DESIGN OF FREQUENCY REGULATION SERVICE MARKET BASED ON PRICE AND DEMAND ELASTICITY BIDS

Transcription

1 DESIG OF FREQUECY REGULATIO SERVICE MARKET BASED O ICE AD DEMAD ELASTICITY BIDS Hadan Zhao and Kanar Bhattacharya Department of Electrcal and Computer Engneerng Unversty of Waterloo, Waterloo, Ontaro, 2L 3G, Canada h3zhao@engmal.uwaterloo.ca anar@ece.uwaterloo.ca Abstract -- In ths paper, an attempt has been made to establsh a maret mechansm for prmary and secondary frequency regulaton servces n the restructured power system envronment. The concept of elastcty of offer prce and elastcty of offer quantty has been proposed. Such a desgn of offer structure helps the provders to respond to the system requrements based on the maret prce varatons n real-tme. Optmzaton models are proposed for auctons that ncorporate servce provder maxmum regulaton constrants and Independent System Operator (ISO) requrements for total regulaton whle mnmzng the total procurement cost of the ISO. The selected servce provders n each area receve a unform maret prce and regulaton servces are actvated by frequency devaton lned- or Area Control Error (ACE) lned-prce sgnals. The dynamc performances of the elastcty based servces are analyzed through the smulaton of a two-step load perturbaton to examne ther regulaton capabltes. Keywords: Ancllary servces, deregulaton, frequency regulaton, maret desgn OMECLATURE ndex referrng to ancllary servce provder j ndex referrng to control area (j A, B) superscrpt for up-regulaton D superscrpt for down-regulaton f system frequency, Hz D area prmary regulaton requrement, p.u.mw/hz D area secondary regulaton requrement K P plant gan, Hz/p.u.MW, K P /D and D s loadfrequency constant, p.u.mw/hz K r hgh-pressure turbne power fracton M upper bound on prmary regulaton, p.u.mw/hz M upper bound on secondary regulaton P prmary regulaton maret prce, $/MWh-Hz P secondary regulaton maret prce, ($/MWh)/MWh T g tme constant of speed governor, s T P plant tme constant, s, T P 2H/fD where H s the nerta-constant, p.u.mw s T r reheat tme constant, s T R tme constant of the hydro governor, s T tme constant of the hydro governor, s T 2 tme constant of the hydro governor, s T t steam-chest tme constant, s T w water startng tme constant, s U bnary varable for selecton of prmary regulaton U bnary varable for selecton of secondary regulaton f ncremental frequency devaton, Hz P D ncremental load demand change, p.u.mw P g ncremental generaton change, p.u.mw P C ncremental consumpton change, p.u.mw P TIE ncremental change n te-lne power, p.u.mw X E ncremental governor valve poston change ρ ACE lned prcng sgnal for control, $/MWh γ prmary regulaton quantty offer, p.u. MW/($/MWh) γ secondary regulaton quantty offer, p.u. MW/($/MWh) η prmary regulaton prce offer, $/MWh-Hz secondary regulaton prce offer, ($/MWh)/MWh η ITRODUCTIO As a prmary requrement n electrcal power systems, the system frequency should be mantaned at the nomnal (6 Hz or 5 Hz) or wthn a narrow margn around the nomnal for satsfactory system operaton. The system frequency s dependent on the real power balance and any msmatch between the generaton and demand results n frequency devaton. When the demand exceeds the supply, t s reflected by a drop n frequency. The speed governors of the generators respond to ths drop by ncreasng ther output nstantaneously. Ths ncrease n generaton together wth some frequency senstve load reducton helps arrest any further fall n the frequency, and s nown as prmary regulaton. Wth prmary regulaton only, a change n system load wll result n a steady-state frequency devaton n the system. Restoraton of the frequency to ts nomnal value requres a supplementary control acton for adjustng the generaton reference set pont of selected generators, and s referred to as secondary regulaton. Ths can be performed through manual adjustment (as n the ordc countres) or Automatc Generaton Control (AGC). Prmary and secondary regulatons together comprse the system frequency control. Tradtonally, all generators wth speed governors partcpate n prmary regulaton whle some selected generators partcpate n secondary regulaton. In deregulated power systems, new paradgms for control are evolvng and several of them are beng managed through the ancllary servces marets. 5th PSCC, Lege, August 25 Sesson, Paper 3, Page

2 Snce the generaton and transmsson actvtes operate as separate busnesses, the Independent System Operator (ISO) has no drect control over generators and therefore has to procure frequency control servces from them (or even from loads). In such an envronment, desgn of proper prcng mechansm for frequency regulaton servces s extremely mportant for proper operaton of the power system. Frequency control as an ancllary servce n deregulated power systems has been dscussed n some of the research lterature. Early n 989, real-tme prcng for the control of frequency and te-lne devatons was proposed []. These prces were derved from the frequency devaton and obtaned through dynamc analyss of the system. Hgher the frequency devaton, more would the prcng penalty be. In [2], the techncal ssues assocated wth load frequency control (LFC) n deregulated envronment were dentfed and two possble solutons- the charged LFC and blateral LFC, were proposed. The objectve of frequency control s to restore both the system frequency to nomnal and the area control error (ACE) to zero. Ths can be mplemented by AGC. A modfed AGC scheme was suggested for prce-based maret operaton n [3]. The AGC smulator could be appled to both pool and blateral marets. Reference [4] follows the deas of [3] and formulates an AGC system tang nto account the effect of blateral contracts by usng the dsco partcpaton matrx. Wth the applcaton of adaptve control, a new AGC scheme based on an onlne dentfcaton of the control area dynamc response was desgned for the Spansh system n [5]. In the orth Amercan power systems, ERC gudelnes provdes for Control Performance Standard (CPS) based on ACE to evaluate the frequency control performance [6]. Reference [7] analyzes and compares the CPS ndces used n orth Amerca, wth the Regulatng Help Indcator (RIH) and Indcator of Regulatng Trajectory Tracng (IRTT) used n Europe and concludes that both are essentally smlar and belong to the same famly. All three ndcators use the sgn of the f to ndcate the error drecton. RIH, IRTT and CPS are respectvely the expresson of zero, frst, and second moment of the frequency error term. Reference [8] also analyzes the CPS crtera and constructs the general crtera for frequency control performance assessment. Reference [9] consders smultaneously energy, AGC, synchronzed spnnng reserve and nonsynchronzed reserves and provdes an optmzaton model that enables a generator to allocate ts power among these varous marets to maxmze ts proft. An automatc balance servce maret that can act as an effectve tool for system frequency control n deregulated systems was presented n []. It was proposed that the partcpants n the maret would respond to frequency lned prce sgnals and provde regulaton servces. The present paper extends the wor reported n [] to construct prce and demand elastcty based offer structure for both prmary and secondary regulaton servces. The selected servce provders are actvated by frequency- or ACE-lned prce sgnals and respond n real-tme. 2 DESIG OF FREQUECY REGULATIO MARKETS The proposed maret structure for frequency regulaton servce and the tme-frame for operaton wll be descrbed n detal n ths secton and s depcted n Fgure. The proposed maret operates n three stagesthe frst stage nvolves recevng offers and maret settlement, the second stage nvolves real-tme nvocaton of the servces through actuatng sgnals and the thrd stage deals wth post-operatonal calculaton of payoffs. Fgure : Prmary and secondary regulaton maret structure and operaton The regulaton servce provders submt ther offers whch nclude prce and quantty. For prmary regulaton, D s assumed constant whch mples that loads do not partcpate n prmary regulaton but only offer for secondary regulaton servces. In prmary regulaton servce, the regulaton quantty R (n MW/Hz) of a generator s determned after the aucton. The selected generators wll adjust R to ther approprate values, whle generators not selected wll operate wth loced governors and thereby not provde prmary frequency regulaton. In ths way, generators can offer for both prmary and secondary regulaton, but n dfferent tmeframes. The prmary regulaton maret operates on a weely bass and the prce remans constant for the whole wee. The generators wll adjust R weely. However, the secondary regulaton maret s an hourly 5th PSCC, Lege, August 25 Sesson, Paper 3, Page 2

3 maret where prces change hourly and generators adjust ther governor set ponts hourly. For example, for the servce provded durng the hour to + (see Fgure ), prmary regulaton servce provders wll submt ther offers one wee n advance,.e., at hour -68, and the maret wll be settled at hour -67. The duraton of the servce provded by the selected generators wll be of one wee from hour -67 to hour +. The secondary regulaton servce provders wll submt ther offers one hour before the actual delvery. Hence, they wll offer at hour - for the servce delvered from hour to hour +. The ISO determnes the unform maret prces for each servce provson accordng to the system regulaton requrement and receved offers by executng an optmzaton procedure. Once ths s complete, the selected generators are actvated n real-tme by prce sgnals derved from the system frequency devaton or ACE. Fnally, at the end of a gven perod payoffs are calculated usng the maret prce, actual frequency devaton, and actual generaton or demand change. 2. Prmary Regulaton Servce The objectve of prmary regulaton s to eep the frequency devaton wthn acceptable bounds when dsturbances occur. 2.. Structure of Prmary Regulaton Offers It s proposed here that the generators wll offer for prmary regulaton servce based on ther droop characterstcs. The offer from a generator comprses a quantty offer γ, and a prce offer η,. However, unle the conventonal offer structure, γ, s the elastcty of quantty per unt maret prce of prmary regulaton offered by generator whle η, s the elastcty of prce per unt of frequency devaton. A comparson of classcal and proposed regulaton structures s shown n Fgure 2. The product, γ,i η,i s equvalent to the classcal value of /R. Fgure 2: Classcal and proposed prmary regulaton structures Example: Consder a 3 MW generator that offers ts servces at a prce of $/MWH for a. Hz change n system frequency. Further, for every % ncrease n maret prce t s wllng to ncrease ts generaton by 2%. If the energy prce s 5$/MWh and system base s 2 MVA, the prmary regulaton offer n terms of prce and demand elastcty, can be wrtten as- $/MWh $/MWh η,.hz Hz 2% 3 MW / 2 MVA % 5$ / MWh γ,.6 p.u.mw $ / MWh From the above t can be stated that the generator s elastcty of prce s $/MWh per Hz, and the elastcty of quantty s.6 p.u.mw, per unt of prmary regulaton prce. Therefore, ths s a typcal offer structure from the generator. Also note that snce there s a lmtaton n the regulaton capablty of each generator, t s necessary for the ISO to ncorporate an upper bound on regulaton, M,. Once all the generators have submtted ther offers, the ISO organzes the offers n ncreasng order of ther prces and the hghest prced offer to ntersect wth the prmary regulaton requrement to determne the maret prce (P ) Procurement of Prmary Regulaton Servce Consderng that the ISO receves offers from the partcpatng generators and the unform maret prce after settlement s P, the ISO s objectve n procurement of the prmary regulaton servce s to mnmze P, whle satsfyng all regulaton constrants. The constrants n ths optmzaton problem can be stated as follows: ) System-wde regulaton requrement: The ISO s requred to mantan at all tmes a mnmum amount of prmary regulaton capablty at ts dsposal. Ths quantty s equal to the classcal R, whch s usually pre-determned and nown from system studes. U, Pγ, D () ) Upper lmt on generator s regulaton capacty: Each prmary regulaton servce provder (generator) s also a compettve maret partcpant. A part of ts capacty s commtted for scheduled generaton and a part of t for the servce. Ths constrant ensures that the regulaton servce from the generator s wthn the requred lmts. U P γ M,...,,,, (2) ) Maret prce for prmary regulaton: Ths constrant ensures that the selected offer prces are less than or equal to the unform maret prce, whch s the hghest accepted offer prce. U η P,...,, (3) 2..3 Real Tme Smulaton of Prmary Regulaton Servce After the maret settlement, the unform maret prce P s determned and sent to the selected generators. The regulaton servce wll be actvated n real-tme when there s a devaton n frequency, through the frequency-lned prce sgnal P Calculaton After real-tme, the payoffs to the servce provders can be calculated by ( CP + P * f * P ) (4) In (4), CP s the avalablty prce of capacty. Even g 5th PSCC, Lege, August 25 Sesson, Paper 3, Page 3

4 f there s not any frequency devaton n real tme, the selected generators can stll receve ths porton of payoff for the provson of on call capacty. The term P P g * f * s the payoff for actual prmary frequency regulaton servce. Snce f and P g are contnuous and tme-varyng, the payoff has to be calculated from dscrete sampled values of the two sgnals. Assumng to be the number of samples n a perod of tme, the payoff functon can be re-wrtten as: CP + K ( P * f * P ) (5) g, 2.2 Secondary Regulaton Servce The objectve of secondary regulaton servce s to restore the system frequency to nomnal after the dsturbance Structure of Offers In ths proposed maret, both generators and customers can offer for secondary regulaton servce based on ther ablty to respond qucly (wthn about mnutes) by ncreasng / decreasng the generaton or consumpton. For up-regulaton servce, the generators offer to ncrease ther generaton whle the customers offer to reduce ther consumpton. And for down-regulaton servce, the generators offer to decrease ther generaton whle the customers offer to ncrease ther consumpton. The up-regulaton offer from generator comprses η, elastcty of quantty, the elastcty of prce per unt of ACE and γ, (as n prmary regulaton). Example: A MW generator offers to provde secondary regulaton at a prce of.4$/mwh for each MW of ACE change. Also t offers that the generaton would respond by a 3% change for a % ncrease n maret prce. For an energy maret prce of 5$/MWh, system base of 2 MVA, the offer can be formulated as- η,.4 $/MWh MWh 3% *MW / 2MVA p.u.mw γ,.3 % *5$ / MWh $/MWh From the above t can be stated that generator s elastcty of prce s.4 $/MWh per unt ACE change and elastcty of quantty s.3 p.u.mw per unt of prce change. Customers can also offer n the same structure. Ths s a typcal offer for secondary regulaton. Also to be noted that snce there s a lmtaton n the regulaton capablty of each generator or customer, t s necessary for t to supply an upper bound on regulaton, M,. Smlarly, generator (or customer ) can offer for down-regulaton based on, and upper bound D M, D γ, D η,. Both the generators and customers are consdered as secondary frequency regulaton servce provders Procurement of Secondary Regulaton Servce The objectve of the ISO managng the secondary regulaton maret s to mnmze the unform maret prce P. The constrants n ths optmzaton problem are smlar to those of prmary frequency regulaton: ) System-wde regulaton requrement: U / D / D / D / D, P γ, D (6) ) Upper lmt on a provder s regulaton capacty: / D / D / D / D U P γ M,,, (7),,, ) Maret prce for secondary regulaton: / D / D / D U η P,,, (8),, Real Tme Smulaton for Secondary Regulaton After the maret settlement, a unform maret prce P s determned and sent to the selected provders. The secondary regulaton servce wll be actvated n realtme through the prce sgnal ρ, when there s a nonzero ACE. The dynamc model of the two-area hydro-thermal system, wth the selected generator dynamcs ncorporated, s shown n Fgure Calculaton After real-tme, wth MP, the spot maret prce of energy, nown as a pror, and the tme-varyng ACE and P g, (or P C, for customers) the payoffs to the secondary regulaton servce provders can be calculated as follows: For generator: K For customer: K ( MP + P * ACE) * P (9) g, ( MP + P * ACE) * P () 3 CASE STUDY C, A two-area nterconnected hydro-thermal power system s used to demonstrate the proposed model for the varous cases. The dynamc model of the two-area hydro-thermal system, wth the selected generator dynamcs ncorporated, s shown n Fgure Maret Settlement By usng the optmzaton model descrbed n Secton-2, the maret was settled. We consder that four generators n area-a and three generators n area-b are selected for prmary regulaton servce. All the four selected generators n area-a receve the unform maret prce of 8.5$/MWh-Hz. The unform maret prce n area-b s 8.8$/MWh-Hz. The selected generators n both areas are shown n Table. 5th PSCC, Lege, August 25 Sesson, Paper 3, Page 4

5 Fgure 3: Dynamc model of prmary and secondary frequency regulaton Gen Area-A Quantty γ,, p.u.mw/($/mwh) Gen Area-B Quantty γ,,.2..5 p.u.mw/($/mwh) Table : Selected Prmary Servce Provders n Both Areas The total prmary regulaton quantty procured by the ISO n each area s.33 p.u.mw/hz and the total secondary up- and down-regulaton procured s.35 and.3 respectvely. After the maret settlement, all the secondary servce provders n both areas are shown n Table 2. The maret prce n area-a for up- and down-regulaton are.27 ($/MWh)/MWh and.25 ($/MWh)/MWh, respectvely. The up-regulaton maret prce n area-b s.3 ($/MWh)/MWh and the down-regulaton maret prce s.29 ($/MWh)/MWh. Provder 4 5 C C2 C3 Area-A Quantty γ,, Up p.u.mw/($/mwh) Down Provder 8 9 C4 C5 C6 Area-B Quantty γ,, Up p.u.mw/($/mwh) Down Table 2: Selected Secondary Servce Provders n Both Areas 3.2 Dynamc Smulaton The system dynamc performances wth the proposed frequency regulaton servces based on elastcty offers are examned through the smulaton of a small perturbaton model of the two-area hydro-thermal system. The transfer-functon model of the system s developed n state-space form by lnearzng the system around a nomnal operatng pont (Fgure 2). The model can be wrtten as follows: 5th PSCC, Lege, August 25 Sesson, Paper 3, Page 5

6 d X dt AX + Γ p () In () X s the state-vector and p s the perturbaton vector. The matrces A and Г are state and perturbaton matrces respectvely, of approprate dmensons, and depend on the system parameters and operatng condtons. It s observed from Table 3 that n area-a Gen-, -2 and -3 provdes prmary regulaton only; Gen-4 provdes both prmary and secondary regulaton, whle Gen-5 provdes secondary regulaton only. They are depcted n the transfer-functon model (Fgure 3). Smlarly for area-b, Gen-6 and -7 provde prmary regulaton only, Gen-8 provdes both prmary and secondary regulaton whle Gen-9 provdes secondary regulaton only, and these have been shown n Fgure 3. Also observe that there are three loads selected n each area for secondary regulaton, whch have been approprately represented n Fgure 3. The system dynamc performance s studed wth the above model, usng the selected prmary and secondary regulaton servce provders, for varous dsturbance condtons. A two-step load perturbaton s consdered n area-a. The frst step s a % ncrease n demand at t s and the second step s a 2.5% ncrease n demand at t s. Fgure 4 shows the dynamc frequency response for the two-step load perturbaton n area-a. Fgure 5 shows the plot of generaton responses from Gen-, -2, and -3 provdng only prmary regulaton servces. Fgure 6 shows output responses of Gen-4 whch provdes both prmary and secondary regulaton servces and Gen-5 whch provdes only secondary regulaton servce. Fgure 7 shows the responses from customer C, C2, and C3 whch provde only secondary regulaton servces. Frequency (Hz) Tme (s) Fgure 4: Frequency response n area-a followng the step load changes Generaton (p.u.mw) 2 x P g P g2 P g Fgure 5: Prmary regulaton of Gen-, -2, and -3 after the step load changes Generaton (p.u.mw) 8 x P g4 P g5 5 5 Tme (s) Fgure 6: Prmary and secondary regulaton of Gen-4 and secondary regulaton of Gen-5 followng the step load changes Consumpton (p.u.mw) x P C P C2 P C Tme (s) Fgure 7: Secondary regulaton responses of customer C, C2, and C3 followng the step load changes Then the same two-step load perturbaton s consdered n area-b. Fgure 8 shows the dynamc frequency response for the two-step load perturbaton n area-b. Fgure 9 shows the plot of generaton responses from Gen-6, and -7 provdng only prmary regulaton servces. Fgure shows output responses of Gen-8 whch provdes both prmary and secondary regulaton servces and Gen-9 whch provdes only secondary regulaton servce. Fgure shows the responses from customer C4, C5, and C6 whch provde only secondary regulaton servces. Frequency (Hz) Tme (s) Fgure 8: Frequency response n area-b followng the step load changes Generaton (p.u.mw) 2 x Tme (s) P g6 P g7 Fgure 9: Prmary regulaton of Gen-6, and -7 after the step load changes Generaton (p.u.mw) P g8 P g9 5 5 Tme (s) Fgure : Prmary and secondary regulaton of Gen-8 and secondary regulaton of Gen-9 followng the step load changes 5th PSCC, Lege, August 25 Sesson, Paper 3, Page 6

7 Consumpton (p.u.mw) x P C4 P C5 P C Tme (s) Fgure : Secondary regulaton responses of customer C4, C5, and C6 followng the step load changes It s seen from Fgure 4 and Fgure 8 that the frequency devaton s wthn. Hz and the system frequency s restored to the nomnal after the perturbaton n both scenaros. The selected servces provders adjust ther output n proporton to ther offer quanttes. 3.3 Calculaton of s The payoffs to the partcpatng servces provders under the two-step load perturbaton n area-a are shown n Table 3. It can be observed that secondary regulaton servce provders from area-a are pad sgnfcantly hgher than the other area provders. Ths s because the step load changes tae place n area-a and the secondary control effort s essentally from ths area s provders. Area-A Generator Customer Provder C C2 C3 Total Prmary, $ Secondary,$ Area-B Generator Customer Provder C4 C5 C6 Total Prmary, $ Secondary,$ Table 3: s for Step Load Changes n Area-A The payoffs to the partcpatng servces provders under the two-step load perturbaton n area-b are shown n Table 4. However, the secondary regulaton servce provders from area-b are pad sgnfcantly hgher than the provders from area-a n ths case because the perturbaton taes place n area-b and the secondary control effort s essentally from ths area s provders. Area-A Generator Customer Provder C C2 C3 Total Prmary, $ Secondary,$ Area-B Generator Customer Provder C4 C5 C6 Total Prmary, $ Secondary,$ Table 4: s for Step Load Changes n Area-B 4 COCLUSIO Ths paper establshes a prmary and secondary frequency regulaton servce aucton mechansm that s based on prce and demand elastcty offers. Such a desgn helps the provders accurately estmate ther capablty to provde the servces dependng on the maret prce. Optmzaton models are proposed for both prmary and secondary regulaton servces. Furthermore, a comprehensve dynamc model of a twoarea nterconnected hydro-thermal power system wth multple generators n each area together wth provson for customers provdng secondary regulaton servce has been developed. Smulatons have been carred out consderng a two-step load perturbaton to examne the prmary and secondary frequency control capabltes of the selected provders. Fnally, a comprehensve payoff calculaton exercse s carred out to determne the payoff to each servce provder. REFERECES [] A. W. Berger and F. C. Schweppe, Real Tme Prcng to Assst n Load Frequency Control, IEEE Transactons on Power Systems, Vol. 4, pp , August 989 [2] R. D. Chrste and A. Bose, Load Frequency Control Issues n Power System Operatons after Deregulaton, IEEE Transactons on Power Systems, Vol., pp. 9-2, August 996 [3] J. Kumar, K. H. g, and G. Sheble, AGC Smulator for Prce-based Operaton -Part I: a Model, Part II: Case Study Results, IEEE Transactons on Power Systems, Vol. 2, pp , May 997 [4] V. Donde and I. A. Hsens, Smulaton and Optmzaton n an AGC System after Deregulaton, IEEE Transactons on Power Systems, Vol. 6, pp , August 2 [5] L. Olmos et al, ew Desgn for the Spansh AGC Scheme Usng an Adaptve Gan Controller, IEEE Transactons on Power Systems, Vol. 9, pp , August 24 [6] orth Amercan Electrc Relablty Councl, ERC Operatng Manual, P-, P-2, June 24 [7]. Maruejouls et al, Measurement of the Load Frequency Control System Servce: Comparson Between Amercan and European Indcators, IEEE Transactons on Power Systems, Vol. 5, pp , ovember 2 [8] G. Gross and J. W. Lee, Analyss of Load Frequency Control Performance Assessment Crtera, IEEE Transactons on Power Systems, Vol. 6, pp , August 2 [9] J. M. Arroyo and A. J. Conejo, Optmal Response of a Power Generator to Energy, AGC, and Reserve Pool-Based Marets, IEEE Transactons on Power Systems, Vol. 7, pp. 44-4, May 22 []J. Zhong and K. Bhattacharya, Frequency Lned Prcng as an Instrument for Frequency Regulaton n Deregulated Electrcty Marets, Proceedngs of IEEE Power Engneerng Socety Annual General Meetng, Toronto, July 23 5th PSCC, Lege, August 25 Sesson, Paper 3, Page 7