16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 010 386 Distribution Systems otage Profie Improvement with Series FACTS Devices Using Line Fow-Based Equations K. enkateswararao, P. K. Agarwa Department of Eectrica Engineering, Maaviya Nationa Institute of Technoogy, Jaipur, India kunche83@gmai.com, pkagra66@gmai.com Abstract-In this paper bus votage improvement of distribution systems with series Fexibe AC Transmission System (FACTS devices is faciitated by a formuation of power fow equations with bus votage magnitudes and ine fows as independent variabes. Since contro variabes such as the ine and bus reactive powers figure directy in the formuation, handing the contro action of FACTS devices in distribution systems is direct and easiy impemented. Using the Breadth-First-Search (BFS, the bus incidence matrix of a radia distribution system is first rendered stricty upper diagona, eading to reduced computationa effort. A the common FACTS device modes under steady-state conditions are easiy incorporated in the new framework by a simpe process of variabe swapping. Using IEEE standard systems, the ine fow-based (LFB formuation is shown to provide easy impementation with mutipe series FACTS devices in the system and enabe direct evauation of the FACTS device ratings. Keywords: Distribution Systems, FACTS, Breadth-First-Search (BFS I. INTRODUCTION Fexibe AC Transmission System (FACTS devices are paying a eading roe in efficienty controing the ine power fow and improving votage profies of the power system network. These new devices can increase the reiabiity and efficiency of transmission and distribution systems. They offer greater fexibiity and contro in operation. Conventiona power fow anayses such as Newton Raphson [1] and Fast Decouped Agorithm [] have been adapted to incude the FACTS device modes [3] in transmission systems. The maor obectives of FACTS devices instaed on a distribution feeder are to improve votage profies, correct power factor, and reduce ine osses. Distribution ines have high R/X ratios, eading to convergence probems in traditiona approaches. Modifications and extensions to standard oad fow agorithms with FACTS devices are reported. Saem et a. [4] have expoited the anaogous mode of thyristor-controedseries-capacitor (TCSC to improve votage contro in a radia distribution system. Garcia et a. [5] derived a modified Newton method in rectanguar Coordinates by requiring an augmented Jacobean matrix to incorporate the additiona series FACTS devices reationships between each contro action and controed variabe. Distribution power fow methods reported in the iterature and actuay impemented prefer to cacuate ine fows and votage magnitudes using forward and reverse sweeps aong a radia ine [6], [7]. Line current and bus votage phasors with simpe votage drop cacuations in the section impedances enabe easy handing of the highy unbaanced nature of the distribution networks. The main obective of this paper is to deveop an LFB formuation of power baance equations for anayzing a radia distribution system that wi efficienty incorporate embedded series and shunt FACTS devices. The LFB equations use bus votage magnitudes and ine power fows as independent variabes and directy reate the FACTS device variabes with system operating conditions. The ine oss terms are the ony noninear terms in the formuation. By adding them to bus power inections, the coefficient matrix of LFB equations is rendered inear. A preiminary Breadth-First-Search (BFS ordering of the branches transforms the coefficient matrix structure to stricty upper/ower diagona and eads to simpe backward/forward substitution for cacuating rea and reactive ine power in each branch and votage at each bus. The FACTS device modes are described first, and the deveopment of LFB equations foows. Numerica exampes, incuding mutipe FACTS devices in the standard IEEE systems, iustrate the power of the new approach. The procedure exhibits good convergence characteristics, high reiabiity, and computationa efficiency. A baanced distribution feeder modeed by the positive sequence impedance is used in the paper, since the aim of this paper is to demonstrate the advantages of the LFB formuation in handing the embedded FACTS devices. FACTS devices can be assumed to be cost-effective when depoyed on the main distribution feeder. II. STATIC MODELING OF FACTS DEICES The concept of FACTS first proposed in 1978 is finding increasing appea in power system panning and operation. Series compensators such as Thyristor Controed Series Department of Eectrica Engineering, Univ. Coege of Engg., Osmania University, Hyderabad, A.P, INDIA.
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 010 387 Capacitor (TCSC, Thyristor Controed otage Reguator (TCR, Thyristor Controed Series Reactor (TCSR, and Thyristor Controed Phase Ange Reguator (TCPAR and shunt compensators such as Static ar Compensator (SC and STATCON. The combined series and shunt FACTS s sampe is Unified Power Fow Controer (UPFC [8]. To deveop the static modes of most FACTS devices, TCSC, TCR, and SC, are speciay discussed in this section and summarized into an integrated FACTS mode. A. TCSC TCSC is defined as a capacitive reactance compensator, which consists of a series capacitor bank shunted by a thyristorcontroed reactor in order to provide a smoothy variabe series capacitive reactance. In the steady-state power fow study, the TCSC can be considered as a static capacitor or reactor offering a reactance x c with a series compensated branch represented by umped equivaent series parameters connected. In most cases, the shunt susceptances of a branch usuay are negected. Therefore, the TCSC s static capacitor wi be directy in series with the ine impedance. B. TCR TCR is considered as the common votage reguator. It is abe to smoothy vary votage magnitude with a tap changing in the contro range of α min < α i < α max. A static mode of TCR with a tap ratio is connected in a series impedance of the distribution ine. C. SC Fig.1. Generic ine segment with FACTS parameters. SC based on thyristors without the gate turnoff capabiity is considered as a shunt-connected static AR generator or absorber. Their output is adusted to exchange capacitive or inductive current. As an important component for votage contro, it is usuay instaed at the receiving bus. In the formuation, the SC has been considered a shunt branch with a compensated reactive power Q SC setting by avaiabe inductive and capacitive susceptances. D. Generic Line Segment with FACTS Parameters Fig. 1 shows the generic mode of a ine segment embedded with series-cass and shunt-cass FACTS devices. Depending upon the FACTS device type, its function in the generic mode can be easiy impemented. Athough designation of sending and receiving ends is arbitrary, ine fow directions are indicated cose to the receiving end. A transformer with tap and phase ange parameters is ocated at the sending end. Additionay, η and x are resistance and reactance of branch ; i and are sending and receiving bus numbers of branch ; and p i and q i are active and reactive power fow at the receiving end of Branch. The generic ine mode is used to derive ine votage drop equations in the LFB formuation. The phase ange parameter is ignored since it is has no significance in radia distribution systems. III. LFB RADIAL DISTRIBUTION POWER FLOW MODEL Since ine fows and bus votage magnitudes are of practica importance in the operation of a distribution system, and the FACTS devices contro these quantities, a power fow mode based on rea and reactive ine power fows and bus votage magnitudes wi enabe easy handing of series and shunt devices. Rea and reactive power baance equations at a buses except the sack bus can be written using the incidence matrix of the network graph [9]. Since a shunt connections are excuded in the incidence matrix, their rea and reactive power contributions are accounted for separatey in the power baance equations. Rea and reactive power oads, shunt capacitors, and ine charging susceptances can be treated as shunt branches. Foowing the traditiona cassification of sack, votagecontroed, and oad buses, the LFB equations are formuated as three sets of equations viz., bus rea and reactive power baance and branch votage equations. A. Genera Power Baance Equations Using a bus incidence matrix A with rows corresponding to a busses other than the sack, the bus rea and reactive power baance can be written as foows: (1 A. p P A'. 0 A. q Q GL GL A'. m H. A is defined as a modified bus incidence matrix with a 1 in set to zero, which makes it easy to incude the ine osses in the power baance equations by using the vectors of branch rea and reactive power osses and m. H is a diagona matrix, whose diagona eements are sums of charging and compensating susceptances at each bus. P GL and Q GL are the bus inection power vectors defined as P GLi = P Gi P Li and Q GLi = Q Gi Q Li, where P Gi, Q Gi, P Li and Q Li are active and reactive generator and oad powers at bus i, i and m i are active and reactive power osses in ine, p and q are rea and reactive ine fow vectors at the receiving end. is the unknown votage vector except at the sack bus. i ( is the square of votage magnitude at bus i. If dispersed generators exist in the distribution system, the corresponding generator buses are cassified into two kinds viz., constant inected power PQ buses or votage-controed P buses. Let n be the tota number of buses and n P and n PQ the number of votage-controed and oad buses, respectivey. Aowing for one sack bus, the tota number of various buses is 0 Department of Eectrica Engineering, Univ. Coege of Engg., Osmania University, Hyderabad, A.P, INDIA.
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 010 388 n = n P + n PQ + 1 (3 The number of unknowns in ( is reduced from n 1 to n n P 1, and the equation is rewritten as A. q Q A '. m H. 0 (4 where a symbos with subscript 1 are the reevant matrices or vectors containing PQ buses ony. B. Branch otage Equations Referring to Fig. 1, the branch votage drop equation can be written as i ( p q i ( r ( x xc (5 t ( ( p q i ( i ( r ( x xc t ( Taking the magnitude of both sides of (6 and rearranging, we get the foowing: 4 i [ r p ( x xc q ] t (7 ( p q ( r ( x x 0 i [ r p xq xcq ] t Where k 1 GL1 1 1 1 c k (8 s ( r ( x x c s p q The branch equation of each ine form as matrix form T T T RP Xq ( A1 A1. k Ac sack (9 Where A C is a bus incidence matrix corresponding to the P buses. is a vector of square of votage of P buses and sack the sack bus. is a diagona matrix of order equa to with the vaues of a tapped transformer equa to the square of the tap vaue. A 1+ and A 1 are obtained from A 1 by setting, respectivey, the negative and positive vaues in A 1 to zero. R and X are diagona ine resistance and reactance matrices. The vector k represents the term on the right side of (8 for a the ines. (6 I. NATURE OF RADIAL DISTRIBUTION NETWORK GRAPH The radia distribution network graph has a tree structure with no oops. The tota number of ines equas the number of buses minus one. Since the pattern of incidence matrix depends on the order of ines and nodes, the incidence matrices in (9 have a structure that depends on the order in which the ines are read from the data. Further, the incidence matrices are square and nonsinguar. Athough BFS and Depth-First Search [10] are two different patterns of tree search methods of graph in widespread use, here BFS is seected to search radia distribution network graph in the LFB mode. The basic idea of BFS is to point out to as many buses as possibe before penetrating deep into a tree. This means that we visit a the buses adacent to the current eve before going on to another one. The brief description of BFS to renumber buses and branches may be summarized in the foowing three steps for buiding an optima BFS tree. 1 Start at source bus as the first eve and fan out to the downstream buses as the next eves. On the same eve, a bus numbers are ordered consecutivey. 3 Branch renumbering is simiar to that of the bus renumbering. At any eve, a branch number is one ess than the upstream bus number. An exampe of using the BFS agorithm is iustrated using the radia distribution system with thirteen nodes and tweve ines of [11] and [1] shown in Fig.. Lines have ony series impedances. The nodes are numbered arbitrariy. This exampe distribution network graph is redrawn in Fig. 3 with bus numbers in sequence starting from 1. Fig. 3. Graph of the IEEE 13-node feeder Fig.. IEEE 13-node test feeder. Department of Eectrica Engineering, Univ. Coege of Engg., Osmania University, Hyderabad, A.P, INDIA.
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 010 389 Fig. 4. Arbitrary order incidence matrix. Athough no. 1 is given to the ony source bus here, the others encirced are arbitrary numbers as given in the origina data ist. This is usefu when the network is reconfigured to meet the demand under different oad and feeder scenarios. The fows in the branches are aways oriented away from the source node, and so the direction arrows are ignored. TABLE I SUMMARY OF FACTS TYPE AND IMPLEMENT IN IEE13-NODE FEEDER FACTS Device Branch Iterations Contro parameter TCR 1-5 t=1.0676 TCSC 1-5 = -0.078 p.u The incidence matrix in Fig. 3, incuding the source node (at root, originay named as 650 caed Bus 1, is shown in Fig. 4. To conform to LFB oad fow equations of the ater section, the rows of the matrix are reated to buses and its coumns to branches. The BFS renumbering is appied to the 13-node test feeder. The optima BFS tree of the IEEE 13-node feeder is shown in Fig. 5. Its reordered incidence matrix, incuding the source node, is shown in Fig. 6. Fig. 6. Reorder incidence matrix for Fig. 5. BFS optima tree.. DECOUPLED LFB MODEL OF RADIAL DISTRIBUTION SYSTEMS Decouped LFB Equations Ap PGL A (10 A GL (11 1q Q A1 H1 T T A1 Ac pv k Rp Xq (1 With BFS ordered ines, the bus incidence matrix and are upper triange matrixes and is a ower triange matrix in nature. Using fat votage profie as starting vaue, the ine fows and may be directy obtained by its backward substitution of (10 and (11. Using the updated p and q into (1, the square votage magnitudes can be cacuated by the forward substitution. There is no need for factorization of the coefficient matrix. The decouped set of equations is easier to code in a program. I. TEST RESULTS IEEE 13- and 34-bus test systems form the basis for testing the LFB formuation. The decouped LFB procedure is appied to the IEEE 13-node test feeder of Fig. with the addition of a singe series FACTS device and the IEEE 34-node test feeder modified with mutipe FACTS devices. A ines have ony resistance and reactance vaues. Base oad fow studies of the exampe systems without any FACTS devices are cacuated. By incuding the FACTS devices, the effect on the votage profies is then studied. A parameters of the modified systems come from [11] and [1]. A convergence toerances are seected as 10 4. TABLE III DEICES IMPLEMENT AND LOCATIONS Fig. 5. BFS numbering tree of the IEEE 13-node system. Case Branch FACTS otage Impement 1 7-8 TCR 1.03 1.014 19-0 TCR 1.0 1.016 7-8 TCSC 1.03-0.037 19-0 TCSC 1.0-0.039 Department of Eectrica Engineering, Univ. Coege of Engg., Osmania University, Hyderabad, A.P, INDIA.
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 010 390 3 7-8 TCR 1.03 1.013 19-0 TCSC 1.0-0.039 4 7-8 TCSC 1.03-0.036 19-0 TCR 1.0 1.015 To contro the votage at bus of the IEEE 13-node feeder to 1.05 p.u., a singe series FACTS device, either TCSC or TCR, is considered in ine 1 on Fig. 5 to reaize this contro obective. The soution converged in five iterations. Tabe I summarizes the resuting FACTS device parameters to reaize the contro obectives. The investigation for these two type FACTS to reaize the same contro obective shows amost the same vaues of their votages of each bus. In addition, their max votage difference at the same bus is beow 0.005 (p.u.. The votage profies in Fig. 7 demonstrate the effect of the FACTS device on improving the votage profie. radia distribution system configuration of Fig. 8 is used to study the effect of mutipe FACTS devices embedded in the system. BFS numbering is isted in Tabe II aong with the origina numbering in the diagram. The IEEE 34-bus system is modified with two FACTS controers with both of TCSC, TCR, or one TCSC and another TCR. The resuts of FACTS device parameters are summarized in Tabe III, which ists FACTS instaation [13] ocations and contro obectives. The LFB approach easiy converged as ong as the equivaent reactance of the ine with a TCSC controed by series capacitor is not cose to zero. The effects on the specified votage profies are shown in Fig. 9. Fig.9. comparison of FACTS effect on votage profies. Fig.7. votage profies after and before facts instaed on the IEEE 13-node test feeder The LFB approach presented in this paper handes mutipe FACTS devices in a system with equa ease. The IEEE 34-bus Fig. 8. IEEE 34-node test feeder. Department of Eectrica Engineering, Univ. Coege of Engg., Osmania University, Hyderabad, A.P, INDIA.
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 010 391 TABLE II IEEE 34-NODE NUMBERINGS DEFINED BY BFS AND THE ORIGIN Department of Eectrica Engineering, Univ. Coege of Engg., Osmania University, Hyderabad, A.P, INDIA.
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 010 39 II. CONCLUSIONS FACTS devices offer a fexibe and comprehensive soution to votage profie contro in distribution systems. The ine fowbased agorithm provides a direct and simpe approach to hande singe or mutipe devices. This wi enabe easy determination of size and pacement of such devices. The ine fow-based equations have constant coefficient matrices and need no updating during the iterative procedure. Breadth first search [14] of the topoogy of the radia network eads to a coefficient matrix structure of LFB equations that is aready in a trianguar form, which resuts in ust one forward or backward substitution in each iteration. This paper demonstrates the ease with which singe or mutipe FACTS devices can be handed by the LFB formuation. Simpe variabe exchange or swap requiring itte change to the overa soution methodoogy enabes the evauation of the contro parameters. IEEE 13- and 34-node standard distribution systems are used to iustrate the method of evauating the FACTS device parameters. Singe and mutipe FACTS devices are considered. Series FACTS devices are empoyed to improve the votage profie. The required device parameters, such as the series capacitance and the shunt ARs, are directy determined. [1] IEEE Distribution Feeder Test Resut. IEEE Distribution System Anaysis Subcommittee. [Onine] Avaiabe: http//ewh.ieee.org/soc/pes/ dsacom/testfeeders.htm [13] Guang Ya Yang; Hovan, TCSC Aocation Based On Line Fow Based Equations ia Mixed-Integer Programming, IEEE Trans. Power Sust., vo.,issue:4,pp.6-69, 007 [14] M. Naork and J. L. Wiener, Breadth-first search crawing yieds highquaity pages, in Proc. ACM 1-58 113-348-0/01/0005, WWW10, Hong Kong, May 5, 001. REFERENCES [1] W. F. Tinney and C. Z. Hart, Power fow soution by Newton s method, IEEE Trans. Power App. Syst., vo. 86, no. 11, pp. 1449 1456, Nov. 1967. [] B. Stott and O. Asac, Fast decouped oad fow, IEEE Trans. Power App. Syst., vo. 93, no. 3, pp. 859 869, May/Jun. 1974. [3] N. G. Hingorani and L. Gyugyi, Understanding FACTS: Concept and Technoogy of Fexibe AC Transmission Systems. New York: IEEE Press, 1999. [4] M. R. Saem, L. A. Taat, and H. M. Soiman, otage contro by tapchanging transformers for a radia distribution network, in Proc. Inst. Eect. Eng., Gener., Transm., Distrib., vo. 144, Nov. 1997, pp. 517 50. [5] P. A. N. Garcia, J. L. R. Pereira, and S. Carneiro, otage contro devices modes for distribution power fow anaysis, IEEE Trans. Power Syst., vo. 16, no. 4, pp. 586 593, Nov. 001. [6] W. H. Kersting, Distribution System Modeing and Anaysis. Boca Raton, FL: CRC, 00. [7] DEWorkstation, Eectric Power Research Institute, Pao Ato, CA. Jan. 1989. [8] L. Gyugyi, T. R. Rietman, S. L.Wiians, T. R. Rietman, D. R. Torgerson, and A. Edris, The unified power fow controer: A new approach to power transmission contro, IEEE Trans. Power De., vo. 10, no., pp. 1085 1097, Apr. 1995. [9] G. W. Stagg and A. H. E_Abiad, Computer Methods for Power System Anaysis. New York: McGraw-Hi, 1971. [10] R. J. Wison and J. J. Watkins, Graphs: An Introductory Approach. New York: Wiey, 1990. [11] W. M. Kersting and L. Wiis, Radia distribution test systems, IEEE Trans. Power Syst., vo. 6, no. 3, pp. 975 985, Aug. 1991. Department of Eectrica Engineering, Univ. Coege of Engg., Osmania University, Hyderabad, A.P, INDIA.