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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 4, OCTOBER 20102851Unbalanced Model and Power-Flow Analysis ofMicrogrids and Active Distribution SystemsMohamed Zakaria Kamh, Graduate Student Member, IEEE, and Reza Iravani, Fellow, IEEEAbstract—This paper presents a three-phase power-flow algorithm, in the sequence-component frame, for the microgrid( grid) and active distribution system (ADS) applications.The developed algorithm accommodates single-phase laterals,unbalanced loads and lines, and three/four-wire distributionlines. This paper also presents steady-state sequence-componentframe models of distributed energy resource (DER) units forthe developed power-flow approach under balanced/unbalancedconditions. The DER models represent the synchronous-generatorbased and the electronically-coupled DER units. Both constantpower (PQ) and regulated-voltage (PV) modes of operation ofDER units are considered. The application of the developedpower-flow method for two study systems is presented. The studyresults are validated based on comparison with the detailed solution of the system differential equations in time domain, using thePSCAD/EMTDC software tool.Index Terms—Active distribution systems, distributed energyresources (DER), microgrids, single-phase laterals, three-phasepower flow.I. INTRODUCTIONRIVEN by environmental, economical, and technical incentives, the integration of distributed energy resources(DER) units into distribution networks close to the loads, isemerging as a complementary infrastructure to the traditionalcentral power plants [1]. A DER unit is either a distributed generation (DG) unit, a distributed storage (DS) unit, or a hybrid ofthe two [2]. Proliferation of DER units, primarily at the distribution voltage levels, has also brought about concepts of the micro[3]–[5] and the active distribution system (ADS)grid[6]–[8]. Theconcept is well defined in the technical literature. An ADS is a distribution network with arbitrary powerflow along the network feeders, where variables are measured(or estimated) and controlled by means of various devices (e.g.,DER units, on-load tap changers, and transformer), based on acentralized and intelligent system. The central control system iscapable of making decisions and operating the system based onmonitoring the network conditions [7]. The ADS ultimate goalis to allow safe penetration of DER units into the current distribution networks and maintain the system stable and reliable [8].DManuscript received July 13, 2009; revised November 13, 2009. First published April 05, 2010; current version published September 22, 2010. Paper no.TPWRD-00522-2009.The authors are with the Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON M5S 3G4, Canada (e-mail:mohamed.kamh@ieee.org; iravani@ecf.utoronto.ca).Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TPWRD.2010.2042825The first requirement for planning, operation, control,(and ADS) is theprotection, and management of theavailability of accurate power-flow analysis results. The conventional power-flow analysis methods, based on the systempositive-sequence representation, that are widely used for largepower transmission systems, are not directly applicable to theand ADS [9]. The reasons are the: relatively high degree of imbalance due to the inherent untransposed structure of three-wire and/orfour-wire three-phase power distribution lines, presence of single-phase laterals, single and two-phase loads,unbalanced three-phase loads [10], presence of three-phase and single-phase electronicallycoupled DG and DS units with various control strategiesand operational modes [11], [12], presence of different types of three-phase rotating machine-based DG units with various control strategies [13], presence of non-dispatchable DG units, for example, windand photovoltaic units [14].Moreover, the production-grade power-flow software tools,which originally have been developed for large-system, are notand ADS analysis. The reason is that theytailored for thelack the flexibility to accommodate DER models and operatingcharacteristics, particularly those of electronically-coupledDER units [15]. Another limitation is that the existing technicalliterature on the steady-state modeling of electronically-coupledDER units assumes only positive-sequence DER representationfor power-flow analysis [15]–[17].The concept of three-phase power-flow analysis has beenextensively addressed in the literature [10], [18]–[27], andthe applicable methods are classified according to the network structure and the adopted reference frame. Based on thephase-frame approach [10], [22]–[24], (i) the forward-backward sweep method [18], and (ii) the compensation method[19]–[21] have been proposed for power-flow analysis of radialfeeders and weakly meshed grids, respectively. The power-flowanalysis of the loop (ring) network structure or the generalnetwork structures are conducted based on Newton-Raphson[24]–[26] and Gauss and/or Gauss-Seidel [10], [22], [23]methods. The sequence-components frame has been usedin [25]–[27] to develop a three-phase power-flow solver forgeneral network topologies with synchronous generating units.Using the sequence-components frame in the power-flow analysis effectively reduces the problem size and the computationalburden as compared to the phase-frame approach. Moreover,due to the weak coupling between the three sequence networks,the system equations can be solved using parallel programming[26].0885-8977/ 26.00 2010 IEEE
2852IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 4, OCTOBER 2010Fig. 1. Schematic diagram of DER unit: (a) SG unit. (b) Electronically-coupledunit.Fig. 2. Generalized sequence-component frame model of DER unit forpower-flow analysis.Motivated by the aforementioned merits of the sequencecomponents for power-flow analysis, this paper developsand thea sequence-frame power-flow solver for theADS. The developed power-flow solver modifies the algorithms presented in [25] and [26] to incorporate models ofelectronically-coupled DER units that include their controlcharacteristics under balanced/unbalanced grid conditions. Inaddition, this paper exploits the concept of the coincidencefactor [28], [29] to accommodate single-phase laterals in thedeveloped sequence-frame power-flow solver. The power-flowalgorithm also accommodates (i) three-phase distribution transformers, (ii) three-phase three- and four-wire distribution lines,and (iii) three-phase (ub)balanced constant power and constantimpedance loads. The accuracy and validity of the developedpower-flow algorithm, including the DER and the single-phaselateral models, were tested on two study-systems and the resultsof several case-studies are compared with those obtained fromthe time-domain analysis in the PSCAD/EMTDC environment.II. STEADY-STATE DER MODELSThis section presents generalized sequence-component framemodels of the: three-phase, directly-interfaced, synchronous generator(SG)-based DG unit, three-phase electronically-coupled DER unit interfaced viaa three-phase, three-wire VSC. It is assumed that the VSCcontrollers tightly regulate the DC-link voltage, and thusthe primary source does not affect the steady-state modelof the unit with respect to its point of connection to the(or ADS). This, in turn, implies that in case ofhostintermittent DG units (e.g., wind and photovoltaic units),adequate storage is interfaced to the VSC dc-side to enableits operation as dispatchable DG units.The models are incorporated in the developed power-flow algorithm of Section III. Fig. 1 shows a schematic diagram of a(or ADS) at the point ofDER unit connected to the hostcommon coupling (PCC). It should be noted that the developedDER model can be enhanced to represent other types of threephase VSC-coupled DER units (e.g., the four-wire VSC-coupled DER units), the permanent-magnet synchronous generatordriven by a micro-turbine or a wind turbine, and the doubly-fedasynchronous generator.The developed model accommodates both PQ and PV modesof operation for directly-coupled and electronically-coupledDER units. Under both operating modes, the positive sequencevoltage of the PCC is used for synchronization [12]. It shouldbe noted that the PCC voltage might be contaminated withthe negative and zero sequence voltage components due to theasymmetries and imperfections in the system. This indicatesthat if the DER unit is synchronized with and controlled togenerate only positive sequence components, its current ex(or the ADS) can include negative andchange with thezero sequence components depending on the control strategy.The VSC-coupled DER units can be augmented with additionalcontrollers to mitigate the negative-sequence current and only[11]. Inexchange positive-sequence current with thesuch a case, the terminal voltage of the VSC-coupled DER unitincludes both positive and negative sequence voltage components. Thus, for both the SG and the VSC-coupled DER units,the active power output of the DER unit is determined based onthe positive sequence voltages and currents. The same conceptis also adopted for the reactive power controller when the PQoperating mode is implemented.A. Positive Sequence ModelBased on the above discussion, Fig. 2 represents the proposed generalized sequence-component frame model of boththe three-phase directly interfaced SG unit and the three-phaseVSC-coupled DER unit. The positive-sequence model of a DERunit also represents its control strategy. If the unit operates in thePV mode (Fig. 2(a)), it is modeled as an ideal voltage sourcebehind the PCC bus. Under this mode of operation, the magnitude of the positive-sequence component of the DER terminalvoltageand the corresponding injected positive-se, both in per-unit, are given byquence real power(1)(2)andare the per-unit positive-sewherequence terminal voltage and the total three-phase injectedactive power of the DER unit, respectively.If the DER unit operates in the PQ mode, its positive-sequence representation is a constant power source (or negativeconstant power load) as shown in Fig. 2(b), [30]. Thus, the posinjected by the DER unit, initive-sequence reactive powerper-unit, is(3)whereis the total three-phase reactive powerinjected by the DER unit. The factor 1/3 in (2) and (3) is usedto calculate the sequence-frame power components from their
KAMH AND IRAVANI: UNBALANCED MODEL AND POWER-FLOW ANALYSIS2853phase-frame counterparts, assuming the same base-power isused in both reference frames. Since the power and voltagesto be regulated are often (practically) those of the PCC bus,the positive sequence impedance of the unit and its terminalvoltage are not shown in Fig. 2(a) and Fig. 2(b).B. Negative and Zero Sequence ModelsDepending on the type (SG or VSC-coupled DER) and thecontrol strategy [11] of the DER unit, the negative and zero sequence current components can also be exchanged between the(ADS) and the DER unit. The proposed generalized negative and zero sequence models of the SG and the three-wireVSC-coupled DER units of Fig. 1 are shown in Fig. 2(c) and(d), respectively.1) SG Unit: For the SG unit, the zero and negative sequenceof the generalized model are [31], [32]admittances(4)whereFig. 3. Alternative VSC output filter configurations., for the filter configurations shown in Fig. 3(a) and Fig. 3(b),is calculated as(9)(10)where , , andare shown in Fig. 3.However, if the unit is controlled to inject balancedthree-phase current components [11], that is, operation basedon dq-current control strategy, then the negative sequenceadmittance of the model is(5)(11)andIn both cases, the zero sequence admittance of the three-wireVSC-coupled DER unit is(6)(12)is the direct (quadrature) unsatuwhereis the reactancerated sub-transient reactance,(resistance) between the neutral of the SG and the ground, andis the armature resistance of the SG.2) Three-Wire VSC-Coupled DER Unit: The magnitude ofthe negative sequence admittance for a three-wire VSC-coupled DER unit is determined based on the control strategy ofthe unit. If the unit is controlled only to generate positive-sequence voltage [12], then the negative sequence admittance of, isthe DER model,The negative and zero sequence admittance of each DER unit issubstituted in the corresponding bus admittance matrix.(7)is the equivalent series impedance of the VSC outputwherefilter between the PCC and the short-circuited VSC terminals.The VSC output filter is used to reduce the harmonic currentinjected in the utility system [33]. The simplest output filtertopology is a first order series-connected inductor Fig. 1(b), foris given bywhichIII. THREE-PHASE POWER-FLOW ALGORITHMThis section presents an algorithm to handle DER units andsingle-phase laterals within the sequence-frame power-flowprogram. Fig. 4 shows the flow chart of the developedpower-flow program including the proposed models of DERunits and single-phase laterals.The first step of the proposed approach is to decompose the(ADS) into a three-phase section and single-phase laterals. Then each single-phase lateral and its associated loadsare lumped and represented by a single-phase load at the nodewhere the lateral is connected to the three-phase system, usingthe concept of coincidence factor (CF) [28], [29]. Hereafter, thisnode is referred to as the “head node.” The equivalent “lumped”load of the lateral is [35](13)(8)is the VSC output filter net reactance (resiswheretance). Other output filter configurations are reported in [34].These alternative configurations lie under either one of the twotopologies shown in Fig. 3. The equivalent series impedance,whereis the number of loads on the lateral, and the coas [35]incidence factor (CF) is determined based on(14)
2854IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 4, OCTOBER 2010Fig. 5. Single line diagram of System-I.untransposed distribution power lines connected to the th bus[26]. Detailed modeling and the model integration of the threephase untransposed power lines, three-phase transformers, andthree-phase (un)balanced loads in a sequence-frame power-flowsolver are available in [25] and [26].Unlike the approach of [27] that requires executing the backward-forward sweep subroutine subsequent to each sequenceframe power-flow iteration in a coupled fashion, Fig. 4 indicatesthat the proposed approach fully decouples the two subroutinesby executing the backward/forward sweep algorithm only onceafter the final convergence of the sequence-frame power-flowalgorithm. Thus, the decoupled algorithm of Fig. 4 is expectedto substantially reduce the execution time and the computationalburden as compared to the coupled approach. This is shown inSection IV.IV. CASE STUDIES AND VALIDATIONSTo demonstrate the application of the developed power-flowmethod and validate the accuracy of the results, the power-flowalgorithm of Fig. 4 was implemented in MATLAB environmentand used to investigate two study systems with different sizesand topologies. The power system sparsity is exploited by usingthe existing MATLAB functions dedicated to solve large andsparse systems of simultaneous linear equations.A. System-IFig. 4. Flowchart of the developed three-phase power-flow algorithm.It should be noted that the coincidence factor method isnot recommended if the single-phase lateral is equipped withvoltage regulating devices or single-phase voltage-controlledDER units. However, to the best of our knowledge, the existingsingle-phase laterals (in North America) have neither of thesetwo features.is thezero- (negative)In Fig. 4,sequence injected current vector, where is the number of theis formulatedsystem buses. The th entry ofby adding the corresponding injected zero- (negative-) sequencecomponents of the loads and the compensation currents of theA single line diagram of System-I, which includes six buses,is shown in Fig. 5. The system of Fig. 5 is selected since itis adequately small to be modeled in detail in a time-domainsimulation tool, and thus the results can be used for verification of the developed DER models and the sequence-framepower-flow part of the algorithm of Fig. 4. System-I reprewhen switch SW issents an autonomous (islanded)open and the system can be effectively reduced to a five-bussystem. This scenario is considered in this work. The systemincludes untransposed lines, unbalanced loads, and distributiontransformers. The system also includes a three-phase shuntcapacitance compensator which is modeled as a three-phaseconstant impedance [25]. To present a more realistic scenarioapplications, the base power is selected at 1 MVAfor theinstead of 33.33 MVA as specified in [25]. The original systemparameters are given in [25].To validate the power-flow results obtained from the algorithm of Fig. 4 and the developed DER models of Fig. 2, a detailed time-domain model of System-I, in the PSCAD/EMTDC
KAMH AND IRAVANI: UNBALANCED MODEL AND POWER-FLOW ANALYSIS2855TABLE IRESULTS OF CASE 1 OF SYSTEM-I. A:PSCAD/EMTDC RESULTS, B: DEVELOPED SOFTWARE RESULTSTABLE IIRESULTS OF CASE 2 OF SYSTEM-I. A: PSCAD/EMTDC RESULTS, B: DEVELOPED SOFTWARE RESULTSTABLE IIIRESULTS OF CASE 3 OF SYSTEM-I. A: PSCAD/EMTDC RESULTS, B: DEVELOPED SOFTWARE RESULTSTABLE IVRESULTS OF CASE-4 OF SYSTEM-I. A: PSCAD/EMTDC RESULTS, B: DEVELOPED SOFTWARE RESULTSenvironment, is also developed. G1 is the slack-bus, and is modeled as an ideal voltage source behind an impedance. It shouldbe noted that in order to handle the active and reactive power, the distributedlimits of the slack bus in an islandedslack bus concept is potentially and advantageous alternative,although it has not been exploited in this work. The load atBus-3 is represented as a constant-power, star-connected load.Corresponding to the following four case studies, G2 representseither of the following DER units:Case 1) An SG unit equipped with voltage regulator and active power controller (an SG operating in the PVmode).Case 2) A voltage-controlled three-wire VSC-coupledDER unit equipped with voltage regulator andactive power controllers (a three-phase three-wireVSC-coupled DER unit operating in the PV mode).Case 3) An SG unit with active and reactive power control(an SG in the PQ mode of operation).Case 4) A current-controlled three-wire VSC-coupled DERunit equipped with the -current controllers [12](a three-phase three-wire VSC-coupled DER unitoperating in the PQ mode).For the first two cases, the voltage controller of the DER unitadjusts the positive sequence voltage component of Bus-4 at1.05 p.u. For the last two cases, the DER unit is controlled toinject 1 p.u. active power at unity power-factor. The study results are summarized in Tables I–IV.Tables I and II show that the magnitude of the phase-voltages of Bus-4 is not 1.05 p.u. However, the positive-sequencevoltage component is successfully regulated at 1.05 p.u. as required. This validates the PV model representation for both theSG and the three-wire VSC-coupled DER units. Moreover, thepositive-sequence components of the bus-voltages, given in Tables III and IV, and the system parameters, given in [25], areused to evaluate the positive-sequence active and reactive powercomponents injected by G2 at Bus-4. The power injected by G2
2856IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 4, OCTOBER 2010Fig. 6. Single-line diagram of System-II [35]. (a) Three-phase part ofSystem-II. (b) Single-phase subnetwork of System-II.is calculated to be 1.0 p.u. active power at unity power-factor, asspecified. This validates the PQ model representation for boththe SG and the three-wire VSC-coupled DER units.The maximum magnitude error for the five busses, in all fourcase studies, is less than 0.3%. The maximum phase error doesnot exceed 0.5%. The good agreement between the results of thetwo solvers indicates that the proposed steady-state DER modelsand the sequence-frame power-flow approach
pled DER units), the permanent-magnet synchronous generator driven by a micro-turbine or a wind turbine, and the doubly-fed asynchronous generator. The developed model accommodates both PQ and PV modes of operation for directly-coupled and electronically-coupled DER
IEEE 3 Park Avenue New York, NY 10016-5997 USA 28 December 2012 IEEE Power and Energy Society IEEE Std 81 -2012 (Revision of IEEE Std 81-1983) Authorized licensed use limited to: Australian National University. Downloaded on July 27,2018 at 14:57:43 UTC from IEEE Xplore. Restrictions apply.File Size: 2MBPage Count: 86Explore furtherIEEE 81-2012 - IEEE Guide for Measuring Earth Resistivity .standards.ieee.org81-2012 - IEEE Guide for Measuring Earth Resistivity .ieeexplore.ieee.orgAn Overview Of The IEEE Standard 81 Fall-Of-Potential .www.agiusa.com(PDF) IEEE Std 80-2000 IEEE Guide for Safety in AC .www.academia.eduTesting and Evaluation of Grounding . - IEEE Web Hostingwww.ewh.ieee.orgRecommended to you b
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