Current compensation in three‐phase power systems

Abstract

In this paper the compensation of reactive and unbalanced currents in three‐phase power systems is discussed. The main result proved is that in sinusoidal steady state any current which corresponds to zero total active power can be compensated by means of a reactive element; the compensation of the reactive currents and the compensation of the unbalanced currents in three‐phase power systems are special cases of this result. The explicit expression of the compensating reactances is derived and the multiplicity of the solutions is discussed. The result is illustrated on some examples.

Reactive power compensation in a multi‐line system under sinusoidal unbalanced conditions

“…The present paper generalizes a result of [1] for three-phase systems to an arbitrary number of phases. It is shown that the reactive compensation element does not require elements between any pair of phases, which would be the straightforward generalization of the results of [1]; it is sufficient to have a star-connected and a circular-connected part.…”

“…It does not require elements between all pairs of phases (which would be the straightforward generalization of the results of [1]); it is sufficient to have a star connected and a circular connected part (that is a scheme with connections only between adjacent phases).…”

Reflections on power theories for poly-phase nonsinusoidal voltages and currents

“…Explicitly: "Find the compensator current which corresponds to zero instantaneous power and which is as small as possible, considering this constraint." The solution can be found in the literature [11], [15], [17], [18], [21]. The second question is dealt with in the next section.…”

“…It is rather obvious that the reactive current component can be generated by means of a set of inductors and capacitors. It has been shown that also the unbalanced current can be generated by inductors and capacitors [6], [18]. The Steinmetz compensation of a single-phase resistive load is a classical example of such compensator.…”

“…• The active current is the current which is taken up by a resistive load with a frequency-independent conductance G = P e(t) 2 rms (18) The load seen from the supply in the compensated situation consists of the actual load and the compensator. The above analysis shows that the the compensated load is a frequency-independent resistor.…”