This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. Copyright @ 2003 IEEEThe use of terminal shunt capacitance has different effects on the displacement factor and distortion factor components of the power factor. These effects are considered for nonlinear loads with ideal supply, and also where the supply impedance exists but is small compared with the load impedance. Optimization of the displacement factor is found to result in reduction of the distortion factor to a minimum value

A. El-Zahab

A.F. Zobaa

A.M. Ibrahim

E. El-Din

M.M. Abdel Aziz

IEEE Transactions on Power Delivery

English

Aziz, MMA

El-Zahab, EE

Ibrahim, AM

Zobaa, AF

Brunel University Research Archive

1450 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 4, OCTOBER 2003Effect of Connecting Shunt Capacitoron Nonlinear Load TerminalsMohamed Mamdouh Abdel Aziz, Member, IEEE, Essam El-Din Abou El-Zahab, Ahmed Mohamed Ibrahim, andAhmed Faheem Zobaa, Member, IEEEAbstract—The use of terminal shunt capacitance has dif-ferent effects on the displacement factor and distortion factorcomponents of the power factor. These effects are consideredfor nonlinear loads with ideal supply, and also where the supplyimpedance exists but is small compared with the load impedance.Optimization of the displacement factor is found to result inreduction of the distortion factor to a minimum value.Index Terms—Distortion, harmonics, power factor.NOMENCLATURECapacitance, F.Displacement factor.Distortion factor of load.Distortion factor after compensation.Minimum value of .rms supply voltage, V.rms current, A.rms value of capacitor current, A.rms value of -th component of load current, A.rms value of supply current, A.rms value of fundamental component of load cur-rent, A.rms value of fundamental component of supply cur-rent, after compensation, A.Current ratio .Voltage ratio .Average power, W.Power factor after compensation.Fundamental phase-angle (displacement angle) ofload current, rad.Fundamental phase-angle of supply current aftercompensation, rad.Fundamental phase-angle of load voltage, rad.Angular supply frequency, rad/s.I. INTRODUCTIONTHE power factor of a load is universally defined as the ratioof the real power input to the volt-ampere product at theterminals [1].For systems with sinusoidal supply voltage (i.e., negligiblesupply impedance) and nonlinear load impedance, the load cur-Manuscript received July 17, 2002.The authors are with the Electrical Power and Machines Department,Faculty of Engineering, Cairo University, Giza 12613, Egypt (e-mail:a.zobaa@eng.cu.edu.eg).Digital Object Identifier 10.1109/TPWRD.2003.817794rent waveform is periodic but nonsinusoidal. It is sometimesconvenient to consider the power factor of such systems as theproduct of a displacement factor and a supply current distor-tion factor. It is only valid for loads with sinusoidal voltage.The displacement factor is partly, but not entirely, related toreactive properties of the load impedance [1]. The distortionfactor is largely related to the degree and kind of nonlinearityof the load impedance. In realistic power supply and distribu-tion systems, the supply has finite and measurable impedance.This can usually be interpreted as series inductance in the supplylines between the generator and the load terminals. If the loadimpedance is nonlinear, the effect of the nonsinusoidal currentdrawn through the supply reactance is to create distorted voltageat the load terminals. When both the voltage and the current atthe supply point are of different nonsinusoidal waveforms, it isgenerally not possible to express the power factor in terms ofdisplacement factor and a supply current distortion factor [2].A straightforward way of obtaining power factor correctionfor loads with a lagging phase-angle is to use shunt capaci-tance at the supply point. For many nonlinear loads comes powerfactor compensation that can be thereby realized even if the loadimpedance is purely resistive.This way of power factor correction installation can be usedwhen it is not necessary to take measures to avoid resonanceproblems or to reduce harmonics. This is generally the casewhen the resonant frequency given by the network inductanceand the capacitance of the power factor correction installationis relatively high and the harmonic content of the network (i.e.,bus voltage and harmonic currents generated by the load) arevery low [3].Harmonic currents tend to flow from the nonlinear loads (har-monic sources) toward the lowest impedance, usually the utilitysource. The impedance of the utility source is usually muchlower than parallel paths offered by loads. However, the har-monic currents will split depending on the impedance ratios.Higher harmonics will flow to capacitors that are low impedanceto high frequencies [2].The main purpose of connecting shunt capacitance is to re-duce the displacement angle between the supply voltage vectorand the fundamental supply current vector, thereby increasingthe displacement factor of the overall burden. The most impor-tant feature, however, is the effect on the overall power factor[4]–[7].This paper considers this effect, with ideal supply, and alsowhere the supply impedance exists but is small compared withthe load impedance.In this analysis, the following assumptions are made.0885-8977/03$17.00 © 2003 IEEEAZIZ et al.: EFFECT OF CONNECTING SHUNT CAPACITOR ON NONLINEAR LOAD TERMINALS 1451Fig. 1. Nonlinear load with nonideal single-phase supply.1) The waveform of the nonlinear load input voltage isundisturbed by connecting the compensating capacitoracross the load input terminals. This assumption willgive reasonable results if the capacitor current is smallrelative to the load current.2) Harmonics of the capacitor current are small relative tothe fundamental [8].3) The harmonic current components drawn from the supplyare not affected by connecting the capacitor across thesupply terminals [9].However, in cases where the assumptions are not valid, theconclusion from this paper will be an approximate estimaterather than an exact solution. To obtain the exact effect insuch cases, one has to study each case individually consideringsimultaneously the effects of supply current and distortedsupply voltage harmonics.II. POWER FACTOR PROPERTIES WITH NONIDEAL SUPPLYConsider a nonlinear load impedance connected to nonideal,sinusoidal supply (i.e., generator), Fig. 1.The supply current is periodic of rms value , and has afundamental component of rms value , lagging by angle(Fig. 2). The supply current distortion factor is givenby(1)Now let a capacitor be connected across the supply terminalsto correct the power factor of the total load. The capacitor willdraw from the supply a sinusoidal current of supply frequencyand rms value . This current adds vectorially to the funda-mental supply current drawn by the load branch to give thefundamental supply current Fig. 2, lagging by . Theload voltage has rms value and a fundamental component ofrms value , lagging by angle , Fig. 2. The input voltageto the load is not sinusoidal and has a distortion factorAccording to the assumptions, the capacitor will draw fromthe supply a supply frequency current of rms valueand phase-angle . This current adds vectorially to theFig. 2. Phasor diagram representing fundamental supply current and loadvoltage components.fundamental supply current drawn by the load branch to givethe fundamental supply current , lagging by , Fig. 2.The harmonic current components drawn from the supply arenot affected by connecting the capacitor across the supply termi-nals and hence the terms of (1) remain constant. Thedistortion factor of the supply current after correction isnow given by(2)For the distortion factor to improve after compensation, it isnecessary thatHence(3)Substituting from (1) and (2) into (3) gives the requirement(4)orThe inequality of (4) is obviously not true for the system. InFig. 2, for example, the displacement factor is increased due tothe capacitor. But in reducing the displacement angle, it is seenthat the value of fundamental component of supply current, aftercompensation, is reduced. It therefore follows from (4) that thedistortion factor is reduced. It also follows that the distortionfactor can only be improved by reducing the displacement factor[10], [11]. Referring to Fig. 2, one can write(5)(6)1452 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 4, OCTOBER 2003Substituting from (5) into (6) gives (See the equation at thebottom of the page) for negative values of (See theequation at the bottom of the page) for positive value of(7)If the value is substituted from (5) into (2) one obtains(8)The overall displacement factor after capacitor correction isnow given Fig. 2 by(9)It has been shown [12] that if the supply voltage distortionfactor is high and the magnitude of the fundamental supplycurrent is greater than that of any higher harmonic, the powerfactor PF after capacitance compensation of the circuit of Fig. 1may be approximated to(10)If is equal to zero, ideal supply, (9) reduces toConsider the following nonlinear load with ,, , , .Fig. 3 shows consistent variations of modified supply cur-rent distortion factor , corrected displacement factor, and modified power factor with the modifiedfundamental supply current phase angle.Variations of modified fundamental supply current phaseangle can be easily converted to corresponding variations in thevalue of compensating capacitor by using (7).Comparing for the case of ideal supply, one can see that thegeneral effect of supply impedance is to shift the fundamentalphase-angle of the distorted supply voltage.Fig. 3 shows also that unlike the case with ideal supply, theminimum supply current distortion factor is not equal to the(a)(b)(c)Fig. 3. Variation of distortion factor (DISF ), displacement factor (DISF),and power factor (PF) with compensated phase-angle  .AZIZ et al.: EFFECT OF CONNECTING SHUNT CAPACITOR ON NONLINEAR LOAD TERMINALS 1453Fig. 4. Distortion factor (DISF ) versus modified fundamental phase-angle for different values of uncorrected fundamental supply current phase angle .maximum power factor. This is due to the effect of the supplyvoltage distortion factor as shown by (10).A set of curves showing supply current distortionfactor versus corrected fundamental supply currentphase-angle for different value of (Fig. 4). Comparingfor the case of ideal supply, one can see that the general effectof supply inductance is to shift the point of minimum distortionfactor by an angle equal to the fundamental phase-angle of thedistorted supply voltage.One may note the following points for the case of ideal supply1) Maximum power factor is obtained at where themodified displacement factor is unity.2) At this value, the distortion factor is a minimum and themaximum realizable power factor is therefore equal to theminimum realizable distortion factor.3) For the range , the three curvesof Fig. 3 are symmetrical about the compensated funda-mental phase-angle axis.4) Although the distortion factor is increased for values of, the total power factor then decreases due to de-crease in the displacement factor. This condition is ac-companied by increased fundamental supply current andincreased transmission loss.5) To increase the compensated distortion factor above itsuncompensated value, angle must be increased be-yond . The effect of such increase is to reduce thepower factor, due to reduction of the displacement factor.As the fundamental phase-angle before compensation isincreased negatively, the minimum distortion factor decreasesand consequently the maximum realizable compensated powerfactor will also decrease.III. MINIMUM REALIZABLE VALUE OF COMPENSATEDDISTORTION FACTORFrom (8)(11)Let the load branch be undisturbed while capacitor isvaried. Parameter , , and of (10) then remainFig. 5. Variation of minimum compensated distortion factor with uncorrectedfundamental phase angle  .Fig. 6. Variation of minimum compensated distortion factor with K .constant while is varied. For a maximum or minimumvalue of distortion factor, one then hasfrom whichso thatIt is clear from Figs. 3 and 4 that represents amaximum. Substituting this value into (10), gives the followingexpression for the minimum value of the modifieddistortion factor(12)If , for ideal supply, (11) reduces to(13)Fig. 5 shows variation of with .Fig. 6 shows variation of with . Variation offunction (11) for changes of shows that , with, when the fundamental supply current is then zero.1454 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 4, OCTOBER 2003One can conclude that for values of , the minimumdistortion factor becomes constant at a value near unity, becauserepresents only a small distortion effect.IV. CONCLUSIONSThe function of terminal shunt capacitance compensation isto reduce the phase (displacement) angle between the funda-mental components of the terminal voltage and current. Whenthe displacement angle is zero, the displacement factor is unityand this can be realized even with nonlinear loads. The powerfactor of the compensated load is then a maximum.The presence of supply reactance causes a nonzero valueof the fundamental load (and supply) voltage phase-angle. Withsupply reactance, an approximate analysis shows that the curvesof displacement factor, distortion factor, and power factor aresymmetrical about axis. The presence of supplyimpedance also reduces the maximum value of power factor re-alizable by shunt capacitance compensation.REFERENCES[1] W. Shepherd and P. Zand, Energy Flow and Power Factor in Nonsinu-soidal Circuits. Cambridge, U.K.: Cambridge Univ. Press, 1979.[2] IEEE Recommended Practices and Requirements for Harmonic Controlin Electrical Power Systems, IEEE Std. 519–1992, June 1992.[3] “Industrial AC Networks Affected by Harmonics-Application of Filtersand Shunt Capacitors,”, IEC 61 642, First ed., 1997.[4] E. F. Eh-Saadany, M. M. A. Salama, and A. Y. Chikhani, “Reductionof voltage and current distortion in distribution systems with nonlinearloads using hybrid passive filters,” Proc. Inst. Elect. Eng.-Gen., Transm.Dist., vol. 145, no. 3, pp. 320–328, 1998.[5] H. Nakano, T. Tanabe, M. Naitoh, Y. Kubota, T. Morita, T. Kimura, M.Matsukawa, and Y. Miura, “Analysis of the current distortion factor ofa three-phase, three-wire system,” Denki Gakkai Zassshi. English, vol.131, no. 4, pp. 1–10, 2000.[6] J. E. Mitchell, “Distortion factor: The new problem of power factor,”INTELEC92, pp. 514–516, 1992.[7] R. Yacamini, “Power system harmonics: Part 3 problems caused by dis-torted supplies,” Power Eng. J., vol. 9, no. 5, p. 233, 1995.[8] IEEE Standard for Shunt Power Capacitors, IEEE Std. 18–1992, Sept.1992.[9] D. E. Rice, “Adjustable speed drive and power rectifier harmonics: Theireffect on power system components,” in Copyright Material IEEE, 1984,Paper no. PCIC-84–52.[10] W. Shepherd, Thyristor Control of A.C. Circuits. Bradford, U.K.:Bradford Univ. Press, 1975.[11] H. Frank and B. Landstorm, “Power-Factor correction with thyristor-controlled capacitors,” ASEA J., vol. 44, no. 6, 1971.[12] H. El-Bolok and W. Shepherd, “The Effect of Source Impedance onthe Performance of Thyristor Controlled Separately-Excited D.C. MotorWith Single-Phase Supply,” P/G School of Electrical and Electronic En-gineering, University of Bradford, U.K., Research Rep., 1980.Mohamed Mamdouh Abdel Aziz (M’80) received the B.Sc. (Hons.), M.Sc.,and Ph.D. degrees in electrical power and machines from Cairo University, Giza,Egypt, in 1970, 1972, and 1975, respectively.Currently, he is Professor of Electrical Power and Machines at Cairo Univer-sity. He was an Instructor in the Department of Electrical Power and Machinesat Cairo University from 1970 to 1972. He was also a Teaching Assistant in theDepartment of Electrical Power and Machines at Cairo University from 1972to 1975. His research interests include cables, contact resistance, harmonics,power quality, photovoltaic systems, and wind energy systems. He is also theauthor or co-author of many referenced journal and conference papers.Essam El-Din Abou El-Zahab received the B.Sc. (Hons.) and M.Sc. degreesin electrical power and machines from Cairo University, Giza, Egypt, in 1970and 1974, respectively. He received the Ph.D. degree in electrical power fromPaul Sabatier, France, in 1979.Currently, he is a Professor in the Department of Electrical Power and Ma-chines at Cairo University. He was an Instructor in the Department of ElectricalPower and Machines at Cairo University from 1970 to 1974. His research areasinclude protection systems, renewable energy, and power distribution. He is alsothe author or co-author of many referenced journal and conference papers.Ahmed Mohamed Ibrahim received the Ph.D. in electrical power engineeringfrom Cairo University, Egypt.His research interests include generation and utilization of electric energy.Ahmed Faheem Zobaa (M’01) received the B.S.(Hons.) and M.S. degrees in electrical power andmachines from Cairo University, Egypt, in 1992and 1997, respectively. He received the Ph.D.degree in electrical power and machines from CairoUniversity, Giza, Egypt, in 2002.Currently, he is an Assistant Professor in the De-partment of Electrical Power and Machines at CairoUniversity. He was an Instructor in the Departmentof Electrical Power and Machines at Cairo Univer-sity from 1992 to 1997. His areas of research includeharmonic problems in power systems, evaluation, and compensation of reactivepower with capacitors and filters, power quality and related areas, photovoltaicsystems: design, performance analysis, and cost benefit analysis, and design andoptimization of wind energy. He is also a Reviewer for many power engineeringjournals and is the author or co-author of many referenced journal and confer-ence papers.Dr. Zobaa is a member of the International Solar Energy Society. On the tech-nical side, Dr. Zobaa is an Editorial Board member for International Journal ofPower and Energy Systems.

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

Distortion factor: The new problem of power factor,”

Energy Flow and Power Factor in Nonsinusoidal Circuits.

for Shunt Power Capacitors,

Power system harmonics: Part 3 problems caused by distorted supplies,”

Power-Factor correction with thyristorcontrolled capacitors,”

Practices and Requirements for Harmonic Control in Electrical Power Systems,

Reduction of voltage and current distortion in distribution systems with nonlinear loads using hybrid passive filters,”

The Effect of Source Impedance on thePerformanceofThyristorControlledSeparately-ExcitedD.C.Motor WithSingle-Phase Supply,” P/G School of Electrical and Electronic Engineering,

Thyristor Control of A.C. Circuits.

Effect of connecting shunt capacitor on nonlinear load terminals

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Effect of connecting shunt capacitor on nonlinear load terminals

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