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... At the initial stage of the power theory development, known since the beginning of the 20th century for sinusoidal AC networks, there were no contradictions in the formulations and calculated expressions [1,2]. Instead of instantaneous values of sinusoidal voltages u(t) and currents i(t), for the convenience of analysis and calculations in the well-known symbolic method, it is proposed to use their effective values U and I. ...
... In this case, the apparent power S consists not only of active power P = U I cos(φ) capable of performing work, but also of ballast reactive power Q = U I sin(φ). The components P and Q make up the power balance S = P 2 + Q 2 , in which the proved orthogonality of P with respect to Q [1,2] is emphasized. ...
... Such approaches were available in early works by Fryze [2,10,11]. In them, inactive power Q q is not divided into components Q and D or the like, but it is defined as a power imbalance: ...
Based on the development of the theory of reactive power and distortion power, starting with the works of Fryze and Budeanu, it has been found that the contradictions in the definition of the components of inactive powers are caused by errors in the introduced intermediate concepts and corresponding calculations when switching to nonlinear and non-sinusoidal AC circuits. The materials of the works of modern researchers and the numerical calculations carried out made it possible to trace the differences between reactive power and distortion power, to confirm the orthogonality properties of the active, reactive power, and distortion power components. The paper defines the conditions for achieving a power balance in an AC network with nonlinear loads, compiled and tested criteria leading to the absence of distortion power in a single-phase AC network. Using the time base of the projection of the generalized vectors in vector diagrams, it is shown that compliance with the criteria for the absence of distortion power does not determine the mutual similarity of the voltage curve with the current curve for a nonlinear load. It has been found that the well-known term “distortion power” has an unfortunate wording, since this power, although it characterizes the interaction of harmonics of currents and voltages with different ordinal numbers, is not determined by the visual similarity or the degree of distortion of the load current waveforms relative to the supply voltage curve.
... In the last two centuries, some authors conceived power theories like Budeanou (1927) [7], Fryze (1931) [8], Akagi (1983) [9], Czarnecki (1984) [10] and Tenti (2003) [11]. PQ theory was first presented by Akagi and other authors and its principle is the instantaneous power calculation in timedomain for three phase systems. ...
... The last three terms can be arranged to one single part as presented in (8). All these parts are orthogonal. ...
... The void current can also be obtained by summing the scattered active and reactive currents and the generated current, as presented in (8). The scattered terms are defined as the difference value of equivalent admittance at different harmonics. ...
... 2. Reactive power denition proposed by Fryze [180] in 1931 is based on the Chapter: 4 ...
... The power theory suggested by Fryze in 1931[180], is depending on a time domain analysis. The current is divided into two portions. ...
... active power Q b as the arithmetic sum of Q h Q b = h=1 V h I h sin θ h was strongly rejected by lots of researchers throughout 90 years of researches as mentioned in the following:a. Fryze in 1931[180], objected Budeanu's theory and he described the necessity to the voltage and current harmonic decomposition before the re- active power could be calculated and relied on the time domain approach. ...
... However, due to nonlinearity in loads and uncertainty in fast increasing distributed renewable generation sources within the new technology of microgrids and smart-grids, the balancing of active power, the provision of reactive power, and also the compensation of harmonics become new critical issues [1], [2]. Therefore, the lack of proper definitions for power components in the case of distorted current and voltage signals has prompted novel power theories [3]- [12]. Active filtering is a compensating strategy that is widely implemented to stand against all the unwanted terms that appear in the current and voltage components [13]- [16]. ...
... Many researchers have redefined power theories under unbalanced, or more generally, distorted current conditions in three-phase systems and a variety of these theories have been introduced [3]- [12]. In general, their research can be divided into two main categories: the first category is the frequencydomain-based approach; and the second category is the time-domain-based approach. ...
... In general, their research can be divided into two main categories: the first category is the frequencydomain-based approach; and the second category is the time-domain-based approach. The time-domain-based approach usually exploits the instantaneous quantities to define the particular current decompositions and power definitions [4]- [12]. The first attempt to solve the problem of defining power components under nonsinusoidal conditions is historically attributed to Budeanu, who used a frequency domain [3]. ...
... In the last two centuries, some authors conceived power theories like Budeanou (1927) [7], Fryze (1931) [8], Akagi (1983) [9], Czarnecki (1984) [10] and Tenti (2003) [11]. PQ theory was first presented by Akagi and other authors and its principle is the instantaneous power calculation in timedomain for three phase systems. ...
... The last three terms can be arranged to one single part as presented in (8). All these parts are orthogonal. ...
... The void current can also be obtained by summing the scattered active and reactive currents and the generated current, as presented in (8). The scattered terms are defined as the difference value of equivalent admittance at different harmonics. ...
The Conservative Power Theory (CPT) is a time-domain theory applicable to any periodic signal, single- or poli-phase system with or without neutral conductor. The principle operation is the orthogonal decomposition of electrical variables, resulting electrical quantities with physical meaning. An important feature of the CPT is the current decomposition. It consists of decomposing any current into five parts. These parts are named as active current, reactive current, scattered active current, scattered reactive current and generated current. This paper presents the application of the current decomposition of the CPT in Distributed Energy Resources (DERs). Initially, clear understanding of how the current decomposition of the CPT is defined and how it is applicable are presented. Further, parts of a nonlinear load current are used as references for two DERs connected at the same Point of Common Coupling (PCC), resulting in a load current sharing. As result, a Supervisory Controller (SC) can increase its options regarding energy management in smart-grids. A case study is conducted in order to show the efficacy of application using current decomposition.
... was strongly rejected by lots of researchers throughout 90 years of researches as mentioned in the following: a. Fryze in 1931 [6], objected Budeanu's theory and he described the necessity to the voltage and current harmonic decomposition before the reactive power could be calculated and relied on the time domain approach. b. ...
... (2) Reactive power definition proposed by Fryze [6] in 1931 is based on the division of the current into two terms as the active current (I a ) and the reactive current (I r ), considering that these terms are orthogonal, then: ...
... Power triangle (S-P-Q) has been introduced first time for time domain by Fryze [6] in 1931, when he defined i aF as the active current and i rF as the reactive current as a part of the time domain description. However, the right-angled triangle power theory is the first attempt to apply (Total-Fundamental-Harmonics) power triangle in the frequency domain in combination with the (S-P-Q) Power triangle. ...
This article presents two new electrical power terms called effective active (P-ef) power term and effective reactive (Q(ef)) power term. These two terms, can approve the orthogonality relationship between fundamental and distorted components. At the same time, these terms are necessary to complete the form of the right-angled power triangle which is compulsory condition to calculate the total apparent (S-t) in the non-sinusoidal systems. This paper also, offers a new definition for the total apparent power S-t or can be called effective apparent power (S-ef) in non-sinusoidal situation in order to avoid the misconception of the old definitions. Moreover, it shows a new power diagram represents all power components in one diagram consists of six right-angled triangles called the right-angled triangle (RAT) diagram. Crown Copyright
... T HE widespread use of nonlinear, time-varying devices, such as those employed in power electronics, has increased the content of nonsinusoidal currents and voltages in power systems. Power theories have been developed by many authors [1]- [14] with the goal of identifying and eliminating nonactive power, or nonactive current. Two different concepts of the nonactive power definition and current decomposition method have been developed: one based on the average value concept and the other on the instantaneous value concept. ...
... Two different concepts of the nonactive power definition and current decomposition method have been developed: one based on the average value concept and the other on the instantaneous value concept. The first was introduced by Fryze [1] and the second was introduced by the so-called " -theory" by Akagi et al. [2]. Both compensation concepts define active and nonactive current and power: the first does not alter the average power transfer and the second does not alter the instantaneous power transfer. ...
... Expression (42) can be simplified and Fryze's definition of active currents [1] in two wires of a single-phase system is obtained (two mutually equal currents of the opposite signs) ...
Based on the condition for the minimum rms value of line currents, a method for improving the power factor in power systems under asymmetrical and nonsinusoidal conditions is presented. This paper offers straightforward and convenient formulations of active currents for the three-phase four-wire, three-phase three-wire, and single-phase systems. Owing to the transformation matrix introduced in this paper, the formulation of active currents is valid regardless of whether the voltages and currents are balanced or unbalanced and it permits any point of the system to be chosen for the voltage reference. Observing the constraints related to the reactive compensators, the line current minimization procedure is used for the determination of optimal compensating capacitances for the three-phase four-wire, three-phase three-wire, and single-phase systems. The optimal reactive compensators based on up to six capacitors are proposed. The definitions of power factors before and after compensation are introduced. The influence analysis of nonactive power compensation on harmonic distortion of line currents has been also performed. Experimental results are obtained to confirm the validity and applicability of the proposed compensation procedure.
... The second of the above mentioned power concepts is based on the theory proposed by Budeanu [14], and its main points are thoroughly discussed in [15], where it is compared to an alternative power decomposition suggested by Fryze [16]. Some additional arguments in favor of the latter were also added in [17]. ...
... Since CSCD is a generalized function whose components are present at cyclic frequencies in, at most, a countable set, Α2 = {α|α = mF}, the application of the decomposition (16) to the term δ(α, f) will allow rewriting Expression (21) in the form: ...
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.
... Actually, a bunch of Non-sinusoidal PTs (NPTs) both for single-phase and three-phase systems have been proposed [30][31][32] since 1920s. In general, these PTs can be categorized into four groups including frequency-domain [33][34][35][36], time-domain [37][38][39][40][41][42], time-frequencydomain [43] and geometric algebra-domain [44,45]. Some of these NPTs are suitable and helpful for identifying the harmonics and reactive power in non-ideal systems, some are the foundation for designing the smart meters, while others may be useful to compensate and suppress the unexpected power components. ...
... However, it is recognized that it is not suitable for non-sinusoidal systems [30]. To explain the power flow in the non-sinusoidal and unbalanced circuits, several different theories [33][34][35][36][37][38][39][40][41][42][43][44] have been proposed and can be categorized into four groups based on their operation domains, namely These NPTs, which are formulated from the bottom-up [36,40,43] or top-down [26,41] perspective, all offer valuable contributions for power analysis. However, some different conclusions may be drawn when different theories are applied in certain cases [69,70] . ...
As the worldwide trend of “carbon neutrality” action spreads, renewable energy substitution for fossil fuels in the electricity sector is inevitable. The traditional power system is updating to a new paradigm of smart grid to promote the consumption of renewable energy and phasing out of fossil fuels. However, this transition would bring about new tremendous challenges on power quality and operation & control of the power system. As the traditional power theories may not be able to handle the non-sinusoidal voltages, unbalanced and/or non-linear loads that are prevalent in evolving smart grid, a novel time-domain Conservative Power Theory (CPT) was proposed in the early 2000 s. So far, more than 190 papers have been published focusing on this attractive theory. This paper gives a summative and comparative overview of CPT and its innovative applications in modern smart grids. Horizontal comparisons among CPT and other common non-sinusoidal power theories are briefly performed and then the mile-stones in CPT’s development are highlighted. Basic power and current definitions under the CPT framework for both single-phase and three-phase systems are described in detail, and four main applications of CPT are discussed, which are load characteristic identification, accountability and revenue, filter and compensation, and power converters. Based on the review, the motivations, definitions, developments, and applications of CPT are comprehensively presented, some possible research aspects of CPT are itemized, and a future vision of CPT-based smart grid scenario is then conclusively predicted.
... It is known that it is enough to allow an artificial delay in opening electronic keys in an alternating current circuit supplying a purely active load in order to form a spectrum of higher current harmonics [23][24][25]. From this spectrum, only the first harmonic of the current will create the component 1 Q . As an example, Figure 1 shows the oscillograms and the spectral composition of the load current at 1 R r.u. in a network with a sinusoidal voltage source 100 U r.u. and frequency 50Hz f , when the delay in opening electronic keys was about 70%, that is, 0.007s. ...
... Therefore, this power does not make sense in the future to decompose into the components p and p . Therefore, ripples of alternating instantaneous power (t) p 3 are distributed in such a way that the total area bounded by the curve (t) p 3 in Figure 2 [23][24][25]. This is due to the fact that one harmonic, characterizing a certain power component, as follows from the properties of the Fourier series, cannot be completely obtained or compensated by a combination of other harmonics. ...
Using the examples of wave and vector diagrams, we study the conditions for the appearance of components of inactive power in an AC network, which are known as reactive power and distortion power. It is shown that the components of the active, reactive power and distortion power are mutually orthogonal and form a power balance, which can be violated mainly due to methodological errors in calculating these components under conditions of non-stationary mode parameters. It is established that the interaction of reactive power and distortion power occurs at the instantaneous power level, and changing their phase shifts allows you to adjust the shape of the resulting power without involving additional active power in the AC network. The results obtained will allow not only to correctly determine the proportion and nature of the components of inactive capacities, which is valuable for solving the problems of optimizing modes in AC networks, but also to create effective technical means of compensating for the identified inactive capacities in the future.
... Известен метод для однофазных сетей, основанный на определении знака и значения мощностей высших гармоник (метод потока активных мощностей), передаваемых от источника искажений в сеть [14]. На основе теории мощности [6,9] такой метод был доработан и применен для многофазных систем, что отражено в работах [7, 8, 13]. Применение метода сопряжено с определением ...
... Известен метод для однофазных сетей, основанный на определении знака и значения мощностей высших гармоник (метод потока активных мощностей), передаваемых от источника искажений в сеть [14]. На основе теории мощности [6,9] такой метод был доработан и применен для многофазных систем, что отражено в работах [7,8,13]. Применение метода сопряжено с определением углов фаз напряжения и тока на высших гармониках. ...
The article discusses the issues of identifying the location of non-linear loads in electrical networks which makes the main contribution to the distortion of the non-sinusoidal voltage and current in the distribution network of an industrial enterprise, including mining enterprises. The existing methods for determining the location of the source of higher harmonic components in voltage and current are considered, their advantages and disadvantages are revealed. The main disadvantages of the methods used include the low accuracy and incorrectness of their use in existing enterprises. When developing a new method, the authors were faced with the task of simplicity of its use in the conditions of industrial operation of electrical equipment and the absolute correctness of the results obtained. The proposed method of identifying the source of higher harmonics is based on the variation of the parameters of the power system, in particular, the change in resistance of power transformers taking into account their transformation ratio. It is shown that by varying the transformation ratio during regulation under load, the total coefficient of the harmonic components of the voltage changes. Based on the constructed dependencies, the variation of the derivative of this function with different variations of the parameters of sources of higher harmonics is analyzed and a method is developed that allows determining the share contribution of consumers to the total harmonic component of the voltage.
... In the last two centuries, some authors conceived power theories like Budeanou (1927) [6], Fryze (1931) [7], Akagi (1983) [8], [9], Czarnecki (1984) [10], and Tenti (2003) [11], [12]. The instantaneous active and reactive power theory, or the PQ theory, was first presented by Akagi and other authors and its principle is the instantaneous power calculation in time domain for three-phase systems. ...
... In the last two centuries, some authors conceived power theories like Budeanou (1927) [6], Fryze (1931) [7], Akagi (1983) [8], [9], Czarnecki (1984) [10], and Tenti (2003) [11], [12]. The instantaneous active and reactive power theory, or the PQ theory, was first presented by Akagi and other authors and its principle is the instantaneous power calculation in time domain for three-phase systems. ...
The staircase modulation strategy is the best choice for Asymmetric Cascaded H-bridge Multilevel Inverter (ACMI) because it makes the output voltage to present a high number of levels and makes one of the ACMI modules to operate at low frequency. However, the staircase modulation is usually employed without giving its deserved attention. This paper presents a clear understanding of the staircase modulation strategy and its applications in both isolated and grid-connected ACMI. The main novelty of this paper is the obtaining of the switching function for each module. The principle of operation is carefully described, also indicating how to command the ACMI transistors. The output voltage of the two superior modules is evaluated for different values of iterations. Special attention is given to the power distribution among the ACMI modules when the staircase modulation is applied. It is demonstrated how the power is processed in each module considering an ACMI with three modules. The analysis is presented showing the staircase modulation within a closed-loop control strategy for isolated and grid-connected modes of operation, showing that the content of this paper is valid for both modes. Experimental results clarify and show the efficacy of the content presented in this paper.
... The authors in this work have adopted the Fryze's approach [31] as the metric for evaluate the power quantities. In [32,33] different interpretations regarding the significance of such terms and metrics can be found. ...
... One the most important motivations regarding the adoption of the Fryze's approach is to assure the real time performance of the meter, considering that the time domain approach needs less processing resource. See [28] and [31] for details on the analytical evaluation. ...
The smart city in urban planning and architecture is a set of urban planning strategies aimed at optimizing and innovating public services so as to relate the material infrastructures of cities “with the human, intellectual and social capital of those who live there” thanks to the widespread use of new communication technologies, mobility, environment and energy efficiency, in order to improve the quality of life and meet the needs of citizens, businesses and institutions. Nowadays we hear more and more about the Internet of Things (IoT). Smart devices connected to the internet are increasing in cities. Cities become smart, but at the same time it is not considered the quality of data that these devices send over the internet. The authors, starting from the experience gained previously, in this work focus on energy efficiency, and in particular how energy measurements are performed and sent. The authors propose a low cost smart electric meter for the measurement of electrical parameters. The meter is capable of adapting to the variability of the grid maintaining a high level of measurement accuracy. On the proposed smart meter two algorithms are developed and compared both in simulation and with real signals.
... Therefore, instead of the classic power analysis in sinusoidal condition, it is necessary to measure active and reactive power with nonsinusoidal signals. Several different interpretations about the significance of such terms can be found in literature ( [14]- [17]): distortion of the network signal required a different analysis, and several of this metric requires the frequency domain analysis. The Fryze's approach has been chosen: this theory is based on considering two types of power terms, active and non-active [14], [17], dividing the load current in two terms, an active one and a reactive one: ...
... Several different interpretations about the significance of such terms can be found in literature ( [14]- [17]): distortion of the network signal required a different analysis, and several of this metric requires the frequency domain analysis. The Fryze's approach has been chosen: this theory is based on considering two types of power terms, active and non-active [14], [17], dividing the load current in two terms, an active one and a reactive one: ...
In recent years, smart devices are increasingly. These devices allow making cities smart, enabling communication...
... where Tx denotes the averaging interval that can be zero, one fundamental cycle, one-half cycle, or multiple cycles, depending on compensation objectives and the energy storage capacity of passive components [13]; p(T) is the instantaneous real power. The instantaneous reactive power theory work can be explained from early definition of non-active current by Fryze [14]. ...
... where VL j is the amplitude of the voltage fundamental com ponent; VL h is the amplitude of the h-th order harmonic; hj is the amplitude of the current fundamental component; hh is the amplitude of the h-th order harmonic, the corresponding average power is and the corresponding rms current is By substituting (17), (18), and (19) in (14) we can obtain the active component of the voltage () VL jhjcosa + VL hhhcosah v p t = ' 2 ' 2 iLj + l'Lh ( hj si n(wot -a) + hh si n (wont + f3h)) (20) ...
This paper is focused on conditioning the voltage and current waveform quality of a hybrid matrix converter that consists of a conventional nine-switch matrix converter and an auxiliary back-to-back voltage source converter. Upon critical evaluation of the existing methods for shunt and series compensation, the fundamental limitations for achieving superior results have been identified. A new strategy based on power averaging for obtaining the reference compensating current and voltage has been proposed. The effectiveness of the proposed method has been verified by the simulation results for both the shunt and series compensation with concurrent presence of the harmonic components in voltages and currents.
... Understanding of the concepts of power theory is important for the compensation of nonsinusoidal load currents as studied by [23,27,28,[54][55][56]. Reactive power in a three phase ac system is related to the energy that circulates between the source and the load and circulates among the phases [56]. ...
... Literatürde değişik koşullar altında farklı güç tanımlamaları yapılmıştır (Budeanu, 1927;Fryze, 1931;Shepherd and Zakikhani, 1972;Sharon, 1973;Kusters and Moore, 1980;Czarnecki, 1985;IEEE, 1988; Slonim and Van der Wyk, 1988; Emanuel, 1990;Filipski, Baghzouz and Cox, 1994;Arseneau et al., 1996). Farklı matematiksel dönüşümler ve teknikler/algoritmalar kullanılarak bu tanımlanan güçlerin hesaplanmaları ve ölçümleri gerçekleştirilmektedir. ...
Sistemler için birçok güç tanımlamaları yapılmıştır. Farklı güç tanımlamaları ve bileşenlerinin doğru bir şekilde hesaplanması ve ölçülmesi son derece önemlidir. Bu amaçla çok sayıda yöntemler ve teknikler geliştirilmiştir. Gerçekleştirilen çalışmada; literatürde tanımlanan gelen-yansıyan-iletilen güç bileşenlerinin geleneksel Fourier dönüşümüne alternatif olarak dalgacık paket dönüşümü kullanılarak hesaplanması önerilmiştir. İlgili güç analizlerini yapmak için etkileşimli grafiksel arayüz programı tasarlanmış; önerilen hesaplama tekniğinin etkinliği ve doğruluğu, gerçekleştirilen benzetimlerle/uygulamalarla gösterilmiştir.
... In contrast to the Fourier transform, the wavelet transform provides a three-dimensional interpretation of the current function under study (voltage, power), primarily in physical space (instantaneous value, time) and in frequency space (amplitude, frequency) [5][6][7]. ...
... In the terms of the circuit the ((), are the smallest currents in rms value, that generate the same power , as the (() currents, while (() are the smallest currents that produce the same instantaneous power ((), as the (() currents. [5][6] [7] [8] 978-1-7281-0750-9/19/$31.00 ©2019 IEEE Global reactive currents (Fryze reactive currents) can be computed with: [5] [6] (() = =(() − − (() ...
... After Budeanu's work, Fryze introduced his theory in the timedomain [7]. In the time-domain approach, voltage and current signals are expressed as a continuous and instantaneous function. ...
The increasing aggregation of renewable-based distributed generating units besides the impressive growing usage of non-linear loads raises unwanted challenges for traditional power terms definition in power engineering. This fact consequently affected the performance of the conventional control frameworks and industrial compensation techniques. In this study, the authors aim to provide an insightful summary over the most recognised time domain-based instantaneous power theories and discuss their advantages and disadvantages within a comprehensive mathematical-conceptual and applicational framework for professionals who are using instantaneous power theories within the smart grid applications. They conclude that there is still a need for a modified power theory which can be validated under non-sinusoidal-unbalanced load/source conditions respecting the physical meaning of different power and current components.
... The expression (18) is known from the works of Fryze S. [5] and it is widely used by specialists. The main disadvantage of the considered expression is the limitation of its application in the form of the requirement that the conductivity value ...
... Therefore, active and reactive power must be measured in non-sinusoidal conditions. Among the different interpretations about the significance of such terms and the metrics ( [14]- [17]), authors chose the Fryze's approach. This theory is based on considering two types of power terms, active and non-active, dividing the load current in two terms, an active one and a reactive one: (1) where (2) The active current [19] term is accountable for the active power. ...
Advanced Metering Infrastructure (AMI) today represents the backbone of Smart City intended as urban area where the most of public services are smart. Smart devices allow cities to be smart, enabling communication also among things and creating a new system nowadays known as IoT (Internet of Things). In particular the smarter the meters, the smarter the City, but the concept of smartness is not univocal. In urban area, smart meters must be accessible, collaborative and accurate. The paper faces this topic, mainly with reference to power measurements and wireless networks. In particular, it describes an innovative solution for electrical power, gas and water metering integration in the same infrastructure. Then it describes metrics and hardware details of a smart electrical power meter and, finally it shows the experimental results of the smart meter metrological characterization.
... The transition of values from the time to the frequency domain is a mathematical decomposition. Consequently, this has resulted in a lot of discussion about the physical interpretation of the concept of electrical power for non sinewave signals [8] [9]. Although this research does not focusses on the physical interpretation of harmonic power, the total power S h related to each specific harmonic h can be calculated and can provide important insights in the network topology. ...
... In the last two centuries, some authors conceived power theories like Budeanou (1927) [6], Fryze (1931) [7], Akagi (1983) [8], [9], Czarnecki (1984) [10] and Tenti (2003) [11], [12]. The instantaneous active and reactive power theory or the PQ Theory was first presented by Akagi and other authors and its principle is the instantaneous power calculation in timedomain for three phase systems. ...
The Conservative Power Theory (CPT) is a time-domain theory applicable to any periodic signal, single- or poli-phase system with or without neutral conductor. The principle operation is the orthogonal decomposition of electrical variables, resulting electrical quantities with physical meaning. An important feature of the CPT is the current decomposition. It consists of decomposing any current into five parts. The label of these parts are active current, reactive current, scattered active current, scattered reactive current and generated current. This paper proposes the application of the current decomposition of the CPT in Distributed Energy Resources (DERs). A Supervisory Controller (SC) uses the current decomposition in a load power sharing strategy. The combination of these two issues is the main contribution of this paper. Moreover, the proposal of this paper is more attractive than the conventional droop strategy since the DERs follow their current reference in a current-controlled mode, making the load sharing faster, more reliable and more accurate. A clear understanding of how the CPT decomposes load currents into its parts is presented as well as the drawback found in droop strategy when dealing with load power sharing. Later, the SC load power sharing strategy is described, indicating that the proposal of this paper makes a SC to have a broad option when managing a smartgrid with dispatchable DERs. A case study with experimental results show the efficacy of applying current decomposition of the CPT in load power sharing strategies.
... Reactive power is something else. So far, reactive power in non-sine periodic modes has not been defined well [4][5][6][7]. IPDME 2017 IOP Publishing IOP Conf. ...
Nowadays, virtually everywhere worldwide, the electricity is paid for based on active and reactive power meters. Higher harmonics appeared to influence the electric power meter readings, and this specifically relates to reactive power. Incorrect power meter readings occur due to different so-called "measuring" protection levels in device circuitry in various devices. The paper analyzes reactive power meter readings of devices from various manufacturers. Based on the analysis, the authors introduce a new approach to evaluating the costs in connection to reactive power generation, transmission and consumption, with current/voltage distortions in power supply lines.
... A reactive power compensation is one of the components of the power grids effective operating. Its theoretical base was developed in first part of the past century by S. Fryze and C. Budeanu [1,2]. Nevertheless, a developing of effective control algorithms of reactive compensators operating continues nowadays in two directions. ...
... Jacobian matrix J is an ( ) n N × matrix, having as its elements the partial derivatives of the signal model (2). If j is an arbitrary row of the Jacobian, then ...
... This theory, uses Fourier series expansion to represent power components of a power grid. The second theory was Fryze's theory in 1931 [3], which uses time domain instead of frequency domain. These two theories opened the way for subsequent theories in order to find out the easiest and the most reliable theories. ...
This paper presents a novel power theory with a new construction of power parameters (consisting of apparent (S), active (P) and reactive (Q) power) for sinusoidal voltage supply with linear and nonlinear loads (nonsinusoidal current). This approach decompose every power parameter into two components (fundamental and distortion), each fundamental component is perpendicular on the distortion component. This theory refutes Budeanu's allegations about the reactive power and power factor calculations and some of IEEE standards 1459-2010 assumptions. Moreover, this paper proves that the total active and reactive power is the result of square root the summation of squares of fundamental and distortion components, and not just the arithmetic summation. The new proposed theory proves that the distortion angle (θn) is not just dependent on the total angle (6>t) and on the fundamental angle (θ1), but dependent on the total current (I1) and the fundamental current (I1). Moreover, it shows a new graphical representation of all power components and presents new formulas building the relationship between the total harmonic distortion (THD) and ((θ), (θ1) and (θ1)) phase angles. The new description of power categories has been supported by diagrams, figures and mathematical formulations. In addition, randomly chosen two circuits have been designed and simulated using Matlab-Simulink program in order to test the validity of the new proposed theory in comparing with Budeanu's and some IEEE standard 1459-2010 equations.
The reactive power and its measurement have been studied in time-domain and frequency-domain approaches in the past. In the present paper a comparison between the two approaches is made and the decomposition of the instantaneous power into various components done by various authors are discussed, their relations with one another are shown graphically for easy understanding and a general expression for each of the power components is developed. The unified expressions, thus obtained after the comparative study of different models, are applied in estimating the capacity of an active filter when used with a passive filter in a system to improve the power factor.
This study deals with a new approach to tackle the challenges encountered in the filters-based reactive power calculation techniques utilized in the control system of Static VAr compensators (SVCs). In this approach, step and time-varying responses are improved by a combination of differential and filter-based methods. Then, optimum values of the main parameters of the low-pass and band-stop filters are determined considering three criteria: accuracy, speed, and capability for following the time-varying loads. To assess the performance of proposed method, a new objective function is introduced, calculated for two sets of signals, captured from a real filed in Mobarakeh Steel Company (MSC) in Isfahan/Iran. Then, the proposed and the other reactive power calculation methods are assessed in practice and simulation. Also, the algorithm is implemented using a TMDSCNCD28335 as the processor to assess the real-time feasibility of the method. To do so, reactive power variation of an electrical arc furnace is emulated in a prototype test bench and the algorithm is run in real-time by the processor during the system operation.
Este artículo tiene como objetivo mostrar el detalle del Standard IEEE 1459-2010 para sistemas monofásicos. Este Standard tiene como objetivo cuantificar la potencia de los sistemas eléctricos; sin embargo, no muestra el detalle de la deducción de las ecuaciones partiendo del esquema circuital. Por lo que la contribución de
este documento es la deducción paso a paso de las ecuaciones partiendo de los voltajes y corrientes del sistema. La deducción se realiza tanto para sistemas monofásicos lineales como para sistemas monofásicos no lineales. Se presenta el detalle del cálculo para la potencia activa, reactiva y aparente y también el cálculo del factor de potencia como de la distorsión armónica.
The article examines the conditions for the appearance of such components of inactive power in electric alternating current networks, which are known as reactive power and distortion power. Through simulation modeling, the validity of the expressions that were obtained analytically and determine the components of inactive power was verified. The validation of expressions based on theoretical concepts. The results are useful in optimizing modes in AC networks and creating effective technical means of compensating latent capacities.
Investigation of the effect of reactive power compensation on the regime parameters and the stability of the electrical system. Determination of the permissible levels of reactive power compensation for the stability of load nodes and synchronous generators. Research in self-excitation area of synchronous generator at reactive power compensation.
Power definitions for polyphase power systems with non-sinusoidal and unbalanced voltages and currents are considered in this paper. Based on application of Fortescue's transformation to time-varying voltage and current space vectors, a new approach to power definitions is proposed. Definitions of the complex, apparent, active and non-active powers in terms of the symmetrical components have been proposed. The analysis related to the influence of zero-sequence voltages to power quantities has been performed. The symmetrical components provide calculation of powers by omitting erroneous contribution of the zero-sequence voltages. A significant property of the proposed power definitions in terms of the symmetrical components is that they are invariant to the choice of the voltage reference. Application of the proposed power definitions in terms of the symmetrical components has been demonstrated by the examples of three-phase three-wire and four-wire systems.
This Chapter focuses on the analysis and implementation of control circuits for shunt active power filters (APF). The selected digital signal processing algorithms which have been designed for the control of active power are investigated. First considered are algorithms with first harmonics detectors based on: IIR filter, lattice wave digital filter, sliding DFT, sliding Goertzel and moving DFT. Next considered is a modified classical control circuit based on a p-q algorithm. Here problems of the active power filter dynamics are discussed. Then follows a description of a modified predictive circuit to eliminate dynamic compensation errors for predictable changes in the load current. The subsequent sections describe a control circuit with filter banks, which allows one to select compensated harmonics. Under consideration are filter banks based on moving DFT algorithms and a p-q algorithm. To conclude this chapter a multirate active power filter is considered, which has a fast response to sudden changes in the load current. The presented algorithms allow a decrease in line current THD ratio from a dozen or so percent to a few percent. This chapter presents simulation and experimental results obtained by the author.
Demand Side Management requires both an adequate architecture to observe and control the status of the power grid and precise and real time measurements on which rely. In case of frequency fluctuations, precision is no more guaranteed so without adding more hardware the authors exploit FFT interpolation to estimate the real frequency of electrical signals. After the discovery phase follows the measurement phase in which a low cost Smart Meter computes the metrics specified in the following chapters. Finally, a comparison among measures taken by a reference instrument and the proposed meter is reported.
The wide application of power electronic equipment results in severe non-sinusoidal phenomena, making the conventional steady-state reactive power theory no more applicable. In order to deal with the harmonic compensation and power factor correction under the non-sinusoidal condition, scholars have carried out lots of research works. This paper discusses and compares several commonly used instantaneous reactive power theories, and pointes out the relationships and differences of them. The work of this paper contributes to better understanding of the instantaneous reactive power theories.
The paper surveys the reactive power definition for non-sinusoidal unbalanced poly-phase systems. Based on minimisation of non-reactive currents of the load, a new definition of reactive power is proposed. The simulation results confirm the validity and applicability of the proposed definitions for a variety of loads.
This article contains analysis of the instantaneous reactive power in case of three phase balanced grid with high harmonics. Methodology and theories are particularly descripted. The type of electric load can be determined based on the proposed reactive power vector analysis.
Two orthogonal decompositions of a total three-phase current are considered for a three-phase system with asymmetric sinusoidal voltage at the connection point of asymmetrical loading. In the first one the total current is represented as an orthogonal sum of balanced and nonbalanced current components, the balanced component containing Fryze's active current (active power). In the second decomposition the total current is represented as an orthogonal sum of pulsed and non-pulsed current components. Both decompositions are used to create the optimal mode of supply with a constant instantaneous power at asymmetrical voltage.
Co-phase power supply technology can solve the problem of three-phase load power imbalance and cancel use of the neutral section insulator, thus being helpful to future development of high-speed railways and heavy-haul railways. The co-phase power supply system was designed by combining the YN, d11 transformer and the integrated power flow controller. The traditional comprehensive compensation current detection method was improved theoretically and was applied in the co-phase power supply system. The simulation results prove as follows: The improved current detection method can test comprehensive compensation currents accurately and on real-time basis; compared with the traditional comprehensive compensation current detection method, the dynamic response velocity and steady state accuracy are improved to a certain extent.
Het elektrische energielandschap heeft het laatste decennium sterke veranderingen ondergaan. Zo zijn er de laatste jaren een groot aantal decentrale generatoren (dg) op het net aangesloten. De aansluiting van dit grote aantal voornamelijk éénfasige dg-eenheden geeft aanleiding tot spanningsproblemen in het distributienet. Dit leidt tot een verminderde netkwaliteit en houdt in dat er steeds een grotere afwijking is van de ideale toestand van spanning en stroom. Het merendeel van de decentrale generatoren wordt via een vermogenselektronische omvormer met het net gekoppeld. Zowel de spanning-stroom relatie als de vermogensuitwisseling worden bij deze vermogenselektronische systemen bepaald door de keuze van de topologie en de sturing. Een geschikte keuze van de hardware in combinatie met de implementatie van een slimme regelstrategie, zal ervoor zorgen dat netgekoppelde omvormers in de toekomst een waaier aan netondersteunende diensten zullen kunnen aanbieden. Hoewel netgekoppelde omvormers veel mogelijkheden bieden in de verbetering van de netkwaliteit, zijn ze op dit moment nog niet in staat om het net tijdens fouten te ondersteunen noch om ongewenste invloeden op het net te verminderen. In dit werk wordt een regelstrategie voorgesteld voor driefasige invertor-gekoppelde dg-eenheden die naast het injecteren van actief vermogen ook aanleiding geeft tot de verbetering van de netkwaliteit.
Historically justified goals of the power theories development, general expectations and mathematical tools used for it are discussed in the paper. General features of the power theory of single-phase circuits with sinusoidal voltages and currents, the only commonly accepted power theory, were used as a reference for the presented discussion. Also discussed in this paper are the major issues of power theories development such as these: Should the power theory be formulated in the frequency or in time-domain? Should it be based on quantities averaged over a period or on instantaneous values? It was shown that in spite of the name "power" theory, the load currents rather than powers convey information on power properties of electrical circuits.
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