Instantaneous Power Components Research Articles

Accounting for a positive, negative and zero sequences power in a three-phase unbalanced electrical system

Purpose. Based on the instantaneous electrical power of a three-phase asymmetric system of sinusoidal periodic current, to determine positive, negative, zero-sequences active and reactive power, as well as invariance power factor. Methodology. In the unbalance case in three-phase electrical system, the electrical energy quality is evaluated by means on voltage and current positive, negative, zero-sequences. At the same time, similar components of active and reactive power have not received practical distribution. But it is precisely in terms of power that electricity is accounted for. The instantaneous power orthogonal components in the time domain are determined using the symmetrical components of voltage and current. Active, reactive powers of positive, negative and zero-sequences are allocated. The result obtained has the property of representativeness, which most of the known results lack. Findings. The three-phase system’s instantaneous power components are analytically determined, including the amplitudes of the oscillating power components. The need to take into account the oscillating instantaneous power components has been proven by means of a graphical interpretation of a special case of the three-phase system mode. As an integral indicator that takes into account the oscillating components of the three-phase system instantaneous power, its root-mean-square value over the repetition period is used. Originality. By calculating the transformer efficiency of the studied model according to the active power positive sequence and the same indicator according to the active power as a whole, it was established, that the component sequence separation affects the results of calculating the generalized indicators, including the power transmission system objects. This can lead to erroneous judgments about the efficiency of the specified facilities functioning. Practical value. The invariance power factor was used to characterize the electrical energy quality level of a three-phase sinusoidal current system in an unbalanced mode.

ANALYSIS OF ENERGY EXCHANGE PROCESSES WHEN BALANCING REGIMES ENERGY SUPPLY SYSTEMS WITH DISTRIBUTED GENERATION

It is shown that maintaining a balance between the production and consumption of electric energy is an important condition for the stable operation of modern energy supply systems. The active increase in the share of renewable energy sources forces the use of new algorithms for balancing demand and supply, in particular, at the expense of flexibility. This implies the need to implement new technological solutions and approaches to balancing the modes of generation and consumption (the ability to quickly respond to changes in demand and supply), which, in turn, requires a detailed analysis of energy exchange processes in electric power systems.
 It is recognized that there is a need for an in-depth analysis of the balance of energy components, and an assessment of electromagnetic compatibility in electric power systems, especially in the conditions of the growing influence of renewable energy sources on local electricity markets. Analysis of various factors influencing technological solutions and cooperation of different market parties are key components for developing effective management strategies and ensuring the stability of the electric power system.
 The peculiarities of the analysis of energy exchange processes in local electric power systems with the determination of exchange capacities, which are integral characteristics of the influence of various factors of the non-acidity of electricity on exchange processes, are considered. It is proposed to balance the components of electric energy on the basis of exchange processes in controlled intersections of local electric power systems using the components of instantaneous power at each energetically constant state. The exchange processes in local electric power systems are analyzed with the selection of different modes of their operation, in particular, when assessing the level of electromagnetic compatibility of the elements of the local electric power systems.
 The introduction of exchange capacities made it possible to develop indicators for assessing the level of electromagnetic compatibility of the elements of the local system. To estimate the share of consumers' contribution to the deterioration of the quality of electricity at the common connection point, an algorithm for evaluating the mutual influence of elements is proposed, with the allocation of the element's contribution to the distortion of electricity in the controlled intersection and the analysis of the magnitude of the influence of distorting factors on electromagnetic processes in the system element.
 An optimization model for achieving the specified levels of balancing (flexibility) in local electric power systems with energy accumulators has been developed.

The power harmonic components distribution study in the power circuit of a dynamic voltage restorer

Purpose. Investigation of the distribution of harmonic power components in the power circuit of a dynamic voltage restorer. Methodology. On the basis of the differential equations of the power circuit of a dynamic restorer, a search for the relationship between the mode parameters and the parameters of the circuit elements is performed. On the basis of the obtained expressions, a model of a dynamic voltage regulator was created using the methods of mathematical modeling in the visual programming environment.. Findings. The equations that reflect the relationship between the mode parameters of a dynamic voltage restorer and the parameters of circuit elements are obtained. As a result of modeling the mode with different harmonic composition of current and voltage, the following features of the distribution of instantaneous power components are revealed. Originality. It has been established that the presence of different current and voltage harmonics acting in the transformer of a dynamic restorer causes additional power harmonics that are transformed in the windings. It is noted that the low-frequency power harmonics of the LC filter dominate on the capacitor, which is connected in parallel to the transformer winding, while the level of high-frequency components caused by PWM modulation for the capacitor and the filter choke differ slightly. The zero-frequency power component of the storage capacitor corresponds to a tripled zero-time power component at the output of the converter, which is due to its operation in three phases. This cannot be extended to the second and third harmonics of the powers of the converter and the capacitor; these components are absent in the latter, which is due to energy exchange processes between the phases of the converter. Practical value. Using the obtained expressions, the principle of determining the parameters of the elements of the power circuit of a dynamic voltage restorer, in particular, the storage elements, is formulated.

Doubly Fed Induction Machine-Based DC Voltage Generator with Reduced Oscillations of Torque and Output Voltage

The doubly fed induction machine (DFIM)-based DC voltage generator is equipped with a stator-connected diode rectifier. The six-pulse diode rectifier as a nonlinear circuit introduces harmonics in the stator and rotor current and distorts the machine stator voltage, as well as the stator flux. This causes electromagnetic torque oscillations and instantaneous power components oscillations. The torque oscillations adversely impact the mechanical parts of the drive-train and oscillations of the p component of instantaneous power influence DC-bus voltage oscillations. The oscillations can be somewhat cancelled by control methods. However, cancellation of electromagnetic torque is not strictly coupled with cancellation of oscillations of the p component of instantaneous power. The paper presents an analysis of influence of the control methods aimed at a reduction of torque oscillations on the output voltage oscillations level in the stand-alone DFIM-based DC voltage generator. Field-oriented control FOC with current controllers and space vector modulation-based direct torque control DTC-SVM with flux module regulation have been compared with control in which electromagnetic torque is one of the commanded variables, whereas the second variable is the dot product of stator flux and rotor current space vectors. The contributions of this paper are the introduction of a new variable in the second control path in the DTC-SVM method instead of flux vector length and the proof that it can reduce torque and DC-bus voltage oscillations in the DFIG-DC system. Additionally, this paper reveals that for proper stator-to-rotor-turns ratio of a doubly fed machine necessary for reduction of the rotor converter power, lower DC-bus voltage can be obtained than is required for full realization rotor side voltage requested by rotor current controllers. This is the reason why, regardless of the control method, torque oscillations cannot be always fully cancelled, and a comparative study of the methods at these conditions has been conducted in simulation and in laboratory tests.

A positive, negative and zero sequences electric power, to improve upon the standard IEEE 1459-2010

PurposesThe purpose of this paper is to identify on the instantaneous electrical power basis of a nonsinusoidal periodic current three-phase asymmetric system, active and reactive positive, negative and zero sequence powers, taking into account higher harmonics. The main power theories, including those embodied in the IEEE 1459 standard, do not allow to evaluate some of power components.Design/methodology/approachA well-known fact is that the three-phase AC system total power with the symmetry of currents and voltages is constant. It corresponds to the electrical energy transfer process in a DC system. In this case, the electrical energy transmission can be taken as high quality. It has been established that the components of active and reactive powers are because of the product of current and voltage of unidirectional sequences. The orthogonal components of the oscillating power are because of the product of the voltage and current components of different sequences, with the exception of the zero sequence.FindingsFor an unbalanced nonsinusoidal mode of a three-phase system, the components of instantaneous power were defined, corresponding to the active and reactive positive and negative and zero sequences powers with the selection of the fundamental and higher harmonics. The active and reactive powers of sequences were divided into two categories – consumed and generated.Originality/valueIt is proposed to use the ratio of “interfere” power RMS value to the total power RMS value to assess the instantaneous power distortion.

The features of the determination and use of instantaneous power components

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Control of Three-Phase Power Electronic Converter With Power Controllers in Stationary Frame

This article concentrates on a three-phase power converter control system that uses voltages and currents in a stationary reference frame. The advantages of such a control system include the lack of transformation between stationary and rotating reference frames and hence, there is no need for an extra algorithm such as a phase-locked loop for the grid voltage phase-angle determination, as the power components are the same in every coordinate system. The method proposed in this article uses proportional-resonant-integral controllers for tracking referenced Akagi's instantaneous power components, which contain intentional oscillations of double grid frequency. Thanks to that, the sinusoidal converter current is maintained despite the negative sequence component in grid voltage. Different targets for converter current asymmetry, from corresponding, through symmetrical, to opposite to voltage asymmetry may be achieved, depending on the operation mode and the demanded power. Moreover, the power limitation method allowing limitation of the phase-current amplitude even for unbalanced phase currents was applied.

Three‐phase converter power control under grid imbalance with consideration of instantaneous power components limitation

Three‐phase converter power control under grid imbalance with consideration of instantaneous power components limitation

Equivalence Analysis of Virtual Synchronous Machines and Frequency-Droops for Inertia Emulation in Power Systems with Converter-Interfaced Renewables

In converter-based AC microgrids, the frequency-droop is widely applied. As a considerable share of installed capacity is replaced by renewable generation, the virtual synchronous machine (VSM) algorithm is presented to address stability issues caused by low-inertia converter interfaces. Recently, droop control loops are also modified to improve stability. The VSM and the frequency-droop are both derived from the property imitation of synchronous generators (SGs) while researched independently. In this paper, by simplifications in the steady state, the expression of the inertia emulation of the VSM algorithm based on the second-order SG model is linearized as a first-order ordinary differential equation. In frequency-droop loops, as the instantaneous power components are commonly passed through a low-pass filter for disturbance rejection, the system function of the droop control can also be transformed into a first-order ordinary differential equation, which is equivalent to that of the VSM under certain conditions. In terms of the inertia constant, the swing equation is normalized under per unit representation. By the same simplification in the VSM linearization, the equivalence between the linearized VSM and the SG is also demonstrated. Therefore, the equivalence among SGs, the VSM, and the frequency-droop are summarized, which provides insights for coordinative control of power converters integrated into current SG dominating power systems. For a specific synchronous generator, the equivalence conditions are verified by simulation.

Automated method for formation and solving the instantaneous power components balances for the analysis of nonlinear electric circuits

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Methodology for Calculating the Parameters of a Reactive Compensator of a Linear Asymmetric Load of a Three-Phase Three-Wire Network

The article describes the method of calculating the parameters of a reactive compensator of a linear asymmetric load of a three-phase three-wire network, which allows to increase the power factor of an asymmetric load to a unit value. It is shown that as a result of the use of a reactive compensator, the power loss in the transmission line can be reduced to two times. In this paper the main equation for the calculation of the parameters of the reactive compensator is derived. The reactive compensator of the circuit with asymmetrical two-arm active load is synthesized. The method is illustrated by an example of a scheme with asymmetric single-cell active load. As known, the unbalanced load of three-phase three-wire power systems leads to a deterioration in the quality of electricity, which manifests itself in the emergence of reciprocal currents and pulsations of instantaneous power, which cause additional losses on the active supports of the transmission line and asymmetry of supply voltages in the nodes of the overall connection of loads. In order to balance the asymmetric stationary linear load, passive filters on reactive elements are effectively used, the calculation of which is based on two approaches: the removal of the pulsating component of instantaneous power and the compensation of the inactive components of the input currents. Among various possible methods, the inductive-capacitive systems are of particular importance. When the limit values of unbalance factor, specified in standards are exceeded, the use of symmetrization systems is required. A symmetrizator should not cause significant active power losses during operation; it implies that the symmetrization process shall be carried out by means of reactive elements (LC) or using active methods (power electronic systems).The purpose of a compensator is to measure adequate electric quantities of the load and generate in the compensator such currents, that the resultant load: compensator-compensated load, as seen from the supply network, was symmetrical, and the fundamental harmonic reactive current drawn from the network did not exceed the value permitted in the supply conditions. In the work vector diagrams of currents and voltages are constructed, power loss is calculated.As a result of the work done, it was established:1) Increasing the power factor of the three-phase system to the maximum unit value leads to a gain in power loss.2) Losses in the wires unbalanced system in 2 times more loss symmetric system, and power factor for unbalanced system in square root of two times less than a coefficient symmetrical.Ref. 3, fig. 8.

Torque Oscillations Cancellation Targets of a Doubly Fed Induction Machine Operating With Unbalanced and Distorted Grid

The paper focuses on the method of vector control of a doubly fed induction machine connected to the unbalanced power network with simultaneous grid voltage harmonics distortions. As the instantaneous values of torque and the qs component of power are independent, torque oscillations during grid voltage harmonics can be achieved for different waveforms of qs power, so a different shape of stator current can be reached at this state. Thus, alternative control targets giving non-oscillatory electromagnetic torque are analyzed and realized in the control. The commanded variables are electromagnetic torque Tem and alternatively, the qs component of stator instantaneous power or a new variable zs calculated in the same way as the qs component of power but the amplitudes of each voltage harmonics are reduced k-times, where k is the harmonic order. The paper discusses how reference stator current vector components can be calculated for each type of torque oscillations cancellation target. The analysis is complemented with a simulation of a 2 MW model and laboratory tests of a small power machine.

Virtual Torque and Power Control of a Three-Phase Converter Connected to an Unbalanced Grid With Consideration of Converter Current Constraint and Operation Mode

The paper presents a three-phase power converter control under grid voltage imbalance. The proposed method adapts the current imbalance in relation to the inverter or rectifier operation. Under the inverter operation, the control target is to have the nonoscillatory p component of instantaneous power and the x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> component of instantaneous virtual torque calculated as the dot product of the grid virtual flux vector and the converter current vector. Then, the phase with lower voltage is supported by higher current. In the rectifier mode, the control target is to have the nonoscillatory q component of power and the T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> component of virtual torque calculated as the cross product of the virtual flux and the converter current. This way, the phase with the highest voltage is loaded by higher current. Unbalanced current obtained in both targets is limited in the way that allows us to limit true phase current and retain sinusoidal current waveforms. However, it does not allow maximum power transfer at the given grid voltage asymmetry, so in order to increase the power value, current progressive balancing is proposed in both operation modes. Finally, converter current balancing is applied also in the case in which a significant amount of reactive power is referenced.

Identification of distribution features of the instantaneous power components of the electric energy of the circuit with polyharmonic current

Many researchers pay attention to the problem of the distortion electric power. The known theoretical results that are reflected in the acting standards are reasonably criticized in the part of the distortion power generation by current and voltage of different frequencies. The paper deals with the approach based on the order of generation of instantaneous electric power components depending on the combination (sum or difference) of current and voltage frequencies. The analytical expressions for the instantaneous electric power components of a harmonic current circuit consisting of a capacitor, an inductance coil and a resistor connected in series are obtained. With this purpose in view, two components – active and reactive – are singled out from the obtained four components of instantaneous power, as well as the orthogonal power components oscillating with double frequency. It is demonstrated that the sum of the squares of the active and reactive components and the sum of the squares of the mentioned orthogonal components coincide and are equal to the total (apparent) power. The used method is developed for the general case of polyharmonic current and voltage. In this case, it is observed that the active and reactive power components can be singled out from the instantaneous power components as orthogonal quadrature components of zero frequency. Though, it is impossible to single out the apparent power. Two numerical experiments with periodic current and voltage, containing three harmonics each, were carried out. The acting values of currents and voltages in each of the experiments were assumed equal. In this case, the amplitudes of the second and the third harmonics exchanged their positions. This example demonstrates that the integral indices of the apparent power and the distortion power, calculated by conventional methods, proved to be the same in both cases, which is incorrect. Under the same conditions, such instantaneous power components whose values turned out to be different for each of the experiments are found among the proposed instantaneous power components. As a result, it is proposed to use a root-mean-square value of the mentioned components for the assessment of the distortion degree in relation to the root-mean-square value of the instantaneous power

Using Passive Two-Port Networks to Study the Forced Vibrations of Piezoceramic Transducers

A generalization and subsequent development of experimental techniques, including methods of studying the phase-frequency relations between the measured components of admittance and instantaneous power are considered. The conditions of electric loading where electric currents, voltages, or instantaneous powers of constant amplitude in the piezoresonators are specified are numerically modeled. It is particularly established that the advanced Mason circuit with additional switch allows acquiring much more data on the forced vibrations of piezoceramic transducers than the classical circuit. The measured (at an arbitrary frequency) voltage drop across the piezoelement, its pull-up resistor, and at the input of the measuring circuit allow determining, with high accuracy, the current, conductivity, impedance, instantaneous power, and phase shifts when the amplitudes of electric current and voltage are given.

Refined calculation of induction motor equivalent circuit nonlinear parameters by an energy method

The topicality of the research aim is caused by the analysis of the processes of energy conversion taking into account the induction motor particular nonlinearities that reveal the physical properties and phenomena in structural materials under the action of electrical and electromagnetic impacts. Taking into consideration the nonlinearities of the induction motor equivalent circuit influences the accuracy of determination of the electric machine operating characteristics. Most conventional methods for parameter identification do not enable assessment of the induction motor nonlinear characteristics and properties. It is proposed to use resistive impedance and inductance dependences on the rotor current to take into account the rotor nonlinear parameters. To form identification equations, the instantaneous power components for the rotor nonlinear resistive impedance and nonlinear inductance have been obtained. The solution of the identification equations resulted in determination of the equivalent circuit electromagnetic parameters taking into account the rotor nonlinear parameters and the amplitudes of the harmonics of the current cosine and sine components of the rotor and magnetization circuit. The results of identification of the induction motor equivalent circuit parameters taking into account the rotor nonlinear parameters have been obtained with sufficient accuracy. This is confirmed by a low error of determination of the electromagnetic parameters. The adequacy of the identified parameters is determined by comparison of the stator current experimental and calculated curves

NETWORK-CENTRIC TECHNOLOGIES FOR CONTROL OF THREE-PHASE NETWORK OPERATION MODES

Purpose. The development of the control system for three-phase network is based on intelligent technologies of network-centric control of heterogeneous objects. The introduction of unmanned aerial vehicles for monitoring of three-phase network increases the efficiency of management. Methodology. The case of decomposition of the instantaneous capacities of the fixed and variable components for 3-wire system. The features of power balance for the different modes of its functioning. It should be noted that symmetric sinusoidal mode is balanced and good, but really unbalanced, if the standard reactive power is not zero. To solve the problem of compensation is sufficient knowledge of the total value of the inactive components of full power (value of the inactive power) without detail. The creation of a methodology of measurement and assessment will require knowledge of the magnitudes of each inactive component separately, which leads to the development of a unified approach to the measurement and compensation of inactive components of full power and the development of a generalized theory of power. Results. Procedure for the compensation of the current of zero sequence excludes from circuit the source, as the active component of instantaneous power of zero sequence, and a vector due to a current of zero sequence. This procedure is performed without time delay as it does not require integration. Only a 3–wire system with symmetrical voltage eliminates pulsations and symmetrization of the equivalent conductances of the phases of the task. Under asymmetric voltage, the power is different, its analysis requires the creation of a vector mathematical model of the energy processes of asymmetrical modes of 3–phase systems. Originality. The proposed method extends the basis of the vector method for any zero sequence voltages and shows that the various theories of instantaneous power three wired scheme due to the choice of a basis in a two-dimensional subspace. Practical value. The algorithm and software implementation for the decomposition of the zero sequence current, which allocated the procedure of obtaining null-balanced vectors of phase and interfacial voltage, calculation of active and inactive instantaneous power is zero balanced mode. The simulation results obtained in the software package Matlab by the method of visual programming in Simulink.

Power oscillation analysis and control of three‐phase grid‐connected voltage source converters under unbalanced grid faults

Control of three-phase grid-connected voltage source converter under unbalanced grid faults greatly depends on the active and reactive powers processed by the converter. The instantaneous active power theory with sequence decomposition is employed to analyse the instantaneous power components, especially the second-order oscillation power. Study shows that the second-order oscillation power comprises two quadrature components, the cosine and sine terms, which are contributed by the average active power and the average reactive power, respectively. This finding sheds insight on the regulation of oscillation power under unbalanced grid conditions. Based on this observation, the authors propose a positive and negative sequence conductance and susceptance control scheme, which enables simple regulation of the active power or reactive power oscillation with the average active power and reactive power control. In addition, the authors investigate the relationship between the positive/negative sequence conductance and susceptance distribution factors with power oscillation and peak current. A maximum current limitation scheme is embedded into the current reference generation block for overcurrent protection. Numerical simulations and prototype measurements verify the accuracy of the analysis and the effectiveness of the control scheme.

Classification of short-circuit faults in high-voltage energy transmission line using energy of instantaneous active power components-based common vector approach

The majority of power system faults occur in transmission lines. The classication of these faults in power systems is an important issue. In this paper, the real parameters of a 28 km, 154 kV transmission line between Simav and Demirci in Turkey's electricity transmission network is simulated in MATLAB/Simulink. Wavelet packet transform (WPT) is applied to instantaneous voltage signals. Instantaneous active power components are obtained by multiplying instantaneous currents obtained from a voltage source side with these WPT-based voltage signal components. A new feature vector extraction scheme is employed by calculating the energies of instantaneous active power components. Constructed feature vectors are treated with a classier for short-circuit faults that occurred in high-voltage energy transmission lines; this is known as the common vector approach (CV A). This is therst implementation of CV A in the classication of short-circuit faults that occurred in high-voltage energy transmission lines. Furthermore, the same feature vector is applied to a support vector machine and articial neural network for a comparison with the CV A method regarding classication performance and testing duration issues. Additionally, a graphical user interface is designed in MATLAB/GUI. Various noise levels, source frequencies, fault distances, fault inception angles, and fault exposure durations can be investigated with this interface. Classication of short-circuit faults in high-voltage transmission line is achieved by using an offline monitoring methodology. It is concluded that a combination of the proposed feature extraction scheme with the CV A classier gives substantially high performance for the classication of short circuit faults in transmission line.

Damping interarea oscillations in power systems using finite time terminal sliding mode control of the unified power flow controller

This paper presents a new nonlinear controller for unified power flow controller (UPFC) based on the Lyapunov's finite time terminal sliding mode concept. Further instead of controlling the direct and quadrature-axis currents of the series voltage source converter (VSC), the instantaneous real-and reactive power components are used as control variables. This mode of control dispenses the unmodelled dynamics of the VSC phase-locked loop system and produces a robust control for the active-reactive power, and dc voltage excursions. Computer simulation results are obtained for a variety of operating conditions for 3-machine 6-bus power system using the finite time terminal sliding mode control and the results are compared with a standard input-output feedback linearisation approach to validate the superiority of the proposed controller.