# Differential Current Protection and Line Impedance Characteristics

Capacitance, inductance, and resistance are all naturally present along miles of power line conductors: capacitance due to electric fields existing within the separation of the lines from one another and from earth ground by the dielectric of porcelain insulators and air; inductance due to the magnetic fields surrounding the lines as they carry current; and resistance from the metal conductors’ length.

The capacitive nature of a power line is evident when that line is open-circuited (i.e. no load connected). For the next few schematic diagrams, only a single phase (one “hot” conductor and one “neutral” conductor) will be represented for the sake of simplicity:

Here, an oscilloscope shows the relative magnitudes and phase shifts of the voltage and current waveforms, allowing us to make determinations of total circuit impedance (Z = V ).

Under typical load conditions, the resistance of the load draws a much greater amount of current than an open-circuited line draws due to its own capacitance. More importantly, this current is nearly in-phase with the voltage because the load resistance dominates circuit impedance, being substantially greater than the series reactance caused by line inductance while being substantially less than the parallel capacitive reactance:

A significant fault behaves like a very low resistance connected in parallel. This not only decreases total circuit impedance but also shifts the phase angle closer toward +90o because now the line inductive reactance is substantial compared to the resistance of the fault. Real transmission lines tend to exhibit shorted impedance phase angles nearer 70 degrees rather than 90 degrees, owing to the effects of line resistance. The exact line impedance phase angle depends on conductor size and separation:

Since line inductance is a fairly linear function of line distance (a longer power line means more inductance, given a fixed inductance-per-mile value), and this inductive reactance is the dominant factor limiting fault current, the magnitude of the fault current becomes an approximate indication of distance between the instrument transformers and the fault.

Article text from Lessons In Industrial Instrumentation by Tony R. Kuphaldt – under the terms and conditions of the Creative Commons Attribution 4.0 International Public License