Static Security Based Available Transfer Capability (ATC) Computation for Real-Time Power Markets

Transcription

1 SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 7, No. 2, November 2010, UDK: : Statc Securty Based Avalable Transfer Capablty (ATC) Computaton for Real-Tme Power Markets Chntham Venkaah 1,a), Dulla Mallesham Vnod Kumar 1,b) Abstract: In power system deregulaton, the Independent System Operator (ISO) has the responsblty to control the power transactons and avod overloadng of the transmsson lnes beyond ther thermal lmts. To acheve ths, the ISO has to update n real-tme perodcally Avalable Transfer Capablty (ATC) ndex for enablng market partcpants to reserve the transmsson servce. In ths paper Statc Securty based ATC has been computed for real-tme applcatons usng three artfcal ntellgent methods vz.: ) Back Propagaton Algorthm (BPA); ) Radal Bass Functon (RBF) Neural network; and ) Adaptve Neuro Fuzzy Inference System (ANFIS). These three dfferent ntellgent methods are tested on IEEE 24-bus Relablty Test System (RTS) and 75-bus practcal System for the base case and crtcal lne outage cases for dfferent transactons. The results are compared wth the conventonal full AC Load Flow method for dfferent transactons. Keywords: Avalable transfer capablty, Intellgent technques, Power system deregulaton, Real-tme power markets, Securty analyss. Introducton The Avalable Transfer Capablty (ATC) of a transmsson network s the unutlzed transfer capablty of a transmsson network for the transfer of power for further commercal actvty, over and above already commtted usage [1]. Power transactons between a specfc seller bus/area and a buyer bus/area can be commtted only when suffcent ATC s avalable. Thus such transfer capablty can be used for reservng transmsson servces, schedulng frm and non-frm transactons and for arrangng emergency transfers between seller bus/area and buyer bus/areas of an nterconnected power system network. Chrste et. al. [2] reported that the US Federal Energy Regulatory Commsson (FERC) began the federal deregulaton process by requrng open access to transmsson servces, so that all companes ownng generaton would have equal opportunty to locate and obtan transmsson servces between ther generaton stes and ther customers. The ATC values for the next hour and for each hour nto the future would be placed on a webste known as the Open 1 Department of Electrcal Engneerng, Natonal Insttute of Technology, Warangal Andhra Pradesh, Inda; E-mal: a) ch.venkaah@gmal.com; b) vnodkumar.dm@gmal.com 269

2 C. Venkaah, D.M.V. Kumar Access Same-tme Informaton System (OASIS), to be operated by Independent System Operator (ISO). Anyone wshng to send a power transacton on the ISO s transmsson system would access OASIS web pages and use the ATC nformaton avalable there to determne f the transmsson system could accommodate the transacton, and to reserve the necessary transmsson servce. Thus the ATC must be computed fast and accurately. Hamoud [3] descrbed a method based on ATC concept for assessng the feasblty of smultaneous blateral transacton and t utlzed the Ontaro Hydro s Probablstc Composte System Evaluaton Program (PROCOSE) whch employs DC Load flow to perform the analyss. Hamoud further [4] proposed a smple, effcent and practcal method employng PROCOSE for determnng the ATC between any two locatons n the system and the ATC s for selected transmsson paths between them. Marja et. al. [5] dscussed some theoretcal aspects of ATC and the problems assocated wth ts evaluaton under open access. Vktor et. al. [6] ncluded ATC n Optmal Transacton Management (OTM) method for remedal transactons curtalment and ths method s found well suted for market-related analyss. Jayashree et. al. [7] proposed a unfed optmzaton model and algorthm for assessng ATC and carryng out Congeston management usng Unfed Power Flow Controller (UPFC) n a deregulated Power Systems handlng both pool and blateral transactons. Ths method used DC Load flow model and repeated Lnear Programmng routne. The dc loadflow-based methods [2-7] are a bt faster than ther ac counterparts but model only real power flow (n Mega Watts) n the lnes rather than MVA, and assume the network to be loss free. Ejebe et. al. [8] presented a detaled formulaton and mplementaton of a fast program for ATC calculaton based on the lnear ncremental power flow approxmaton. Frad et. al. [9] presented a method to calculate energy transacton allocaton factors for allocaton of any nonlnear transmsson system quantty to the actve transactons placed on a transmsson system. Ashwan and Srvastava [10] proposed a methodology based on AC Power Transfer Dstrbuton Factors (ACPTDF) to allocate the actve power loadng n transmsson lnes. The methods based on power transfer /outage dstrbuton factors [8-10] can cater to only the scenaros that are too close to the base case from whch the factors are derved. Jan et. al. [11] presented an approach based on RBF neural network to rank contngences expected to cause steady state bus voltage volatons. Ejebe et. al. [12] mplemented a methodology developed for rankng transmsson lne outages and generator outages accordng to the severty of ther effects on bus voltage or lne flows. Wu [13] proposed a novel algorthm for contngency ATC computaton and a senstvty analyss for system uncertantes. Luo et. al. [14] proposed a neural network soluton methodology for the problem of real power transfer capablty calculaton. The Quck prop algorthm 270

3 Statc Securty Based Avalable Transfer Capablty (ATC) Computaton... s utlzed to tran the neural network for estmatng the transfer capablty and the nputs to neural network are generator status, lne status and load status. The artfcal neural network (ANN) method [14] requres a large nput vector so that t has to oversmplfy determnaton of ATC by lmtng t to a specal case of power transfer to a sngle area from all of the remanng areas. So ths method s unable to track down the bus-to-bus transactons, whch s the true sprt of deregulaton. The Adaptve Neuro Fuzzy method has a lmtaton wth the unversal ndex as all the lne outage cases are consdered for two categores leadng to naccurate ATC values n most of the lne outage cases. Kharuddn et. al. [15] proposed a novel method wth the full detals for determnng ATC n a large power system from only three nput varables through fuzzy modelng. Kharuddn et. al. [16] ntroduced the concept of varable slack bus and the source bus s assgned to slack bus for ATC computaton. The ATC s computed based on the hghest possble ncrement of snk bus load above the base case. Here, ANN technques have not been ntegrated wth fuzzy systems for fast ATC computaton. In ths paper to overcome the above lmtatons, to reduce the computatonal burden and to execute ATC n real tme dfferent Artfcal Intellgence (AI) technques vz., Back Propagaton Algorthm (BPA), Radal Bass Functon (RBF) Neural Network and Adaptve Neuro Fuzzy Inference System (ANFIS) have been utlzed and compared wth the AC Load flow based ATC. These methods are tested on standard IEEE 24-bus [17] Relablty Test System (RTS) and 75-bus [18] practcal system, for base case and crtcal lne outage cases, for dfferent transactons. In recent years, hybrd fuzzy neural networks have attracted consderable attenton for ther useful applcatons n such felds as control, pattern recognton, mage processng, forecastng etc. In all these applcatons, there are dfferent fuzzy neural network archtectures proposed for dfferent purposes and felds. The ntegrated system wll possess the advantages of both neural networks (e.g. learnng abltes, optmzaton abltes, and connectonst structures) and fuzzy systems (e.g humanlke IF-THEN rules thnkng and ease of ncorporatng expert knowledge). In ths way, one can brng the low-level learnng and computatonal power of neural networks nto fuzzy systems and also hgh level, humanlke IF-THEN rule thnkng and reasonng of fuzzy systems nto neural networks. Thus, on the neural sde, more and more transparency s pursued and obtaned ether by pre-structurng a neural network to mprove ts performances or by a possble nterpretaton of the weght matrx followng the learnng stage. On the fuzzy sde, the development of methods allowng automatc tunng of the parameters that characterze the fuzzy system can largely draw nspraton from smlar methods used n the connectonst communty. Thus, neural networks can mprove ther transparency, makng them closer to fuzzy systems, whle fuzzy systems can self adapt, makng them 271

4 C. Venkaah, D.M.V. Kumar closer to neural networks. Integrated systems can learn and adapt new assocatons, new patterns and new functonal dependences. Ths paper s organzed as follows. Secton 2 detals the problem formulaton of ATC computaton for real-tme power markets. Secton 3 gves an nsght nto Artfcal Intellgent methods (BPA, RBF and ANFIS) applcaton for ATC computaton. Secton 4 llustrates legbly the effectveness of utlzaton of ntellgent methods on standard IEEE 24-bus system and Practcal Indan 75-bus system. The conclusons are presented n Secton 5. 2 Problem Formulaton The ATC problem for real-tme applcaton has been attempted n two dfferent ways ) Neural Network approach and ) Adaptve Nero Fuzzy approach. For a gven source-snk par, tracng the least ndrect path usng lne mpedance data, dentfes the neghborng bus. The one havng the least mpedance among all the possble ndrect paths s chosen. If there are a number of buses on the chosen ndrect path between a source and a snk then the bus mmedately after the source s labeled as the neghborng bus. A new unversal ndex (γ) has been proposed to represent a gven operatng condton of a power system takng nto account demands at all the buses except the snk and neghborng bus. At the snk bus load s to be ncreased untl t volates the thermal lmt and the neghborng bus s a generator bus. Hence the loads are consdered at these two buses. The Unversal ndex ( γ ) s defned as N γ= P, (1) = 1, Ns, Nn where P d s demand (MW) at bus, N s the total number of buses, N s and N n are snk and neghborng bus and A max s the thermal load ablty (MVA) of the lne havng the hghest lmt n the system. The Performance Index (PI) for the purpose of contngency screenng [11, 12] to dentfy the crtcal lnes s defned as 2 N v α Δv PI = lm = 1 2 Δv, (2) sp lm max mn where v = v v Δ v = v v /2, v s post outage voltage Δ and ( ) magntude at bus ; s specfed voltage magntude at bus. d α s user defned constant (Generally taken as 1), and sp v 272

5 Statc Securty Based Avalable Transfer Capablty (ATC) Computaton Input varables The nputs to the neural network play a vtal role to extract the features. Therefore to compute ATC between a gven par of source-snk buses n a large system, only three nputs are consdered to a neural network for base case. These are snk bus njecton ( P s ), the neghborng bus njecton ( P n ) and the unversal ndex ( γ ) for the base case. Bnary nputs are used to represent crtcal lne outages n addton to the base case nputs. The snk and neghborng bus njectons are the dfferences between respectve local generaton and demand n MW Neural network approach Apart from three nputs vz. the snk bus njecton ( P s ), the neghborng bus njecton ( P n ) and the unversal ndex ( γ ), the crtcal lne outages are represented by bnary nputs that represent for each crtcal lne outage condton. For example, two nput bnary varables can represent four condtons: 0 0 normal operatng condton (Base case); 1 0 crtcal lne-2 outage; 0 1 crtcal lne-1 outage; 1 1 crtcal lne-3 outage. Smlarly to represent number of lne outages (NL) we need only maxmum of log 2 ( NL +1) nputs. Moreover by consderng only crtcal lne outages the number of nputs wll be decreased Adaptve Neuro Fuzzy Inference System (ANFIS) approach In Adaptve Neuro Fuzzy Inference System approach n addton to the three base case nputs, Category Index (C) s used to represent varous crtcal lne outages. Thus total nputs consdered here are the snk bus njecton ( P s ), the neghborng bus njecton ( P n ), the unversal ndex ( γ ) and the Category Index (C). The total number of nputs to the Adaptve Neuro Fuzzy Inference system ncludng crtcal lne outages s reduced to four. Compared to the neural network crtcal lne outage representatons, only one nput category ndex (C) s requred to represent crtcal lne outages n the Adaptve Neuro Fuzzy Inference System vz. C = 1 for normal operatng condton (Base case); C = 3 for crtcal lne-2 outage; C = 2 for crtcal lne-1 outage; C = 4 for crtcal lne-3 outage. 273

6 C. Venkaah, D.M.V. Kumar As the number of nputs to the ANFIS are reduced to four compared to Neural Network approach (nputs are fve consderng crtcal lne outages), the computatonal tme wll be reduced drastcally. 3 Artfcal Intellgent (AI) Models 3.1 Back Propagaton Algorthm (BPA) A schematc dagram of the topology of BPA s shown n Fg. 1. Ths network conssts of a set of n nput neurons, m output neurons and one hdden layer of k ntermedate neurons. Data flows nto the network through the nput layer, passes through the hdden layer and fnally flows out of the network through output layer. The network thus has a smple nterpretaton as a form of nput-output model, wth network weghts as free parameters. Such networks [19] can model functons of almost any arbtrary complexty, wth the number of layer and number of neurons n each layer, determnng the functon complexty. In Fg. 1 the nput sgnal X ( = 1,, n) are multpled by the weghts W j ; then operated on by the actvaton functon f ( x ) to produce the b j of the hdden layer. Smlar operatons can be made on outputs of the network. Here n bj = f XW j, (3) = 1 where f s a transfer functon of actvaton functon, whch can take the form of non-lnear functon. For the non lnear sgmod functon f ( ) ( 1 e x x ) 1 = +. (4) Fg. 1 Topology of a three layered MLP. 274

7 Statc Securty Based Avalable Transfer Capablty (ATC) Computaton... Tranng s a procedure used to mnmze the dfference between outputs of Mult-layer Perceptron (MLP) and the desred values by adjustng the weghts of the network. Sets of nput vectors are presented to the network untl tranng s completed. Once the network s traned the new nput data s presented to the network to determne the output. 3.2 Radal Bass Functon (RBF) Neural Network A potental advantage of Radal Bass Functon Network (RBF) s ts ablty to augment new tranng data wthout the need for retranng. RBF has only one nonlnear hdden layer and lnear output layer. Durng tranng, all of the nput varables are fed to hdden layer drectly wthout any weght and only the weghts between hdden and output layers have to be modfed usng error sgnal. Thus, t requres less tranng tme n comparson to BPA model. Fg. 2 Radal Bass Functon Network model. The RBF Neural Network s shown n Fg. 2. The RBF network [11] hdden layer has non-lnear Gaussan functon, whch s defned by a center poston and a wdth parameter. The wdth of the RBF unt controls the rate of decrease of functon. The output of the th unt a ( x p ) n the hdden layer s gven by where a ( xp) 2 r xjp x j = exp, (5) 2 j= 1 ψ x j s centre of th RBF unt for nput varable j, 275 Ψ s wdth of th RBF unt, x jp s j th varable of nput pattern p and r s dmenson of nput vector. The connecton between the hdden unts and the output unts are weghted sums. The output value O qp of the q th output node for p th ncomng pattern s gven as

8 C. Venkaah, D.M.V. Kumar H 276 ( ) O = w a X + w, (6) qp q p qo = 1 where w q s weght between th RBF unt and q th output node, w qo s basng term at q th output node and H s number of hdden layer (RBF) nodes. The parameters of the RBF unts are determned n three steps of the tranng actvty. Frst, the unt centers are determned by some form of clusterng algorthm. Then the wdths are determned by a nearest neghbor method. Fnally, weghts connectng the RBF unts and the output unts are calculated usng delta rule. 3.3 Adaptve Neuro Fuzzy Inference System (ANFIS) The fuzzy logc has two man advantages. The way fuzzy logc tackles the dmensonalty of a problem s computatonally more effcent than that by other artfcal ntellgence (AI) technques (such as ANN, expert system, etc.). Another advantage s that fuzzy logc can capture uncertantes nherent n an ncomplete or reduced set of data. It s noteworthy that rgorous mathematcs ntensve conventonal methods have none of these two advantages Fuzzfcaton of Inputs Each of the nputs s converted from a sngle crsp value nto a maxmum of two fuzzy values usng the wdely used trangular functons that may overlap wth one another as shown n Fg. 3. The x -axs n Fg. 3 represents the crsp values of th nput ( I ) whle the y-axs shows membershp grade ( μ ) that may vary from 0.0 to 1.0. Each trangle has a fuzzy attrbute that can be coded by a lngustc varable (e.g., low ) or a number mplyng level of fuzzness (e.g., 1). However, for the sake of mathematcal representaton, a number s used. The total number of such attrbutes or trangles for th nput s denoted by m. The x coordnates of three vertces of each trangle are respectvely a j, c j f and b j, when j = 1, 2,, m. Equaton (7) shows crsp ( I ) to fuzzy ( I ) converson for th nput [15] f f I = { 1, } I c1; I = { m}, I > cm, (7) f I = 1,2, 2,3,... m m, c < I c, {( ) ( ) ( )} 1, 1 m where = 1, 2,3, 4 (.e., for ATC determnaton), I 1, I 2, I 3 and I 4 are P s, P n, γ and C, respectvely. The membershp grade ( μ ) correspondng to each fuzzy value of gven crsp nput can be obtaned usng (8):

9 Statc Securty Based Avalable Transfer Capablty (ATC) Computaton... I aj f μ = ; aj I cj, j I, j c a ( ) I bj f μ = ; j j,, j c I b j I b c ( ) j j j j where j mples the numbers pcked up by the th f nput s fuzzy value ( I ) as n (7). (8) Fg. 3 Trangular membershp functon for th nput Inference on ATC The rule-base relatng ATC to the nputs for a large system s developed usng Sugeno fuzzy model. A set of frst-order polynomal equatons s used to nfer a crsp value of ATC from crsp values of four nputs. It should be noted that a gven set of crsp values for the four nputs wll not fre all of the 4 rules rather q number of rules when 1 q 2 (.e., one to sxteen rules). Ths s because, as shown n (7), each nput s crsp value has a maxmum of two fuzzy values. The requred overall crsp value ATC s obtaned as n (9) that uses weghted average of the ndvdual crsp outputs from each of the fred rules, that s ATC o AT C = o q ( μ ATC ) o o q where o mples each of the fred q rules, and μ o s as n (10): μ o o 4 = 1 m, (9) 277

10 C. Venkaah, D.M.V. Kumar μ = o 4 μ, (10) = 1 where μ 1, μ 2, μ 3, μ 4 are the membershp grades calculated usng (8) f f f f respectvely, for the four nput fuzzy values (.e. I1, I2, I3 and I 4 ). 4 Smulaton Results 4.1 ATC for blateral transactons on IEEE 24-bus RTS The IEEE 24-bus RTS [17] has been used to compare the performance of proposed Neural Networks & ANFIS methods wth that of full AC load flowbased ATC determnaton. The par of buses 23 (source) and 16 (snk) s consdered for llustratng the determnaton of ATC. The path has been dentfed as the one havng the least mpedance path among all of the ndrect paths that connect 16 to 23. Ths has led to selecton of bus 13 as the neghbor to ths source snk Generaton of patterns The Tranng and Testng patterns are generated usng load-flow, treatng bus 23 as slack, 16 and 13 both as PV (.e., bus wth specfed real power and voltage) buses. The other bus types were retaned as what those should be n a normal load flow. The load at snk bus (No. 16) was ncremented n steps of 10 MW to repeat the load flow untl thermal lmt s exceeded n any lne of the test system. The maxmum possble ncrement acheved above base-case load at the snk bus was the ATC for the correspondng case Tranng Tranng sets provded to the neural network are representatve of the whole state space of concern so that the traned system has the ablty of generalzaton. Tranng patterns for the IEEE 24-bus RTS are composed of: Load levels of 50%, 75%, and 100% of base case whle all lnes n operaton wth dfferent Snk bus njecton. Contngency rankng s done on ths system. It s found that the lnes 7, 18 and 37 are the frst three crtcal lnes for the IEEE 24-bus RTS. Sngle Lne outage of these lnes at 50%, 75%, and 100% of base load wth dfferent Snk bus njecton are consdered for the pattern generaton. Total 240 patterns are generated randomly, Out of whch 180 patterns are used for the tranng and the remanng novel 60 patterns whch are not the part of tranng pattern are used for the testng consderng base case as well as the crtcal outage cases. There are 180 tranng patterns n total coverng the base case and three crtcal lne outage cases are consdered. 278

11 Statc Securty Based Avalable Transfer Capablty (ATC) Computaton Testng The traned neural network and ANFIS was tested usng 60 patterns, whch are composed of 30 load varaton cases and 30 crtcal lne outage cases wth dfferent snk bus njectons. None of these 60 patterns were used n the tranng of the neural network. 4.2 ATC for blateral transactons on 75-bus practcal system The 75-bus practcal system [18] has been used to compare the performance of proposed Neural Networks & ANFIS methods wth that of full AC load flow-based ATC determnaton. The par of buses 14 (source) and 5 (snk) s consdered for llustratng the determnaton of ATC. As there s no drect path between the source bus and snk bus one of the effectve generator buses connected to the ndrect path between buses 14 and 5 s taken as the neghborng bus. So generator bus 6 s taken as the neghborng bus Generaton of patterns The load at snk bus (No. 5) was vared n steps of 5 MW to repeat the load flow untl thermal lmt s exceeded n any lne of the system. The maxmum possble ncrement acheved above base case load at the snk bus was the ATC for the correspondng case Tranng Tranng sets provded to the neural network are representatve of the whole state space of concern so that the traned system has the ablty of generalzaton. Tranng patterns for the 75-bus system are composed of: Load levels of 25%, 50% and 75% of base case whle all lnes n operaton wth dfferent Snk bus njecton. Contngency rankng s done on ths system. It s found that the lnes 25, 22, 19 are the frst three crtcal lnes for the 75-bus system. Sngle Lne outage of these lnes at 25%, 50% and 75% of base load wth dfferent Snk bus njecton are consdered for the pattern generaton. Total 300 patterns are generated randomly, Out of whch 210 patterns are used for the tranng and the remanng novel 90 patterns whch are not the part of tranng pattern are used for the testng consderng base case as well as the crtcal outage cases. There are 210 tranng patterns n total coverng the base case and three crtcal lne outage cases are consdered Testng The traned neural network and ANFIS was tested usng 90 patterns, whch are composed of dfferent loadng cases and dfferent lne contngency cases wth dfferent snk bus njectons. None of these 90 patterns were used n the tranng of the neural network. 279

12 C. Venkaah, D.M.V. Kumar 4.3 Back Propagaton Algorthm (BPA) for IEEE 24-bus RTS Input layer The nput layer conssts of fve neurons to gve nputs Snk bus njecton ( P s ), Neghborng bus njecton ( P n ) and Unversal Index ( γ ) and 2 bnary nputs are selected to represent four cases as below. 0 0 for Base case; 1 0 for crtcal Lne-18 outage; 0 1 for crtcal Lne-7 outage; 1 1 for crtcal Lne-37 outage Output layer The output layer has only one neuron whose output s the ATC from bus 23 to bus Hdden layer The neural network wth one hdden layer wth 9 neurons has been consdered by ht and tral, whch has provded mnmum error. Fg. 4 shows graphcally the BPA based ATC as compared to exact values of ATC as determned from AC load flow based calculaton [16] for IEEE 24-bus RTS. Fg. 4 IEEE 24-bus RTS comparson of BPA Neural Network ATC and AC LF based ATC Back Propagaton Algorthm (BPA) for 75-bus practcal system Input Layer The nput layer conssts of fve neurons to gve nputs Snk bus njecton ( P s ), Neghborng bus njecton ( P n ) and Unversal Index ( γ ) and 2 bnary nputs are selected to represent four cases as below. 280

13 Statc Securty Based Avalable Transfer Capablty (ATC) Computaton for Base case; 1 0 for crtcal Lne-22 outage; 0 1 for crtcal Lne-25 outage; 1 1 for crtcal Lne-19 outage Output Layer The output layer has only one neuron whose output s the ATC from bus 14 to bus Hdden Layer The neural network wth one hdden layer wth 9 neurons has been consdered by ht and tral, whch has provded mnmum error. Fg. 5 shows graphcally the BPA based ATC as compared to exact values of ATC as determned from AC load flow based calculaton [16] for 75-bus practcal system. Fg bus practcal system comparson of BPA Neural Network ATC and AC LF based ATC. 4.5 Radal Bass Functon Neural Network (RBFN) for IEEE 24-bus RTS & 75-bus practcal system To demonstrate the effectveness of the proposed RBF model, t has been traned and tested wth the patterns generated as dscussed n Sectons 4.1 and 4.2. The RBF model used here has same 5 neurons n the nput layer, 1 neuron n the output layer as utlzed for BPA. The number of hdden neurons selected as 75 wth Gaussan densty functon. Eucldean dstance-based clusterng [11] technque has been employed n ths paper to select the number of hdden (RBF) unts and unt centers. The normalzed nput and output data are used for tranng of the RBF neural network. The optmal learnng s acheved at the 281

14 C. Venkaah, D.M.V. Kumar global mnmum of testng error. It was observed that the tranng n ths case was faster and also ts performance was better as compared to the BPA model. The tranng of RBF neural network requres less computaton tme as compared to the BPA model, snce only the second layer weghts have to be calculated usng error sgnal. The tranng of RBF network has been made stll faster by applyng adaptve learnng rate and momentum. Fg. 6 IEEE 24-bus RTS comparson of RBF ATC and AC LF based ATC. Fgs. 6 and 7 shows graphcally the RBF neural network estmates for ATC as compared to exact values of ATC as determned from AC load flow method, for the IEEE 24-bus RTS and 75-bus practcal system respectvely. Fg bus practcal system comparson of RBF ATC and AC LF based ATC. 282

15 Statc Securty Based Avalable Transfer Capablty (ATC) Computaton Adaptve Neuro Fuzzy Inference System (ANFIS) for IEEE 24-bus RTS & 75-bus practcal system ATC between a gven par of source-snk buses n a large system s determned usng the same nputs as gven n BPA and RBF methods, except nstead of takng bnary nput varables for crtcal lne outage condtons, a sngle varable s taken and t s gven a separate nteger value to dstnct each outage case. The nputs thus become Snk bus njecton ( P s ), neghborng bus njecton ( P n ), Unversal Index ( γ ) and category Index(C). The C value has been specfed for the IEEE 24-bus RTS s as follows: C=1 for Base case; C=3 for crtcal lne-18 outage; C=2 for crtcal lne-7 outage; C=4 for crtcal lne-37 outage. The C value has been specfed for the 75-bus practcal system s as follows: C=1 for Base case; C=3 for crtcal lne-22 outage; C=2 for crtcal lne-25 outage; C=4 for crtcal lne-19 outage. These four nputs are fuzzfed and ATC has been calculated. The numbers of fuzzy sets (attrbutes) chosen are respectvely 3, 5, 3 and 4 for P s, P n, γ and C. The lngustc attrbutes correspondng to three levels are low, medum, and hgh respectvely. Snce the neghborng bus may also have generaton n excess of ts local load, ts membershp levels are fve mplyng negatve hgh, negatve low, zero, postve low, and postve hgh, respectvely. For tranng by ANFIS, the MATLAB Fuzzy Toolbox [20] was used. Fg. 8 shows graphcally the ANFIS estmates of the ATC as compared to exact values as determned from AC load flow based calculaton for IEEE 24-bus Relablty Test system. The ATC values calculated for dfferent test cases by the three methods are gven n Table 1 for Base case and lne outage cases along wth the AC Load Flow based ATC values. Out of 60 test patterns the frst 30 patterns presented n Table 1 correspond to normal operatng condton and the remanng 30 patterns n Table 1 correspond to crtcal lne outages wth 10 patterns for each lne. Fg. 9 shows the comparsons of ANFIS based ATC and AC LF based ATC results for the 75-bus practcal system. 283

16 C. Venkaah, D.M.V. Kumar Fg. 8 IEEE 24-bus RTS comparson of ANFIS ATC and ACLF ATC. Table 1 ATC between bus 23 and bus 16 for IEEE 24-bus RTS (Base Case & Crtcal Lne Outages). Test AC LF BPA RBF ANFIS Test AC LF BPA RBF ANFIS Patterns ATC(pu) ATC(pu) ATC(pu) ATC(pu) Patterns ATC(pu) ATC(pu) ATC(pu) ATC(pu)

17 Statc Securty Based Avalable Transfer Capablty (ATC) Computaton... Fg bus practcal System comparson of ANFIS ATC and ACLF ATC. Test Patterns: : crtcal lne-7 outage; 41-50: crtcal lne-18 outage; 51-60: crtcal lne-37 outage. The ATC values computed for dfferent test cases on 75-bus practcal system by the three methods are gven n Table 2 for base case and lne outage cases along wth the AC load flow based ATC values. Test AC LF Patterns ATC(pu) Table 2 ATC between bus 14 and bus 5 for Practcal Indan 75-bus system (Base Case & Crtcal Lne Outages). BPA ATC(pu) RBF ATC(pu) ANFIS ATC(pu) 285 Test AC LF Patterns ATC(pu) BPA ATC(pu) RBF ANFIS ATC(pu) ATC(pu)

18 C. Venkaah, D.M.V. Kumar Test AC LF Patterns ATC(pu) Table 2 (contnuaton) ATC between bus 14 and bus 5 for Practcal Indan 75-bus system (Base Case & Crtcal Lne Outages). BPA ATC(pu) RBF ATC(pu) ANFIS ATC(pu) Test AC LF Patterns ATC(pu) BPA ATC(pu) RBF ANFIS ATC(pu) ATC(pu) Test Patterns: : crtcal lne-25 outage; 46-65: crtcal lne-22 outage; 66-90: crtcal lne-19 outage. 286

19 Statc Securty Based Avalable Transfer Capablty (ATC) Computaton... The tranng and testng tmes of the ntellgent technques vz. BPA, RBF and ANFIS have been compared n terms of CPU tme (n seconds) for computng ATC for both the systems are as shown n Table 3. Table 3 Comparson of CPU Tme (n seconds). Test System BPA RBF ANFIS Tranng IEEE 24-bus RTS bus Practcal System Testng IEEE 24-bus RTS bus Practcal System It s found from Table 3 that all the proposed ntellgent technques took very less tme to compute ATC. The smulaton was carred out n Pentum 4 CPU, 3.00 GHz, 496 MB of RAM Personal Computer. 5 Concluson In ths paper to make use ATC calculatons n real tme, Artfcal Intellgent methods vz.: ) Back Propagaton Algorthm, ) Radal Bass Functon Neural Networks, and ) Adaptve Neuro Fuzzy Inference System are utlzed and compared wth the Full AC Load Flow method. To compute ATC between source and snk three nputs are consdered ) Snk bus njecton (P s ), ) Neghborng bus njecton (P n ) and ) Unversal ndex (γ). Whereas for the crtcal lne outage cases apart from these three nputs two more addtonal nputs are consdered for the Back Propagaton Algorthm (BPA) and Radal Bass Functon Neural network (RBF) whereas only one addtonal nput s consdered for the Adaptve Neuro Fuzzy Inference System (ANFIS) to dentfy a partcular crtcal lne outage. The proposed method has been tested on IEEE 24-bus Relablty Test System and 75-bus practcal System. The mean absolute error for base case and crtcal lne outage case utlzng BPA neural network were found to be pu and pu respectvely for IEEE 24-bus RTS and the correspondng values for 75-bus practcal system are pu and pu respectvely. For the Radal Bass Functon (RBF) Neural network, the mean absolute error for base case and crtcal lne 287

20 C. Venkaah, D.M.V. Kumar outage case were found to be pu and pu respectvely for IEEE 24-bus RTS and the correspondng values for 75-bus practcal system are pu and pu respectvely. Whereas for the Adaptve Neuro Fuzzy Inference System (ANFIS), the mean absolute error for base case and crtcal lne outage case were found to be pu and pu respectvely for IEEE 24-bus RTS and the correspondng values for 75-bus practcal system are pu and pu respectvely. The CPU tme requrement of the ANFIS method s ndependent of the system sze and also t requres only four nputs rrespectve of sze of the system. The number of rules and parameters related to fuzzy model are ndependent of the system sze. Hence the Adaptve Neuro Fuzzy Inference System (ANFIS) method can be used on larger systems for real-tme power markets. 6 References [1] Avalable Transfer Capablty Defntons and Determnaton, North Amercan Electrc Relablty Councl, June 1996, [2] R.D. Chrste, B.F. Wollenberg, I. Wangesteen: Transmsson Management n the Deregulated Envronment, Proceedngs of the IEEE, Vol. 88, No. 2, Feb. 2000, pp [3] G. Hamoud: Feasblty Assessment of Smultaneous Blateral Transactons n a Deregulated Envronment, IEEE Transactons on Power Systems, Vol. 15, No. 1, Fe. 2000, pp [4] G. Hamoud: Assessment of Avalable Transfer Capablty of Transmsson Systems, IEEE Transactons on Power Systems, Vol. 15, No. 1, Feb. 2000, pp [5] M.D. Ilc, Y.T. Yoon, A. Zoban: Avalable Transmsson Capacty (ATC) and ts Value under Open Access, IEEE Transactons on Power Systems, Vol. 12, No. 2, May 1997, pp [6] V. Maksmovc, I. Skokljev: Remedal Transactons Curtalment va Optmzaton, Serban Journal of Electrcal Engneerng, Vol. 6, No. 1, May 2009, pp [7] R. Jayashree, M.A. Khan: A Unfed Optmzaton Approach for the Enhancement of Avalable Transfer Capablty and Congeston Management usng Unfed Power Flow Controller, Serban Journal of Electrcal Engneerng, Vol. 5, No. 2, Nov. 2008, pp [8] G.C. Ejebe, J.G. Waght, M. Santos-Neto, W.F. Tnney: Fast Calculaton of Lnear Avalable Transfer Capablty, IEEE Transactons on Power Systems, Vol. 15, No. 3, Aug. 2000, pp [9] A. Frad, S. Brgnone, B.F. Wollenberg: Calculaton of Energy Transacton Allocaton Factors, IEEE Transactons on Power Systems, Vol. 16, No. 2, May 2001, pp [10] A. Kumar, S.C. Srvastava: AC Power Transfer Dstrbuton Factors for Allocatng Power Transactons n a Deregulated Market, IEEE Power Engneerng Revew, Vol. 22, No. 7, July 2002, pp [11] T. Jan, L. Srvastava, S.N. Sngh: Fast Voltage Contngency Screenng usng Radal Bass Functon Neural Network, IEEE Transactons on Power Systems, Vol. 18, No. 4, Nov. 2003, pp

21 Statc Securty Based Avalable Transfer Capablty (ATC) Computaton... [12] G.C. Ejebe, B.F. Wollenberg: Automatc Contngency Selecton, IEEE Transactons on Power Apparatus and Systems, Vol. PAS-98, No. 1, Jan/Feb. 1979, pp [13] Y.K. Wu: A Novel Algorthm for ATC Calculatons and Applcatons n Deregulated Electrcty Markets, Internatonal Journal of Electrcal Power and Energy Systems, Vol. 29, No. 10, Dec. 2007, pp [14] X. Luo, A.D. Patton, C. Sngh: Real Power Transfer Capablty Calculatons usng Multlayer Feed-forward Neural Networks, IEEE Transactons on Power Systems, Vol. 15, No. 2, May 2000, pp [15] A.B. Kharuddn, S.S. Ahmed, M.W. Mustafa, A.M. Zn, H. Ahmed: A Novel Method for ATC Computatons n a Large Scale Power System, IEEE Transactons on Power Systems, Vol. 19, No. 2, May 2004, pp [16] A.B. Kharuddn, S.S. Ahmed: Slack-load Bus Par Technque usng Full AC Load Flow Algorthm for On-lne Determnaton of ATC, 2 nd World Engneerng Congress, July 2002, pp [17] The IEEE Relablty Test System, A Report Prepared by the Relablty Test System Task Force of the Applcaton of Probablty Methods Subcommttee, IEEE Transactons on Power Systems, Vol. 14, No. 3, Aug. 1999, pp [18] I.J. Raglend, N.P. Padhy: Solutons to Practcal Unt Commtment Problems wth Operatonal Power Flow and Envronmental Constrants, IEEE Power Engneerng Socety General Meetng, Montreal, Canada, June [19] L. Fausett: Fundamentals of Neural Networks, Prentce-Hall, [20] MATLAB Fuzzy Logc Toolbox User s Gude Verson 2,