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Residual Voltage Formula Relay Protection

Fiber and communications infrastructure knowledge brief Published 10 Mar 2024

Prepared for preliminary research by the METRA knowledge desk. Confirm optical interfaces, port or core capacity, electrical input and output, enclosure protection, thermal design and installation limits against current standards and product documentation.

Residual voltage in relay protection is calculated as the phasor sum of the three line-to-earth voltages, often expressed as VR=VA+VB+VC.

Definition and Concept

Residual voltage, also called zero-sequence voltage, is the voltage measured by a relay to detect earth faults. It is obtained by summing the three phase-to-ground voltages as phasors: VR=VA+VB+VC where VA,VB,VC are the line-to-earth voltages of phases A, B, and C, respectively. In a balanced three-phase system under normal conditions, VR=0.

During a single line-to-ground fault, VR becomes non-zero and is used to trigger protective relays. Residual Voltage Transformer (RVT) ConnectionResidual voltage is typically measured using a Residual Voltage Transformer (RVT).

The RV

T secondary is connected in open-delta across three-phase VTs or a five-limb three-phase VT to obtain the true residual voltage. The connection ensures that: Healthy system: VR=0 Unearthed neutral with single line-to-ground fault: VR=3VS, where VS is the phase voltageSolidly earthed system: VR=VS This configuration allows the relay to detect earth faults accurately without being affected by the normal phase voltages.

Calculation Using Symmetrical Components

Residual voltage can also be expressed using zero-sequence components: V0=VA+VB+VC3 The relay measures VR=3V0 in an unearthed system or VR=V0 in a solidly earthed system. This approach is widely used in digital relays, where the zero-sequence voltage is computed from phase voltage vectors.

Practical Notes

Ensure the phase alignment of voltage and current coils in the relay for correct operation.

The RV

T ratio and connection type must match the system grounding method to avoid false tripping. For double-phase-to-ground faults, the residual voltage vector aligns with the healthy phase and is equal to one-third of its amplitude. By applying these formulas and connection principles, engineers can accurately calculate residual voltage for relay protection and set appropriate relay thresholds.

Residual Voltage Formula Relay Protection - METRA FIBER MARKET [PDF]

Residual Voltage Formula Relay Protection

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Technical note

This reference is intended for preliminary fiber and communications infrastructure research. Optical interface, fiber type, port or core capacity, electrical input and output, enclosure protection, cooling, installation limits and applicable standards must be verified for the specific project.

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