Inter national J our nal of Electrical and Computer Engineering (IJECE) V ol. 8, No. 4, August 2018, pp. 1997 – 2013 ISSN: 2088-8708 1997       I ns t it u t e  o f  A d v a nce d  Eng ine e r i ng  a nd  S cie nce   w     w     w     .    i     a    e    s    j    o    u    r    n    a    l     .    c     o    m     GENCO Optimal Bidding Strategy and Pr ofit Based Unit Commitment using Ev olutionary P article Swarm Optimization Illustrating the Effect of GENCO Mark et P o wer Adline K. Bik eri 1 , Christopher M. Muriithi 2 , and P eter K. Kihato 3 1,3 School of Electrical, Electronic, and Information Engineering, Jomo K en yatta Uni v ersity of Agriculture & T echnology , K en ya 2 Department of Electrical and Po wer Engineering, T echnical Uni v ersity of K en ya, K en ya Article Inf o Article history: Recei v ed October 27, 2017 Re vised April 10, 2018 Accepted: May 3, 2018 K eyw ord: Profit Based Unit Commitment EPSO PSO GENCO Mark et Po wer Dere gulated Electricity Mark et ABSTRA CT In dere gulated electricity mark ets, generation compani es (GENCOs) mak e unit commit- ment (UC) decisions based on a profit maximization objecti v e in what is termed profit based unit commitment (PB UC). PB UC is done for the GENCOs demand which is a summation of its bilateral demand and allocations from the spot ener gy mark et. While the bilater al demand is kno wn, allocations from the spot ener gy mark et depend on the GENCOs bidding strate gy . A GENCO thus requires an optimal bidding strate gy (OBS) which when combined with a PB UC approach w ould maximize operating profits. In this paper , a solution of the combined OBS-PB UC problem is presented. An e v olutionary par - ticle sw arm optimization (EPSO) algorithm is i mplemented for solving the optimization problem. Simulation results carried out for a t est po wer system with GENCOs of dif- fering mark et strengths sho w that the optimal bidding strate gy depends on the GENCOs mark et po wer . Lar ger GENCOs with significant mark et po wer w ould typically bid higher to raise mark et clearing prices while smaller GENCOs w ould typically bid lo wer to cap- ture a lar ger portion of the spot mark et demand. It is also illustrated that the proposed EPSO algorithm has a bet ter performance in terms of solution quality than the classical PSO algorithm. Copyright c 2018 Institute of Advanced Engineering and Science . All rights r eserved. Corresponding A uthor: Adline K. Bik eri School of Electrical, Electronic, and Information Engineering, Jomo K en yatta Uni v ersity of Agriculture & T echnology P .O. Box 62000-00200, Nairobi, K en ya. Email: adlinebik eri@gmail.com 1. INTR ODUCTION T raditionally , one of the most important aspects of po wer system operation is the prior scheduling of generating units also referred to as unit commitment (UC) [1, 2, 3]. UC schedules are usually determined on a week-ahead, day-ahead, or e v en just a fe w hours before operation. Prior scheduling of generating units increases ef ficienc y by ensuring a least-cost operating re gime while k eeping system reliability . In traditional, re gulated en vironments, UC is done from a “ least-cost” point-of-vie w [4]. While in the v ery short-term rule-of-thumb methods can be applied, po wer utilities usually in v est in system optimization softw are as the e xtra cost resulting from non-optimal operation could be significant. UC in dere gulated mark ets tak e a dif ferent approach. Unlik e the re gulated en vironment, the independent system operator (ISO) who is in char ge of ensuring that demand is met does not o wn or operate an y generating units [5, 6]. The ISO recei v es supply bids from the v arious generation companies (GENCOs) in the system and then allocates the demand to these GENCOs based on a cheapest-first method. The GENCOs in the system thus ha v e to compete for a proportion of the demand so as to mak e mone y . In some systems, apart from the allocations J ournal Homepage: http://iaescor e .com/journals/inde x.php/IJECE       I ns t it u t e  o f  A d v a nce d  Eng ine e r i ng  a nd  S cie nce   w     w     w     .    i     a    e    s    j    o    u    r    n    a    l     .    c     o    m     ,  DOI:  10.11591/ijece.v8i4.pp1997-2013 Evaluation Warning : The document was created with Spire.PDF for Python.
1998 ISSN: 2088-8708 in the ISO operated ener gy mark et ( spot mark et ), GENCOs may independently ne gotiate bilateral supply contracts with consumers though the y may ha v e to use the ISO’ s transmission netw ork to deli v er agreed po wer [6]. Each indi vidual GENCO still has to dra w up its o wn generations schedules especially because operational constraints on generating units such as minimum-up time or minimum-do wn times could significantly eat into a GENCOs profit if not properly considered in the operational planning stage. A GENCO’ s UC schedule is based on e xpected own demand from both the spot and bilateral ener gy mark ets with the aim of maximizing profits [7]. Thus, in dere gulated mark ets, UC is done from a profit maximization point of vie w hence the term profit based unit commitment (PB UC) [8]. Ho we v er , the allocation from the spot ener gy mark et depends lar gely o n a GENCO’ s bidding strate gy [9]. The GENCO may either lo wer its bids aiming t o increase its allocation or raise its bids so as to raise the electricity prices which means that the GENCO’ s o wn demand and hence its UC schedule depends significantly on its adopted bidding strate gy . An important determinant of a GENCO’ s bidding strate gy in the spot mark et is its mark et po wer i.e. the GENCO’ s ability to alter the mark et price and allocations in the mark et. A GENCO whose actions cannot af fect the mark et equilibrium is refe rred to a price tak er and con v ersely , a GENCO whose actions significantly af fect the mark et is referred to as a price mak er . Electricity mark ets usually assume an oligopolistic structure characterized by se v eral price tak ers and one or tw o price mak ers; usually lar ge companies that are of fshoots of the pre vious re gional or national ut ilities prior to dere gulation [10]. Since the GENCO’ s mark et po wer can influence the mark et price, it is a significant consideration in the determination of an optimal bidding strate gy (OBS) and hence the solution of the PB UC problem. Se v eral approaches for the solution of the PB UC problem ha v e been proposed in literature. Classical mathematical methods such as Priority Listing (PL), Dynamic Programming (DP), Branch and Bound, Mix ed Inte ger Programming (MIP), and Lagrangian Relaxation ha v e been proposed in [11, 12]. Ne wer , heuristi c based methods such as Genetic Algorithm (GA), Ant colon y optimization (A CO), P article sw arm optimization (PSO), and Artificial bee colon y (ABC) ha v e been proposed in [13, 14, 15]. Hybrid methods that combine tw o or more solution approaches ha v e also been proposed [16, 17]. Heuristic based methods pro vide the adv antages of a more thorough search of the solution space and being less prone to getting s tuck at local optimum solutions. Also, there is a reduced mathematical computation b urden since these method don’ t require the computation of gradients which may be quite dif ficult in certain instances. The e v olutionary particle sw arm optimization (EPSO) algorithm [18, 19, 20], which combines the classical PSO algorithm with e v olutionary programming (EP) concepts, is one of the most promising algorithms for the solution of v arious po wer system operation optimization problems. It has been sho wn that EPSO has better con v er gence characteristics than the con v entional PS O and usually gi v es better results. In this paper , an EPSO algorithm based solution methodology is proposed to solv e the combined optimal bidding strate gy and PB UC problem. The application of the proposed solution methodology is il lustrated for se v eral GENCOs of dif fering sizes operating in a test po wer system. The rest of the paper is or g anized as follo ws. Section 2. introduces the concept of GENCO bidding strate gies in electricity mark ets with an illustration of ho w a GENCO can set its bidding strate gy to increase its profits. Section 3. introduces the general EPSO algorithm. The problem formulation is gi v en in section 4. and the proposed solution algorithm in section 5.. Numerical simulations are presented in section 6. while conclusions are gi v en in section 7.. 2. GENCO BIDDING STRA TEGIES IN ELECTRICITY MARKETS In dere gulated electricity mark ets, electric ener gy is sold either through bilateral agreements between GENCOs and consumers or through an electricity pool operated by an independent system operator i.e. the elec- tricity spot mark et [21]. In the case of the bilateral mark et, the b uyer and seller agree on a transaction price from which the GENCO meets all costs for transmission, distrib ution, and other ancillary services. The electricity pool is ho we v er operated by an independent system operator ISO who recei v es and aggre g ates hourly ener gy supply bids from GENCOs and hourly demand bids from consumers after which a mark et clearing price (MCP) is deter - mined [6]. The GENCOs are allocated portions of the demand based on a cheapest-bid first while ensuring system reliability and security . The MCP is defined as the cost of supplying the last MW of demand and all GENCOs who recei v e load allocations for the gi v en hour are paid at this price irrespecti v e of their bids. Each GENCO will combine the bilateral demand with the allocation from the spot mark et as its own demand and from this data dra w up a UC schedule based on a profit maximization objecti v e. Since the spot mark et allocation is based lar gely on the GENCO’ s bid and those of its competitors, the GENCO bid decisions significantly af fect its allocation and hence its profits. Should a GENCO ha v e enough influence, it could af fect the IJECE V ol. 8, No. 4, August 2018: 1997 – 2013 Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE ISSN: 2088-8708 1999 mark et clearing price and consequently its profits. The magnitude of this influence defines the GENCO’ s mark et po wer . Un de r perfect competition, so as to maximize its profits, a GENCO should bid at its mar ginal cost (cost of supplying an e xtra MW of elect ricity) [9]. Ho we v er , depending on the mark et en vironment, the GENCO could increase its profits in one of tw o w ays: The GENCO could l o we r its bid ( bid low ) thereby potentially increasing its allocation in the spot mark et though this could reduce the MCP . Bidding lo w is justified if the reduced re v enue due to the lo wer pric es is co v ered by the increased re v enue due to a lar ger allocation. The could raise its bid ( bid high ) thereby potentially reducing its allocation in the spot mark et b ut increasing the MCP . This is justified if the increased re v enue due to the higher prices co v er the re v enue lost due to a smaller allocation. A minimal e xample to illustrate the spot mark et dynamics follo ws ne xt. The GENCO mar ginal cost curv e forms the basis of its bidding strate gy . The mar ginal cost curv e is a plot of the incremental cost of po wer generation ag ainst the total po wer output for a GENCO. Mathematically , M C i – the mar ginal cost curv e for GENCO i is gi v en by: M C i = @ C T i @ P T i ; (1) where C T i is the total operating cost of GENCO i when supplying a total of P T i MW . Assuming a quadratic cost curv e for GENCO costs, C T i is gi v en by: C T i = N X j =1 a ij + b ij P ij + c ij P 2 ij ; (2) and P T i = N X j =1 P ij : (3) In (2) and (3) a ij , b ij , and c ij are the coef ficients of the quadratic cost curv es for unit j operated by GENCO i while P ij is the output of unit j operated by GENCO i . Consider tw o GENCOs each o wning one generating unit with cost characteri stics sho wn in T able 1. The mar ginal cost curv es for the tw o GENCOs are plotted in Figure 1(a) sho wing that GENCO G1 has the cheaper generating unit of the tw o GENC Os. If each GENCO submits its mar ginal cost curv e as its supply curv e, the combined system supply curv e will be as sho wn i n Figure 1(b). Assuming a nominal system demand of 200 MW with a linear demand curv e a s sho wn in Figure 1(b), the mark et equilibrium will then be the point at which the tw o curv es intersect. When read from Figure 1(b) this point is ( P d = 200 MW , MCP = $ 30 : 78 = MWh ). When e xtrapolated to the supply curv es of the tw o GENCOs, G1 and G2 will supply 144 : 4 MW and 55 : 6 MW respecti v ely . T able 1. Example GENCO cost characteristics GENCO P min i 1 P max i 1 Cost Equation C T i ( P ij ) G1 0 300 25 P 11 + 0 : 020 P 2 11 G2 0 150 28 P 21 + 0 : 025 P 2 21 No w , consider a case where GENCO G1 submits bids where the gradient of its mar ginal cost curv e is multiplied by a f actor 1 . Its bid curv e, B C 1 is then gi v en by: B C 1 = b 11 + 1 2 c 11 P 11 = 25 + 0 : 04 1 P 11 (4) A v alue of 1 > 1 raises the bid curv e abo v e the nominal meaning that the GENCO bids high while a v alue of 1 < 1 means that the GENCO bids low . The ef fect of 1 on the MCP and the GENCO allocations is illustrated in Figure 2 for v alues of 1 = 0 : 8 , and 1 = 1 : 2 . The results are summarized in T able 2 sho wing that as 1 increases, the MCP increases, GENCO G1’ s allocation reduces (as does its re v enue and costs) b ut its profit increases. GENCO Optimal Bidding Str ate gy and Pr ofit Based Unit Commitment using Evolutionary ... (Adline K. Bik eri) Evaluation Warning : The document was created with Spire.PDF for Python.
2000 ISSN: 2088-8708 0 50 100 150 200 250 300 350 20 22 24 26 28 30 32 34 36 38 40 $30.78/MWh 144.4 MW 55.6 MW GENCO Output [MW] Marginal Cost [$/MWh]     GENCO G1 GENCO G2 0 50 100 150 200 250 300 350 400 450 20 22 24 26 28 30 32 34 36 38 40 $30.78/MWh 200 MW Power Supply / Demand [MW] Electricity Price [$/MWh]     Supply Curve Demand Curve (a) (b) Figure 1. (a) Mar ginal cost curv es for tw o GENCOs and (b) mark et equi librium obta ined from the intersection of the aggre g ated supply curv e and the system demand curv e. 0 50 100 150 200 250 300 350 20 22 24 26 28 30 32 34 36 38 40 GENCO Output [MW] Marginal Cost [$/MWh]     GENCO G1 GENCO G2 µ 1  = 0.8 µ 1  = 1.0 µ 1  = 1.2 0 50 100 150 200 250 300 350 400 450 20 22 24 26 28 30 32 34 36 38 40 Power Supply / Demand [MW] Electricity Price [$/MWh]     Supply Curves Demand Curve µ 1  = 0.8 µ 1  = 1.0 µ 1  = 1.2 (a) (b) Figure 2. Illustration of the ef fect of GENCO G1’ s bid strate gy on (a) the demand allocations and (b) the MCP . T able 2. Ef fect of GENCO bidding strate gy on spot mark et prices, allocations, re v enues, costs, and profits 1 MCP P 1 Re v enue Cost Profit [$ = MWh] [MW ] [$ = h] [$ = h] [$ = h] 0 : 8 30 : 15 161 : 01 4 ; 854 : 98 4 ; 543 : 87 311 : 11 1 : 0 30 : 78 144 : 44 4 ; 445 : 68 4 ; 028 : 40 417 : 28 1 : 2 31 : 29 130 : 97 4 ; 097 : 48 3 ; 617 : 21 480 : 27 A plot of the GENCO profit ag ainst the v alue of i for the tw o GENCOs acting indi vidually is illustrated in Figure 3 which sho ws that the tw o GENCOs achie v e maximum profits at dif ferent v alues of i ( 1 = 1 : 9 and 2 = 0 : 6 ). These results sho w that the lar ger GENCO G1 should bid high to increase its profits while con v ersely , the smaller GENCO G2 should bid low to increase its profits. 3. EV OLUTION AR Y P AR TICLE SW ARM OPTIMIZA TION Ev olutionary particle sw arm optimization (EPSO) is a heuristic optimization algorithm based on a com- bination of the e v olutionary programming (EP) and particle sw arm optimization (PSO) concepts [18, 19, 22]. As with the classical PSO algorithm [23], candidate solutions (particles) are mo v ed around the solution space in search of the best possible solution. Each particle defines a position in the solution space and during successi v e iterations, the particles are mo v ed to w ards the best sol utions disco v ered at the gi v en point in the solution process. The EPSO particle mo vement rule used in updating the particle position i s similar to the PSO particle update equation in that a particle mo v es to w ards its o wn personal best solution that it achie v ed so f ar ( pB est ), as well as to w ards the global best ( g B est ) solution which is best among the best solutions achie v ed so f ar by all particles present in the IJECE V ol. 8, No. 4, August 2018: 1997 – 2013 Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE ISSN: 2088-8708 2001 0 0.5 1 1.5 2 2.5 3 −200 −100 0 100 200 300 400 500 600 700 Bid Factor,  µ Profit [$/h]     GENCO G1 GENCO G2 Figure 3. Illustration of the ef fect of the bid f actor i on GENCO profits. population. One important dif ference in the EPSO algorithm is that the g B est position is “disturbed” hence the particles don’ t just aim for the already found g B est position b ut rather for the re gion around the g B est position which may actually be better than the already found g B est [18]. One of the main challenges of the classical PSO algorithm is parameter tuning i.e. the determination of the best algorithm parameters to gi v e the best solution. The EPSO algorithm addresses this challenge by progres- si v ely “mutating” the weight parameters with successi v e it erations. Thus, as the algorithm progresses, the weight parameters also e v olv e to w ards the best v alues. The basic structure of EPSO as originally e xplained in [18] carries out the follo wing processes at each iteration: REPLICA TION - each particle is replicated a number of times. MUT A TION - each particle has its weights mutated. REPR ODUCTION - each particle (original and replicas) generates an of fspring according to the particle mo vement rule using the mutated weights. EV ALU A TION - each of fspring has its fitness e v aluated. SELECTION - the best particles between the original set and the mutated set survi v e based on a stochastic tournament to form a ne w generation. After a certain pre-set number of iterations (generations), the particle with the global best solution is stored as the optimal solution. Incorporation of the Darwinistic characteristics of mutation and sele ction allo ws the EPSO algorithm to tak e adv antage of the f aster con v er gence characteristics of Ev olutionary Programming (EP) strate gies [19]. 4. PR OBLEM FORMULA TION Under the dere gulated en vironment each indi vidual GENCO seeks to capture a significant proportion of the spot electricity mark et and then determine a generation schedule that maximizes its profit based on e xpected prices at each scheduling period. If the GENCO can significantly af fect the electricity price at a gi v en hour , then the GENCO can set up its bid to dri v e up profits at the specified hour . The GENCO’ s decision is then tw o-fold: (1) ho w to set up its bidding strate gy either to capture a lar ger portion of the spot mark et or to dri v e up the electricity price, and (2) ho w to schedule the generating units to maximize its profit gi v en the e xpected prices. This optimization problem is formulated here as an optimal bidding st rate gy - profit based unit commitment (OBS- PB UC) problem. Re v enues from both the day-ahead spot ener gy and reserv e mark ets and the GENCO’ s bilateral contract commitments are considered. The objecti v e function and the operational constraints are e xplained in the follo wing subsections. 4.1. Objecti v e Function Profit ( P F ) is defined as the dif ference between re v enue ( R V ) obtained from sale of ener gy and reserv e and the total operating cost ( T C ) of the GENCO. The objecti v e function is thus gi v en as: Maximize P F = R V T C : (5) GENCO Optimal Bidding Str ate gy and Pr ofit Based Unit Commitment using Evolutionary ... (Adline K. Bik eri) Evaluation Warning : The document was created with Spire.PDF for Python.
2002 ISSN: 2088-8708 4.1.1. GENCO Re v enue In (5), R V is gi v en by: R V = H X h =1 R V p h + R V r h ; (6) where R V p h and R V r h are the re v enues from the ener gy mark et and the reserv e mark et at hour h respecti v ely . H is the number of hours in the scheduling horizon. R V p h is calculated as: R V p h = h s P h s + h b P h b + h s h b P h b ; (7) where h s and h b are the ener gy prices at the spot mark et and bilateral mark et respecti v ely at hour h , P h s and P h b are the po wer supplied to the spot mark et and bilateral mark et respecti v ely at hour h , and is a contract of dif ferences f actor [24]. The first term in (7) represents re v enue from the ener gy sold at the spot mark et, the second term represents re v enue from bilateral contracts, while the third term represents re v enue from contracts of dif ferences. Contracts of dif ferences are usually included in bilateral contracts to compensate suppliers and consumers for dif ferences between the bilaterally agreed prices and the pre v ailing mark et price [24]. Re v enue from reserv e sales R V r h is gi v en as: R V r h = h r N X j =1 P max j P h j ; (8) where h r is price of reserv e capacity at hour h , P max j is the maximum capacity of unit j , and P h j is the output of unit j at hour h . N is the total number of generating units. In (8), the same price is assumed for both spinning and non-spinning reserv e. If the pricing is dif ferent, the equation could be split to ha v e tw o terms accounting for each type of reserv e. 4.1.2. GENCO Costs T otal cost T C is a sum of generator fuel costs ( F C ) and start up costs ( S U C ) for all N units o v er the entire scheduling period of H hours gi v en as: T C = H X h =1 N X j =1 F C h j + S U C h j ; (9) where F C h j = a j + b j P h j + c j P h j 2 ; (10) and S U C h j = j 1 U h 1 j U h j ; (11) where j = ( C S C j if P h t = h C S hr j U t j C S hr j H S C j if P h t = h C S hr j U t j < C S hr j : (12) In (11) and (12), U h j is the status of unit j at hour h i.e. U h j = 0 if unit j is OFF at hour h and U h j = 1 if unit j is ON at hour h . j is the start up cost coef ficient for unit j which is either the cold start cost C S C j if the duration unit j has been ON is less than its cold start hour C S hr j or the hot start cost H S C j otherwise. 4.2. Operational Constraints The GENCO operational constraints are gi v en as: (a) Po wer balance constraints N X j =1 P h j = P h s + P h b 8 h (13) IJECE V ol. 8, No. 4, August 2018: 1997 – 2013 Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE ISSN: 2088-8708 2003 (b) Generation limit constraints U h j P min j U h j P h j U h j P max j 8 i; 8 h (14) (c) Generator ramp up constraints P h j P h 1 j R U j 8 i; 8 h (15) (d) Generator ramp do wn constraints P h 1 j P h j R D j 8 i; 8 h (16) (e) Generator minimum up time constraints U h j = 1 if U t j U t 1 j = 1 ; for h = t; :::; t + M U T j 1 (17) (f) Generator minimum do wn time constraints U h j = 0 if U t 1 j U t j = 1 ; for h = t; :::; t + M D T j 1 (18) In (15) and (16), R U j and R D j are the hour -to-hour ramp-up and ramp-do wn limits on unit j respecti v ely . In (17) and (18), M U T j and M D T j are the minimum-up-time and minimum-do wn-time limits on unit j respecti v ely . Constraints (14) to (18) define unit operation limits and are similar to the formulation of a traditional utility’ s cost mi nimization UC problem [25]. Constraint (13) – the po wer balance constraint – states that the GENCO’ s total output at an y gi v en hour must equal its o wn load which is the sum of it s e xpected spot mark et allocation P h s and its bilateral mark et commitment P h b . While the bilateral mark et load w ould typically be agreed upon long in adv ance, the spot mark et allocation w ould depend on the GENCO’ s bidding strate gy . A GENCO can predict the v alues of P h s and h s using its bidding strate gy and the e xpected com petitor bid curv es. Generally , P h b and h b can be treated as constants while P h s and h s are v ariables dependent on the mark et dynamics. A GENCO w ould act in the day-ahead mark et to af fect the v alues of P h s and h s so as to increase its profits. A second significant dif ference between the formulations of the OBS-PB UC problem and the traditional UC problem is the absence of a minimum spinning reserv e constraint [25] in the ne w formulation. This is because, supply of reserv e, as well as other ancillary services, is not the responsibility of the GENCO. The ISO ensures the supply of such ancill ary services by eng aging the GENCOs. A GENCO thus gets payments for supply of both spinning and non-spinning reserv e as gi v en in the re v enue equation (6). The adequac y of the reserv e i s ensured by the ISO by aggre g ating reserv es from all GENCOs participating in the electricity mark et. 5. OBS-PB UC SOLUTION METHODOLOGY In this section, the procedure adopted in this paper to solv e the OBS-PB UC problem is outlined. Sec- tion 5.1. e xplains the procedure adopted to determine the profit corresponding to a gi v en bidding strate gy while section 5.2. details the step-by-step procedure implemented to select an optimal bidding strate gy using the EPSO algorithm. 5.1. Pr ofit Maximization Pr ocedur e As illustrated in section 2., a GENCO can opt to bid high or bid low with respect to its mar ginal cost curv e aiming to maximize its profits. Assume a linear reference mar ginal cost curv e gi v en by 1 : M C ref = + P h T ; (19) where and are the mar ginal cost curv e coef ficients for the GENCO and P h T is its total output at hour h . Then, let h be the bid curv e multiplying f actor at hour h so that the GENCO bid curv e at hour h is gi v en by: B C h = + h P h T : (20) The v alue of h then defines the GENCO’ s bidding strate gy at hour h . F or a scheduling period of H time periods, the set of bid f actors U = 1 ; 2 ; 3 ; : : : ; H constitutes the GENCO’ s bidding strate gy . 1 the subscript i indicating the GENCO number is dropped to impro v e readability of the equations. GENCO Optimal Bidding Str ate gy and Pr ofit Based Unit Commitment using Evolutionary ... (Adline K. Bik eri) Evaluation Warning : The document was created with Spire.PDF for Python.
2004 ISSN: 2088-8708 Figure 4. Profit Maximization procedure for a gi v en bidding strate gy . F or a gi v en bidding strate gy , the procedure used to determine a profit maximization schedule is sho wn in Figure 4. Gi v en a particular bidding strate gy , the reference mar ginal cost curv e, forecasted competitor bid curv es, and the hourly demand curv es, the GENCO can forecast the mark et’ s supply and demand curv es and hence the mark et equilibrium point as illus trated in section 2.. As seen from Figure 4, this gi v es the GENCO’ s spot mark et allocations and the MCPs (spot mark et prices). The spot mark et data is then combined wi th the bilateral mark et data (demand and prices) which is fed to a profit maximization algorithm to determine the optimal UC schedules and hence the profit associated with the bidding strate gy U . 5.2. EPSO Algorithm Dif ferent bidding strate gies gi v e dif ferent s pot mark et allocations and hence dif ferent optimal UC sched- ules. Thus, an algorithm that determines the optimal bidding strate gy is implemented in this paper using the EPSO algorithm [18]. In the solution of the OBS-PB UC problem, a particle represents a candidate solution to the problem which in this case is a set of bid f actors with one bid f actor for each time period of the scheduling hori- zon. Gi v en a scheduling period of H hours, the j th particle after k iterations U j ;k = f 1 j ;k ; 2 j ;k ; 3 j ;k ; : : : ; H j ;k g represents a position in the H -dimension solution space. The particle also has an associated v elocity V j ;k = f v 1 j ;k ; v 2 j ;k ; v 3 j ;k ; : : : ; v H j ;k g and an associated set of weights W j ;k = f w 0 j ;k ; w 1 j ;k ; w 2 j ;k g . The v elocity represents a direction in which the particle is mo ving in the solution space while t he weights go v ern the direction of par - ticle mo v ement. w 0 j ;k go v erns the particle’ s inertia habit, w 1 j ;k go v erns its memory habit, while w 2 j ;k go v erns its cooperation habit [18]. A step by step outline of the procedure used to solv e the OBS-PB UC problem using the EPSO algorithm follo ws. Step 1 : Initialization : Randomly initialize J particles U j ; 0 j = 1 ; 2 ; : : : ; J . Each particle is a set of H bid f actors defining a particular bidding strate gy . F or each particle, an optimal unit commitment schedule is obtained using the profit maximization procedure sho wn in Figure 4. The obtained profit P F j ; 0 is the particle’ s initial fitness v al ue. Each initialized particle is stored as pB est j ; the corresponding fitness v alues as the best fitness v alues; and the fittest particle of all initialized particles as initial g B est . Step 2 : Set the algorithm generation counter k = 1 . Step 3 : Set the particles counter j = 1 . Step 4 : Replication Each particle is replicated R times i.e. R ne w particles are created as: U r j ;k = U j ;k ; r = 1 ; 2 ; : : : R : (21) Step 5 : Set the particles replica counter r = 0 . Step 6 : Mutation The weights for replica r of particle j are mutated as: w l ;r j ;k +1 = w l ; 0 j ;k + w l N (0 ; 1) ; l = 0 ; 1 ; 2; (22) where w l is the standard de viation of the random mutation of weight parameter w l . IJECE V ol. 8, No. 4, August 2018: 1997 – 2013 Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE ISSN: 2088-8708 2005 Step 7 : Repr oduction A ne w of fspring is generated according to the particle mo vement rule 2 : U r j ;k +1 = U r j ;k + V r j ;k +1 ; r = 0 ; 1 ; 2 ; : : : R ; (23) where V r j ;k +1 = w 0 ;r j ;k V r j ;k + w 1 ;r j ;k pB est j ;k U r j ;k + w 2 ;r j ;k g B est k U r j ;k : (24) In (24), the g B est k v alue is disturbed to gi v e g B est k using: g B est k = g B est k + g N (0 ; 1) (25) where g is the standard de viation of the random disturbance of the g B est v alue. Step 8 : F itness Evaluation An optimal UC schedule is obtained using the procedure described by Figure 4. The profit obtained from the optimal UC schedule is is the of fspring’ s fitness. Step 9 : Increase the replica counter by 1. If all replicas ha v e been e v aluated, go to Step 10, else go back to Step 6. Step 10 : Updating pB est The fitness v alues of particle j ’ s of fspring are used to update the pB est j ;k . Step 11 : Selection One of fspring is chosen to survi v e to the ne xt generation through a stochastic tournament. The stochastic tourna- ment is carried out as follo ws: The fittest between the particle’ s of fspring is determined. This particle survi v es to the ne xt generation with a probability p l uck while the other particles survi v e with a probability (1 p l uck ) =R . If p l uck is set to 1 then the best particle will al w ays be chosen (pure elitism selection) while if p l uck is set to 1 = ( R + 1) , there will pure random selection. Step 12 : Increase the particle counter by 1. If all particles ha v e been e v aluated, go to Step 13, else go back to Step 4. Step 13 : Updating g B est The original g B est k 1 v alue and the highest profit from the pB est j ;k v alues are used to update the g B est k v alue. Step 14 : Increase the algorithm generations counter by 1. If K generations ha v e been e xhausted, go to Step 15, else go back to Step 3. Step 15 : Store g B est K and its corresponding UC schedule as the optimal solution and ST OP . 6. RESUL TS AND DISCUSSION 6.1. T est System The IEEE 118-b us system data [26, 27] w as used to simulate a dere gulated electricity mark et en vironment with three GENCOs of dif ferent sizes in terms of installed capacity of generators. The three GENCOs operate se v eral of the 54 thermal units in the IEEE 118-b us test system and the generating units data are gi v en in T ables 3, 4, and 5 for GENCOs A, B, and C respecti v ely . The generator cost coef ficients are scaled up from the v alues gi v en in [27] so as to gi v e more realistic ener gy prices. Based on the installed capacity , GENCO A controls 60% (4340 MW out of 7220 MW) of the system capacity; GENCO B controls 30% (2140 MW out of 7220 MW); while GENCO C controls 10% (740 MW out of 7220 MW) of the system capacity . The reference linear mar ginal cost curv es for each of the three GENCOs and the aggre g ated system mar ginal cost curv e are sho wn in Figure 5. The mar ginal cost curv es sho w that GENCO A operates the cheaper units while GENCO C operates the most e xpensi v e units. Nominal mark et clearing prices h s corresponding a spot mark et demand P h D can be read of f from the aggre g ated reference mar ginal cost curv e of Figure 5(b). Additionally , linear demand curv es are assumed for v arious load le v els with a per -unit gradient of 5 i.e. h s = h s P h T =P h T = 5 : (26) 2 U 0 j ;k refers to the original particle while U 1 j ;k , U 2 j ;k ; : : : refer to the replica particles. GENCO Optimal Bidding Str ate gy and Pr ofit Based Unit Commitment using Evolutionary ... (Adline K. Bik eri) Evaluation Warning : The document was created with Spire.PDF for Python.
2006 ISSN: 2088-8708 Equation (26) implies that a 100% increase in the spot mark et price w ould result in a 20% reduction in the spot mark et demand. A 24-hour (day ahead) scheduling period is applied and the load le v el is sho wn in Figure 6. Apart from the allocations in the spot mark et, GENCO A is assumed to ha v e a bilateral load demand equi v alent to 10% of of the system spot mark et demand (Figure 6) at a constant price of $ 45 = MWh . A contract of dif ferences f actor ( in equation (7)) is set at 0 : 1 . GENCOs B and C are assumed to ha v e no bilateral commitments. The price of reserv e po wer (both spinning and non-spinning) is set at a constant $ 4 : 50 = MW . T able 3. GENCO A ’ s Generator Data Unit No. of P min i P max i Capacit y a b c MUT MDT R U RD HSC CSC CShr Code Units [MW] [MW] [MW] [$/h] [$/MWh] [$/MWh 2 ] [hrs] [hrs] [MW] [MW] [$/h] [$/h] [hrs] A1 2 100 420 840 128.32 16.68 0.0212 10 10 210 210 250 500 20 A2 8 100 300 2400 13.56 25.78 0.0218 8 8 150 150 110 220 16 A3 2 50 250 500 56.00 24.66 0.0048 8 8 125 125 100 200 16 A4 1 50 200 200 13.56 25.78 0.0218 8 8 100 100 400 800 16 A5 3 25 100 300 20.30 35.64 0.0256 5 5 50 50 50 100 10 A6 2 25 50 100 117.62 45.88 0.0195 2 2 25 25 45 90 4 T otal 18 4340 T able 4. GENCO B’ s Generator Data Unit No. of P min i P max i Capacit y a b c MUT MDT R U RD HSC CSC CShr Code Units [MW] [MW] [MW] [$/h] [$/MWh] [$/MWh 2 ] [hrs] [hrs] [MW] [MW] [$/h] [$/h] [hrs] B1 1 10 0 350 350 65.92 21.50 0.0060 8 8 175 175 100 200 16 B2 1 10 0 300 300 65.92 21.50 0.0060 8 8 150 150 440 880 16 B3 2 5 0 200 400 78.00 26.58 0.0088 8 8 100 100 100 200 16 B4 8 2 5 100 800 20.30 35.64 0.0256 5 5 50 50 50 100 10 B5 1 2 0 50 50 117.62 45.88 0.0195 2 2 25 25 45 90 4 B6 8 5 30 240 63.34 52.49 0.1393 1 1 15 15 40 80 2 T otal 21 2140 T able 5. GENCO C’ s Generator Data Unit No. of P min i P max i Capacit y a b c MUT MDT R U RD HSC CSC CShr Code Units [MW] [MW] [MW] [$/h] [$/MWh] [$/MWh 2 ] [hrs] [hrs] [MW] [MW] [$/h] [$/h] [hrs] C1 4 2 5 100 400 20.30 35.64 0.0256 5 5 50 50 50 100 10 C2 1 3 0 80 80 48.66 30.94 0.0918 3 3 40 40 45 90 6 C3 6 5 30 180 63.34 52.49 0.1393 1 1 15 15 40 80 2 C4 4 5 20 80 35.90 75.39 0.0566 1 1 10 10 30 60 2 T otal 15 740 0 500 1000 1500 2000 2500 3000 3500 4000 4500 10 20 30 40 50 60 70 80 90 GENCO output power [MW] Marginal Cost [$/MWh]     GENCO A GENCO B GENCO C 0 1000 2000 3000 4000 5000 6000 7000 8000 10 20 30 40 50 60 70 80 90 Aggregated GENCO output power [MW] Marginal Cost [$/MWh]     Aggregated for all GENCOs (a) (b) Figure 5. (a) Indi vidual mar ginal cost curv es for the three GENCOs and (b) aggre g ated system mar ginal cost curv e. First, in section 6.2. a discussion of the nominal system equilibrium is presented i.e. the mark et prices, spot mark et load allocations, and e xpected GENCO profits (results of the PB UC) if each GENCO were to bid its IJECE V ol. 8, No. 4, August 2018: 1997 – 2013 Evaluation Warning : The document was created with Spire.PDF for Python.