Time-domain formulations for apparent power using collective rms and polar coordinates

This paper may be considered as a continuation of the paper “A new IEEE Std 1459-2000 - Compatible time-domain formulation for apparent power” published in Electric Power Systems Research from Elsevier. It also presents the development of new time-domain equations related to the definition of apparent power however using collective rms values and using polar coordinates values. These equations give exactly the same results of IEEE Std 1459-2000 and FBD methods. All of them have no restriction with regard to asymmetric, unbalanced and/or distorted signals. The application of these formulations involves an adequate quantity of samples, obeying the Nyquist Criterion, which can be used in numeric meters for power measurements. One of the advantages of using these formulations presented in this paper is their simplicity. The polar coordinate decomposition, for example, uses only basic mathematics operations. Illustrative examples using simulation cases are showed, which have confirmed that the equations in time-domain here developed are corrected and that both principal approaches, American (IEEE Std 1459) and European (FBD method), lead to similar results, with a small divergence only if the voltage homopolar component is present.