D.Chattopadhyay K.Bhattacharya Jyoti Parikh. Indira Gandhi Institute of Development Research. Gen.Vaidya Marg, Coregaon (East),. Bombay-400 065, India.
IEEE Transactions on Power Systems, Vol. 10, No. 4, November 1995
2014
OPTIMAL REACTIVE POWER PLANNING AND ITS SPOT-PRICING: AN INTEGRATED APPROACH D.Chattopadhyay
K.Bhattacharya
Jyoti Parikh
Indira Gandhi Institute of Development Research Gen.Vaidya Marg, Coregaon (East), Bombay-400 065, India Abstract: The paper presents an integrated framework to analyze the issues of reactive power planning alongwith reactive power pricing. The planning problem involves optimal placement and sizing of capacitors in a network such that operating and investment costs are minimum. A simple bus-wise cast-benefit analysis (CBA) scheme is proposed which involves solving a modified optimal power flow problem (OPF') iteratively. The proposed CllA incorporates detailed hourly loading conditions at a bus and achieves a fairly accurate estimate of the benefits from capacitor placement. The formulation is directly handled by the well known MINOS code and is solved efficiently. It obviates the need to introduce integer variables and is thus suitable for large system applications. A two-part reactive power spot-pricing scheme is formulatcd, by which the investment and operational costs can be recovered by the utility. The proposed reactive power price has two parts a fixed part to account for the Investment costs of new capacitor at a bus and a variable spot price to account for the operating costs incurred in supplying the additional reactive power from generating units.
-
1. INTRODUCTION The reactive power planning (RPP) problem involves optimal allocation and sizing of reactive power sources at load centres to improve the system voltage profile and reduce losses. Howcvcr, cost considerations gcnenlly limit the extent to which this can be applied. The criteria uscd for RPP has been to minimize the losses [I-21, the cost of new reactive power sources (capacitors) [3] or a combination of the two [4,51. Rama Iyer et al.[l] proposed an algorithm to minimize power losses by optimal placement of capacitors. A linear Mixed Integer Programming (MIP) problem is solved by decomposing it into two smallcr sub-problems using the Bender's Decomposition method. A linear programming model has b a n proposed in [2] to minimize the transmission losses by adjusting transformer tap settings, VAr injections etc. which are obtained from a modified Jacobian matrix. Aoki et a1.[3] have suggested an approximation melhod for solving the RPP problem in an MIP framework using the 95 WM 204-8 PWRS A paper recommended and approved by t h e IEEE Power System Engineering Committee of t h e IEEE Power Engineering S o c i e t y f o r p r e s e n t a t i o n a t t h e 1995 LEEE/PES Winter Meeting, January 29, t o February 2, 1995, New York, NP, Manuscript suDm,mitted June 28, 1994; made a v a i l a b l e f o r p r i n t i n g December 19, 1994.
principle of recursive linear programming. Deeb and Shahideh ur [4] have analyzed the RIP problem in a lin&orm considering- all load buses as candidates for VAr sources, different loadings and various contingency cases using the Bender's Decomposition method. In a later work [5]:the authors proposed a Cross Decomposition algorithm which is highly efficient m solving multi-area pow@ systems. Reactive power pricing in. real-time (spot-pricing) addresses the important issue of providing information to both $e utility and consumers about the true burden on the system, in terms of cost and other system parawters viz. voltage drops and increased transmission losses, from time to time. Berg et al.[6] indicated the inadequacy of the existing reactive power pricing policy based on power factor penalties. Baughman and Siddiqui [7] have presented a real-time pricing scheme of reactive power, similar to that of real power proposed by Scheweppeet al.[8]. Real-time pricing of reactive power has been shown to perform better than the power factor penalty scheme in terms of providing incentives to all customers to reduce their consumption of reactive power irrespective of their power factor. The present work combines the issues of RPP and reactive power pricing in an integrated framework. The RPP problem involves optimal placement and sizing of ca acitors at load buses such that the investment costs as welfas the operation costs are minimum. A simple bus-wise cost-benefit analysis (CBA) scheme has been presented to estimate the benefits from capacitor placement. While the proposed algorithm obviates the need for inteqer variables, it encompasses all the features associahi with the MIP formulation of RPP viz. different dimet&sizes of reactive power sources (which can include fixed reactive equipment, switched capacitors or static VAr compensators) and different costs associated with different size groups. Further, a two-part reactive power spot-pricing scheme is formulated, by which the investment and operational costs can IC recovered by the utility. The proposed reactive power price has two parts- a fixed part to account for the investment costs of new capacitor at a bus and a variable part to account for %eoperating costs incurred in supplying the additional reactive power from generating units. a. b. c.
d.
Following are the salient features of this work all load buses have been considered as candidate buses for installation of capacitors. criterion used for the RPP problem is minimization of system generating costs as well as cost of adding new capacitors. a simple algorithm has been proposed to perform a bus-wise cost-benefit analysis (CBA) in order to decide upon the optimal capacitor placements and their sizes. This a1 orithm obviates the use of inte er variables and mafes use of a series of modiffed optimal power flow (OPF') computations. the model formulation is in a format which can
0885-8950/95/$04.00 0 1995 IEEE
2015
e. f.
directly be handled by the well known MINOS code 193 and is solved efficiently. hourly load curve for each bus has becn considercd for the sclcction of capacitors, thus giving a more accurate estimate of the benefits therein. a bus-wise two-part tariff scheme for reactive power is proposed. It comprises a fixed part to recover the investment costs and a variable part reflecting the operatin costs incurred by the utility in supplying the resi ual reactive power requirement
d
2. MODEL FORMULATION
Nomenc:lature: COST Objective function (investment cost of capacitors and real power generation cost, $/Hr) Generator i cost characteristic Marginal cost of reactive power generation at bus i ($/p.u.MvAr/hr) LSF Load scaling factor BCR Benefit to Cost Ratio N Total number of buses Number of generating buses NG NL Number of load buses Number of buses with capacitors installed NC Index for buses i, j I Set of buses requiring VAr support L Set of candidare buses considered for capacitor installation, initially &=I, ...,NL) Real power generation at bus i @.u.MW) Reactive power generation at bus i @.u.MVAr) Real power demand at bus i @.u.MW) Reactive power demand at bus i @.u.MVAr) Reactive power support from new capacitor at bus i (p.u.MVAr) Voltage at bus i @.u.) Element of network admittance matrix (p.u.) Phase angle of Yi, (radians) Voltage angle at bus i (radians) Power transfer on line i-j (P.u.) Maximum power transfer limit (P.u.) Maximum reactive power support possible to add (p.u.MVAr) Real power generation limits at bus i Pub, Pgi" tP.U.MW) Reactive-power generation limits at bus i Qu-9 Qgi(p.u.MVAr) Limits on bus voltage levels (P.u.) v,v"" CAPCOST Cost of installing new capacitor ($/p. u.MVAr-hr) 2.1 Optimal allocation and sizing of capacitors A modified OPF formulation is used for allocation and sizing of capacitors on the load buses. These additional sources are required to provide the necessary reactive ower support at load buses, more so, during the peak loads. PF is computed for every hour of the load curve. The modified OPF objective function comprises the aggregate cost of generation and cost of adding new capacitors. This is different from the earlier studies [1-51
a
where transmission loss minimization or "cost" of transmission loss were considered for mininnkation. If system parameters viz. voltage, line flows etc. are within their specilicd limits, the utilities would operate on a least-cost schedule. Considering the "cost of generation" objective function, somewhat higher losses would be incurred since cheaper generating sources, e.g. pit-head plants, hydro stations etc. generally located away from load centres, would be predominantly used, to meet the demands. But it might be worthwhile for the utility to bear thls additional loss rather than switch generation to relatively expensive units located nearer to load centres. In this context, an analysis of loss vs. cost trade-off is carried out to get an insight mto the choice of planning criteria. The modified formulation of the OPF problem is described below: Objective Function: COST
-
Ci(P,,) + i r No
Qc,€APCOST i c NL
The system operating constraints are the following: a. Load Flow Equations:
- ~IV,I~JCY~,J~OS(~,+~~-~J AT
P , - pd, for i
-
j-1
1,....,N
b. Generating Limits: PI'* I PI, I p*,-
Q,-
IQ,,
(5)
e,,-
for i = 1,...,NG c. Voltage Limits:
-
IV! Constant I V q I V,l IP-l
for i = 1,...JVG for i 1,......&L
-
(7)
d. Transmission Limits:
V i j ; i#j
P , IP , e. Var injection limits: Qe,s
Q,
for i
-
1,..$A5
(9)
The modified OPF solution obtained using MINOS code, gives the amount of reactive power support needed at each load bus at each hourly load conditioc.. The utility would seek an analysis of whether new reactive power sources would be cost-effective i.e., would they provide a favourable benefit-to-cost ratio (BCR) when they arc, actually installed.
2016
An explicit cost-benefit analysis (CBA) is carried out to determine which of the capacitors are cost-effective and in which size. The outcome of CBA is incorporated in the OFF computation in an iterative way, to arrive at the global optimal solution. The following steps give the overall capacitor addition, sizing and CBA scheme (Fig.1):
Skp-1: Perform OPF computations considering the hourly load demands at each bus. The solution would rovide the amount of VAr support required at load Ewes i, [(i E I) and (I EL)], fy each hour. (L) includes all load buses to start with. Step2 Wirh the estimated VAr requirement, determine the standard size of capacitor unit to be installed at each bus i, (i E I) and the capital c a t thus incurred (in $/MVAr-Kr: considering a 10-year life of the equipment). This gives the preliminary allocation and sizin of capacitors. I Step-3: The marginal bene it from capacitor addition on i-th bus is calculated as follows: remove i-th bus capacitor and rerun the modified OPF keeping other things unchanged. The difference in the Objective function is the marginal benefit from capacitor addition on bus i. Step-4: If BCR for capacitor on bus i exceeds uqity, select it, This is done for all i and the set of capacitors selected is available (i = 1,...,NC). If BCR IS less than unity, consider a capacitor of lower rating and r d c u l a t e BCR to check if a lower rating could be selectecl. Else, the bus capacitor is rejected. Step-5: M d f y set L by removin all the rejected buses and go to Step-1. Go to Step- only when all buses in the modified set [L) have BCR> 1 i.e., all buses in (L) areselected, {L) = (I). Step6 Perform OPF computations considering only the selected bus camcitors. If this gives a feasible OPF solution, this Selection is final.Step-7: If Step-6 results in violation of any of the constrmts, capacitors are includel in succession at buses, where they were re'ecteci in Step-4, in the decreasing order of their BdRs till a feasible solution is attained.
B
%
2 2 Two-part pricing scheme for reactive power Reacuve power pricing should mover the capital investments, in the form of installing capacitors at load buFs, and marginal cost of reactive power generrtion. The reactwe power pricing and ca citor sizing and hcement problems need to be consider in an integrated ramework to ensure that both investment and operating costs are recovered in a manner equitable to utility and the customers. The CBA ensures that placement of capacitors are beneficial to the system. The pricing scheme should enable the utility .to recover its expenditure on installation of capacitors while ensuring that the customers do not pay excessively even if there exists strict voltage constraints. To illustrate the last point, case study results of [7] (Section IV) may be noted: as the volta e limit is tightened from 0.9 p.u to 0.966 p.u for bus#4, ke reactive wer price changes drasticall from $0.56/MVAr-h to %R52/MVAr-h and is about 2.H times higher than the rice of active power. This scheme, however, seerns to be un air, since it passes on the burden of meeting the voltage constraints solely to the customers by charging an exorbitant price, when the utility can resort to installation of
e8a
P
P
capacitors to esse out the vo
FIG.1 SCHEME FOR OPTI5fAL ALLOCATION AND SIZING OF CAPACITORS
and charge a
fixed amount for the same, if i cost-effective utility could (Le., BCR > 1). For the ab0 install capacitor at bus ##4and charge a fixed component of $24lMVAr/day (assuming a capacity cost of $lOO/kVAr and a 10-year life) dongwith a variable component of $0.56/MVAr-h. This section presents a two-part pricing scheme for reactive power cornpnsing a fixe0 part U, cover the capital
2017
s
expenditure on new ca acitors and a variable part to cover the opcratiny costs. The ccision w inslall capdciurs at ccrlain load buses follows from the optimal allocation and sizing scheme proposed in Scction 2.1. The reactive power price at these buses would include the fixed part also, while the other buses would have only the variable operating cost. The fixed part of the price would be a periodical payment based on the annualized capital cost of the capacitor in $/MVAr, similar to the connection charge levied in India [lo] for real power. The variable part is similar to the hourly spot-pricing scheme proposed in [7]. The real-time price of reactive power based on marginal cost at a particular bus and at a particular hour is given by:
where pi- and p, in are the Lagrangian multipliers associated with the uppcr and' lower limits of reactive power generation respectively (Eqn.6).
3.2 Allocation and sizing of capacitors A. 5-Bus System:
Step-1: The base case OPF is solved for each hourly loading condition considering the objective function (1). All load buses (#3. #4 and #5) are initially considered to be equi ped with capacitors with Q, = 0.2 p.u.MVi!r.
Step-2: Table2 shows the VAr requirements at each load bus for different loading conditions. The preliminary selection of capacitor at a load-bus is made on the basis of the maximum VAr requirement at that bus, over the load curve. A capital cost of $100.O/kVAr is assumed for the resent studies. Considering a 10year life period opthe equipment, the cost would a proximately be $24.0/MVAr/Day i.e. $%OO.O/p.u.MVAr/Day (on a 100 MVA Base) Given below are the preliminary sefection of capacitors at load-buses and their capital costs. Bus #3 = 0.2 p.u.MVAr ($480.O/Day) Bus #4 = 0.2 p.u.MVAr ($480.O/Day) Bus #5 = 0.2 u.MVAr ($480.O/Day)
Table-2: VAr requirement (in p.u.M$r) LSF Bus 13
3. ANALYSIS A 5-Bus system [111, the IEEE 30-Bus system and
Bur Y4
Bur YS
0.0056 0.0540
0.01 14 0.0777 0.1202
0.0274 0.1074 0.1613 0.2000
1.2 1.3
0.1080 0.2000
0.2OoO
1.4
0.2000
0.2000
a 60-Bus system (comprising two interconnectedIEEE 30-Bus systems) are considered for the purpose of demonstrating the proposed algorithm. The generating unit characteristics and bus-wise load demand curves for a typical day are given in Section-6.
0.7 0.8 0.9 1.o 1.1
3.1 Choice of a planning criterion
Different generation schedules would result from cost or loss as minimands. Table-1 shows the trade-off between the two ob'ectives considering a loading of LSF=O.7. The system cost ddfers significantly between the two cases i.e cost or loss minimization. The intermediate cases are obtained by minimizing cost subject to an upper limit on the total loss. It is seen from Table-1 that there is a eneration switching from the expensive unit (gen #2) to the cfeaFr-unit (gen #1) when cost is minimized, thereby incurrin addibonal system losses. However, it may be worthwhile k r the uulity to bear this additional loss and operate at minimum system costs, rather than switch generation to relatively expensive units located nearer to load Centres and reduce the losses.
0.018
Cost
($/hr) 6521.7
P.1 (p.u.MW)
p,, (p.u.MW)
0.500
0.673
(Minimum Loss) 0.02
6399.0
0.593
0.581
0.0225 0.025 0.027
62412 6161.6 6125.1
0.753 0.878 0.982
0.424 0.301 0.200
W i u m Cos0
Based on the above analysis, the cost minimization criterion has been used in the following analysis.
0.1848
0.2oOo 0.2oOo 0.2oOo
a
Step-3: As seen from Ste -2, load-buses #3, #4 and #5 would require ad itional reactive power support under higher loading conditions. However, it is worth examining whether installation of capacitor banks on these buses would prove to be costeffective. To this effect, a Cost-Benefit Analysis (CBA). as described in Fig.1, 1s tamed out. The syrbm cost increases when the capacitor from a pmcuhr bus is removed. This difference in cost is the marginal benefit from this capacitor. Table-3 gives the results.
Table-1: Loss vs. Cost Trade-off
Loss (in p.u.MW)
at load buses for different LSF
LSF
Table-3: Calculation of Marginal Bewfits in S CapaCitoF Capacimr Capacitor on Bur 15 ($1 on Bur Y4 ($) on Bus U3 ($) 0.W
0.7 0.8 0.9 1 1.1
0.00 0.00 0.00 0.00 0.12
0.00 0.00 0.24 0.65
12 1.3
1.55 8.03
2.54 957
.o
1.4 17.85 ............................................................................... Tolnl 82.65
benefit for the day ($1
20.05
0.00 0.17 1.93 4.50 8.30
13.23 22.69
640.13 ...............2072.85 ......
99.15
2018
Step-4: The BCR for the three load buses arc evaluated as: BUS#3: $82.65/$480.0 = 0.17 BUS#4: $99.15/$480.0 = 0.206 Bus #5: $2072.85/$480.0 = 4.32 Since the benefit-to-cost ratio for a capacitor on bus #5 is substantially high, thus bus #5 is selected for installation of capacitor. Even for smaller ratings of capacitors, the BCR is less than unity for buses #3 and #4. steps: The set of buses (L) to be considered for installation of capacitors is modified by rejecting buses #3 and #4. Step-6: Now, an OPF computation is carried out considering capacitor on bus #5 only. It is found that, the voltage conscraints are violated for higher loadings. Therefore, additional reactive power support is needed at some other load bus(es), inspite of their low BCR. step7: From Step-4, it is seen that the capacitor on bus #4 has higher BCR as compared to that on bus #3. Hence, bus #4 is also selected for instaliing ca acitor. Another OPF computationensured that this sektion gives feasible solution for all loading conditions considered. Thus, the selection (on bus #5 and bus #4) is final.
Table-& SelccUon of bus capacitors fur IEEE 30-bus system Initial choice of Buses i E I with Buses rejected No. capacitors {set I E L) BCb1 from (L)
Itn.
1
As seen from Table-4, after the first OPF computations there were 10 load buses requiring VAr support. However, only capacitors on buses #7 and #30 had a higher benefit than cost. Hence the others were rejected from the set of candidate buses (L). Because of the highly reactive power loaded condition assumed for the system, some more new buses were selected for capacitor placement, in the second OPF run. However, these also had a BCR less than 1. The iterative scheme converges to the final solution when all the buses selected for capacitor placement have BCR more than 1. It is to be noted that, on1 a subset of buses are considered for selection which gradualry reduces, till the final solution is attained, when no further bus capacitors are rejected.
C. 60-Bus System
The analysis is further extended to an interconnected
system with dispersed eneration from sources having a wide range of costs. A &-Bus interconnected power system
(comprising two interconnected IEEE 30-Bus systems or Areas) is considered, where Area-1 has a high reactive power demand (power factor=O.85 for all buses) and expensive generators while Area-2 has cheaper generatin sources and light reactive power load (power factoh0.95 k r all buses). Analysis has been carried out to find an optimal mix of reactive power Compensation and transfer of power from
Y7 (0.2) #30 (0.1)
#4
W6 119 P21 #24
t26 #27 t29
......"..................................................................................................................... 2
#3 (0.05) #7 (az) I f 18 (0.05) Y20 (0.1) U22 (0.1)
#7 (0.2)
#30 (0.15)
#3 #i8
820 t22 W23 t25 W28
U23 (0.05) U25 (0.1) #28 (0.1) #30 (0.15)
............................................................................................................................. 3
B. IEEE 30-Bus System
In a large power s stem, there may be instances when some new buses are serected after a bus capacitor with BCR less than unity is dropped from the set of candidate buses (L). Stated alternatively, there may be some new members in the set I in a subsequent iteration when (L)is modified to reject some of the buses. The IEEE 30-bus test system is considered to demonstrate this phenomenon for one loading condition (peak load, LSF=1.4). The reactive power demands are increased considering a power factor of 0.85 at all buses to represent a heavily reactive power loaded system. The optimal allocation and sizing scheme described earlier, i applied and the iterative selection process of capacitors for the IEEE 30-bus &est system is shown in Table4
#4 (0.1) #6 (0.1) #7 (0.2) #19 (0.1) #21 (0.1) #24 (0.05) #26 (0.05) #27 (0.05) #29 (0.05) t30 (0.1)
#7 (0.2) #9 (0.1) #IO (0.15) 115 (0.1) #17 (0.05) 5130 (0.15)
17 (0.2)
#7 (0.2) #14 (0.1) #16 (0.2)
#7 (0.2) P14 (0.1) t16 (0.2)
#30 (0.15)
Y9 110 #15 #17
...................-......................................................................................................... 4
None
t30 (0.2) t30 (0.2) kigureo m 0 d e n e the capacilor rallngo HI p.u.MVAr
kea-2 to kea-1. to keep the system costs at minimum. The performanceof the capacitor selection algorithm has remained satisfactory for this test case also. Area-2 supplies 1.55 p.u.MW cheaper surplus power to meet 57% of kea-1 demand even if such transfers lead to relatively high system losses. Also, a Group of ten buses is selected for capacitor installation, having an aggregate BCR of 1.215, to keep the voltages within limits. The scheme ensures accurate calculation of benefits and global optimal solution with good convergenceproperties.
3 3 Evaluation of reactive power price The proposed reactive power price has two parts - a fixed part component to account for installation cost of new capacitor at buses where they are installed (which could be charged periodically) and an hourly spot price to account for the operating costs incurred to supply the ddditional reactive power from enerating units. Considering the 5-bus system, evaluation ofthe fixed part component for load buses #4 and #5 are based on their capital costs, as given in Step-2 (Section 3.2). Since there is no additional capacitor requirement at bus #3, hence no fixed part component is charged at this bus. To determine the variable operahng costs of supplying additional VAr requirements, OPF computationsare carried out without the capacitors on buses #4 and #5. However, the reactive power demand at these buses are reduced by an amount Q for different hours. The marginal cost of providing this reduced reactive power demand at buses #4 and #5 is the spot prices for these buses. For bus #3, the
2019
marginal cost is calculated based on the reactive power demand which is kept unchanged. At the generating bus, the price of reactive power is zero till the reactive power generating capacity limits (Qs- and Q "") are reached. The spot prices at buses #3, #4 and #5 are &own in Fig.2. I
V0L138, Jm.91, pp.27-38. N.Deeb and S.Shahidehpour, "Cross decomporition f a multi-area optimal readive power planning". IEEE Trans. on Power Systems, VOLPWRS-8,N ~ . ' 9 3 pp. , 1539-1544. S.V.Berg, J.Adams and B.Niekum, "Powerfactors and the efficient pricing and production of reactive power". The Energy Journal, VOl.4. pp.93-102. M.LBaughman and S.N.Siddiqi, "Real-time pricing of d v e power: 'Iheory and case study resulu", IEEE Tra~u.an Power Systeans. Vd.F'WRS-6. Feb.'91, pp.23-29. F.C.Schweppe, M.C.Caramanir, R.D.TPbon and REBohn, Spot pricing qfelectricity. Kluwer Academic Publishers. 1988. A.Brodte, D.Kendri& and A.Meeraur, GAMS - A User's Cuidc. The Saartific Press, 1988. London Economics Re-, India-Lung k m issues in the power sector, VOLS. 1990. G.W.Stagg and A.H.El-Abiad. Cmnputer methods in power system analy.?l.McGrpw-HiU Inc.. 1968.
[SI [6]
1
[7] [SI 191 [lo] 1111
6. APPENDIX
The 5-bus system considered. ir deecribed in detail in [111 while the IEEE 30-bus system has been widely used [SI. The bus loadings have, however, been considered to vary over a day. Hourly loads at each bur have been evdved by using a Losd Scaling Fawhere. LSF varies ftun 0.7 to 1.4. ' h e generating unit cost characteristic u d limits an given in Table 5.
4. CONCLUDING REMARKS The paper presents a simple approach to reactive power planning and combines this issue with that of reactive power pricing so as to recover the costs of installing new capacitors at load buses. The criterion used in the reactive power planning problem is to minimize the system generating cost and the cost of adding new capacitors. All load buses have been considered as possible locations for installation of capacitors. A simple algorithm has been proposed to perform a bus-wise cost-benefit analysis (CBA) to decide upon optimal capacitor placements and their sizes. This algorithm obviates the use of integer variables and makes use of a series of modified o timal power flow (OPF) computations. Avera e hourly loacfcurve for each bus, has been considered for 8 e selection of capacitors. This gives a more accurate estimate of the benefits therein. A 5-bus system, the IEEE 30-bus test s stem and a 60-Bussystem have been used to demonstrate $e effectiveness of the proposed scheme. A bus-wise, twopart tariff scheme for reactive power has been proposed comprising a fixed part component which recovers the investment costs incurred and a real-time part to reflect the operating costs incurred by the utility while supplying the residual reactive power requirement. The fixed part could be realized on the basis of a periodical payment similar to the connection charge levied in India [lo] for real power.
5. REFERENCES [l]
[2]
[3]
[41
S.Rama Iyer, K.Ramachandran and S.Hariharan,"Optimal reactive power allocation for improved system perfonnance", IEEE Trans. on Power Apparatus and Systems, VoLPAS-103, June'84, ~p.1509-1515. J.Qiu and S.Shahidehpour, "A new approach for minimizingpower losses and improving voltage profile", IEEE Trans. on Power Systems, Vol.PWRS-2, May'87, pp.287-295. K.Aoki, M.Fan and A.Nishikori, "Optimal VAR planning by approximation method for recursive mixed-integer h e a r programming", IEEE Trans. on Power Systems, Vol.F'~S-3. N O V . ' ~pp.1741-1747. ~. N.Deeb and S.Shahidehpour. "Decompositim approad for minimizing real power losses in power systems", Proc.IEE. Pan-C,
Table I:Generator characlerbtlfl
s 11
12
4
m s 600 600 600
4
m
2940 4212
c, $AI
1250 532
P,& Mw
P,Mw
Qd
MVAR
50
150
-lw
20 20
150 150
-40
................................................................................................................... Y5 18
111 #I3 134 155 1%
4668
481
-10 -40
-6 -6 -10 -40
................................................................................................................... 120 1200 1020 50 300 120 120
612 1380
480 720
50 40
300 300
-100
Q-
MVAR
150 50
40 40 24
24 40 M
150
D.Chattopadhyay obtained his B.E. in Mechonicol Engineering from Regional Engineering College, Durgapur ( I d a ) in 1990. Cumntly, he ir w o h g towarda his Ph.D. at the Indira Gandhi Institute of Dexelopnent Research, Bombay, India. His research interests include economic operntion of power systems, environmental and demand-side management aspects. K.Bhattacharya obtained his B.Tech in 1986, M.E.from B.LT.Mesra. Ranchi, in 1988 and Ph.D. from Indian Institute oi Techndogy, Delhi in 1993. all in Electrical Engineering. Presently, he b i . r the faculty of Indira Gandhi Instiwte of Development Research, Bombay. Hb research interests include power system operations planning. stability and unmL
Jyoti Parikh received her M.Sc from the University of Cplifomh, Berkeley and Ph.D. in theoretical Nuclear Physics from the University d Maryhd at College Park. She has worked at the IntemotiollPl Institute of Applied Systems AnalysiB (KIASA),Austria for eight years on energy and enviraUnent problems of the developing countries. Currently, she is a !&xior Professor at the Indira Gandhi Institute of Development Researd. Bombay. She was Senior Consultantfor the World Bank study on Indian Power Sector to set Up a power system simulation model for the regimal grids d India. She ir on the editorial hard of rhe international journal Utilitk Policy. Her research interests include power systems operatiom planning, prihg poli~y. environmental and demand-ride managanent aspects. She has p l b b h d extensively in i n t e m a u d journal. of reputr.
2020
DISCUSSION Subir Sen and D.P. Kothari (Centre for Energy Studies, Indian Institute of Technology, New Delhi, India): The authors are to be commended for presenting an integrated approach to optimal reactive power planning and its spot pricing to different test systems. However, we would like to seek the authors' clarification on the following points:
1. In the paper it is assumed that reactive power can flow from one voltage level to other. However, the basic principle of reactive power compensation in integrated network is complete avoidance of VAR flow from one voltage level to other yoltage level during normal network condition. Otherwise this may lead to heavy voltage drop in the system and may take the system towards voltage instability. It would be highly appreciated if the authors may express their views on the same alongwith the study results. This would immensely help further research in this area.
D.Chattopadhyay, K.Bhattacharya and Jyoti Parikh:
We appreciate the discussers' interest in this work. We have the following response to offer: 1.
In this work, the reactive power demand at a load bus is met by an optimal mix of shunt compensation and reactive power generation from generating sources, such that operational and investment costs are minimum. The RPP problem presented here involves solving this modified OPF formulation which includes voltage constraints at all load buses and line flow constraints. Under heavy reactive loading in the system, which could lead to voltage instability, the optimal mix would change towards higher reactive compensation, subject to the same objective of reducing overall costs.
2.
Section 3.1 adequately discusses why cost has been considered as an objective function. It has been clearly demonstrated that there exists a trade-off between the cost and loss minimization objectives. It can be seen that following a minimum loss criterion Ieads to high cost of generation (Table-1). This is different from the earlier studies [l-51 where transmission loss minimization or "cost" of transmission loss were considered for minimization. If system parameters viz. voltage, line flows etc. are within their specified limits, it would always be desirable for the utilities to operate on a least-cost schedule.
3.
The test cases presented in the paper were carefully coined so as to cover the possible complexities which may arise in a real-life system. For example, we have considered a case (Section 3.1.B) where some new buses are selected when capacitoi in some other bus is dropped and a system with dispersed generation from demand centers with a wide range of costs (Section 3.1.C). Efforts are underway to develop an OPF model for an Indian utility which will subsequently be used for RPP using the methodology presented. However, we have encountered problems in getting data on certain parameters like generator cost characteristics which do not exist in published form. Once we have access to the complete database on network, we would come up with our findings.
2. In the paper the minimisation of cost has considered as the objective. However, to get an optimal solution the transmission loss(which shall increase with low voltage condition in the network) should also be considered as another objective. Has any such type of studies been carried out ? Please clarify.
3. It would have been better if the authors would have explained their approach/model through an actual reallife system rather than a sample test system. It would have been welcome if the authors would present the excellency of their approach through a practical operating system alongwith complete system data. Finally, we would appreciate the authors' responses and congratulate them dn their excellent presentation and look forward to their further investigations in the field. Manuscript received March 7, 1995.
Manuscript received April 10, 1995.
