundamental concepts and common problem types to build your problem-solving skills.

Protection relays are the core components that detect faults and initiate tripping. Understanding their characteristics, such as pickup current, time multiplier settings, and inverse time characteristics, is vital for solving numerical problems.

Distance relays measure the impedance to the fault. Numerical problems often involve calculating fault impedance, fault location, and determining if a fault is within the protected zone of a specific relay.

The impedance to a fault ($Z_f$) is calculated as $Z_f = V_f / I_f$, where $V_f$ is the voltage at the relay location and $I_f$ is the fault current. For a transmission line with impedance per unit length ($z$), the fault location can be determined if the relay measures $Z_f$ and the line impedance up to the relay is known. The fault distance is then $d = Z_f / z$. Problems often involve calculating the apparent impedance seen by the relay under various fault conditions, including the effect of source impedances and mutual coupling.

Differential protection compares the current entering a protected zone with the current leaving it. Numerical problems typically involve calculating the differential current and understanding the effect of CT (Current Transformer) ratios and tap settings.

For a protected zone, the sum of currents entering should equal the sum of currents leaving under normal conditions and for external faults. For internal faults, the currents will not balance, creating a differential current that operates the relay. The differential current ($I_{diff}$) is often calculated as $I_{diff} = I_{primary\_in} - I_{primary\_out}$, where currents are referred to the primary side using CT ratios. Problems might involve calculating the operating current for internal faults or the restraining current for external faults, considering CT saturation effects or tap settings on the relay.

These are communication-assisted protection schemes. Numerical problems might involve calculating the time taken for a signal to travel, the attenuation of signals, or the coordination of communication channels.

Carrier current protection uses power line communication for signal transmission. Problems can involve calculating the time delay introduced by the communication channel or the signal strength required. Pilot wire protection uses dedicated wires. Numerical problems might involve calculating the loop impedance of the pilot wires or the voltage/current levels for fault detection.

To excel in numerical problems, consistently practice with past GATE questions. Break down each problem into smaller steps: identify the protection scheme, list the given parameters, determine the required calculations, and apply the relevant formulas. Pay close attention to units and CT/PT ratios.