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Non-periodic currents: Their properties, identification and compensation fundamentals
Abstract
Before the area of power electronics was developed, nonperiodic
currents occurred in distribution systems, apart from arc furnaces
supply, mainly during switching and faults. Now, such currents are
produced at normal operation of some power electronics equipment. Power
electronics enables very fast control of processes and energy flow.
Nonperiodic currents are a by-product of such a fast control.
Identification of nonperiodic currents and their compensation is the
subject of this paper. The paper discusses the main properties of
nonperiodic currents, provides their classification and introduces a
concept of coperiodic, noncoperiodic and quasi-periodic currents as well
as the concept of interharmonic noise and quasi-harmonics. The paper
provides fundamentals of quasi-periodic current compensation and
discusses a hybrid control algorithm of a hybrid compensator
... In the mathematical sense, a signal is considered non-periodic if it does not have a complete pattern within a measurable constant time frame. To reconcile the definition of the non-periodic signal in power system and mathematics, Czarneski [2] proposed a classification of the waveforms based on their periodicity, namely, co-periodics, non-coperiodics, and quasi-periodics. A co-periodic quantity has an integer multiple of the power system frequency. ...
... Two widely used devices for load current compensation are active filters and passive filters [2]. Passive filters, though straightforward and inexpensive as compared to active filters, may bring a high possibility of the amplification of inter-harmonics noise components of the current [6], which makes them not practically applicable for non-periodic load compensation. ...
... Czarnecki et. al [2] proposed a hybrid active filter that consists of a frequency domain method for the compensation of reactive powers and a time-domain method for the compensation of non-periodicity. ...
This paper presents a new technique for the compensation of non-periodic load current. The method provides control references for three co-located devices, each corresponding to one moving calculation window and one decomposed part of the compensated current. They are slow compensator with high power rating, large calculation window, and low switching frequency; fast compensator with lower power rating, shorter calculation window, and higher switching frequency; and the reactive compensator which is an ordinary static VAR compensator (SVC). A fuzzy based adaptive window is proposed for the slow compensator to find the optimum window for different load characteristics. The technique is evaluated using real-world data and controller hardware-in-the-loop (HIL) implementation.
... Many of the loads encountered in modern power electronics cause a significant level of nonsinusoidal and/or nonperiodic voltage and current disturbances in electrical power systems. Arc furnaces, welders, and motor drives are typical nonlinear loads that can cause not only characteristic harmonics (frequency integer multiple of the line frequency) but also subharmonic (frequency lower than the line frequency) and stochastic nonperiodic (frequency higher than the line frequency but not the integer multiple of the line frequency) components to appear in the spectra of voltages and currents [1][2][3][4][5]. ...
... The harmonic currents will produce voltage distortions that can affect other sensitive loads at points of common coupling (PCC) as they interact with the impedance of an electrical distribution system. These current and voltage waveforms are considered as nonperiodic, although mathematically the currents may still have a periodic waveform; in any event, the period of the currents is not equal to the period of the line voltage [1,2]. The effects of nonperiodic components of voltage and current are similar to those caused by harmonics. ...
... The effects of nonperiodic components of voltage and current are similar to those caused by harmonics. They may contribute to power loss, disturbances, measurement errors, and control malfunctions, and thus to the degradation of the power quality in distribution systems [2]. In addition, voltage sags are one of the most important power quality problems in the distribution system and are usually caused by fault conditions or by the starting of large electric motors [6]. ...
This paper presents a 3-phase, 4-wire unified series-parallel active filter (USPAF) system for periodic and nonperiodic disturbance compensation using a generalized nonactive power theory. The USPAF system consists of a series active filter (AF), parallel AF, and split DC-link capacitors with the midpoint of the DC-link connected to the neutral wire. The generalized nonactive power theory is applicable to singlephase or multiphase, sinusoidal or nonsinusoidal, periodic or nonperiodic, and balanced or unbalanced electrical systems. The theory was implemented previously in a parallel AF. In this study, the USPAF system is proposed to compensate for the nonsinusoidal and nonperiodic currents and voltages. Distorted source voltages, source voltage sag, and unbalanced nonlinear load current compensation were simultaneously tested in the experiments. Subharmonic and stochastic nonperiodic current and voltage compensation were simulated in MATLAB/Simulink. Simulation and experimental results verified the validity of the generalized nonactive power theory for the compensation of periodic (nonsinusoidal) and nonperiodic current and voltage disturbances with the USPAF system.
... Many of the loads encountered in modern power electronics cause a significant level of nonsinusoidal and/or nonperiodic voltage and current disturbances in electrical power systems. Arc furnaces, welders, and motor drives are typical nonlinear loads that can cause not only characteristic harmonics (frequency integer multiple of the line frequency) but also subharmonic (frequency lower than the line frequency) and stochastic nonperiodic (frequency higher than the line frequency but not the integer multiple of the line frequency) components to appear in the spectra of voltages and currents12345. The harmonic currents will produce voltage distortions that can affect other sensitive loads at points of common coupling (PCC) as they interact with the impedance of an electrical distribution system. ...
... The harmonic currents will produce voltage distortions that can affect other sensitive loads at points of common coupling (PCC) as they interact with the impedance of an electrical distribution system. These current and voltage waveforms are considered as nonperiodic, although mathematically the currents may still have a periodic waveform; in any event, the period of the currents is not equal to the period of the line voltage [1,2]. The effects of nonperiodic components of voltage and current are similar to those caused by harmonics. ...
... The effects of nonperiodic components of voltage and current are similar to those caused by harmonics. They may contribute to power loss, disturbances, measurement errors, and control malfunctions, and thus to the degradation of the power quality in distribution systems [2]. In addition, voltage sags are one of the most important power quality problems in the distribution system and are usually caused by fault conditions or by the starting of large electric motors [6]. ...
This paper presents a 3-phase, 4-wire unified series-parallel active filter (USPAF) system for periodic and nonperiodic disturbance compensation using a generalized nonactive power theory. The USPAF system consists of a series active filter (AF), parallel AF, and split DC-link capacitors with the midpoint of the DC-link connected to the neutral wire. The generalized nonactive power theory is applicable to single-phase or multiphase, sinusoidal or nonsinusoidal, periodic or nonperiodic, and balanced or unbalanced electrical systems. The theory was implemented previously in a parallel AF. In this study, the USPAF system is proposed to compensate for the nonsinusoidal and nonperiodic currents and voltages. Distorted source voltages, source voltage sag, and unbalanced nonlinear load current compensation were simultaneously tested in the experiments. Subharmonic and stochastic nonperiodic current and voltage compensation were simulated in MATLAB/Simulink. Simulation and experimental results verified the validity of the generalized nonactive power theory for the compensation of periodic (nonsinusoidal) and nonperiodic current and voltage disturbances with the USPAF system.
... Non-linear non-stationary currents (also known as non-periodic currents) are known to be problematic to power systems. Arc furnaces, cycloconverters, adjustable speed drives, as well as transient disturbances are the typical sources that generate non-linear nonstationary currents [Czarnecki, 2000;and Tolbert et al., 2003]. This also includes currents with sub-harmonics as well as super-harmonics [Tlusty et al., 2012]. ...
... This also includes currents with sub-harmonics as well as super-harmonics [Tlusty et al., 2012]. The compensation with the conventional power theories becomes erratic due to the energy flow in the presence of non-linear non-stationary currents differs from that in the presence of only reactive, unbalanced, and harmonic currents [Czarnecki, 2000]. ...
... Czarnecki [Czarnecki, 2000] suggested that non-linear non-stationary currents should be compensated along with harmonics by the same device that reduces the reactive and unbalanced currents. He also pointed out that this can be achieved through the proper choice of measurement and digital signal processing procedure as well as the right control algorithm. ...
This paper describes an active power filter (APF) control strategy, which
eliminates harmonics and compensates reactive power in a three-phase four-wire
power system supplying non-linear unbalanced loads in the presence of
non-linear non-stationary currents. Empirical Mode Decomposition (EMD)
technique developed as part of the Hilbert-Huang Transform (HHT) is used to
singulate the harmonics and non-linear non stationary disturbances from the
load currents. The control strategy for the APF is formulated by hybridizing
the so called modified p-q theory with the EMD algorithm. A four-leg
split-capacitor converter controlled by hysteresis band current controller is
used as an APF. The results obtained are compared with those obtained with the
conventional modified p-q theory, which does not possess current harmonics or
distortions separation strategy, to validate its performance.
... These currents interact with the impedance of the power distribution system and disturb voltage waveforms at point of common coupling (PCC) that can affect other loads. These waveforms are considered as non-periodic for the period of the currents is not equal to the period of the line voltage [1], [2]. ...
... These currents interact with the impedance of the power distribution system and disturb voltage waveforms at point of common coupling (PCC) that can affect other loads. These waveforms are considered as non-periodic for the period of the currents is not equal to the period of the line voltage [1], [2]. The effects of non-periodic components of voltages and currents are similar to that caused by harmonics. ...
... The effects of non-periodic components of voltages and currents are similar to that caused by harmonics. They may contribute power loss, disturbances, measurement errors and control malfunctions, thus degradation of the supply quality in distribution systems [2]. Additionally, voltage sags are one of most important power quality problems in the distribution system and usually caused by fault conditions or by the starting of large electric motors [5]. ...
In this paper, a generalized non-active power theory based control strategy is implemented in a 3-phase 4-wire combined series-parallel active filter (CSPAF) system for periodic and non-periodic waveforms compensation. The CSPAF system consists of a series active filter (SAF) and a parallel active filter (PAF) combination connected a common dc-link. The generalized non-active power theory is valid for single-phase and multi-phase systems, as well as periodic and non-periodic waveforms. The theory was applied in previous studies for current control in the PAF. In this study the theory is used for current and voltage control in the CSPAF system. The CSPAF system is simulated in Matlab/Simulink and an experimental setup is also built, so that different cases can be studied in simulations or experiments. The simulation and experimental results verify that the generalized non-active power theory is suitable for periodic and non-periodic current and voltage waveforms compensation in the CSPAF system.
... Generally, power electronic converters generate harmonic components with frequencies that are integer multiplies of the line frequency. However, in some cases, such as line commutated three-phase thyristor based rectifiers, arc furnaces and welding machines are typical loads, the line currents may contain both frequency lower than the line frequency (subharmonic) and frequency higher than the line frequency (stochastic non-periodic, the wave-shape and amplitude are constantly changing) components but not integer multiple of the line frequency [1][2][3][4][5]. These waveforms are considered as non-periodic, although mathematically the currents may still have a periodic waveform, but in any event, the period of the currents is not equal to the period of the line voltage [1,2]. ...
... However, in some cases, such as line commutated three-phase thyristor based rectifiers, arc furnaces and welding machines are typical loads, the line currents may contain both frequency lower than the line frequency (subharmonic) and frequency higher than the line frequency (stochastic non-periodic, the wave-shape and amplitude are constantly changing) components but not integer multiple of the line frequency [1][2][3][4][5]. These waveforms are considered as non-periodic, although mathematically the currents may still have a periodic waveform, but in any event, the period of the currents is not equal to the period of the line voltage [1,2]. The non-periodic components can occur as well in the source voltage. ...
... The effects of non-periodic components of current and voltage are similar to that caused by harmonics. They may contribute power loss, disturbances, measurement errors and control malfunctions, thus degradation of the power quality in distribution systems [2]. ...
... Despite the clear interest in power quality [5], and the large number of studies of the influence of harmonics on power grids, there has not been much attention paid to the study of interharmonics, so it is necessary to look deeper into the causes that provoke them, as well as the consequences they have [6,7]. Currently, they are not a real or compelling problem, but it is expected that in the future they may become so, therefore it is necessary to pay attention to this problem [8]. ...
... The voltage waveform is transformed into geometric domain using (6), so that the geometric voltage is as follows ...
The calculation of power flow in power systems with the presence of harmonics has been properly studied in the scientific literature. However, power flow calculation considering interharmonic components is still an open question. Traditional methods based on the IEEE1459 standard have proven to be valid and accurate only for linear and sinusoidal systems, but have been criticized for non-linear and non-sinusoidal systems because they are not able to explain correctly the current and voltage interactions beyond the active power. This paper proposes the use of a novel mathematical framework called geometric algebra (GA) to study the power flow considering the interaction of current and voltage harmonics and interharmonics. The use of GA enables the precise determination of the direction and magnitude of the total and single active power flow for each component, as well as other power elements related to the non-active power due to cross interaction. Moreover, this paper makes a novel contribution to the definition of interharmonics in geometric algebra space that has not been done before. To test the validity of the method, both linear and non-linear circuits are proposed and solved by applying voltages and currents with harmonic and interharmonic components. The results obtained show that power flow can be analyzed under the prism of the principle of energy conservation (PoCoE) in a way that allows a better understanding of the power spectrum due to the interaction of harmonics and interharmonics of voltage and current.
... Despite the clear interest in power quality [5], and the large number of studies of the influence of harmonics on power grids, there has not been much attention paid to the study of interharmonics, so it is necessary to look deeper into the causes that provoke them, as well as the consequences they have [6,7]. Currently, they are not a real or compelling problem, but it is expected that in the future they may become so, therefore it is necessary to pay attention to this problem [8]. ...
... The voltage waveform is transformed into geometric domain using (6), so that the geometric voltage is as follows ...
The calculation of power flow in power systems with the presence of harmonics has been properly studied in the scientific literature. However, power flow calculation considering interharmonic components is still an open question. Traditional methods based on the IEEE1459 standard have proven to be valid and accurate only for linear and sinusoidal systems, but have been criticized for non-linear and non-sinusoidal systems because they are not able to explain correctly the current and voltage interactions beyond the active power. This paper proposes the use of a novel mathematical framework called geometric algebra (GA) to study the power flow considering the interaction of current and voltage harmonics and interharmonics. The use of GA enables the precise determination of the direction and magnitude of the total and single active power flow for each component, as well as other power elements related to the non-active power due to cross interaction. Moreover, this paper makes a novel contribution to the definition of interharmonics in geometric algebra space that has not been done before. To test the validity of the method, both linear and non-linear circuits are proposed and solved by applying voltages and currents with harmonic and interharmonic components. The results obtained show that power flow can be analyzed under the prism of the principle of energy conservation (PoCoE) in a way that allows a better understanding of the power spectrum due to the interaction of harmonics and interharmonics of voltage and current.
... However, in some cases, such as cycloconverters and linecommutated three-phase thyristor-based rectifiers, the line currents may contain both sub-harmonics (frequency lower than fundamental frequency) and super-harmonics (frequency higher than fundamental frequency but not an integer multiple of it). These waveforms are considered as nonperiodic , although mathematically the currents may still have a periodic waveform, but in any event, the period of the currents is not equal to the period of the fundamental voltage [1], [2]. ...
... However, in some cases, such as cycloconverters and linecommutated three-phase thyristor-based rectifiers, the line currents may contain both sub-harmonics (frequency lower than fundamental frequency) and super-harmonics (frequency higher than fundamental frequency but not an integer multiple of it). These waveforms are considered as nonperiodic , although mathematically the currents may still have a periodic waveform, but in any event, the period of the currents is not equal to the period of the fundamental voltage [1], [2]. An arc furnace is an example of a non-linear load that may draw rapidly changing non-sinusoidal currents from the source, that is, the current wave shape is constantly changing. ...
This paper presents a new definition of non-active current, which is valid for single-phase and polyphase systems as well as for periodic and non-periodic waveforms. The definition is applied to a shunt compensation system, and different cases of non-periodic current compensation are studied. A variety of compensation characteristics of non-periodic currents and the rating requirements for the compensator are illustrated by simulation.
... These currents are considered as non-periodic, though mathematically they may still have a periodic waveform. The period of the currents is not equal to that of the line voltage [8], [9]. Most previous efforts [1]-[5] focused on the compensation of periodic non-sinusoidal currents. ...
... These currents are considered as non-periodic, though mathematically they may still have a periodic waveform. The period of the currents is not equal to that of the line voltage [8], [9]. Most previous efforts [1][5] focused on the compensation of periodic non-sinusoidal currents. ...
Compensation of irregular currents such as those associated with arc furnaces, transient disturbances, and power electronic converters is presented. The compensation is based on a well-defined nonactive current definition. The basic concepts required in the definition of nonactive current are presented and illustrated by compensation simulations for a variety of different types of nonperiodic currents found in distribution electrical systems, including disturbance, subharmonic, and stochastic currents. Further, based on the compensation objectives for different types of load waveforms, the specifications such as current ratings or capacitance requirements of the active filter are also presented.
... However, in some cases, such as cycloconverters and linecommutated three-phase thyristor-based rectifiers, the line currents may contain both sub-harmonics (frequency lower than the line frequency) and super-harmonics (frequency higher than the line frequency but not the integer multiple of line frequency). These waveforms are considered as non-periodic, although mathematically the currents may still have a periodic waveform, but in any event, the period of the currents is not equal to the period of the line voltage [1],[2]. Arc furnaces are another example of a non-linear load that may draw non-periodic currents because they draw rapidly changing power from the source and the waveshape and amplitude are constantly changing. ...
This paper presents a discussion of the compensation of non-periodic currents such as those associated with arc furnaces. Based on the compensation objectives for different types of load waveforms, the energy storage requirements of the compensator are also presented. Further, basic concepts required in the definition of nonactive current are presented and illustrated by simulations for a variety of different compensation characteristics of non-periodic currents. Key Words non-active power, reactive power, compensator, nonperiodic current, arc furnace 1.
... Non-integer multiple harmonics are defined as non-periodic currents in [7] , and the compensation is discussed. Nonperiodic currents are also discussed in [8]. The diversity of the features of nonlinear currents makes it difficult to get one definition that fits all situations, and the compensation of such currents is quite difficult. ...
This paper presents a generalized nonactive power theory, in which the instantaneous currents (active and nonactive) and instantaneous powers (active and nonactive) are defined. This theory is implemented in a parallel nonactive power compensation system. The theory is valid if the system is three-phase or single-phase, sinusoidal or non-sinusoidal, periodic or non-periodic, balanced or unbalanced. Four cases, three-phase balanced RL load, three-phase unbalanced RL load, diode rectifier load, and single-phase RL load are tested in the experiments. Subharmonic load compensation and non-periodic load compensation are simulated in Matlab. The simulation and experimental results not only verify the validity of the theory, but also show that this theory can perform instantaneous nonactive power compensation with fast dynamic response
... Non-integer multiple harmonics are defined as non-periodic currents in [7] and the compensation is discussed. Nonperiodic currents are also discussed in [8]. The diversity of the features of non-periodic currents makes it difficult to get one definition that fits all situations, and the compensation of such currents is quite difficult. ...
This paper presents a theory of instantaneous nonactive power/current. This generalized theory is independent of the number of phases, whether the load is periodic or non-periodic, and whether the system voltages are balanced or unbalanced. By choosing appropriate parameters such as the averaging interval T<sub>c</sub> and the reference voltage V<sub>p</sub>, the theory has different forms for each specific system application. This theory is consistent with other more traditional concepts. The theory is implemented in a parallel nonactive power compensation system, and several different cases, such as harmonics load, rectifier load, single-phase pulse load, and non-periodic load, are simulated in MATLAB. Unity power factor or pure sinusoidal source current from the utility can be achieved according to different compensation requirements. Furthermore, the dynamic response and its impact on the compensator's energy storage requirement are also presented.
... T HE WIDESPREAD use of nonlinear loads and power electronics converters, such as cycloconverters and linecommutated three-phase thyristor-based rectifiers, has increased the generation of nonsinusoidal and nonperiodic currents and voltages in power systems [1], [2]. An arc furnace is an example of a nonlinear load that may draw rapidly changing nonsinusoidal currents. ...
... Therefore, the traditional power quality indexes cannot be used since they are found upon the periodicity of the considered signal. However, some very interesting contributions regarding this problem have recently appeared in specialized literature [14] [16]. In particular, in [14] a new index, the short-term harmonic distortion index, has been defined; it refers to an aperiodic signal to which a windowed Fourier transform (WFT) has been applied. ...
DC arc furnaces are more and more applied in large industrial systems and represent one of the major sources of perturbations for the feeding system. This paper deals with the problem of the dc arc modeling using three well-known chaotic attractors (Rössler, Chua, and Lorenz attractors). A new tuning procedure is adopted to determine the most adequate parameters of the attractors to model the dc arc furnace. Waveform distortions and voltage fluctuations indexes are calculated from the simulation results of a whole existing plant and compared with measured data. The proposed models of dc arc furnace can be used to assess the impact in terms of power quality of the dc arc furnace when planning new plants or evaluating the performances of compensating devices.
Symmetry is not only used to simplify the analysis of three-phase electrical systems, but it is also used to define its voltages, currents and loads. When the loads are symmetrical, the currents of a three-phase AC system are expected to be symmetrical as well. Given the proper conditions, in converters such as the matrix converter (MC), the output voltages and currents are expected to be sinusoidal with periodic symmetry. However, in some cases this symmetry is broken so that, there appears nonlinear behaviors such as quasiperiodicity and so on. Based on simulations and experiments, this paper focuses on an analysis of a quasiperiodic behavior and the presence of a DC component in the output currents of a Venturini modulated MC. The presence of such behaviors in the output currents indicates that the symmetry in a period is broken. The broken symmetries appear when the input and output frequencies are mismatched. In addition, this paper shows the possibility to recover the symmetry of the output currents of the MC. The method for symmetry recovery is based on a time-delayed feedback control. The simulation and experimental results indicate the possibility of attenuating the quasiperiodic behavior and DC component.
This paper presents a general definition of nonactive current/power and the implementation for a shunt compensation system. This definition is universal for different loads, such as nonperiodic, unbalanced or single phase, and also flexible in terms of the compensation results. Unity power factor, pure sinusoidal source current, or zero nonactive power supply from the utility can be achieved according to different compensation requirements. In addition, the corresponding current rating and energy storage requirements of the compensation system are also presented.
Based on a new definition of nonactive current/power, this paper presents the application of a parallel active filter for the compensation of nonperiodic currents. Analysis of the compensation characteristics required for a variety of nonperiodic currents such as those associated with arc furnaces is presented. In addition, the corresponding current rating and energy storage requirements of the compensator are also presented.
A great variety of features of nonperiodic currents make
experimental study on their properties, identification and compensation
confined to only particular cases dependent on the loads used. To
overcome this obstacle, a device can be developed that, supplied from a
three-phase power grid, would have the line currents controlled, at the
operator's discretion, by a computer. This device is referred to as a
phantom load in the paper. The phantom load described is built of two
three-phase current inverters, a measurement and digital signal
processing unit for the vector control of the inverters, a PC for
generating the required waveform of the phantom load line currents and
for its control, as well as a synchronization unit. The synchronization
unit provides the synchronization of the current waveform generated in
the computer with the supply voltage of the supply power grid of 60 Hz
frequency. The paper discusses the operational principle of such a
device
The sections in this article are
Power Theory of Systems with Nonsinusoidal Voltages and Currents
Fourier Series
Properties of Harmonics' CRMS Vaues
Harmonics in Linear Circuits with Lumped RLC Parameters
Harmonics of Symmetrical Three‐Phase Quantities
Instanteneous Power in Single‐Phase Circuits
Active Power in Single‐Phase Circuits
Apparent Power in Single‐Phase Circuits
Budeanu's Reactive and Distortion Powers
Current's Physical Components Power Theory of Linear, Time‐Variant Loads
Current's Physical Components and Powers of Single‐Phase Harmonic Generating Loads
Three‐Phase Systems — Doubts with Respect to Apparent Power Definitions
Currents' Physical Components of Three‐Phase, Linear, Time‐Invariant ( LTI ) Loads
Currents' Physical Components and Powers of Three‐Phase Harmonic Generating Loads
Instantaneous Reactive Power p‐q Theory
Advanced Topics That Have Not Been Discussed
For the most general case of electrical polyphase circuits under non-sinusoidal, unbalanced but steady-state working conditions there are different definitions of active quantities needed for power transfer and non-active quantities which could be compensated without changing the average power transfer. In practice normally the load is varying with time, therefore it is interesting how the definitions of power quantities can be extended to dynamic working conditions and what are the results of compensating non-active quantities in such cases. Even if the load does not change with time after the start of a controllable compensator, the complete system is time varying. For this case it is shown how the non-active quantities as defined within the FBD Method can be determined under dynamic conditions. For two simple circuits simulations are presented which show the dynamic performance of an ideal controllable compensator with a control scheme based on the FBD Method.
Reactive power compensators with thyristor switched inductors and
shunt capacitors enable adaptive compensation at the price of an
harmonic distortion increase. This distortion is even higher if the
compensator is controlled asymmetrically to reduce the effects of the
load unbalance. Harmonic distortion may increase, moreover, because of
the compensator resonance with the supply system reactance. This paper
suggests a modification of the balancing compensator structure that
reduces the harmonic currents injected by the compensator into the
supply. The structure suggested also reduces the possibility of the
compensator resonance with the supply source inductance. The paper
discusses the required control range of the compensator susceptances and
their frequency properties and suggests an efficient method of measuring
the load parameters needed for VAr compensator control
A theoretical basis for describing the energy properties of
circuits with nonperiodic voltage of finite energy is formulated. It is
shown that the current in such a circuit can be decomposed into three
orthogonal components related to three different phenomena that are
responsible for the current value. This decomposition not only explains
the energy properties of such circuits, but it also forms the basis for
the source current minimization. Conclusions are drawn about
measurements that are required for this purpose