theoretical concepts for reactive power generation including control aspects. Impedance and phase balancing of induction. a r c - - and siigle phase electric ...
POWER FACTOR CORRECTION AND LOAD BALANCING IN THREE-PHASE DISTRIBUTION SYSTEMS *Bh
SIX&, Anuradha Saxena and D.P.Kothari Center for Energy Studies *Department of Electrical Engineering IIT, Hauz khas, New Delhi-110 016, INDIA
ABSTRACT - This papr deals with the different methods for compensating unbalanced three phase loah. Compensation of grounded, ungrounded star connected and delta connected three phase unbalanced load has been camed out. Three schemes haw been proposed for neutral current compensatfon. A common approach has been folbwed fir power factor correction and load bahcing. Simulated resulrs ma1 that aper covnsmon all three supply currents are in phme with their respectiw phase wltages with equal magnitude resulting in a balanced load on supply system. L INTRODUCTION In recent years, there has been greatly increased demand for controllable var sources to compensate large industrial loads such as electric arc fiunaces, electric traction, commercial li&ting, air conditioning etc. If not compensated, these loads create system unbalance and lead to wide ffuctuations in the supply voltages. Such supply system can not be used to feed sensitive loads like computers, electronic equipment etc. Tbe importance of balanced load on the supply system has already been felt by power experts a long back [1-21. The presence of unbalanced load results in reactive power burden and excessive neutral current, which in turn results in low system efficiency, poor power factor and disturbance to other consumers. Innumerable control methods have been proposed to draw balanced supply currents if reactive load is fed fiom balanced supply system. Gyugyi [3] discussed few basic theoretical concepts for reactive power generation including control aspects. Impedance and phase balancing of induction a r c - - and siigle phase electric traction as a load have been presented by Tremayne [4] and Knechke [5], respectively. A very conceptual approach for realizing balanced load while feeding single phase R-L load is reported by Kern et al [6] and three phase load by Sadek [7l. However, a new criterion based on optimization of the nns values of line currents is used fir evaluating the reactive elements required for compensation in threephase threemire system by Vasu et al [8] and minimization of power line loss for optimal reactive power compensator has been discussed by Lin e4 al [SI. Further, the idea of electronic compensator has been introduced to compensate the reactive
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currents but only with arc-furnace as a load by Cox and Mihod [101. Sumi et al [111 have described the system outline and operating results of 20 MVA static Var Generator. An analysis to determine the response of the STATCON in transmission line is provided by Schauder and Mehta [12]. Kearly et al have worked on microprocessor controlled model construction network for dism'bution feeder [131. Ng et al [141 have used fuzzy approach for placing the capacitors in distribution system. The vast majority of the work is restricted to single phase line to line loads, thrwphase, three-wire loads. However, this paper is an attempt to compensate all kinds of three-phase unbalanced loads i.e. grounded load, ungrounded star connected and delta connected unbalanced loads. In a three-phase, four-wire system under normal operating condition with the loads reasonably balanced, the current in the neutral is expected to be small, typically not more than 20 percent of the normal load current in the phases. However, excessive neutral current phenomenon arises, especially in unbalariced circuits such as fluorescent lighting loads. This type of system in particular, results in excessive neutral current, which can potentially af€ect both the neutral conductor and the transfonner to which it is connected. The objective of this paper is to balance a three-phase, fourWire system feedig a three-phase, four-wire unbalanced load and thee-phase, three-wire unbalanced load. Three schemes have been presented for neutral current compensation. Each scheme suggests selection of different reactive elements for making the load balanced and resistive at supply end. It also proposes the selection of optimized set out of three compensation methods according to nature of load. The basis of forming three sets lies on the selection of phases for neutral current compensation namely a-b, b-c and c-a Thereby forming three solutions for one instant in case of three phase grounded unbalanced load (Fig. l(a)). Moreover, a uni6ed approach is devised for compensation of three phase, three wire load. IL SYSTEM DESCRIPTION System considered consists of a balanced three phase supply feeding the unbalanced loads. Fig. l shows the line diagram
representation of loads where supply voltages are: v , = IvI LOO; v ba = JVIL120"; v , = IVIL240" For three-phase unbalanwd grounded load as shown in Fig. 1 (a), three schemes have been presented and then three-phase threewire unbalanced load has been compensated using a common scheme. First scheme considers phases b and c vig.2(a)), second scheme selects phases a and b (Fig.2(b)) and third scheme chooses phases a and c (Fig.2(c)) for neutral current compensation. Suppose P, Pb and Po are three loads of lagging power factor cos@, cos% and cos@, respectively fed from balanced supply. The current carried away by neutral U is given by summation of b, Ihl and I^j (load currents). I,, can be neutralized by injecting a current I, equal in & t u d e and 180" out of phase fiom z. L current stands for neutral compensation current and 8 is the neutral current compensating angle. After neutral curreat compensation the load becomes equivalent to three-phase three-wire unbalanced load (Fig.l(b)), this is transformed to equivalent delta connected load (Fig.(c)). Three phase unbalanced delta co~ected load is cornpensated by two sets of lossless elements (susceptances) one for power factor correction (B*,, Bboi and B ml ) and other for line currents balancing (Bsb2, kZ and B d ) as shown in Fig.3. EL NEUTRAL CURRENT COMPENSATION Neutral current compensation can be achieved by any one of the following three schemes. A. First Scheme This scheme realizes the b a l a n d operation by providing neutral current compensation in phases b and c, for three-phase fourwire load as shown in Fig.2(a). The nature of passive lossless compensating elements will depend on angle of neutral compensation current L i.e. 8. Reactive elements chosen for b and c phases will be decided by angles P and 7. The angles p and 7 are the angles of compensating elements Z, and Z , . These two impedances being lossless reactive elements (either capacitive or inductive) thus, these angles (B and 7) will be SO". If angle is -909 then selected element will be an inductor, i f * then it will be a capacitor: For 3O° i,t, and -&. Fig.qc) shows the balanced load currents i, & and i, after compensation Fig.7(a) presents the load aments L, ,,i and L in case of three phase delta connected load. Fig.7(b) shows the balanced phase current i, which at any instant is the sum of i d , - L , U and - b . Where ia and b. are the currents flowing in susceptances placed for unity power factor correction and load balancing in phases a-b and cia. Lastly, Fig.7(c) shows the voltage v, and three balanced supply currents i, 4 and b drawn by load thereby presenting balanced load to the supply system.
93.4mH in phases a-b, b-c and c-a, respectively. Third scheme uses two capacitors of 65.58pF and 21.91pF and an inductor of 115.7mH in phases a-b, b-c and c-a respectively. After compensation all currents are in phase with their respective voltages and power consumed per phase is equal as given in Table 1. Table 2 presents the compensation results for three phase star ~ ~ e c t e d ungrounded load. For the given load specifications, capacitors of 380.8pF. 59.65pF and 290.8pF are needed in between phases a-b, b-c and c-a respectively for reactive power/power factor compensation. Further, load balancing requires two capacitors of 82.54pF, 11.62pF in phases a-b, b-c and one inductor of 107.6mH in phase oa Last column of table shows per phase current and per phase power after compensation. Table 3 shows the results corresponding to three phase unbalanced delta connected load. For the given load values, two capacitances of values 184.9pF, and 254.6pF are needed in phases a-b and c-a fbr power fkctor correction and no capacitive or inductive element in phase b-c for power factor correction is needed. Load balancing requires an inductor of 213.3mH in phase a-b, a capacitor of 94.89pF in phase b-c and an inductor of 213.4mH in phase e a . Last column shows that equivalent balanced per phase power is 19.99kW and current is 78.7A.
VI. CONCLUSIONS Three different compensation schemes for unbalanced three phase four wire load have been investigated. All the three schemes are able to make the system perfectly balanced. A common scheme for three-phase three-wire unbalanced load (either star connected or delta c~~ected) has been adyzed and found to balance the load completely. These schemes can be realized by variable lossless impedance compensators using elements which may knction as variable reactances. Results may be utilized for the proper design of a controller for balancing the loads in three phase ac system. VlL ACKNOWLEDGEMENT The fitst author gratefblly acknowledges the "Council of Scientific and Industrial Research, INDIA" for the financial support receiving under the Senior Research Fellowship scheme, Award No. 9/143(285)/94-EMR-I, because of which this work reported in this paper was possible.
Relevant waveforms for three phase grounded star connected unbalanced load, three phase ungrounded star connected u n b d d load and three phase delta connected load have also been devised. Fig. 5 shows the results corresponding to a load of 15kW 0.8pf lagging, 20kW unity pf and 25kW 0.85pf lagging in three phase grounded star connected load configuration (as shown in Fig. l(a)). FigS(a) indicates the load currents id it^ and L and neutral current i,. Figs. 5(b), 5(c) and 5(d) depict the neutral current compensation by the three schemes. It has been clearly shown in Fig.S@) that at any instant sum of i b , i, and i, is zero, which effectively represents the neutral current elimination by the first scheme. Fig.S(c) shows the neutral current compensation by second scheme and at any instant the sum of w, ihoc and i,, is zero. In FigS ( d ) according to the third scheme, neutral current compensation is carried out in phases a and c and i n is neutralized by i, and w Figs. 5 (0, 5 (g) and 5(h) give the detailed description of balanced load current i, when balancing is done by the three schemes. F i g . 5 0 shows that current i, is equal to sum of id, i* and -i, which is expected according to the first scheme. Similarly Figs S (g) and 5 0 ) indicate that sum of idi, , i& and -i is equal to i. Finally, FigS(e) shows the voltage v, and the three balanced supply currents 4, & and h obtained after compensation by all the three schemes. Fig.6 gives the appropriate waveforms for three phase ungrounded star connected unbalanced load and Fig.7 for three phase delta co~ected unbalanced load. Fig.Ci(a) shows the equivalent load current w &, &.i in case of three phase ungrounded star connected load. Fig.6(b) produces i current
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REFERENCES 1. L.Gyugyi, R.AOtto and T.H.Putman, "Principles and application of static thyristor-conuolled shunt compensators", IEEE Trans. on PAS, vo1.97, no. 5, pp 1935-1942, 1978. 2. L. Gyugyi,"Reactive power generation and control by thyristor circuits", EEE Trans. on Ind. Appl., v01.MlS,no.S,pp 521-531, 1979. 3. L.Gyugyi,"Power electronics in electric utilities: static var compensators", Proc. IEEE, vol.76, no.4, pp 483494, 1988. 4. J.F.Tremayne,"Impedance and phase balancing of mainsfiequency induction fiirnaces", EE Proc., vol.130, pt.B, n0.3, pp 161-170, 1983. 5. T.AKneschke,"Control of utility system unbalance caused by single-phase electric traction", IEEE Trans. on Ind. Appl., v01.21, n0.6, pp 1559-1570, 1985. 6. k K e m and G.Schroder,"A n o d approach to power fkcm control and balancing problems", Proc. of Cod. JEEEIECON Record, pp 428-433, 1994. 7. M.Z.E1 Sadek., "Balancing of unbalanced loads using static var compensators", Electr. Pow. Syst. Res., vol.12, pp 137-148,1987.
8. E.Vasu, V.V.B.Rao, P.Sankaran,"An optimization criterion for three phase reactive power compensation", EEE Trans. on PAS, ~01.104, no.11, pp 3216-3220, 1985. 9. C.E. Lit& T.C.Chen and C.L.Huang,"A real time calculation method for optimal reactive power compensator", IEEE Trans. On Pow. Syst., vo1.4, n0.2, pp 443-652, 1989. 10. MD.Cox, AMirbod," A new static var compensator for an arcifinace", IEEE Trans. on Pow. Syst. voI.PWRS-1, 110.3,pp 110-119,1986. 11. Y.Sumi,Y.Harumoto,T.Hasegawa,M.YanoandK.Ikeda," New static VAR control using force-commutated inverters", IEEE Trans. on Pow. App. and syst., vol. PAS100, no.9, pp 4216-4224, 1981. 12. C.Schauder and H.Mehta, "Vector analysis and control of advanced static VAR compensators", IEE Proc.-C, ~01.140, pp 299-306, 1993. 13. J.K&y, AY.Chilchani, RHackam, M.M.A.Salama and V.H. Quhana," Microprocessor controlled reactive power compensator for loss reduction in radial distribution feeders", IEEE Trans. on Pow. Del., vo1.6, no.4, pp 18481855,1991. 14. H.N.Ng, M.M.A.Salama and AY.Ch&hani," Capacitor placement in distribution systems using fuzzy technique", IEZE Canadian Conference on Elecuical and Computer Engineering pp 790-793, 1996.
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TABLE 3.1: Compensation of three-phase unbalanced grounded load Load Specifications : ( 15kW 0.8 pf, 20kW unity pf, 25kW 0.85 pf) Schemes
First Scheme
For neutral current compensation Lbnc=10.3mH C c ,=205.3 pF
For power factor/ reactive power compensation
Load balancing Compensating I Elements
Per phase power Current(A)
(kW) &
C^ISO^F
C a ,=69.7 p F poh= 19.99; I,=78.7L0" Cte2=37.9^F ^=78.72; 1^78.7/120° 13,-78.7/240° Lca2=94.0mH *"
b,=257.6pF Cbcl=290.7^F
Second Scheme
L,=49.3np &=8.51mH
Cabl=328.6pF cl=355.9pF C a ,=219.9 p F
Ca,,=67.2pF ? , = 19.99; I,=78.7L0" C k2 =41.2 p f L=78.72; Isb=78.7L 120" L 4 ~ 93.4mH 1, = 78.7L240"
Third Scheme
C,=982.2 p F C,, = 1188.9pF
Labl = 153.5& L l =471.2mH L,,=51.41mH
CaU=65.58pF k = 19.99; Cbc2=21.91pF bz78.72; L d = 115.7mH 1
I,=78.7L0" ISb=78.7L 120" ,=78.7L240"
TABLE 3.2: Compensation of three-phase star connected ungrounded load 1oa Specifications
Equivalent A- For power Factor/ oa oaaancing connected load reactive power Per phase power compensation Compensating Elements (kW) & current (A)
2,=3.44 L 36.9" 2,=11.3L12.8"- c abl =380.8 pF C au =82.54pF P,=20.41; 1,=80.4L0" Z,=3.23L0" Z,=7.21L7.76" C bcl =59.65 p F CbcZ=11.62p [ ,=80.4; 1,=80.4L120" 1, = 80.4L240" Z c ,=2.19L31.8" 2,=7.69L44.6" Cc,,=290.8pF Lca=107.6mH
TABLE 3.3: Compensation of three-phase unbalanced A-connected load Load Specifications
Equivalent A Tor power Xoad Balancing connected load factor\ reactive Power Compensating Per phase power compensation Elements (kW) & current (A)
Pab= 15kW0.8pf Zab = 10.3 L 36.9" C ab , = 184.9pFLa,=213 L a ,=213.3mH k',,,,=19.99; I,=78.7L0" Pk=2OkW 1.0 pf Z,=9.68 LO" C bcl =0.00pF Ck2=94.89pF$,=78.72;Is F$,=78.72;Isb=78.7L120" Isc=78.7Z240° Pc,=25 kW 0.85 pf Z,,=6.58L31.8" CCa,=254.6pFLC L C a = 2 1 3 . 4 m H
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cnc
c Toil Grounded star connected
(a)
(a) First scheme (cornpensation in b and c phases)
'an1
a
ao NZonl
bnl v
cnl (bl Ungrounded star connected
(bf Second scheme (compensation in a and b phases)
ca
(c) Delta connected
(c) Third scheme (compensation in a and c phases Fig.2 Neutral current compensation of three phase unbalanced grounded load
Fig. 1 Representation of three phase unbalanced load
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BCQ1
Vbn
Fig. 3 Representation of equivalent balanced load
Fq. 4 (a)Using first scheme for three phase grounded star connected unbalanced load
-Ica anc
Ibei
\
cnc
Fig. 4 (b) Using second scheme for three phase grounded star connected unbalanced load VQn lab
Figt(c) Using third scheme for three phase grounded star connected unbalanceCI load ad ab
'be
bn ca
Fig.4(d)For three phase ungrounded star connected unbalanced load
F;g.L(e) For three phase delta connected unbalanced load
Fig.L Phasor representations for compensations of all kinds of load
486
no. mi"
/ ibnc
.•ibnc EO.M-
•• A
/ \ / •• // \\'. .'Y ;\;\' / i\ i\ vy '>' V t
N
-ianq
\
/
«,•• «. Fig 5(a) Load currents and neutral current
Fig.5(b) Neutral current compensation in first scheme
TirE (SEO
Fig.5(c) Neutral current compensation by second scheme
Fig.5(d) Neutral current compensation by third scheme
~zsr Fig.5(e) Voltage van and three balanced supply currents
Fig.5(0 Current ia balancing by tlrst scheme
Fig.5(g) Current ia balancing by second scheme
Fig.5(h) Current ia balancing by third scheme
Fig.5. Waveforms lor compensation of three phase grounded load (Load specifications: 15kW 0.8 pf lag, 20kW unity pi, 25 kW 0.85pf lag)
e.ee-
-80.00-)0.00
0.01
0.02 TIE (SEC)
,,1,1, 0.03
0.04
Fig 7(a) Load currents when load is delta connected
Fig 6(a) Load currents in delta equi. of ungrounded star load
\ /
-100.00-
0.00
0.01
0.02 TIE ( SEC1
0.03
0.04
0.00
Fig 6(b) Current isa balancing
0.
01
0.02 TIE ( SEC1
0.03
^
0.04
Fig 7(b) Current isa balancing
Fig 7(c) Voltage van and three phase balanced supply currents
Fig 6(c) Voltage van and three phase balanced supply currents Fig 6 Waveforms for compensation of three-phase ungrounded S&K connected load
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Fig 7 Waveforms for compensation of three-phase delta connected load
