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Transmission-Line Differential Equations

Transmission-Line Differential Equations

Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...

Differential Relays

Differential Relays

Differential relays are used to protect generators, buses, and transformers by comparing electrical quantities at different points. When a fault occurs, the difference in current between the two points triggers the relay to operate, opening the circuit breaker. Under normal conditions, the current entering (i1) and leaving (i2) a generator are equal. When a fault occurs, however, these currents become unequal, and the difference current flows in the relay operating coil, causing the relay to...

Line Protection with Impedance Relays

Line Protection with Impedance Relays

Coordinating time-delay overcurrent relays in complex radial systems and directional overcurrent relays in multi-source transmission loops can be challenging. Impedance relays address these issues by responding to the voltage-to-current ratio, specifically measuring the apparent impedance of a line. These relays become more sensitive during faults as current increases and voltage decreases, thereby reducing the apparent impedance.
Under normal conditions, low load currents keep the measured...

Reclosers and Fuses

Reclosers and Fuses

Automatic circuit reclosers enhance the protection of distribution circuits by interrupting and auto-reclosing an AC circuit according to a preset sequence. They effectively manage temporary faults on overhead distribution lines, often caused by tree limbs or wildlife, by briefly disrupting service to improve overall reliability. However, contact with reclosers or energized broken conductors on the ground can pose serious hazards.
A comprehensive protection scheme for radial distribution...

Parallel RLC Circuits

Parallel RLC Circuits

Street lamps equipped with RLC surge protectors are an excellent example of applying circuit analysis in practical scenarios. These surge protectors safeguard the lamp's components against sudden voltage spikes.
A simplified parallel RLC circuit model with a DC input source generating a step response is employed in this context. When the switch is turned on, Kirchhoff's current law is applied, leading to a second-order differential equation.

Reducing Line Loss

Reducing Line Loss

In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.
With a step-up transformer at the source, the voltage is increased, thereby reducing the current in the transmission lines since power loss in...

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Related Experiment Video

Updated: May 22, 2026

Comparative Study of Simulation of Temperature Rise in Ring Main Unit

Comparative Study of Simulation of Temperature Rise in Ring Main Unit

Published on: July 5, 2024

Differential protection scheme for transmission lines with end-of-line UPFC compensation using sequential current

Jai Prakash Sharma¹, Ravi Shankar Tiwari¹, Om Hari Gupta²

¹Electrical Engineering Department, GLA University Mathura, Bharthia, UP, 281406, India.

Scientific Reports

|May 20, 2026

Summary

A new protection strategy using differential current sequence components accurately detects faults in transmission lines with Unified Power Flow Controllers (UPFC). This method enhances power system reliability under dynamic conditions.

Keywords:

Differential protection Dynamic compensation Sequence current components Transmission line UPFC

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Last Updated: May 22, 2026

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Published on: July 5, 2024

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Published on: June 27, 2025

Area of Science:

Electrical Engineering
Power Systems Engineering

Background:

Increasing power demand strains transmission infrastructure, necessitating advanced solutions like Flexible AC Transmission System (FACTS) devices.
Unified Power Flow Controllers (UPFCs) offer independent active and reactive power control, enhancing transmission line capability but complicating protection.
Traditional protection relays may be less effective with UPFC integration.

Purpose of the Study:

To develop and validate a novel protection strategy for transmission lines with end-line UPFC compensation (ELUC).
To ensure reliable and accurate fault detection despite dynamic system conditions and UPFC operation.

Main Methods:

A protection algorithm based on differential current sequence components was designed.
Simulations were performed using MATLAB Simulink.
Validation included real-time simulation and assessment across diverse fault scenarios.

Main Results:

The proposed scheme demonstrated high selectivity and accuracy in fault detection.
Performance was evaluated under various fault types, locations, resistances, UPFC modes, and synchronization errors.
Real-time simulations confirmed the algorithm's effectiveness in dynamic conditions.

Conclusions:

The differential current sequence component-based protection strategy is effective for transmission lines with ELUC.
The method provides reliable fault detection, improving power system stability and reliability.