Currents' Physical Components Research Articles

Compensation of Budeanu’s Reactive and Complemented Reactive Currents in Extended Budeanu Theory in 3-Phase 4-Wire Systems Powered by Symmetrical Nonsinusoidal Voltage Source

The result of continuous efforts in the development of power theory, Budeanu’s power theory was successfully extended. The mathematical description that has been proposed is based on another concept, namely the Currents’ Physical Components (CPC) theory. With CPC theory, it was possible to describe, in the original Budeanu theory, the components of the load current, including the Budeanu distortion current. The Budeanu distortion current can have a maximum of five components associated with different physical phenomena and related to the equivalent parameters of the load. This article discusses passive compensation, which provides compensation for the Budeanu reactive current and the Budeanu complemented reactive current due to the known equivalent load parameters associated with the reactance elements. In addition, the article refers to a very important aspect when determining the parameters of a passive compensator, i.e., choosing parameters in such a way that the compensator simultaneously compensates for the reactive current and the unbalanced current. The article presents five methods relating to the determination of compensator parameters. Two methods are related to the reactive current compensation only for the first harmonic without affecting the unbalanced current. The next three methods relate to the compensation of the Budeanu reactive current and the consideration of the unbalanced current. Calculations and simulations were performed for all five methods, the results of which are presented and analyzed in this publication. The Matlab/Simulink R2023a environment was used as the calculation and simulation software.

Description of a three-phase, four-wire system with a nonlinear receiver and an asymmetric voltage source using CPC power theory

This article mathematically describes a three-phase, four-wire circuit in the case of a nonlinear, unbalanced load, asymmetry of the power source with a periodic, non-sinusoidal waveform. This description uses Currents' Physical Components (CPC) power theory for three-phase circuits. Determining the energy flow between the source and the load is possible by decomposing the phase current into components depending on the physical nature of the phenomena in this circuit. Mathematical relationships were determined enabling decomposition into components depending on the direction of energy flow and the causes of their creation. A calculation example using the determined relationships and calculation results has been presented. The presented computational concept is important for mathematical analyzes in circuits with nonlinear three-phase receivers. Knowing the nature of physical phenomena, it is possible to perform measures that limit the value of the current supplying the load.

Decomposition of the Voltages in a Three-Phase Asymmetrical Circuit with a Non-Sinusoidal Voltage Source

This article presents the concept of a mathematical description of a three-phase, four-wire asymmetrical electric circuit in decomposition into Voltages’ Physical Components (VPC), associated with distinctive physical phenomena in the load. This is an alternative method of mathematical description to the Currents’ Physical Components (CPC) still being developed since the end of the last century. According to previous studies, the improvement of the power factor in three-phase systems is possible by observing several components. Compensation for the scattered power is possible only by using a reactive compensator connected in series with the load. Thanks to the presented analytical method, it is possible to design compensators connected in series with the load. The VPC power theory opens the possibility of improving the power factor in three-phase networks for loads with asymmetry between phases. Due to the unfavorable impact of high currents on the compensator branches, the method proposed in the article can improve the energy quality in local low-power grids. However, the possibility of its practical use in high-power industrial networks is questionable.

Comparison and extension of advanced frequency domain non-active power decompositions

This research paper introduces new prospects in the field of power quality and energy transmission efficiency analysis and system design methodology through advanced frequency-domain power definitions. This proposal presents an improved extension of the power theory Currents’ Physical Components (CPC) by L.S. Czarnecki and compares its improvements with the CPC and an extension of the CPC by H. Lev-Ari. This proposal increases the resolution of physical phenomena reducing the power quality and hence contributes to its analysis and improvement. For this purpose, four additional non-active power components compared to the CPC are introduced. In contrast to the extension by H. Lev-Ari, these additional components are obtained from different definitions. In particular, the decomposition of the unbalance component into a spectral uniform and a spectral non-uniform component is novel to frequency-domain power definitions. As the CPC and its extension through H. Lev-Ari already decompose the collinear and shift components into spectral uniform and non-uniform components, the proposal for the unbalance components finally completes this structure. This yields a consistent and intuitive designation of physical phenomena related to spectral non-uniformity constituting as a concretization to the well-known distortion non-active power. Conclusive examples illustrate this improvement using the appertaining non-active power components.

Improved CPC-based parameter calculation of passive balancing compensation in three-phase four-wire systems with unbalanced loads

The unbalanced loads in low voltage three-phase four-wire(3P-4W) systems increase the energy and the voltage losses of the power supply system, and even cause serious voltage deviations. The passive compensation method using the Currents’ Physical Components (CPC) – based power theory does not consider the voltage losses of phase and neutral line impedances, and it is only suitable for the situations of symmetrical voltage. Under the conditions of supply voltage distortion, load unbalance and the consideration of line impedances, this paper improves the calculation method of passive compensation parameters oriented the current components in four-wire systems, which can make the system work efficiently with the fundamental optimal working current balanced without harmonic amplification. The effectiveness and adaptability of the proposed method to the background conditions are verified, based on the comparison of MATLAB / Simulink simulation results.

Cooperation of a Non-Linear Receiver with a Three-Phase Power Grid

This article presents an analysis of electrical parameters in a three-phase circuit characterized by the generation of harmonics. The Currents Physical Components (CPC) power theory for three-phase circuits were used. Relationships for three-wire circuits were used, and mathematical relationships were determined to enable decomposition into those components that depend on the direction of energy flow and the reasons for their creation. A calculation example using the previously determined dependencies was presented, and the results of the calculations were discussed. When mathematical analyses are required in circuits with non-linear receivers, and in particular, when there is a cooperation of several such receivers with a common power grid, the calculation concept presented is important. The generation of identical harmonic orders by several receivers causes a disturbance in the direction of energy flow in the power grid. For this reason, the case of a non-linear receiver generating harmonics of orders that has existed before in the power grid seems very interesting. Determining the value of individual powers can be used to estimate the impact of individual receivers on the quality of electricity.

Extension and Correction of Budeanu Power Theory Based on Currents’ Physical Components (CPC) Theory for Single-Phase Systems

In 1927, the most recognized power theory in the frequency domain was proposed by Budeanu. The second power theory in the frequency domain, which is currently catching a lot of supporters, is the approach proposed by Czarnecki. Both theories have common features in the form of the description of active power and are completely different in terms of the description and interpretation of reactive power. This article presents the possibility of using mutual elements of both approaches: thus, it is possible to interpret the physical meaning of the reactive power (reactive current) proposed by Budeanu and the power before the deformation obtained from the mathematical description.

Experimental Evaluation of Distortion Effect for Grid-Connected PV Systems with Reference to Different Types of Electric Power Quantities

Aware of the fact that the installed PV capacity and its power production rapidly increased in the last decade, with the huge impact that has been done to the power system, the distortion effects for grid-connected PV systems with reference to different types of electric power quantities will be presented in this article. The impact of the frequent fluctuation of solar irradiance on the behavior of the grid-connected PV system, due to cloud movements and resulting shadows and in terms of power quality and the evaluation of power components, is the topic of analysis in this research. Besides the simulation results of certain study cases, an experimental evaluation of electric power quantities on an actual PV system in real weather conditions was also performed. The experimental setup, formed through the combination of a PC and multifunctional I/O board with an appropriate software solution, was established and used for obtaining the target results. The methodology used for the evaluation of electric power quantities relied on the current physical components (CPC) theory for power definition. The experimental results were obtained for three different cases, namely, the low, medium, and high solar irradiance cases. On the basis of these results, the conclusions about distortion effects are given.

An Approach for Power Quantification Based on Stockwell Transform and CPC Power Theory

This article presents a power calculation method for non-sinusoidal signals with non-stationary characteristics based on currents’ physical components (CPC) power theory and the discrete Stockwell transform (DST). The DST independently localizes the real and imaginary components of the spectrum at any given time interval, being suitable for analyzing non-stationary waveforms. The proposed method allows for an instantaneous tracking of the power components defined in CPC power theory based on a time–frequency analysis provided by the DST. Thus, the proposed method is able to identify alterations in the harmonic content, and consequently track variations on the powers, in all time instants. The proposed method is validated using non-stationary signals, including a scenario with frequency deviation, presenting rather promising results when compared to the Fourier-based approach. Additionally, the proposed method is also assessed in noisy environments by inserting an additive Gaussian noise, based on real oscillographic records, presenting a good performance, which attests its suitability for power quality (PQ) analysis and power calculation.

Application of Enhanced CPC for Load Identification, Preventive Maintenance and Grid Interpretation

Currents’ Physical Components (CPC) theory with spectral component representation is proposed as a generic grid interpretation method for detecting variations and structures. It is shown theoretically and validated experimentally that scattered and reactive CPC currents are highly suited for anomaly detection. CPC are enhanced by recursively disassembling the currents into 6 scattered subcomponents and 22 subcomponents overall, where additional anomalies dominate the subcurrents. Further disassembly is useful for anomaly detection and for grid deciphering. It is shown that the newly introduced syntax is highly effective for identifying variations even when the detected signals are in the order of 10−3 compared to conventional methods. The admittance physical components’ transfer functions, Yi(ω), have been shown to improve the physical sensory function. The approach is exemplified in two scenarios demonstrating much higher sensitivity than classical electrical measurements. The proposed module may be located at a data center remote from the sensor. The CPC preprocessor, by means of a deep learning CNN, is compared to the current FFT and the current input raw data, which demonstrates 18% improved accuracy over FFT and 45% improved accuracy over raw current i(t). It is shown that the new preprocessor/detector enables highly accurate anomaly detection with the CNN classification core.

CPC-Based Minimizing of Balancing Compensators in Four-Wire Nonsinusoidal Asymmetrical Systems

The article presents the possibility of using the currents’ physical components (CPC) theory to generate the reference current of the active power filter (APF). The solution proposed by the authors is based on the cooperation of minimizing balancing compensators (MBC), which, due to their use in 4-wire systems, have been divided into two structures. The first compensator, which purpose is to minimize and balance the reactive current and the unbalanced current of the zero sequence, is built in the star system (STAR-MBC). The purpose of the second compensator, which operation occurs in the delta system (DELTA-MBC), is to minimize and balance the other two components, i.e., the unbalanced current of the negative sequence and the unbalanced current of the positive sequence. The two structures cooperating with each other significantly reduce the currents associated with the reactive elements, i.e., reactive current, and the unbalanced current. As mentioned, these currents are reduced but not compensated to zero or to the reference value. In order for the compensation and balancing to bring the preferable effect, an APF system should be included, which will cooperate with MBC compensators. This solution is presented in this publication. The control of the active part of the hybrid active power filter (HAPF), which was presented in the paper, consists of the reflection of the waveform of the nonsinusoidal active current. In this approach, no current shift in relation to voltage is obtained, but the waveforms of these quantities remain distorted. The reactive current is compensated and the unbalanced currents are balanced. The second definition of generating a reference current can also be used. Through this approach, the active current with a sinusoidal waveform is achieved. The second approach allows for an additional reduction of the three-phase RMS value of the load’s current. In both of these approaches, the active currents flowing through the lines will reflect the amplitude and phase asymmetry that is present in the supply voltage. The APF system will follow the changes in power or load conditions and generate the correct value for the reference current. The calculations presented in the article, as well as the current and voltage waveforms, were created as a result of the constructed mathematical models, which were used for theoretical illustrations. Calculations and waveforms were generated based on a script written in Matlab.

Adaptive Balancing by Reactive Compensators of Three-Phase Linear Loads Supplied by Nonsinusoidal Voltage from Four-Wire Lines

A method of the design of an adaptive balancing reactive compensator in four-wire systems with linear loads and nonsinusoidal voltage is described in this article. The method of compensation is founded on the Currents’ Physical Components (CPC) – based power theory of three-phase systems with nonsinusoidal voltages and currents. The compensator is built of two sub-compensators of Y and  structure, respectively. The Y compensator reduces the reactive current and the zero sequence symmetrical component of the unbalanced current. The  compensator reduces the negative sequence symmetrical component of the unbalanced current. The positive sequence symmetrical component of the unbalanced current and the scattered current remain uncompensated. It is because shunt reactive compensators do not have any capability for that. Thyristor Switched Inductors (TSIs) enable the susceptance control of the compensator branches, referred to in the article as Thyristor Controlled Susceptance (TCS) branches. Periodic switching of thyristors in these branches causes the generation of harmonic currents, in particular the third-order harmonic. Moreover, in the presence of the supply voltage harmonics, a resonance of the equivalent capacitance of the compensator with the distribution system inductance can occur. These two harmful phenomena in the compensator suggested were reduced by the selection of a special structure of the TCS branches and their LC parameters. The presented method of the adaptive compensator synthesis was verified in the article with a numerical example and results of computer modeling of the load with an adaptive compensator.

Performance Parameters of Electric Arc Furnaces Based on the Current's Physical Components Power Theory

Electric arc furnaces (EAFs) are processes with an intensive consumption of energy; in modern arc furnaces, the specific energy conception range is around 0.5 MWh per ton of produced liquid steel. In such furnaces, small improvements in efficiency represent significant savings. Electric arcs are highly nonlinear and chaotic, and their use in the arc furnaces for scrap melting introduces a very high harmonic distortion in the power systems. To improve the understanding of power phenomena at the arc furnaces, this article proposes the application of the current's physical components power theory, and based on this analysis, an interpretation of each current component is provided. Real EAF voltage and current measurements are computed for a complete melting and heating process. This article proposes the use of the current components as performance indicators and gives some ideas about how to improve the operation and control to optimize the electrical energy used at the arc furnaces.

Two-stage reactive compensation in a three-phase four-wire systems at nonsinusoidal periodic waveforms

The improvement of the power factor in three-phase, four-wire, stationary, unbalanced and linear loads, supplied from an ideal and symmetrical source at nonsinusoidal periodic waveforms, is the subject of this article. The case of an ideal source or a source that has a negligibly low internal impedance was considered. The analysis was based on the load current decomposition, according to the Current Physical Components (CPC) theory. The paper presents fundamentals of design of reactive compensators for compensation of the reactive and unbalanced currents of linear time invariant (LTI) loads supplied with nonsinusoidal voltage in four-wire systems. A reactive balancing compensator consists of two compensators working in a star and triangle configuration. The article presents the method of calculating the parameters of such a compensator using the CPC power theory. It was proved that the reactive and unbalanced components of current can be fully compensated in the reactive compensator also in the case of nonsinusoidal waveforms in power networks.

Currents' Physical Components (CPC) - based Power Theory A Review Part I: Power Properties of Electrical Circuits and Systems

Currents' Physical Components (CPC) - based Power Theory A Review Part I: Power Properties of Electrical Circuits and Systems

The use of CPC theory for energy description of two nonlinear receivers

The article concerns a mathematical description of electric power in the case of two nonlinear receivers connected to a common supply network. This description was made on the basis of the fundamental CPC (Currents' Physical Components) power theory. This theory was developed for one nonlinear receiver. In the case of two nonlinear receivers of the same type, i.e. when the harmonics generated by them are created equal, the CPC theory requires some modification. This issue is important when it is necessary to determine the components of currents in an energy system supplying two nonlinear receivers.

Currents' Physical Components (CPC) of the Supply Current of Unbalanced LTI Loads at Asymmetrical and Nonsinusoidal Voltage

Currents' Physical Components (CPC) of the Supply Current of Unbalanced LTI Loads at Asymmetrical and Nonsinusoidal Voltage

Development History of the Currents' Physical Components (CPC) - Based Power Theory

Development History of the Currents' Physical Components (CPC) - Based Power Theory

ORTHOGONAL COMPONENTS OF THE THREE-PHASE CURRENT AT ASYMMETRICAL ACTIVE - REACTIVE LOAD IN 4-WIRE CIRCUIT

Purpose . For the unbalanced sinusoidal mode with asymmetric voltage in 3-phase 4-wire circuits to receive the orthogonal 4-component decomposition of 3-phase current, are classified symmetry/asymmetry of active and reactive load elements separately. Methodology . The methodology is based on the vector approach, which with one voice allows to analyze the energy characteristics of a 4-wire and 3-wire circuits as balanced and unbalanced modes. At asymmetrical voltage the matrix representation methodology of the equivalent conductivities is used. Results. For 3-phase 4-wire network with a sinusoidal unbalanced mode with asymmetric voltage obtained 4-component orthogonal decomposition of the 3-phase current. The components have a clear electro-energetic sense and are classified irrespective by the load condition. Originality . The resulting decomposition current develops the theory Currents' Physical Components (CPC) for 4-wire circuit with asymmetric voltage. For the first time the unbalanced current is classified by activity and reactivity of asymmetry load elements. Practical value. Practical value of the obtained orthogonal decomposition current and the power equation is a possibility of their utilization for the increase both quality of delivery and quality of consumption of electrical energy.

Accurate CPC Power Analysis under Extreme EAF's Distortion Conditions

Electric Arc Furnaces (EAF) are huge energy consumer. However due a limited power calculation the maximum electrical efficiency is not obtained. Most of the applications in market report the usage of non valid power quantities in EAF power control system. Because the extreme distortion conditions of power phenomena produced by the nonlinearity of the load in the EAF, the implementation of Current's Physical Components (CPC) power theory has the potential of describing more accurate the physical load conditions and the electric power phenomenon during the Heat Process. Each one of the current components proposed by CPC offer useful information of the load condition, and give indicators which can be useful as stability indicators of the process for a better identification of the EAF stage.