Calculation of Relay Protection Impedance

Relay protection impedance is calculated by measuring the line impedance, converting it to relay secondary impedance using CT and VT ratios, and setting zone reaches based on desired protection coverage.

Step 1: Calculate Line Impedance

The first step is to determine the primary line impedance of the transmission line. For a three-phase line, the positive sequence impedance is calculated as: Z₁ = R + jX where R is the line resistance and X is the line reactance per unit length, multiplied by the line length in kilometers to get the total line impedance in ohms (primary side) .

Step 2: Convert to Relay Secondary Impedance

Relays operate on secondary voltage and current, so the primary impedance must be converted using the CT and VT ratios: Z_secondary = Z_primary × (CT ratio / VT ratio) Here, the CT ratio is the primary current divided by the secondary current, and the VT ratio is the primary voltage divided by the secondary voltage. This ensures the relay sees the correct impedance corresponding to the actual line .

Step 3: Determine Zone Settings

Distance relays typically have multiple zones of protection:

• Zone 1: Instantaneous tripping for 80–85% of the line. Z1 = Zone1% × Z_line
• Zone 2: Covers 100% of the line plus 20–50% of the next line, with a time delay for coordination. Z2 = Zone2% × Z_line + portion of next line impedance
• Zone 3: Backup protection for far-end faults, often covering the next two line sections. Z3 = Zone3% × Z_line + next line impedance .

Step 4: Include Ground Fault Compensation (if needed)

For single line-to-ground faults, zero-sequence compensation can be applied: K0 = (Z0 - Z1) / (3 × Z1) This adjusts the apparent impedance seen by the relay to account for ground return paths .

Step 5: Check Load Encroachment

The relay must distinguish between normal load and fault conditions. Calculate the load impedance: Z_load = (Line Voltage)² / Load MVA Compare this with the relay settings to ensure the relay does not trip under normal load .

Step 6: Verify and Document

• Ensure CT and VT ratios are correct.
• Confirm zone reach percentages and time delays.
• Test the relay with secondary impedance values.
• Document assumptions and compare results with protection standards and relay manuals . By following these steps, you can calculate the relay protection impedance accurately, set appropriate zone reaches, and ensure reliable operation of distance relays under fault conditions.