Analyzing Faulted Transmission Lines: Phase Components as an Alternative to Symmetrical Components
Protection engineers are often interested in calculating the steady-state voltages and currents on faulted transmission lines. This necessitates the use of accurate fault solution techniques. The most commonly taught and used methods involve symmetrical components. Symmetrical components are advantageous in that they yield multiple decoupled systems that are simple to solve. This simplicity was crucial before the advent of digital computers. With modern computers, it is equally easy to perform calculations with phase components (A, B, C) or with symmetrical components (positive, negative, zero). With symmetrical components, different circuit topologies must be used for different fault types, which can be inconvenient in practice. Additionally, symmetrical component techniques commonly assume line transposition and give oversimplified results for real-life cases. This paper presents phase-domain solution methods as an alternative to symmetrical components. Phase-domain analysis allows all ten common shunt faults to be modeled using a single circuit topology. In exchange for this convenience, the phase domain approach must account for mutual coupling between the three phases of a transmission line. However, this in turn allows phase-domain analysis to be used to model untransposed transmission lines without compromising the accuracy of the solution. This paper presents a general derivation for a steady-state, phase-domain transmission line solution and illustrates its practical use through several examples. Steady-state signals can be reliably used for testing traditional phasor-based relays. This steady-state solution is then translated into a time-domain equivalent, which numerically solves differential equations to accurately model the transition between prefault and fault states. Accurate modeling of state transitions makes this solution suitable for testing relays that use incremental quantities.