Unbalanced Three-phase Systems Research Articles

Modeling and analysis of unbalanced distribution system using object-oriented methodology

An object-oriented (OO) model for three-phase unbalanced distribution system is proposed and implemented. Single-phase system components are initially modeled using object-oriented methodology. Later, it is extended to unbalanced three-phase distribution system using the “composition” technique of object-oriented design. The main features of object-oriented methodology such as “inheritance”, “aggregation”, “association” and “polymorphism” have been exploited to obtain a better software model. Three-phase distribution load flow analysis and short circuit analysis modules have been developed using the proposed object model. The performance of the developed software has been tested on IEEE 13-Node, IEEE 34-Node and IEEE 123-Node distribution systems.

Object Modeling of Balanced and Unbalanced Distribution Systems for Power Flow Analysis

Most of the distribution systems are usually unbalanced and radial or near radial (weakly meshed). Presently, the integration of dispersed generations with the distribution system is becoming more popular. This article proposes a new object-oriented software modeling for distribution system power flow analysis. Object-oriented design of radial distribution system, assuming balanced operation, is obtained. Extensibility property of the object-oriented design is exploited to extend the radial system model to weakly meshed system and to incorporate the dispersed generations. The “composition” technique of object-oriented design has been employed to model the unbalanced three-phase system using the objects of balanced system. The modeled objects are implemented in C++ and the robustness of the developed power flow program has been tested for various balanced (10-bus, 33-bus, 69-bus, IEEE 37-bus) and unbalanced (IEEE 13-bus, IEEE 34-bus, IEEE 123-bus) test systems.

Continuation Three-Phase Power Flow: A Tool for Voltage Stability Analysis of Unbalanced Three-Phase Power Systems

In this paper, a continuation three-phase power flow (CTPFlow) approach in polar coordinates, which can be used to analyze voltage stability of unbalanced three-phase power systems, is proposed. Using CTPFlow, the PV curves of unbalanced three-phase power systems can be obtained. It is found that the patterns of the PV Curves of unbalanced three-phase power systems are quite different from that of balanced three-phase power systems or positive-sequence power systems. The investigations indicate that a CTPFlow is needed where there are unbalanced network or loads existing in a system. Numerical examples are given to illustrate the approach.

Modelling of Power Components in Non-sinusoidal Power Systems Using Hilbert Transform

AbstractThis article presents a Hilbert transform-based approach of power components definition in non-sinusoidal power systems. Instantaneous phasors of current and voltage, apparent power, and power factor are also defined. The proposed Hilbert transform-based method is applicable to sinusoidal or non-sinusoidal, single-phase systems as well as balanced and unbalanced three-phase systems. The method is also applicable in the presence of interharmonics. The properties and physical meanings of defined power-related quantities are discussed in detail. The presented method leads to the formulas used in the conventional RMS concept method. Study cases of power systems at different loads are examined to test the validity and practicability of the proposed approach.

Modelling of Power Components in Non-Sinusoidal Power Systems Using Hilbert Transform

This article presents a Hilbert transform-based approach of power components definition in non-sinusoidal power systems. Instantaneous phasors of current and voltage, apparent power, and power factor are also defined. The proposed Hilbert transform-based method is applicable to sinusoidal or non-sinusoidal, single-phase systems as well as balanced and unbalanced three-phase systems. The method is also applicable in the presence of interharmonics. The properties and physical meanings of defined power-related quantities are discussed in detail. The presented method leads to the formulas used in the conventional RMS concept method. Study cases of power systems at different loads are examined to test the validity and practicability of the proposed approach.

Two digital filtering algorithms for fast estimation of symmetrical components in a power system: a static estimation approach

This paper presents the application of two digital filters working together for fast estimation of power systems symmetrical components. The three-phase unbalanced system is transformed to two phases using α–β-transformation. Using such a transformation, harmonics of order 3 and their multiples, in the input signal, are suppressed. Having identified the two-phase voltages, the positive and negative sequence phase voltage can be calculated using a constant transformation matrix. The zero sequence component is easily estimated by averaging the unbalanced three-phase voltage at every sample instant. Least error square algorithm is used to identify the magnitude and phase angle of sequence components from the available samples of the specified component.

An algorithm for estimating fault location in an unbalanced three-phase power system

A new algorithm for estimating fault location on a transmission line, as well as the fault type, is studied and tested using simulation data obtained from the Electromagnetic Transient Program (EMTP). The proposed algorithm is based on the least absolute value estimation approach (LAV), and uses digitized samples of post-fault voltage and current waveforms at the relay locations. The proposed algorithm is applied to two different models of the transmission line. The first model is a three phase long transmission line, while the second model is a three phase three terminals transmission line. The measurements taken at the relay location do not need to be synchronized. Effects of critical parameters on the behavior of the proposed algorithm and on the estimated fault location are examined. A computational comparison between the proposed algorithm and the least errors square (LES) is presented in the paper.

A new approach to an individual‐phase reactive power compensator for nonsinusoidal and unbalanced three‐phase systems

AbstractMany researchers have attempted to clarify the definitions of active power, reactive power, active current, reactive current, etc. for unbalanced and nonsinusoidal three‐phase situations. The so‐called pq theory has given a new definition of instantaneous reactive power, and it has been discussed and developed by many authors. In this paper, the merits and demerits of the instantaneous reactive power compensator are discussed. It is shown theoretically that applying instantaneous reactive power compensation to unbalanced three‐phase systems has a serious disadvantage in that it causes third‐order harmonic currents on the source side, which problem cannot be avoided. To overcome this problem the authors propose a new approach, and name it the “quasi‐instantaneous” reactive power compensator. It compensates individual‐phase reactive currents. The basic principles of the quasi‐instantaneous reactive current compensator are discussed in detail, and its validity is confirmed using digital simulation. In particular the authors show that the power factor of each phase becomes unity on the source side, but the source currents remain unbalanced when the proposed method is applied. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 139(3): 73–81, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.1162

Current control of unbalanced electrical systems

The vector modeling approach is employed to describe the behavior of unbalanced three-phase (three-wire), unbalanced two-phase and single-phase systems. In the case of single-phase systems, a fictitious circuit is introduced in order to create the vector model. Continuous-time and discrete-time current controllers based on the vector approach are presented. The current control scheme is based on two controllers, one for the positive sequence and another for the negative sequence. The controllers are implemented in the synchronous reference frame and in the stationary reference frame. In the stationary reference frame, the use of the same integral gains for both controllers simplifies the equations of the control law especially for single-phase systems. Simulation and experimental results obtained with a pulsewidth modulation voltage-source inverter supplying unbalanced systems are presented.

A New Approach to Individual-Phase Reactive Power Compensator for Non-Sinusoidal and Unbalanced Three-Phase Systems

Many researchers have attempted to clarify the definitions of active power, reactive power, active current, reactive current, etc. for unbalanced and non-sinusoidal three-phase situations. The so-called pq theory has given a new definition of instantaneous reactive power, and it has been discussed and developed by many authors. In this paper, the merits and demerits of the instantaneous reactive power compensator are discussed. It is shown theoretically that applying instantaneous reactive power compensation to unbalanced three-phase systems has a serious disadvantage in that it causes third-order harmonic currents on the source side, which problem cannot be avoided. To overcome this problem the authors propose a new approach, and name it the “quasi-instantaneous” reactive power compensator. It compensates individual-phase reactive currents. The basic principles of the quasi-instantaneous reactive current compensator are discussed in detail, and its validity is confirmed using digital simulation. In particular the authors show that the power factor of each phase becomes unity on the source side, but the source currents remain unbalanced when the proposed method is applied.

Modeling and control of unbalanced three-phase systems containing PWM converters

This paper proposes two complex vector models to characterize unbalanced three-phase four-wire systems that contain pulsewidth-modulated voltage-source converters (PWM-VSCs). In the first case, the three-phase system is decomposed in orthogonal odq components. A complex vector model is then built from the dq and o components. In the second case, a complex vector model is introduced by decomposing the system in three single-phase systems. In both cases, an orthogonal, fictitious circuit is introduced to handle a single-phase system, such as the homopolar system or each one of the three single-phase systems that compose a three-phase four-wire system. From the vector models, two digital controllers, which employ two different reference frames, are proposed. Also, the use of the same gains for both controllers simplifies the equations of the controller in the stationary reference frame. As an example, current control in a PWM-VSC system is presented.

Automated system for measuring electrical three-phase power components

This paper describes an automated system, using the software LabVIEW and an experimental setup including a digital oscilloscope equipped with general purpose interface bus (GPIB) interface, to measure the instantaneous and average power components of generic three-phase electrical systems. The system is being used as an academic laboratory tool for teaching concepts on generic three-phase electrical power systems to third-year electrical engineering students. The method is based on a generalized instantaneous power theory and can be applied to balanced or unbalanced three-phase power systems feeding linear or nonlinear loads. Details of the methodology, comprising acquisition, and signal processing are presented. Examples of three-phase balanced and unbalanced power system measurements are displayed.

Three-phase power flow calculations using the current injection method

This paper presents a new sparse formulation for the solution of unbalanced three-phase power systems using the Newton-Raphson method. The three-phase current injection equations are written in rectangular coordinates resulting in an order 6n system of equations. The Jacobian matrix is composed of 6/spl times/6 block matrices and retains the same structure as the nodal admittance matrix. Practical distribution systems were used to test the method and to compare its robustness with that of the backward/forward sweep method.

Analysis of the current distortion factor of a three-phase, three-wire system

In a balanced three-phase system, the three-phase current distortion factor of three-phase ac power sources has been expressed by applying the conventional single-phase current distortion factor, which is defined for a single-phase system. However, in an unbalanced three-phase system, it is difficult to express the three-phase current distortion factor for distorted three-phase ac currents by means of the conventional single-phase current distortion factor. For instance, the conventional current distortion factors for three-phase ac currents are usually different from each other in the unbalanced three-phase system. To solve the above problem, this paper proposes a novel definition of the three-phase current distortion factor. The proposed three-phase current distortion factor is quite effective for the unbalanced three-phase system as well as the balanced three-phase system. © 2000 Scripta Technica, Electr Eng Jpn, 131(4): 1–10, 2000

A novel approach to the design of a shunt active filter for an unbalanced three-phase four-wire system under nonsinusoidal conditions

A new approach is presented for the design of a shunt active filter in a three-phase, four-wire distribution system with unbalanced, distorted sources and unbalanced loads. The purpose of the shunt active filter is to provide compensation currents such that the source needs to supply balanced (positive-sequence) fundamental source current at unity power factor even though the load consumes harmonic currents as well as positive, negative, and zero-sequence currents. A major feature of the proposed approach is that it does not require symmetrical component transformation to transform the three-phase voltages and currents to /spl alpha/-/spl beta/-o quantities. This makes practical implementation of the proposed method easier than the symmetrical component transformation approach. In addition, the power factor of the positive-sequence fundamental component is close to unity and only positive-sequence power is supplied by the source. The effectiveness of the proposed control algorithm is demonstrated by computer simulation and experimental results of a shunt active filter for a three-phase four-wire distribution system with distorted, unbalanced source voltages and unbalanced loads.

Reactive power compensation and load balancing for unbalanced three-phase four-wire system by a combined system of an SVC and a series active filter

A combined reactive power compensation method of a static VAr compensator (SVC) and a series active filter is described for unbalanced three-phase four-wire distribution feeders with harmonic distortion. The SVC which consists of Δ-connected thyristor-controlled reactors, Y-connected thyristor-controlled reactors and passive filters, acts as a classic reactive power compensator for load balancing and power factor correction. The small rating active filter is used to improve the filtering characteristics of the passive filter in the SVC and suppress possible resonance between the system impedance and the passive filter. Simulation results performed by the electromagnetic transients program show that the proposed reactive power compensation configurations can effectively balance currents, correct power factor and eliminate harmonic currents.

Harmonic and reactive power compensation based on the generalized instantaneous reactive power theory for three-phase four-wire systems

This paper presents harmonic and reactive power compensation based on a generalized theory of instantaneous reactive power for three-phase power systems. This new theory gives a generalized definition of instantaneous reactive power, which is valid for sinusoidal or nonsinusoidal and balanced or unbalanced three-phase power systems with or without zero-sequence currents and/or voltages. The properties and physical meanings of the newly defined instantaneous reactive power are discussed in detail. A harmonic and reactive power compensator based on the new theory for a three-phase harmonic-distorted power system with zero-sequence components in the load current and/or source voltage is then used as an example to show harmonic and reactive power measurement and compensation using the new theory. Simulation and experimental results are presented.

96/05019 An active filter for an unbalanced three-phase system using the synchronous detection method

96/05019 An active filter for an unbalanced three-phase system using the synchronous detection method

Application of Kalman filtering for online estimation of symmetrical components for power system protection

This paper presents a new model that enables linear Kalman filtering (KF) to be applied for the direct estimation of symmetrical components in unbalanced three-phase systems. Computational experiments implementing KF using both synthetic and actual data sets are reported. It is shown that Kalman filtering models are well suited for symmetrical component estimation online. The effects of sampling rate, data window size and frequency drift on the optimal estimates are also studied.

Identification and tracking of harmonic sources in a power system using a Kalman filter

In this paper, two problems have been addressed on harmonic sources identification: the optimal locations of a limited number of harmonic meters and the optimal dynamic estimates of harmonic source locations and their injections in unbalanced three-phase power systems. Kalman filtering is used to solve these problems. System error covariance analysis by the Kalman filter associated with a harmonic injection estimate determines the optimal arrangement of limited harmonic meters. Based on the optimally-arranged harmonic metering locations, the Kalman filter then yields the optimal dynamic estimates of harmonic injections with a few noisy harmonic measurements. The method is dynamic and has the capability of identifying, analyzing and tracking each harmonic injection at all buses in unbalanced three-phase power systems. Actual recorded harmonic measurements and simulated data in a power distribution system are provided to prove the efficiency of this approach.