VOLTAGE UNBALANCE IN LOW VOLTAGE DISTRIBUTION NETWORKSVin - PDF document

VOLTAGE UNBALANCE IN LOW VOLTAGE DISTRIBUTION NETWORKSVinícius Santos Valois – COPEL – Companhia Paranaense de Energia, BrazilCarlos Márcio Vieira Tahan – University of São Paulo, BrazilNelson Kagan – University of São Paulo, BrazilHector Arango – EFEI – Federal School of Engineering at Itajuba, BrazilSUMMARYThis paper presents a methodology formeasuring, monitoring and controllingvoltage unbalance in electrical powerdistribution networks. The distribution ofsingle-phase and double-phase loadsalong the network and their randominstant demand values can be consideredas the main causes to voltage unbalancein three-phase distribution systems.The work considers voltage unbalancemeasurements carried out in a Braziliandistribution company located in the Stateof Paraná, namely COPEL – CompanhiaParanaense de Energia.Since voltage unbalance gradually affectsequipment, this disturbance should bedealt with by statistical analysis.Regarding voltage regulation and voltageunbalance, a world-wide tendency is toconsider their monitoring and measuringon 10 minute intervals along a 1 weekstudying the opportunity of usingdigital simulations for the analysis ofvoltage unbalance disturbances;comparing field measurements andresults from simulations;proposing preliminary standardsregarding voltage unbalance to beapplied in low and medium voltagedistribution systems in Brazil. VOLTAGE UNBALANCE IN LOW VOLTAGE DISTRIBUTION NETWORKSPaulo Vinícius Santos Valois – COPEL – Companhia Paranaense de Energia, BrazilCarlos Márcio Vieira Tahan – University of São Paulo, BrazilNelson Kagan – University of São Paulo, BrazilHector Arango – EFEI – Federal School of Engineering at Itajuba, BrazilINTRODUCTIONThere has been a growing concern to supply power tocustomers mainly when their processes are based onsusceptible loads. In such scenario power qualitybecomes extremely relevant. Reliability indices andvoltage levels, for instance, are parameters much moreregulated now. Other power quality phenomena are alsobeing taken care of in much more detail, such as voltagesags, harmonic distortion, voltage and current unbalanceand so forth.This paper presents a methodology for measuring,monitoring and controlling voltage unbalance inelectrical power distribution networks. The distributionof single-phase and double-phase loads along thenetwork and their random instant demand values can beconsidered as the main causes to voltage unbalance inthree-phase distribution systems.Contrary to some other disturbances in electrical powersystems, for which the performance is evident for theordinary customer, voltage unbalance belongs to thosedisturbances in which their perceptible effects areproduced in the long run.Voltage unbalance leads to a sharp decrease on theefficiency of three-phase induction motors. In Brazil,50% of the electric energy is absorbed by industrialcustomers. Since induction motors represent the largestportion of industrial loads, it is seen that the voltageunbalance should be carefully studied and controlled.This work considers voltage unbalance measurementscarried out in a Brazilian distribution company locatedin the State of Paraná, namely COPEL – CompanhiaParanaense de Energia.Since voltage unbalance gradually affects equipment,this disturbance should be dealt with by statisticalanalysis. Regarding voltage regulation and voltageunbalance, a world-wide tendency is to consider theirmonitoring and measuring on 10 minute intervals alonga 1 week period.OBJECTIVESThe main objectives of this paper are as follows:to study the opportunity of using digital simulationsfor the analysis of voltage unbalance disturbances;to compare field measurements and results fromsimulations;to propose preliminary standards regarding voltageunbalance to be applied in low and medium voltagedistribution systems in Brazil.BASIC CONCEPTSVoltage unbalance in three-phase distribution systemsregards the changing in phase angles and/or in themagnitude of voltage phasors. The main causes leadingto voltage unbalance are the following ones.Unsymmetrical distribution systems, that isequipment and phase conductors present differentimpedance values.Unsymmetrical loads, such as arc furnaces, singleand double phase loads;Different voltage drops due to differences in mutualimpedances between phase conductors and betweenphase conductors and ground. This depends on thespatial configuration of conductors.Low voltage distribution networks – the main focus ofthis paper – introduce a small amount of voltageunbalances due to their impedances. The main cause canbe considered as the current unbalance, due to thedistribution of single-phase and double-phase loadsalong the network, such as public lighting andresidences.COMPUTING THE VOLTAGE UNBALANCEINDEXThe voltage unbalance index is generally related to thenegative symmetrical component system. This is due tothe large number of pieces of equipment that have theirefficiency and life affected, mainly the ones likegenerators and motors (based on rotating magneticfields), where the major part of electrical energy istransformed.Phase-to-phase and phase-to-ground voltage unbalanceindices () are equal and given by the followingequation: where are positive and negative sequencephase-to-ground voltages and are positiveand negative sequence phase-to-phase voltages. Equation (1) allows for the computation of voltageunbalance in a system by using phase-to-phase voltagesonly. Such computation is carried out by utilisingvoltage magnitude only whereas methods based onphase-to-ground voltages require the magnitude andphase angles. However such method demands lots ofarithmetic operations. The CIGRÉ method was chosento be used, since it is derived from the CO-SENOSmethod, that keeps the accuracy. The voltage unbalanceindex can be readily determined by the followingequation: (2)where: A variant of the above method is here named CIGRÉ-2and is based on the relative deviations in phase-to-phasevoltage magnitudes d d and d , with respect theaverage value , given by: where: MABABVVV-=d MBCBCVVV-=d, and Equation 3 is a simpler calculation method as comparedto equation 2, though there is a slight loss in accuracy.ALLOWED VOLTAGE UNBALANCE INDICESBrazilian standards do not establish limits for voltageunbalance indices as yet. There are some references tothose indices in norms that regulate equipment tests andstandards [7] [8]. Table 1 shows a comparative figure ofadopted limits in world-wide standards.Table 1 – Voltage unbalance limitsVoltage UnbalanceImmunity LevelsCompatibility Level(95% probabilityof not exceeding theamount) StandardsNormalconditionMajority ofsingle anddouble phaseloadsSamplingPeriod EN501602 %3 %10 min1 week NRS-0482 %3 %10 min1 week(*) (*) this standard considers the maximum daily voltage unbalance index INFLUENCE OF NETWORK IMPEDANCES ONVOLTAGE UNBALANCENetworks can contribute on voltage unbalance due tothe unsymmetrical spatial configuration of conductors.This leads to different phase voltage drops due todifferent mutual impedances. In order to evaluate thiseffect on the voltage unbalance, a number ofsimulations were carried out on low voltage networks.Voltage drops due to mutual inductances areproportional to the flowing electric current and to theconductor length. Thus, a typical distribution networkbranch was assumed to have the current fixed by themaximum allowed voltage drop. In order to ensure thecurrent balance, a three-phase balanced resistive loadwas considered to be installed in the receiving bus. Twodifferent conductor configurations were considered inthe simulations, as shown in figure 1. vertical configurationtriangle configuration (A, B and C are phase conductors and N is the ground conductor)Fig. 1 – Conductor configurationsTable 2 presents the computed voltage values and thecorresponding voltage unbalance indices () alongthe branch, for different distances () from the source.Table 2 – Voltage unbalance due to different conductorconfigurationsVertical ConfigurationTriangle configuration(b) VabVbcD%VabVbc 100219.10219.10219.100.00219.09219.09219.090.00 150211.14212.53211.800.38211.75211.75211.750.00 180206.45208.68207.540.62207.47207.47207.470.00 200203.36206.15204.760.79204.67204.67204.670.00 Results shown in Table 2 confirm the small influencefrom conductor configuration on the voltage unbalanceindices.PROBABILISTIC COMPUTATIONAL MODELTO EVALUATE VOLTAGE UNBALANCEA computational model was developed to evaluatevoltage unbalance indices in electrical powerdistribution networks. The model considers a three- phase representation of the network, taking into accountmedium and low voltage network branches as well asdistribution transformers (three-phase transformers orbank of single-phase transformers), capacitor banks, etc.The load flow method is carried out as many times asnecessary following a Monte Carlo method thatrandomly generates scenarios in a given instant alongthe load daily curve.Load modelling to support such simulations is the resultof an extended load demand measurement campaigncarried out in the 90´s to stratify all customersconnected to distribution networks in Brazil. Thismethod classifies residential customers according todifferent ranges for monthly consumed energy andcommercial and industrial customers according to theiractivities. Other load categories were also considered,such as public lighting. Each customer is modelled byits corresponding typical daily load curve. For every 15minute intervals the probability distribution curve isgiven to be used by the Monte Carlo simulation method.Figure 2 illustrates a typical probability distribution forthe demand in residential customers during the peakload period (from 8 to 9 pm). Consumo 200-400kWh hora {20,20:15,20:30,20:45}0.20.40.60.80.3750.751.1251.52.14210.71d(t)/dmedfreqüênciaFig.2 Probability distribution (density and cumulative)curves for residential customers, monthly energyranging from 200 to 400kWhMEASUREMENT RESULTSSince there are too many low voltage networks in thedistribution company, network selection criteria to carryout measurements were adopted. A criterion was chosento select those networks more likely to have voltageunbalance, such the ones having predominantly single-phase and double-phase loads, having highertransformer loading, voltage drop and dispersion ofloads along the network. The selected networks weresubmitted to simulations by using the developedsoftware and to measurement in the field during oneweek and demand values stored on 15 second intervals.A low cost electronic meter was used to monitor lowand medium voltage networks.Table 3 shows a compilation of the main networkcharacteristics taken from COPEL´s data base. The tablealso presents the number and monthly energy ofresidential (R), commercial (C) and industrial (I)customers as well as total (T) figures. Table 4 shows themost relevant voltage unbalance results obtained fromthe measurements.Table 3 – Characteristics of the selected low voltagenetworksCUSTOMERS CaseNetw.Transf.LNumber ofcustomersMonthly energy (kWh) #Code(kVA)(m)RCITRCIT 1C014875,0781126040313325314263668728637 2C095045,0401550055125250012525 3C099445,0399710203761265971967414052 4C131775,0518106030010916145810016955 5C380745,048797040101162292179018408 6C421145,03826902071105322241012773 7C483575,06949901031032091918056321662 8C497475,064211802012020722554021276 9C517445,0394260032995830136910952 10C621245,0485720072124660012466 11C9079112,53123507034570383152323813428 12C4617112,5582681604881450218584429837384 Table 4 – Results from field measurementsVoltage Unbalance Index(%)Probability of VoltageUnbalance CaseNetMax. Value95% Value #CodeInst.AverageInst.AverageInst.AverageInst.Average 1C01483.72.61.71.497.6499.2199.82- 2C09505.53.42.22.092.8595.8499.0599.70 3C09942.91.91.30.999.07--- 4C13174.53.52.52.483.2685.8798.7499.50 5C38073.52.11.51.198.9899.8899.96- 6C42114.13.01.81.797.6298.9199.87100.00 7C48353.92.81.71.598.0899.7099.94- 8C49744.32.81.81.596.6298.5899.55- 9C51743.02.21.41.399.3899.80100.0- 10C62123.92.51.41.199.2899.8099.95- Extreme (*)5.503.502.502.4083.2685.8798.7499.50 (*): maximum voltage unbalance indices and minimum probabilities Results obtained in table 4 lead to the followingpreliminary conclusions:All low voltage networks meet the criterion that95% of the measured voltage unbalance indices areless than or equal to 3%;Only two low voltage networks do not meet thecriterion that 95% of the measured voltageunbalance indices are less than or equal to 2%;Maximum instantaneous voltage unbalance indicesare less than 5.5%;Such results are a consequence of good networkmanagement procedures. EVALUATION OF VOLTAGE DROPS BYMEASUREMENT AND BY THE DISTRIBUTIONNETWORK MANAGEMENT SYSTEMThe existing distribution management system running atCOPEL does not determine voltage unbalance indices.It only provides the distribution of total power flows ineach of the three phases of the transformer, estimatedfrom the billed customer energy values.However, the system provides the minimum voltagelevel in the distribution network, by considering thenominal voltage (220V) in the low voltage transformerbus. The voltage drops are evaluated at each branch, asa function of load demands and cable characteristics,what leads to the determination of the maximumnetwork voltage drop.Table 5 shows voltage drop values () determined bythe distribution management system and obtained fromthe field measurements. The latter are the voltage dropvalues considering probability lower than 3%.Table 5 – Voltage drop values (measurement anddistribution management system)Network ManagementSystemMeasurement CaseNetCodeV (volt)V (volt) IdealActualIdealActualVabVbcVca 1C01486.6910.05205.28197.89209.00209.00208.00 2C09506.168.81206.45200.62210.00209.00206.00 3C09943.327.74212.70202.97206.00207.00207.00 4C13173.9310.64211.35196.59218.00212.00212.00 5C38074.708.50209.66201.30205.00205.00205.00 6C42112.206.13215.16206.51216.00212.00212.00 7C48356.248.41206.27201.50207.00205.00205.00 8C49746.919.87204.80198.29203.00201.00200.00 9C51745.318.42208.32201.48211.00209.00209.00 10C62123.8110.47211.62196.97214.00215.00213.00 It is seen that the network management system providesmore conservative results, mainly for the values withprobability lower than 3%.Taking case #1, for instance, there was a 199Vinstantaneous registered value, closer to the oneevaluated by the network management system. Howeversuch value does not affect negatively customerequipment due to its low probability (0.0025%). In suchlocation, a 206.5V voltage level corresponds to the 1%probability whereas 208.5V corresponds to 3%probability.VOLTAGE UNBALANCE INDICES USING THEMONTE CARLO SIMULATION METHODTable 6 compares the maximum voltage unbalanceindices obtained from simulation and frommeasurement.By analysing the maximum values of voltage unbalanceindices shown in table 6, one sees that the simulationmethod is rather more conservative. However oneshould not discard such simulations from a networkmanagement system. The main causes for suchdifferences can be explained by the methodologyadopted, where 500 possible load unbalance scenarioswere analysed for each selected instant in the dailycurve. Such a high number of network conditions leadsto the evaluation of extreme cases and thus leading tomore conservative results. Also, while loads weremodelled by 15 minute measurements, simulations wereconsidered in 3 hour intervalsTable 6 – Maximum voltage unbalance indicesNetworkSimulationInstantaneousMeasurement 1C01485.873.7 2C09506.435.5 3C09947.652.9 4C13175.274.5 5C38078.103.5 6C42114.834.1 7C48359.053.9 8C49747.874.3 9C51745.633.0 10C62128.583.9 It is seen however that such discrepancies arediminished when analysing probabilistic results. Figure3 shows results for case #1.Table 7 shows probabilities associated to voltageunbalance indices lower than 2% and 3%, obtained frommeasurements and simulations.If one considers the criterion of 95% of monitoredvalues not exceeding 3%, measurement and simulationsfor cases shown in table 7 lead to the same conclusions.When adopting the 2% limit, more conservative resultswhere obtained when using the simulation method, whatis adequate for network management systems.Table 7 – Probabilistic results – measurements andsimulations (probability of voltage unbalance)MeasurementSimulations CaseNet #CodeInst.AverageInst.Average 1C014897.6499.2199.82-96.0098.00 2C095092.8595.8499.0599.7097.0099.00 3C099499.07---95.00- 4C131783.2685.8798.7499.5096.0098.00 5C380798.9899.8899.96-95.0097.00 6C421197.6298.9199.87100.0094.9097.00 7C483598.0899.7099.94-94.0097.00 8C497496.6298.5899.55-94.0097.00 9C517499.3899.80100.00-98.0099.50 10C621299.2899.8099.95-89.5095.80 Fig. 3 – Simulation and field measurement results Simulations Instantaneous Average Volta g e Unbalance Index (%) Fre q uenc y (%)CONCLUSIONSVoltage unbalance indices determined in fieldmeasurements are considered to be low, possibly dueto network management procedures adopted in thecompany. In such procedures, load current unbalanceare avoided by an appropriate distribution of single-phase and double-phase customers along thedistribution network. Simulation results were validatedmainly when considering that 95% of the time thevoltage unbalance index is inferior to 3%. Theprobabilistic method should therefore be incorporatedinto the company´s network management system. Lowcost measurement instruments were shown to beeffective enough for monitoring voltage unbalanceindices. Although results point out that simulationshould be included in the distribution managementsystem, when considering the 96 simulations (oneevery 15 minute period) throughout a daily cycle (24h)and the large number of low voltage distributionnetworks (COPEL has approximately 250,000distribution transformers), the computation time couldrestrict the application of the method. A veryinteresting approach would be to consider techniquesbased on Artificial Neural Networks (ANN). In suchapproach, the procedure is divided into two phases:training and application. The training phase is based onthe data base for load curves and customers connectedto the system, on simulations and on measurementcampaigns. The voltage unbalance indices would bestored for each type of distribution network, where thetype would be defined by given attributes such as loadbalance amongst phases, network length, cablecharacteristics, voltage drops, number of customers ineach category, monthly energy, etc.. In the followingphase, having known the network attributes andcorresponding loads, the software would be able toestimate the resulting voltage unbalance index. Asimilar procedure was successfully applied to adistribution transformer loading management system[9] [10].REFERENCESESBrazilian legislation (DNAEE 46 and 47). 197878CIGRÉ A new simple and effective approximateformulation for the determination of three-phaseunbalances by the voltmeter method. Belgique,CIGRÉ, 1986, 1986NEMA Standards Publication n. MG-1-19877BERNDT, M. M.; SCHMITZ, N. L. Derating ofPolyphase induction motors operated with unbalancedline voltages.s.W. EDWARD REID, O. Power quality issues –standards and guidelines. IEEE Transactions onIndustry Applications. V.32, n.3, p.625-632,May/June. 1996..EUROPEAN STANDARD– EN50160. Voltagecharacteristics of electricity supplied by publicdistribution systems. Brussels, CENELEC, 1994..NRS 048-1:1996 ELECTRICITY SUPPLY –QUALITY OF SUPPLY Overview of implementationof standards and procedures. South Africa. 1996..EUROPEAN COMMITTEE FORELECTROTECHNICAL STANDARDIZATION –CENELEC Voltage caracteristics of ElectricitySupplied by Public Distribution systems.s.J. A JARDINI; H. P. SCHMIDT Seleção eclassificação de transformadores de distribuiçãoutilizando redes neurais. Internal Report – Departmentof Electrical Engineering – University of São Paulo.o.J. A JARDINI; H. P. SCHMIDT S. U. AHN C. M. V.TAHAN C. C. B. OLIVEIRA “DistributionTransformer Loss of Life Evaluation: A NovelApproach Based on Daily Load Profiles” a serpublicado no PES Transaction (paper 99WM 402 ).