Optimization of Ancillary Services for System Security: Sequential vs. Simultaneous LMP calculation

Transcription

1 Optmzaton of Ancllary Servces for System Securty: Sequental vs. Smultaneous LM calculaton Sddhartha Kumar Khatan, Yuan L, Student Member, IEEE, and Chen-Chng. Lu, Fellow, IEEE Abstract-- A lnear optmzaton problem s formulated to enable the Independent System Operator (ISO) to make least cost decsons for purchasng ancllary servces. The ISO s responsble for adjustng the schedules resultng from the market clearng process to elmnate congeston [1]. Both the sequental and the smultaneous DC formulatons for congeston management and ancllary servces selecton are optmzed and compared as to ther optmalty. In a smultaneous approach the complex nterplay of dynamc nteractons whch truly represents the actual operaton s taken nto consderaton. Hence the combned optmzaton s more practcal from the pont of actual operaton of the power system. It s shown n the results that optmalty s acheved by smultaneously handlng congeston and ancllary servces. Load senstvty studes are done at each of the load buses to see the system mpact and predct the LM at each load bus. A Locatonal Margnal rce (LM) smulator based on a generalzed n-layer feed forward artfcal neural network (ANN) whch uses an error-backpropogaton algorthm (LMS mnmzaton) s developed to ncorporate the nherent uncertantes n the market envronment, load forecastng and other factors. It can also serve as a useful tool when there are mssng nputs. Index Terms ANN, ancllary servce, lnear programmng,lm, power market. T I. INTRODUCTION HE deulaton of the electrcty market has ncreased the challenges to mantan the system securty and relablty. The system s beng operated closer to lmts. The responsblty of mantanng the securty and relablty rests on the ISO. At the same tme the ISO should pursue the goal of maxmum socal welfare by choosng least cost optons for mantanng the desred reserve, ulaton and other ancllary servces and adjustng schedules for congeston management. Ancllary servces are generally referred to as those servces other than energy that are essental for ensurng the relable operaton of the electrcal grd. FERC has determned that the followng sx ancllary servces may be ncluded n an open access transmsson tarff: (1) schedulng, control and Sddhartha Kumar Khatan s wth the Department of Electrcal Engneerng, Iowa State Unversty, Ames, Iowa, 11 USA (e-mal: skhatan@astate.edu). Yuan L s wth the Department of Electrcal Engneerng, Iowa State Unversty, Ames, Iowa, 11 USA (emal: tua@astate.edu) Chen-Chng Lu s wth the Department of Electrcal Engneerng, Iowa State Unversty, Ames, Iowa, 11 USA (e-mal: lu@astate.edu ). dspatch; (2) reactve power supply and voltage control; (3) ulaton and frequency response; (4) energy mbalance; () operatng reserve (spnnng and non-spnnng) [2]. In the present formulaton only ulaton and spnnng reserve are consdered. These are ancllary servces actually avalable n the electrcty markets. In the market envronment the cost of next MW at any node (load bus) remans the same when there s no congeston. On the other hand, there s dfferental prcng or LM when the transmsson system s congested and one causng the congeston has to pay more. LM s a standard way for congeston management. Therefore load senstvty studes are mportant to reflect the mpact of load ncrease at a node on the system n terms of LM. There are standard software packages for the calculaton of LM. However loss of nformaton or bad nformaton, delayed nformaton, nadequate nformaton can all lead to mparment. Moreover there s nherent uncertanty n the market envronment and t s practcally mpossble to accurately model the non lnear market dynamcs whch would reflect the output n ts true sense. The correctness of the output s mportant. The above factors of uncertanty and mportance of LM motvated the modelng of the LM calculaton n a market envronment through a neural network confguraton. enetc algorthms are a category of evolutonary algorthms whch are used for optmzaton problems. These technques are not very effectve aganst estmaton problems. Support Vector Machnes and Artfcal Neural Networks are effectve machne learnng algorthms as they provde real tme estmaton on testng set once they are properly traned. Thus, ther use allows dynamc estmaton of LM. However, Support Vector Machnes orgnally solve only bnary classfcaton problems. Thus the choce of ANN s sutable for LM predcton. Unlke k-nearest neghbors and case based reasonng technques whch are lazy learnng technques; neural networks are generally referred to as eager learnng algorthms because they generalze the observatons for nferences before processng the query. Reference [3] uses a combnaton of fuzzy nference system and least square estmaton for forecastng prce n a day ahead market. Reference [4] uses ANN for System Margnal rce (SM) forecastng and [] uses extended Kalman flter based ANN to predct market clearng prce (MC). Nether of them /8/2. 8 IEEE. 321

2 consders congeston and has nputs such as system demand, reserves, gas and ol prces and past MCs and SMs. The current study s not exhaustve wth ard to the sutablty and avalablty of the nputs correspondng to the output. However the proposed method provdes a wndow nto a drecton whch s promsng and can become more attractve wth detaled studes usng real data from the market and more thorough parameter analyss and selecton of optmal performance network for a wde range of nputs. The proposed model can be used for prce forecastng wth the demand forecast data whch s avalable wth every utlty. II. ANN ARCHITECTURE In ths paper a generalzed n-layer feed forward artfcal neural network [6]-[8] whch uses an error-backpropogaton algorthm (LMS mnmzaton) was mplemented n the Vsual Basc (VB 6.) programmng language. The program can allow for a general number of nputs, hdden layers, hdden layer elements, and output layer elements. Two hdden layers were found to be suffcent n solvng a problem of ths sze and therefore the archtecture was reduced to a four-layer feed forward network. A four-layer feed forward network conssts of a set of sensory unts (source nodes) that consttute the nput layer, two hdden layers of computaton nodes, and an output layer of computaton nodes. The followng notaton s generally used to refer to a partcular type of archtecture that has two hdden layers: (# nputs)-(# hdden neurons)-(# hdden neurons)-(# outputs). For example, the notaton refers to an ANN archtecture that takes n 1 nputs (features), has 2 hdden layers consstng of 4 neurons each, and produces 1 output. The terms elements, nodes and neurons are nterchangeable and refer to the same entty. Fg. 1 shows the Mult-layer Feed-forward Network. mportant because, otherwse, the nput-output relaton of the network could be reduced to that of a sngle-layer perceptron. The computaton of the δ (local gradent) for each neuron of the multlayer perceptron requres that the functon ϕ(.) be contnuous. In other words, dfferentablty s the only requrement that an actvaton functon would have to satsfy. For ths problem, an asymmetrc hyperbolc tangent functon (tanh) was chosen for whch the ampltude of the output les nsde the range 1 y j +1. Snce, we requre the fnal outputs to be real values nstead of bnary outputs; a lnear combner model was used for neurons n the output layer, thus omttng the nonlnear actvaton functon C. Learnng Rate arameter η The learnng-rate parameter s denoted by η. The backpropagaton algorthm provdes an approxmaton to the trajectory n weght space computed by the method of steepest descent. The smaller one makes the learnng-rate parameter η, the smaller wll the changes to the synaptc weghts n the network be from one teraton to the next and the smoother wll be the trajectory n weght space. Ths mprovement, however, s attaned at the cost of a slower rate of learnng. If, on the other hand, one makes the learnng-rate parameter η too large so as to speed up the rate of learnng, the resultng large changes n the synaptc weghts assume such a form that the network may become unstable (.e., oscllatory). For ths problem, a smooth learnng curve was acheved wth η of.1 D. erformance Measure (RMSE) In order to track the performance of the network the Root Mean Squared Error (RMSE) at the end of each epoch was calculated. An epoch s defned as one full presentaton of all the tranng vectors to the network. The RMSE at the end of each epoch s defned as: N 2 [ d j Y ( X j )] RMSE = j = 1 N where d j s the desred response for the nput tranng vector X j, and N s the total number of nput vectors presented to the network for tranng. In order for the network to learn the problem smoothly, a monotonc decrease n the RMSE s expected wth ncrease n the number of epochs. Fg. 1. Mult-layer Feed-forward Network A. Intalzaton of weghts The frst step n back-propagaton learnng s to ntalze the network. It s recommended that the ntalzaton of the synaptc weghts of the network be unformly dstrbuted nsde a small range. A range of (-.2, +.2) was used for random ntalzaton of all synaptc weght vectors n the network for ths study B. Non Lnear actvaton functon The model of each neuron n the hdden layer(s) and output layer of the network ncludes nonlnearty at the output end. The presence of a nonlnear actvaton functon, ϕ(.), s III. FORMULATION OF THE OTIMIZATION ROBLEM The objectve of the aucton market could be to mnmze the socal cost or mnmze the procurement cost. The socal cost refers to the actual cost of the requred servces and the procurement cost refers to the cost to procure the requred servce. So the drect objectve s to mnmze the product of the prce and amount or capacty of all the ancllary servces. The general constrants consdered are system reserve and ulaton requrements, maxmum ramp rates, maxmum and mnmum bd block amounts, unt capacty lmts, system relablty, securty and so on. A. DC ower Flow Model The DC power flow formulaton gnores reactve power, assumes all the voltages are at 1. per unt, and gnores lne 322

3 conductance. Ths makes the power flow a lnear set of equatons, whch can be solved drectly. = Bδ (1) where Bus power njecton B Imagnary part of bus admttance matrx δ Bus voltage angle DC power flow model s used to calculate the lne flow. B. Objectve functon The basc objectve s to make the devatons from unconstraned market equlbrum mnmum and also mnmze the cost of the ancllary servce, such as ulaton and reserve. 1) Congeston management objectve functon Schedulng Coordnators (ISO s clents) submt schedules showng how much power they want to transport and where t wll come from. ISO takes all the schedules and runs them through a large computer program (schedulng nfrastructure) to determne the chances of traffc jam (overloadng of the transmsson system) or congeston. If there s no congeston, ISO gves schedulng coordnators green lght to proceed. Otherwse the ISO gves schedulng coordnators opportunty to ether sell off or buy more power, wth ISO eventually choosng least-cost optons C s = c Δ, j D, k Q 2) Ancllary Servces Objectve Functon mn [ V, θ, j D, k Q ( c ( c res res + e + π e res res res res τ τ ) + where: (MW) s the amount of ulaton cleared at each bus, each schedulng coordnator; c (/MW) s the bd prce of capacty reservaton for ulaton purposes; e (/MWh) s the bd prce of the energy output from ulaton sources; a (/MWh/mn) s the bd prce for the ulaton adder, R s the generaton ramp rate (MW/mn); τ (h) s the tme requrement for the speed of response of ulaton; )] (2) (3) res (MW) s the amount of reserve cleared; c res (/MW) s the res bd prce of capacty reservaton for reserve; e (/MWh) s the bd prce for the energy output from reserve; τ res (h) s the tme requrement for the actvaton of reserve; π res (,1] s the probablty of spnnng reserve actvaton. 3) Decson varables If a congeston takes place, the schedulng coordnators have to sell or buy more power. That s, the real power out of the generaton unt has to be adjusted, whch s marked res as Δ,, sc ' k ' C. Constrants, sc ' k ',, sc ' k '. 1) Congeston management and lne flow constrant To deal wth congeston management, only the te lne flow s checked. The nequalty constrant s of the followng form: H 1 δ = HB Fmax (4) where F max The maxmum lne flow Because =, + Δ () old where, old The orgnal generaton amount So we get, HB Δ, sc1 + HB Δ, sc2 Fmax HB, old (6) HB Δ, sc1 HB Δ, sc2 Fmax+ HB, old (7) For other constrants please see [1]. IV. ILLUSTRATION A. Test system The test systems used was the -bus TI/SSe test system, shown n Fg. 2. Two schedulng coordnators, SC1 and SC2, and three major congeston zones are assumed. The lmtng constrant s the transfer capablty from area 3 nto area 1. Both SC1 and SC2 have generaton avalable at buses 11, 12, 1, 6, 31 and 38 and serve loads at 7 load buses. In ths example, no congeston management or ancllary servce bds are submtted by the demand sde. Both SCs submt adjustment bds for congeston management at all sx generator buses and also bds for all types of ancllary servces. The basc nformaton about the two SC s s shown n Table

4 2 Before 2 After Fg. 2 The one lne dagram of the test system TABLE 1 THE INFORMATION FOR BOTH SCHEDULE COORDINATORS Lne Number Lne Number Fg. 4 The result of sequental optmzaton SEQ SEQ SIM B. Sequental vs. Smultaneous Optmzaton The dfference of lne flow before and after optmzaton n the case of smultaneous and the sequental optmzaton of the congeston and the ancllary servce are shown n Fg. 3 and Fg. 4 respectvely. Fg. shows a comparson of the generaton output for the smultaneous and the sequental approaches. Lne Flow Before Lne Number Fg. 3 The result of smultaneous optmzaton After Lne Number SEQ SIM Fg. Comparson of generaton output In Table 2 the objectve value s presented to compare the optmalty. As expected the objectve functon value n the case of the smultaneous optmzaton approach s better. Ths s due to the fact that n a smultaneous approach the couplng constrants and the complex nterplay of dynamc nteractons whch represents the actual operaton are taken nto consderaton. Hence the combned optmzaton s more practcal from the pont of actual operaton of the power system. It s shown that the optmalty s acheved by smultaneously handlng congeston and ancllary servces. TABLE 2 OTIMAL VALUE method Objectve value () sequental smultaneous C. Locatonal Margnal rce One of the most used methods to manage congestons s through the LM. After the calculaton of the LM, the customers n a congested area may have to pay a hgher prce. Therefore t s mportant to study the load senstvty of the dfferent nodes to dentfy the mpact of load ncrease on the system and the resultng LM. The LM shown n Table 3 s calculated smultaneously wth ancllary servce optmzaton. The results shown n Fg. 6 and Table 4 are the generator outputs before optmzaton and then after smultaneous optmzaton and for 1 MW of load ncrease on bus 13 for the purpose of LM calculaton. 324

5 TABLE 3 THE BUS LM Load Bus Real Load (/MW) OLD OLD OT_SIM LM_BUS V. ANN MODELIN FOR REDICTIN LM 1) ANN Inputs and Outputs The generator output of the sx generators of each of the schedulng coordnators obtaned from Matlab smulaton of the test system at dfferent load level at each of the seven load buses are shown to be reasonably good ndcators of LM, the output. A bus test power system model was smulated n Matlab 7.1. Loads and njectons were smulated and lne power flow and LM were computed for 1 cases. The data was used (7%) for tranng and (2%) for testng 2) Results and Dscusson The twelve generator outputs were used as nputs. However after the senstvty analyss t s found that only fve of them were havng any mpact on the output. So these fve generator output were used n tranng. They are generators a1 to a. In the Fg. 8 below the nput output characterstc of these fve generators to the output s shown Fg. 6 eneraton changng TABLE 4 OLD, OT AND LM ENERATION AMOUNT Sc1 Sc2 Old Opt LM Old Opt LM bus 1 bus bus bus6 32 bus bus9 bus Fg. 8 The I/O characterstcs The generators a1-a correspond to 12-SC1, 38-SC2, 12- SC2, 1-SC2, 31-SC1 and 6-SC1.The four layer feed forward network used were and The number of epochs used was. The results for the tranng curves and the LM predcton for both the cases are presented n the fgures below. Fg. 9 shows the tranng curve for the network for LM at a partcular node Fg. 7 LM vs. Load ncrease Then the load at one of the load buses was sequentally ncreased wth a step of 1 MW to the maxmum of MW. Ths was repeated for each of the seven load buses. The Fg. 7 shows the trend n the LM for each node wth the ncrease n load at that bus only. Ths s useful nformaton assumng bd prces to be same for adjustment and ancllary servces. Ths nformaton can also be used by a utlty (LSE) to make decsons ardng generaton from own generators or to purchase from the market. Fg. 9 The tranng curve for Fg. 1 and Fg. 11 show the predcted and the Target LM on dfferent scales. The average absolute error n ths case s 27%. 32

6 tranng data, wth lttle or no dfference, because the network tends to learn the values. However t s a challenge to dentfy the optmal set of nput varables whch have hgh senstvty to LM. It s n the scope of our future work to consder load uncertanty, lne flow, and load forecast data to optmze the network for best performance and also use that for prce forecastng purposes because load forecast data are avalable. Also t wll be nterestng to use tme dependent networks such as recurrent networks to model the market envronment. Fg. 1 The LM Smulator output for test data () Fg. 12 and Fg. 13 show the tranng curve for the ---1 network for LM at a partcular node. The average absolute error n ths case s 18%. Fg. 11 The result of smultaneous optmzaton VI. CONCLUSIONS The proposed ANN can be very attractve for estmaton of the LMs under the stuaton of uncertanty and mssng nformaton. ANN models are good unversal functon approxmators and easy to tran. Neural Networks are amongst the most robust machne learnng tools for estmaton. They take tme to tran but once traned they can process and estmate output n real tme. The only condtons unfavorable to ANNs are the cases where supervsed learnng s constraned due to lack of nput data or tranng tme. DC formulaton usng L s very effcent and robust for congeston management and ancllary servces optmzaton to make least cost decsons. Smultaneous optmzaton s more accurate and makes sense n a coupled envronment but the sequental approach s easer to perform. VII. ACKNOWLEDMENT We gratefully acknowledge the help of Dr. Kasthurrangan opalakrshnan n codng for the neural network. Fg. 12 The tranng curve for ---1 REFERENCES [1] M. bescu and C. C. Lu, Optmzaton of Ancllary Servces for System Securty, roc. Internatonal Symp. Bulk ower Systems Dynamcs and Control, Santorn, reece, Aug [2] M. Shahdehpour, H. Yamn, and Z. L, Market Operatons n Electrc ower Systems, New York: A John Wley & Sons, Inc. 2 [3] L,.; Lu, C.-C.; Mattson, C.; Lawarree, J.; Day-Ahead Electrcty rce Forecastng n a rd Envronment, ower Systems, IEEE Transactons on Volume 22, Issue 1, Feb. 7 age(s): [4] B. R. Szkuta, L. A. Sanavra, and T. S. Dllon, Electrcty rce Short Term Forecastng Usng Artfcal Neural Networks, IEEE Trans. ower Syst., vol. 14, no. 3, pp , Aug [] L. Zhang and. B. Luh, Neural Network-Based Market Clearng rce redcton and Confdence Interval Estmaton wth an Improved Extended Kalman Flter Method, IEEE Trans. ower Syst., vol., no. 1, pp. 9 66, Feb.. [6] S. Haykn, Neural Networks: A Comprehensve Foundaton, Macmllan College ublshng Company, Inc., New York, NY, [7] D.C. ark, M.A El-Sharkaw, R.J. Marks 11, L.E. Atlas, and M.J. Dunborg, "Electrc Load Forecastng Usng An Artfcal Neural Network", IEEE Transactons on ower Systems, Vol. 6, No. 2, May 199 1, pp [8] Fg. 13 The LM Smulator output for test data (3) It s concluded that neural network modelng for predctng LM can be a very useful tool (wth proper tranng) because t can be used onlne to meet the performance requrement. It s however mportant not to over tran the network wth 326