This paper contributes to narrowing the long-standing theoretical gap with power theory (or “power definitions”) for nonlinear ac switching circuits. The true instantaneous energy transformation and storage components of ac circuits are identified from the Poynting Theorem. This paper tackles the problem of power identification from the most general form of energy conservation. Therefore, it is no longer necessary to mathematically “define” powers to fit the engineering solution of a problem. The identification technique does not present problems with physical meaning since it is in full agreement with Maxwell's Equations. In this paper, the method is applied to the identification of the power components of single-phase switched circuits. Instantaneous energy is decomposed only into energy transformed (related to active power) and energy stored (related to reactive power). Examples that have caused physical interpretation problems with other power theories are presented for illustration and validation.

AC Power Theory From Poynting Theorem: Accurate Identification of Instantaneous Power Components in Nonlinear-Switched Circuits

The author discusses in depth the instantaneous reactive power (IRP) theory. The paper is interesting and theoretically profound. However, the discusser does not agree on the author's assertion that power properties are expressed in terms of three kinds: active, reactive, and unbalanced power. The decomposition seems to be meaningful only under a strictly restricted condition: a three-line system with sinusoidal symmetrical positive-sequenced voltages. A theory based on a restricted condition should not be used as a standard to criticize the other theory.

Discussion of "Instantaneous Reactive Power p-q Theory and Power Properties of Three-Phase Systems"

Traditional electrical power theories and one of their most important concepts—apparent power—are still a source of debate, because they present several flaws that misinterpret the power-transfer and energy-balance phenomena under distorted grid conditions. In recent years, advanced mathematical tools such as geometric algebra (GA) have been introduced to address these issues. However, the application of GA to electrical circuits requires more consensus, improvements and refinement. In this paper, electrical power theories for single-phase systems based on GA were revisited. Several drawbacks and inconsistencies of previous works were identified, and some amendments were introduced. An alternative expression is presented for the electric power in the geometric domain. Its norm is compatible with the traditional apparent power defined as the product of the RMS voltage and current. The use of this expression simplifies calculations such as those required for current decomposition. This proposal is valid even for distorted currents and voltages. Concepts are presented in a simple way so that a strong background on GA is not required. The paper included some examples and experimental results in which measurements from a utility supply were analysed.

https://www.mdpi.com/2227-7390/9/11/1295/pdf

Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions

This paper presents an analysis of some of the definitions of power factor as applied to nonlinear and unbalanced systems and gives alternatives to the use of a single power factor. The three most important practical functions of power factor for linear balanced circuits are the computation of the increment in the transmission losses, the computation of the required reactive compensation and the information to specify (or design) machines. So far, the three have not been considered simultaneously for nonlinear and unbalanced circuits. In the paper we show that, for the general case, the three purposes cannot be achieved consistently with only one power factor. We propose alternatives that are completely general and applicable to linear and/or nonlinear, balanced and/or unbalanced circuits. In addition, we present a strategy for the optimal reactive compensation that yields the minimum transmission losses.

A practical approach to power factor definitions: transmission losses, reactive power compensation, and machine utilization

This paper proposes a cyclostationary based approach to power analysis carried out for electric circuits under arbitrary periodic excitation. Instantaneous power is considered to be a particular case of the two-dimensional cross correlation function (CCF) of the voltage across, and current through, an element in the electric circuit. The cyclostationary notation is used for deriving the frequency domain counterpart of CCF—voltage–current cross spectrum correlation function (CSCF). Not only does the latter exhibit the complete representation of voltage–current interaction in the element, but it can be systematically exploited for evaluating all commonly used power measures, including instantaneous power, in the form of Fourier series expansion. Simulation examples, which are given for the parallel resonant circuit excited by the periodic currents expressed as a finite sum of sinusoids and periodic train of pulses with distorted edges, numerically illustrate the components of voltage–current CSCF and the characteristics derived from it. In addition, the generalization of Tellegen’s theorem, suggested in the paper, leads to the immediate formulation of the power conservation law for each CSCF component separately.

Cyclostationary Approach to the Analysis of the Power in Electric Circuits under Periodic Excitations

Summary form only given as follows. This paper presents a time domain model for the representation of powers in linear and nonlinear electrical circuits. The model can account, in a physical (or engineering) sense, for "active and reactive powers" as functions of time. The model is based on the time domain decomposition of the instantaneous power p(t) into two components: p(t)=a(t)+r(t). Where, a(t) represents the instantaneous power consumed by the (linear or nonlinear) load. The information regarding the store/restore process is contained in r(t). In contrast with the traditional frequency domain model in which powers are defined orthogonal (i.e. S/sup 2/=P/sup 2/+Q/sup 2/+D/sup 2/+...) and therefore they do not interact with each other, the proposed model permits the interaction of active and reactive powers at every instant. Using the model of the paper we can obtain the instantaneous power needed for compensation of both wave shape and power factor.

L.M. Hernandez

Papers

Physical time domain representation of powers in linear and nonlinear electrical circuits