A DISTRIBUTION COMPANY ENERGY ACQUISITION MARKET MODEL WITH INTEGRATION OF DISTRIBUTED GENERATION AND LOAD CURTAILMENT OPTIONS

Transcription

1 A DISTRIBUTION COMPANY ENERGY ACUISITION MARKET MODEL WITH INTEGRATION OF DISTRIBUTED GENERATION AND LOAD CURTAILMENT OPTIONS Rodrgo Palma-Behnke José Lus Cerda A. Department of Electrcal Engneerng Unversty of Chle Av. Tupper 007, Santago, Chle Abstract: Ths work presents a novel day-ahead energy acquston model for a dstrbuton company (DsCo ) n a compettve market based on Pool and fnancal blateral contracts. The market structure encompasses wholesale generaton companes, dstrbuted generaton (DG) unts of ndependent producers, DG unts owned by the DsCo, and load curtalment optons. Thus, whle satsfyng ts techncal constrants, the DsCo purchases actve and reactve power accordng to the offers of DG unts, customers, and the wholesale market. The resultng Optmal Power Flow (OPF) model s mplemented wth an obect-orented approach, whch s solved numercally by makng use of a branch and border sequental quadratc programmng algorthm (SP). The model s valdated n test systems and then appled to a real case study. Results show the general applcablty of the proposed model, wth potental cost sav ngs for the DsCo. Fnally, the analyss of Lagrange multplers gves valuable nformaton, whch can be used to mprove the market desgn and to extend the use of the model to a more general market structure such as a power exchange. Keywords: Dstrbuted Generaton, Market Desgn, OPF, Ancllary Servces, uadratc Programmng. I. INTRODUCTION DG can be defned as the ntegrated use of small generaton unts drectly connected to a dstrbuton system or nsde the facltes of a customer [1]. The potental development of DG s sustaned n the followng factors: ncreasng power qualty requrements, avodng or shftng nvestment n transmsson lnes and/or transformers, ohmc losses mnmzaton, envronmental protecton, and exstence of hgh energy prces at retal level [1-4]. Tradtonally, a DsCo purchases energy from wholesale market, at a hgh voltage level, and then transfers ths energy to fnal customers. Nevertheless, the restructurng process of the energy sector has stmulated the ntroducton of new agents and products, and the unbundlng of tradtonal DsCo nto techncal and commercal tasks, ncludng the provson of ancllary servces []. In ths context, the obectve of ths work s to make a contrbuton to the knowledge of the techncal and commercal ntegraton of DG unts n market desgn alternatves. The study focuses on the development of a day-ahead energy acquston model for a DsCo, whch operates n a compettve market based on a Pool and fnancal blateral contracts, wth ntegraton of DG nsde ts control area at Lus S. Vargas lvargasd@ng.uchle.cl Aleandro Jofré aofre@dm.uchle.cl Center of Mathematcal Modelng& Department of Mathematcal Engneerng Bco. Encalada 10, Santago-Chle medum voltage level (subtransmsson). Dfferent products (actve and reactve power) and techncal operatonal constrants are explctly taken nto account n the proposed dspatch model called Dstrbuted Company Acquston Market (DCAM). In Secton II DG technologes are brefly revewed dstngushng ther man characterstcs n the context of a compettve market. In Secton III, a Dstrbuton Company Acquston Market (DCAM) for a DsCo s descrbed. Secton IV presents the structure of the resultng mathematcal optmzaton problem and the soluton algorthm. In Secton V the proposed method s valdated n test systems and ts man features are dscussed. In Secton VI the DCAM s appled to a real case study, where network data of the man dstrbuton company n Chle and the external representaton of the nterconnected system are used. Fnally, analyss, conclusons, and future research work n the feld are presented n secton VII. II. DISTRIBUTED GENERATION TECHNOLOGIES Accordng to some authors, n the future a substantal share of electrcty wll be produced by technologes assocated wth DG []. These technologes encompass a wde range of subcategores characterzed by fuel type, generaton capacty, envronmental mpact, and operaton flexblty. Currently the most common technology used for DG under 1 MW, are motors and turbnes propelled by desel and other fossl based combustbles [1,,5]. These unts usually have low captal cost, hgh rank of operaton, fast start-up capablty, sound electrc converson effcency, and good operatng relablty. In addton, small conventonal ndustral gas turbnes, n the range of 1-0 MW, are commonly used n combned heat and power facltes, whch take advantage of the steam producton capablty. Ther mantenance costs are slghtly lower n comparson wth other engnes, whle electrcal converson effcency ncreases []. Applcatons on mcroturbnes have become well known for ther effcency and relablty [,4,6]. Indvdual unts range from kw, but can be combned readly nto a system of multple unts. Another mportant feature of these unts s ts low combuston temperature, whch can assure low NO x emssons levels. Hydraulc mcroturbnes correspond to small hydraulc generatng unts. Ther benefts are the low envronmental contamnaton, low mantenance costs and hgh effcency. Fuel cells (FC) are an emergng technology wth compact, quet power generators that use hydrogen and oxygen to 1

2 produce electrcty. These unts are able to convert fuels (rch n H ) to electrcty at very hgh effcences (35%- 60%) as compared wth conventonal technologes. The DC-current produced by FC can be transferred to the power system by usng nverters. Emsson of NOx and CO related wth ths technology refers to the reformer process (producton of hydrogen) n the case of usng fuel (as natural gas, methanol, etc.) [, 4, 7]. The Photovoltac Systems (PV) are also a popular renewable resources technology. The power of a sngle module vares between 50 and 100W and ts effcency s near 15%. Usually PVs are bult n arrays wth seres and parallel connectons, and coupled to the network thorough an nverter. PV systems show hgh nvestment and very low mantenance costs [, 4, 5]. In the last two years, wnd generaton ncreased dramatcally ther share n worldwde electrcty nstalled generaton capacty. About 4.5 GW of capacty were nstalled only n 000, mantanng ths tendency untl year 003 [] 1. For wnd and PV technologes the emssons of ar pollutants are neglgble. Irrespectve of the specfc DG technology, when nterconnected to a power grd ether they use a synchronous generator or a power electronc nverter [4]. Consequently, from a steady state pont of vew, these dfferent technologes can be represented by standard load flow equatons wth mnmum and maxmum power lmts (actve and reactve), complex power lmt and voltage lmts at the connecton busbar. III. DISTRIBUTION COMPANY ACUISITION MARKET (DCAM) DESCRIPTION In ths secton a general formulaton of the DsCo acquston market model s descrbed. 3.1 General Market Structure The general framework consders dfferent DG technologes nsde a DsCo control area. DGDC Wholesale Energy Market Seller DGI Buyer Seller Buyer DsCo Buyer Load Interconnected Systems DsCo: Dstrbuton Company that operates the facltes and buys energy, ether through fnancal blateral contracts or n the Pool. Wholesale Market: It s the wholesale market of the entre nterconnected system whch establshes a prce boundary wth DCAM. In other words, the wholesale market provdes energy at a gven (or estmated) prce. Ths s the typcal case n Pool or fnancal blateral contracts market structures. DGI: Dstrbuted generaton unts nsde the DsCo control area. These unts are managed or owned ndependently from the DsCo. From the market pont of vew DGI unts send energy offers (prce and quantty) to DsCo. DGDC: Dstrbuted generaton unts nsde the DsCo control area, whch are managed or owned by the DsCo. Loads : Customers served by the DsCo, whch have flexble contracts wth load curtalment and Demand Sde Management (DSM) orented optons. DCAM s organzed as a Day ahead-market wth hourly actve power offers from DGI, DGDC and the wholesale market. In addton, DCAM manages the cost of unserved energy for all the Loads wth curtalment optons. Also, DCAM manages an ancllary servces market for reactve supply. The DsCo as a whole must be compled wth a defned hourly power factor lmt and t must mantan voltage profle wthn a desgnated band. To fulfll these requrements the DsCo receves reactve power offers from the DGI and manages the reactve supply of DGDC as well as ts own compensaton devces. Note that n the case of Power Exchange (PX), prces and quanttes (MWh) are fxed as a result of a prce clearng procedure. In addton, n physcal blateral contracts schemes, usually prces and quanttes (MWh) are also fxed n a negotated agreement that defnes a purchase schedule. In Secton 6. an extenson of the proposed model n the context of a PX s further dscussed. 3. Techncal Coordnaton Requrements The DCAM must handle the techncal coordnaton among the DsCo, the nterconnected power grd, DGDC unts, DGI unts and Loads. Fgure summarzes these nterrelatons. Fgure 1: General Market Structure In Fgure 1 the DsCo acquston market DCAM s shown n dashed lne as part of a more general market structure. Ths structure encompasses pool markets and fnancal blateral contracts. These defntons of market agents are as follows: 1 Reported by Wndpower Fgure : Techncal Coordnaton Requrements

3 In Fgure four nterconnectng substatons (four step down transformers n ths case) between the power grd and the DsCo control area are shown. In the general case, each sector of the nterconnected system maybe connected to neghborng sectors by te transmsson lnes as well. As a result, the actve and reactve power transfers between the network and the DsCo are gven by the sum of the actve (P ) and reactve ( ) nectons n the four nterconnectng substatons. In order to manage the techncal coordnaton of the entre system the proposed model s composed of the followng basc functons: Equvalent system: An equvalent system for the external network s needed for a sutable modelng of power transfers between the power grd and the DsCo control area. Ths equvalent model allows DCAM to take decsons leadng to a feasble operaton condton for the entre network. Power Factor Computaton: In order to montor the power factor lmts, the DsCo must compute the aggregaton of reactve and actve power transfers n all nterconnectng substatons. Optonally, specfc lmts can be consdered for each nterconnectng substaton. Power Flow Constrants Identfcaton [8-18]: Ths module calculates actve and reactve power balance n each node, power flow lmts on branch elements (lnes, transformers, FACTS), voltage operaton ranges n each bus, and generaton lmts for each unt. Margnal Unt Identfcaton: For the economcal analyss of the system, the margnal prce unt should be dentfed at each hour. Usually t corresponds to a generatng bus nsde the external equvalent system. Insde the DsCo control area, a careful network model of the subtransmsson system s also recommended. An mportant assumpton here s that subtransmsson networks (n the range of 1 to 66 kv) are balanced n normal operaton. Ths assumpton s supported by feld current measures, whch show at most a 5% of current unbalance n chlean subtransmsson networks. Ths lmt s n the range of nternatonal standards. The followng coordnaton requrements are dentfed for ths model: DGI unt offers. DGI unts must nform the DsCo about an exstng dspatch schedule resultng from the partcpaton n the Pool or from a physcal blateral contract. In addton or alternatvely, DGI unts can send offers for reactve and actve generaton to the DCAM. DGDC unt dentfcaton: It dentfes DGDC unts that are owned or managed by the DsCo. Load offers: It dentfes Load contracts, wth detaled cost nformaton for unserved energy ranges, that must be submtted to the DCAM. All the above nformaton s suppled to the DCAM, n order to obtan an estmaton of the prcng for actve and reactve power and, subsequently, to take a decson on the correspondng purchases n the energy and ancllary markets. Thus, the proposed DCAM defnes the supply of electrcal energy and the reactve power related ancllary servces for the DsCo [19]. The outputs and servces suppled by DCAM n the day-ahead market can be summarzed as follows: Energy (actve power) bought at the wholesale market, Energy (actve power) bought at the DGI, Energy (actve power) obtaned from the DGDC, Load curtalment (unserved energy of customers), Voltage and power factor control. 3.3 Acquston Market Modelng Gven the set of coordnaton requrements descrbed above, the DsCo must decde the energy purchases that maxmze ts expected beneft. As the market works on an hourly bass, we use average power nstead of energy as optmzaton varables. The DCAM receves offers and cost nformaton of the market partcpants as follows: Wholesale Market Prce: It s defned as the DsCo estmated acquston prce for actve power from the nterconnected system (P DC ). In Pool based markets t corresponds to the clearng prce. DGI offers: These ndependent generatng unts send offers to the DCAM n form of blocks, for each hour, for actve (Pr DGI ) and reactve power. These offers could ether be the whole capacty of DGI, or the dfference between the capacty of DGI and the compromsed (and scheduled) energy n the wholesale market (P DGI,WS ). To dstngush between capactve and nductve reactve power, the offers are further classfed nto two types: - Reactve Power Inecton Prce Pr RI,DGİ - Reactve Power Absorpton Prce Pr RA,DGI. DGDC prce: As these unts belong to the DsCo, they nform ther varable operaton cost to the DCAM drectly. In ths work the followng convex quadratc functon cost s used: C = α + β P + γ P (1) DGDC DGDC DGDC where P DGDC s the actve power generaton of DGDC unt, whle α, β, and γ are postve coeffcents of the quadratc cost functon. Note that β corresponds to the margnal generaton cost when γ s zero. On the other hand, the reactve power must comply wth the operaton constrants of these unts [9]. Therefore, ts cost s mplctly obtaned from the Lagrange multplers of the optmzaton problem and no explct cost model for reactve power s requred [1]. Loads: Curtalment optons of fnal retal customers nsde the DsCo control area are also modeled as a convex quadratc cost functon. Ths functon s as follows [9,16]: C U = δ P + τ P () U U where P U s the unserved energy at load, whle δ, and τ are coeffcents that quantfy the cost of the unserved In the case of Chle there s a mandatory pool market structure wth audted costs, where regulated prces for the DsCo are recalculated each sxth month by the regulatory entty wth varatons dependng on peak load hours [0]. 3

4 energy for the DsCo. Loads outsde the DCAM system are not consdered wth curtalment optons n ths model. The DsCo s defned as the market operator of the DCAM, whch does the prce estmaton and the optmzaton procedure for the hourly acquston of actve and reactve energy (power). IV. DCAM OPTIMIZATION MODEL The DCAM descrbed n Secton III can be formulated for each tme perod as a mathematcal optmzaton problem (OP). The resultng nonlnear OP s solved usng a Sequental uadratc Programmng (SP) based procedure [16, ]. 4.1 General Structure OP n 3 represents the general structure of the proposed model. Mn Z = f ( x r ) r s.t. gx ( ) = 0 (3) h( x r ) 0 x r x r x r mn max Ths structure corresponds to a mnmzaton problem derved from a general OPF formulaton [8-18]. The obectve functon f( x r ) represents the DsCo costs for supplyng ts demand. The set of constrants and bounds correspond to the steady state operaton constrants of the system and operaton lmts of the devces. 4. Obectve Functon and Varables The resultng quadratc obectve functon for DCAM s as follows: r f( x) = PrDGI PDGI + CDGDC PDGDC + P DC P n + = DGI = DGDC unts unts ( ) + Pr + Pr + RA,DGI RA,DGI RI,DGI RI,DGI = DGI DGI = unts unts + C Uk k= loads DC ( P ) Uk (4) DGI unts, as depcted n Secton 3.3, offers actve power P DGI, reactve absorbed power RA,DGI, and reactve nected power RI,DGI at gven prces. DGDC unts nform ther operaton costs as a quadratc functon (Eq. 1) of actve power necton P DGDC. Unserved energy costs for each load are also re presented as a quadratc functon (Eq. ) of the amount of unserved power P U. Fnally, P n refers to the total mported energy from the power grd (wholesale market) at a gven prce (PDC). The decson varables are ordered n vector form as r x = [ P,, P,, V, δ, t,, V, G P, n G n, U out, U RA,DGI, t RI,DGI SVC ]. UPFC (5) The frst group of varables between P G and V UPFC are tradtonal OPF system modelng varables [8-18]. P G and G represent the total actve and reactve power necton of each generatng unt ncludng the two types of DG (P DGDC and P DGI ). Note that n the case of P DGI, nectons compromsed and scheduled at the wholesale market are not ncluded. P U and U refer to actve and reactve unserved energy n each load. V and d are the nodal voltage magntud and angle, respectvely. Transformers wth tap changng capabltes are represented by t t varables. FACTS devces are modeled through specalzed varables SVC and V UPFC explaned n detal n reference [16]. The rest of the varables n vector x v followng optmzaton varables: correspond to the P n : total actve power flow nected n the control area, n : total reactve power flow mported to the control area, out : total reactve power flow exported to the power grd, RA,DGI : reactve power absorbed by th DGI unt, RI,DGI : reactve power nected by th DGI unt. The obectve functon has the general matrx form: T 1 T Z = α + cx+ xx (6) Where, a corresponds to the aggregated fxed costs, c T s the vector of lnear cost coeffcents vector, s the quadratc cost coeffcents matrx. 4.3 Constrants The proposed OP exhbts equal (E), unequal (UE), lnear (L), and nonlnear (NL) constrants that can be summarzed as follows: Power Balance (E, NL). These are the nodal actve and reactve power balances [16]. Ther general form s GN P + P V V y G U P cos( θ θ φ ) = 0 L N GN N LN LN N (7) + G V V y S + U L sn( θ θ φ) = 0 (8) SN LN LN N Where N={1,...,n} s the node set for a network wth n nodes or buses, GN, LN, SN and UN ( N) are the sets of generators, loads, SVC and UPFC devces connected to a node N. In addton, y and φ correspond to the elements of the nodal admttance matrx. Note that n P L the necton of ndependent DG already compromsed and scheduled at the wholesale market are dscounted. These DGI nectons are parameters n the optmzaton model. Power Factor Control (E, L). These constrants mantan the load power factor, wthn specfed margns, for loads nsde the DsCo control area. They are as follows: PL P = 0 LN k N (9) U U k DC L where N DC s the set of load nodes wth curtalment optons. 4

5 FACTS Devces (NL). These are the operatonal constrants for each UPFC devce n the system. Please see detals n reference [16]. Transmsson Lne Lmts (UE, NL). These constrants represent the power flow lmts on transmsson lnes. Two alternatve models are proposed: By usng actve power flow transmsson lmt θ δ δ θ P : y V cos( ) + V V y cos( ) < P (10) By usng current lmt I : ( δ δ θ ) y V + V + V V cos( ) < I (11) Power Factor (PF) Lmt for the DsCo (UE, L). Ths constrant s defned as follows: nected (1) tan( φ) where nected = n+ out Pn As tan(φ) functon has postve and negatve sgns, ths constrant s further dvded nto the followng two constrants n out tan( φ) and -tan( φ) (13) Pn Pn Where P n 0, n 0, out 0 The relatons between the reactve power varables and OPF system varables are as follows P = y V cos( θ ) + y V V cos( δ δ θ ) (14) n Control Area nected Control Area = [ y V sn( ) + y V V sn( δ δ θ )] Control_ Area Control_ Area θ (15) In addton, ether n or out must be zero,.e., they must fulfll the followng relaton, n out = 0 (16) Ths s known as the complementary condton. DGI Reactve Power (E, L). Ths constrant ensures the reactve power balance for each DGI unt. = + DGI RADGI, RIDGI, wth 0 and 0 RI, DGI RADGI, (17) Where DGI represents the total reactve power generated by the unt. Note that as a result of the optmzaton process ether RI,DGI or RA,Dg (or both) are zero. Bounds (UE, L). All optmzaton varables are subect to the followng operatonal constrants Voltage Magntude: Generaton Ranges: P Gmn Gmn G V Gmax mn V V (18) max P P (19) (0) G Gmax Note that n the case of DGI when there s energy already compromse and (scheduled) n the wholesale market, P Gmax corresponds to the dfference between DGI generaton capacty and P DGI,WS. 4.4 Branch and Border - SP (BBSP) The resultng OP s defned as a nonlnear optmzaton problem wth a quadratc obectve functon and nonlnear equalty and nequalty constrants. Wth the consderaton of Equaton 16, the OP requres the modelng of nteger varables [3,4]. Thus, the OP becomes a mxed nteger nonlnear optmzaton problem. In prevous research work, the authors have appled successfully the SP methodology for the soluton of the tradtonal OPF formulaton [16,]. In the present applcaton a new combned Branch and Border-SP (BBSP) methodolo gy s developed. The new requrements can be summarzed as follows: Increased number of varables (Eq. 5), Increased number of NL,E constrants (Eqs. 14, 15), Increased number of L, NL, E constrants (Eqs. 13,17), Changes n the Jacoban and Hessan Matrx [16], Two addtonal nteger varables due to Eq. 16. Fgure 3 shows the general structure of the BBSP algorthm. Fgure 3: The Structure of Branch&Border-SP Algorthm The convergence crteron consders both, the requrements of the mnmzaton of the obectve functon and the satsfacton of the constrants [5], whch nclude the fulfllment of equaton 16. Therefore, the convergence crteron uses a combnaton of the followng parameters: Cost Mnmzaton: The absolute value of the dfference between operatonal costs of two consecutve teratons, defned as ε COST, must be smaller than a certan percentage of the average cost. Satsfacton of the Power Flow Constrants: The sum of the resduals of the rght sde of the power flow constrants, defned as ε RHS, n the subproblem must be smaller than a percentage of the total system demand [8-18] 5

6 q (k) q (k 1) (k) (k 1) q + q ε (1) COST 100 (k) DTP + DT I ε () RHS 100 Equaton 16, whch s known n optmzaton as a complementary condton, usually causes convergence problems to the algorthms [4]. For ths reason, t s necessary to use an alternatve approach known as Branch and Border. Ths heurstc procedure conssts of an nterventon of the optmzaton algorthm, forcng the varables n and out to satsfy the complementary condton defned by Equaton 16. In fact, after fulfllng the convergence crtera of the OPF [8-18], or f the maxmum number of teratons of the routne (n=n) s acheved, the reactve power nected s computed as follows: = ( y V sn( θ ) + y V V sn( δ δ θ (3) INJECTED )) ControlArea ControlArea Then, the verfcaton of complance wth Equaton 16 s carred out accordng to the followng crtera: If INJECTED >0 out =0 and n=1 (start teratons agan), If INJECTED <0 n =0 and n=1 (start teratons agan). DCAM s mplemented n JAVA and s currently a functon n a larger research platform for power system analyss called DeepEdt, whch has been developed by the Area of Energy of the Department of Electrcal Engneerng at the Unversty of Chle [6] 3. V. VALIDATION AND TEST STUDY In ths secton applcatons of DCAM on a test network are shown to gve an overvew of the capabltes of the model. 5.1 Base Case The test network s composed of two busbars, three generators, and two loads, as shown n Fgure 4. Each busbar represents a dfferent system Control Area, whch are nterconnected through an equvalent transmsson lne. P Busbar1 + Busbar1 P Busbar+ Busbar Fgure 4: Two Busbar Network P DGDC P DGI The DsCo s feed through busbar, whereas the wholesale energy s produced by the system equvalent generator Gs 3 DeepEdt Homepage: at node 1. DGI stands for ndependent generaton unts and DGDC for generators belongng to the DsCo. Both DGI and DGDC are n servce connected to busbar. DGI actve power necton s fxed n 10 MW due blateral contracts, whle DGI reactve power consumpton (lmted to 10 MVAr) can be purchased by the DsCo. Most of the operatonal constrants are fxed due to the capabltes of the equpment. However, the power factor constrant depends on the operaton and, n some cases, cannot be fulflled. In fact, based on the experence of DsCo s n the Chlean market, ths constrant s very senstve to revenues as nvolves fnes when the DsCo requres more reactve power than the establshed n the contract from the producer company. For ths reason, we nvestgate the behavor of DCAM when PF lmts are changed (lmt n Eq. 1). Table 1 summarzes the characterstcs of the two busbar network wth a nomnal voltage of 0 kv. In the tests both, the wholesale market prce (P DC ) and the varable cost for the DGDC unt (β ) are set to 0 $/MWh. On the other hand, DGI unts are assumed renewable-based resources wth varable costs of (5$/MWh). For these unts the actve power necton lmt s set to 10 MW. Table 1. - Characterstcs of the two Busbar Network. System Data DGDC Actve Power Generaton Lmt MW 0 DGDC Reactve Power Generaton Lmt MW 10 DGI Actve Power Generaton Lmt MW 10 DGI Reactve Power Generaton Lmt MW 10 R', Transmsson Lne Ohm/Km X', Transmsson Lne Ohm/Km Length of Transmsson Lne km 300 Economc Data P DC $/MWh 0 ß $/MWh 0 Pr DGI $/MWh 5 Pr RI,DGI $/MVArh 1 Pr RA,GI $/MVArh 1 In order to compare the results of DCAM wth centralzed optmzaton, n all cases an OPF [8-18] s run to acheve the optmal operaton. Ths reference operaton condton (base case) consders no costs for reactve power generaton from DGI and voltage varatons between 0.9 and 1.1 pu are allowed at each busbar. 5. Test network results DCAM s solved for dfferent power factor lmts rangng from PF=0 to PF=1. Table summarzes the smulaton results for a specfc hour. As expected, centralzed OPF reaches the lowest operaton costs of $155.9, as shown n the frst row. Notce that OPF soluton takes 10 MVAr from DGI. However, from the DsCo pont of vew, the optmal soluton s dfferent, as ts costs nclude the acquston of reactve power generaton of ndependent producers (raw RA,DGI ). 6

7 Table.- Test Network Results. DCAM OPF PF [0-0.89] PF 0.9 PF 0.95 PF 0.97 PF 1 Operatonal Cost $ Actve Power Generaton P Busbar1+PDGDC+PDGI MW Reactve Power Generaton(*) Busbar1+DGDC+ DGI MVar Total Actve Losses MW Unserved Load MW System Actve Power Inyecton PBusbar1 MW System Reactve Power Inyecton Busbar1 Reactve Generaton DG(*) R_DG MVar MVar Actve Power Margnal Cost $/MW Reactve Power Margnal Cost $/MVar Voltage Busbar 1 kv Voltage Busbar kv (*) Note that DGDC and DGI do not absorb reactve power, hence both RA,DGDI and RA,DGI are zero. In all smulatons DGI actve power (P DGI ) and DGDC actve (P DGDC ) and reactve power ( RI,DGDC ) acheved ther upper bounds (10 MW, 0 MW, and 10 MVAr respectvely). As DCAM performs losses reducton from the DsCo pont of vew, t uses the most of ts own generaton (10 MW n unt DGDC). A smlar argument explans the behavor of voltage at busbar 1, whch s set n ts upper lmt of 4 kv n all smulatons. On the other hand, busbar vares ts voltage between the gven boundares n order to mantan the load flow balance. For power factor lmts between 0 and 0.89, DCAM (thrd column) optmal solutons are all the same, as the power factor constrant (Eq. 1) s not actve. For greater power factor lmts, operatonal costs ncrease due to the reactve power purchased by the DsCo to the DGI ( RA,DGI raw n Table ). Thus, although actve losses are decreased, the total cost ncreases as the PF gets closer to 1,.e., purchasng reactve power s more expensve than savng n losses. It was found that when the power factor constrant s greater than 0.97, ndependent generator DGI acheved ts reactve power necton lmt (10 MVAr). In ths pont, the only alternatve to satsfy the PF s by load curtalment. Ths stuaton s shown n Table for a PF=1, where 4.1 MW of unserved load are shed. At ths pont, the system operaton costs ncrease dramatcally due to the unserved load costs (500 $/MWh). 5.3 The role of constrants In ths subsecton, results for PF=1 are studed n more detal (last column n Table ). As PF=1 mposes Busbar1 =0, f we take angle reference at bus 1, the actve and reactve power reachng bus from bus 1 may be wrtten as P P P R = V Busbar1 Busbar1 L Busbar Busbar 1 V V Busbar1 Busbar1 Busbar P = V Busbar 1 Busbar 1 X L (4) (5) As the lne consumes reactve power, s negatve Busbar and the DsCo must nect reactve power nto the transmsson lne at busbar. At frst, DCAM attempts to mnmze by settng Busbar V at ts upper lmt. Busbar 1 Secondly, t reduces the actve load, whch n turn reduces P Busbar1. For the gven condton and data, the only way to do that s va unserved load n Load1 or Load. In addton, Equaton 9 mposes a power factor control constrant for unserved loads. Consequently, unserved reactve power mples unserved actve costs. Results show unserved actve power of 4.1MW and 8. MVAr of reactve power at Load. Therefore, the selecton of load curtalment s chosen to mnmze costs, n ths case s Load as t allows less actve power unserved load. Furthermore, Fgure 5 shows the behavor of busbar margnal cost and unserved actve power for dfferent PF values. For PF=0.9 a mnmum marg nal cost s acheved (optmal combnaton of loss reducton and reactve power purchase). Also, after a power factor of 0.97 margnal costs ncrease rapdly as unserved loads ncrease. These results ndcate that DCAM s able to optmze the revenues for the DsCo by combnng the purchase of actve and reactve power from the system (Gs), the ndependent generators (DGI) and ts own unts (DGDC). [MW] PF=0 PF=0.89 PF=0.9 PF=0.95 PF=0.96 PF=0.97 PF=0.98 PF=0.99 PF=1 Unserved Load Actve Power Margnal Cost Fgure 5: Busbar Unserved Load and Margnal Cost. VI APPLICATION TO A REAL NETWORK An applcaton to a real dstrbuton company n the Chlean Central Interconnected System (CIS), adapted for a future scenaro wth hgh penetraton of DG, s presented n ths secton. 6.1 System Descrpton The DsCo, named RM, s fed by 5 step down substatons from the CIS system. RM serves nearly 5 mllon people n the central part of the country. A scheme showng the man features of RM and CIS s presented n Fgure 6. The base case corresponds to a low demand scenaro wth a supply profle of 75% of hydropower and 5% of thermal unts. The wholesale prce P DC s set to 0$/MWh [0]. The actve power generaton costs for DG are around 10% above P DC, whereas for the reactve power the cost s set around 1% to 3% of the actve power costs, dependng on geographcal locaton of GD unts. Reference [7] contans detaled nformaton of the smulated system. 0.0 [$/MWh] 7

8 RM DsCo: - 0 DGDC unts - 40 DGI unts - 84 nodes - Demand (891.8MW) Fgure 8: Reactve Power Inectons Fgure 8 shows that when lower power factors are mposed, the DCAM gets the reactve power from a mx of the CIS, the ndependent DG and ts own DG. When the power factor s ncreased the acquston comes manly from pro ducers located n ts own area,.e., from DGDC and DGI. Fnally, when a unty power factor s mposed, DsCo only acqures reactve energy from ts own DGDI as the unserved load decreases the reactve requrements. Ths pattern s smlar to the one analyzed n the test example of Secton 5. Operatonal costs are shown n Fgure , ,0 OPERATIONAL COSTS 50056,0 Fgure 6. Real Case Study Rest of CIS: -33 generators -70 nodes -Demand (161.6 MW) The resultng optmzaton model s composed of a vector wth 851 varables and 466 constrants. Man results for actve and reactve power are shown n Fgures 7 and 8. Fgure 7 shows that DCAM model renders a mx for actve power generaton acquston. For power factor lower than 0.98 optmal mx s 605 MW from CIS, 35 MW from own DG and 50 MW from ndependent producers nsde DsCo s area. 450,0 400,0 350,0 300,0 50,0 00,0 150,0 100,0 50,0 0,0 fp=0.9 fp=0.98 fp=1 Power Factor Fgure 7: Actve Power Inectons Pn P DGI P DGDC When an extreme condton of unty power factor s mposed, the DCAM performs load sheddng by usng the load curtalment optons from some consumers. Total unserved load s 86 MW. MVAr 00,0 180,0 160,0 140,0 10,0 100,0 80,0 60,0 40,0 0,0 0,0 fp=0.9 fp=0.98 fp=1 Power Factor nyected DGI DGDI US$ 40056, ,0 0056, ,0 56,0 fp=0 fp=0.9 fp=0.95 fp=0.98 fp=0.99 fp=1 Power Factor Fgure 9: Operatonal Costs Operatonal costs show a stable behavor before the load sheddng s performed. Ths result confrms agan the patterns observed n the test system,.e., the man varable affectng costs, s the unserved load from consumers wth load curtalment optons. Resultng losses are shown n Fgure 10. MW fp=0 fp=0.9 fp=0.95 fp=0.98 fp=0.99 fp=1 Power Factor Fgure 10: Actve Power Losses Losses along wth the acquston of reactve power are key ele ments n cost optmzaton. Fgure 10 shows a wde range of varaton for the losses (nearly 15%), whch underlnes the flexblty of DCAM to fnd the optmal soluton. 6. Comments DCAM was conceved for markets based on Pool and fnancal blateral contract. However ts applcaton n a Power Exchange context s possble by usng the tool to analyze the behavor for dfferent bddng scenaros. Consequently, market agent strateges can be tested usng DCAM n ths envronment. Thus, for dfferent estmated clearng prces (P DC ) n the day-ahead market, DsCo optmal purchases can be obtaned. Wth ths teratve scheme a DsCo bddng curve for the day-ahead market. Smlarly, n the negotaton process for physcal blateral contracts DCAM can be used as a smulaton tool to explore the best alternatves for the DsCo. 8

9 VII. CONCLUSIONS The proposed DCAM model, based on an OPF approach, s desgned for a compettve market scenaro wth DG unts both, nsde (DGDC) and outsde (DGI) the DsCo control area. The compettve scenaro s characterzed by an actve partcpaton of new market agents, such as DG unts, customers wth load curtalment optons, and talored contracts wth reactve and voltage lmts. Results on a test network and a real dstrbuton company show that DCAM s able to obtan the best mx of energy acquston from the wholesale market and the DG unts, whle satsfyng steady state operaton standards and rules mposed by contracts. A specal feature of DCAM s ts ablty to handle power factor constrants, whch have become ncreasngly mportant as they are lnked to power qualty and power grd securty. For these reasons PF constrants appear n most contracts among DsCos and generatng companes n modern markets. In addton, Lagrange multplers provde the opportunty cost for the DsCo to satsfy the correspondng PF related constrant. Load curtalment optons are also part of the agreements that can be ncorporated nto DCAM. Results ndcate that the optmzaton process can sometmes ncrease the unserved energy to maxmze DsCo s revenues. Ths feature s very mportant as t ntroduces flexblty n the demand sde and, consequently, mproves market competton. Lagrange multplers resultng from the optmzaton procedure allow the dentfcaton of valuable nformaton for market desgn purposes. Test results show that busbar margnal costs (actve and reactve) provde convenent nvestment sgnals for new DG and reactve power compensaton equpment. Fnally, from the regulatory entty pont of vew, the proposed method can be used to sze the mpact of volaton of power factor and voltage lmts on the operaton of the system. The ongong work s centered n extendng the tme horzon of the method to a context monthly decson, ncludng accurate operaton models and specfc techncal constrants of dfferent technologes, and the desgn of an ancllary servces market. Also, future research wll focused on expandng DCAM to ncorporate DGI nectons at low voltage dstrbuton systems, whch normally does not operate under balanced condtons. Ths s a senstve topc as a growng number of monophasc DG s expected n the near future. VIII. ACKNOWLEDGMENT Ths paper has been partally supported by grants Fondecyt #100801, # , ICM Complex Engneerng System and the Facultad de Cencas Físcas y Matemátcas of Unversty of Chle. IX. REFERENCES [1] Ackermann, T., Andersson, G., Söder, L., Electrcty Market Regulatons and ther Impact on Dstrbuted Generaton, Conference on Electrc Utlty Deregulaton and Restructurng and Power Technologes 000, Cty Unversty, London, 4 7 Aprl , pp , IEEE 000. [] Organzaton for economc co-operaton and development, Dstrbuted Generaton n Lberalzed Electrc Markets, Internatonal Energy Agency, ISBN: , 00. [3] Kncad, D., The role of dstrbuted generaton n Compettve Energy Market, Gas Research Insttute, Dstrbuted Generaton Forum, March ( [4] Saks Melopoulos A. P., Dstrbuted Energy Source: Needs for Analyss and Desgn Tools, IEEE, Vancouver Summer Meetng, Brtsh Columba, Canada, 001. [5] Canever D., Dudgeon G.J.W., Massucco S., Mc Donald J.R., Slvestro F., Model Valdaton and coordnated operaton of a photovoltac Array and desel power plant for dstrbuted generaton. IEEE PES, Vancouver Summer Meetng, Brtsh Columba, Canada [6] Lasseter R., Dynamc models for mcro-turbnes and fuel cells. IEEE PES, Vancouver Summer Meetng, Brtsh Columba, Canada, 001. [7] Web Ste The Hydrogen & Fuel Cell Investor, [8] Carpenter, J., Contrbuton a l etude du Dspatchng Economque, Bulletn de la Socete Francase des Electrcens, Vol. 3, pp , Aug [9] A. Wood, B. Wollenberg, "Power Generaton, Operaton and Control", nd Ed, John Wley and Sons Inc. New York, ISBN: , [10] E. El-Hawary, "Optmal Power Flow: Soluton Technques, Requrements, and Challenges", IEEE Tutoral Course N 96, [11] H. Glavtch, R. 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Torres, R.A.: "OPF Wth SVC and UPFC Modelng for Longtudnal Systems", IEEE Transactons on Power Systems, Volume: 19, Issue: 4, Nov. 004, pp [17] Ambrz-Pérez H., Fuerte-Esquvel C., "Advanced SVC Models for Newton-Raphson Load Flow and Newton Optmal Power Flow Studes", IEEE Transactons on Power Systems, Vol. 15, No. 1, Feb. 000, pp [18] Lma, F.G.M., Soares, S., Santos, A., Jr, Akmeda, K.C. and Galana, F.D., "Numercal experments wth an optmal power flow algorthm based on parametrc technques", IEEE Transactons on Power Systems, Vol. 16, No. 3, Aug. 001, pp [19] Narnder K. Trehan, Ancllary Servces Reactve and Voltage Control, US Nuclear regulatory Commsson, Maryland, ISBN: , 000. [0] Natonal Energy Commsson, Chle, Nodal Prces, October of 001. Interconnected System Central (SIC), Techncal Report (n spansh). ( Oct

10 [1] Momoh, J.A.; VAr prcng and control n the compettve market, Power Engneerng Socety Summer Meetng, 00 IEEE, Volume: 3, 1-5 July 00 Pages:143 vol. 3. [] R. Fletcher, "Practcal Methods of Optmzaton", John Wley & Sons, ISBN: , New York, [3] M. Bazaraa, Sheral H.,Shetty C., "Nonlnear Programmng", John Wley & Sons, ISBN: , New York, [4] George L. Nemhauser, Laurence A. Wolsey, Laurence A. Wolsey. Integer and combnatoral optmzaton, New York, John Wley, [5] Ravndra S., Lasdon L., Computatonal Experence wth a Safeguarded Barrer Algorthm for Sparse Nonlnear Programmng, Computatonal Optmzaton and Applcatons archve, Kluwer Academc Publshers, Vol. N 19, Issue 1, Aprl 001, pp , ISSN: [6] Palma, R., Moya, O., Vargas, L.,"Obect-Orented Smulaton Software for a Compettve Envronment - Applcaton to Transmsson Expanson Plannng", The Frst EPRI Latn Amerca Conference & Exhbton: Toward a Mature Electrcty Market Through Tecnology, R&D, and Busness Vson, Ro de Janero, Brasl, 8-30 Novembre, 001. [7] Electrcal Engneerng Department, Unversty of Chle, Homepage : X. BIOGRAPHIES Rodrgo Palma B. (IEEE Senor Member) receved hs B.Sc. and M.Sc. on Electrcal Engneerng from the Pontfca Unversdad Católca de Chle and Dr.-Ing. from the Unversty of Dortmund, Germany. He s currently a professor n the Electrcal Engneerng Department at the Unversty of Chle. Hs research feld s the plannng and operaton of electrcal systems n compettve power markets and new technologes. José Lus Cerda A. was born 1978 n Santago, Chle. He receved hs B.Sc. n Electrcal Eng neerng from the Unversty of Chle, of Santago, of Chle. He s currently workng as a research assstant n the feld of market smulaton and analyss of electrc power systems. Lus S. Vargas (IEEE Senor Member) receved the Electrcal Engneer dploma (1985) from the Unversdad de Chle, Santago, Chle. He obtaned hs M.Sc. degree from Unversdad de Chle n 1987 and hs Ph.D. degree n Electrcal Engneerng from the Unversty of Waterloo, Canada. From 1994 he has worked at the Unversdad de Chle where currently he s an Assocate Professor. Hs man research nterests are n the areas of supply and demand forecastng, and expanson plannng of energy systems. Aleandro Jofré was born n Santago, Chle. He receved the Mathematcal Engneerng dploma n 1984 from Unversdad de Chle, hs Ph.D. n Appled Mathematcs (1989) from Unversty of Pau, France and Habltaton Degree (1995) n France. He s currently a professor at Department of Mathematcal Engneerng and Deputy Drector of Centre for Mathematcal Modelng. 10