FACTS: Basic Concepts – Power Transfer

The power flowing across an arbitrary power transmission line depends on the sending end voltage (V₁), receiving end voltage (V₂), line impedance (Z = R + jX) and the phase difference between the sending and receiving terminals.  Since the line resistance (R) is usually very small compared to its reactance (X), that term is negligible in the Power Transfer Equation (Equation 1, below).

The second equation indicates that the power factor (the cosine of the angle between current and voltage) has a direct impact on total power transfer. Power factor is somewhat like a measure of efficiency: it’s the ratio of real power delivered to your circuit compared to “apparent power”, which is temporarily absorbed by reactive elements like capacitors and inductors (also called reactors) and then returned to the generator.  This is because these are energy storage devices.

Lastly, equation 3 indicates the amount of thermal power lost dissipated to the resistance of the power line. It is converted to heat at a rate proportional to the apparent power flow, which is why a poor power factor is particularly bad for the grid — it means more power is lost due to heat in the transmission line. Since current results in heating of the line, excessive current will cause the line to physically droop. It becomes dangerous because it increases the likelihood that the line will contact another phase (line-to-line fault) or ground (via a tree or house, for example).

As a result, power factor (and subsequently, apparent power flow) affect the power system’s economic viability and profitability.

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This article was taken from a report which I co-authored. It was submitted to ECE3333: Power Systems I, taught by Professor Rajiv Varma at the University of Western Ontario in Spring 2009.

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