Impact of Population of Group Search Optimizer on Bidding Strategies in Deregulated Electricity Market

Transcription

1 Internatonal Journal of Electroncs Engneerng Research. ISSN Volume 9, Number 2 (2017) pp Research Inda Publcatons Impact of Populaton of Group Search Optmzer on Bddng Strateges n Deregulated Electrcty Market Naresh Kumar Yadav Department of Electrcal Engneerng D. C. R. Unv. of Sc. & Tech; Murthal (Sonepat)-Haryana, Inda Abstract Ths paper studed the smplfed model for bddng strategy from the tradtonal b-level bddng model, whch has been developed n our prevous work. To transform the model nto a sngle level maxmzaton problem, earler, the researchers have adopted Karush Kuhn Tucker (KKT) optmalty condtons. Nevertheless, the proft maxmzaton problem wth KKT optmalty condtons poses a great challenge. Further, the complexty ncreases n the deregulated envronment whle the transmsson constrants become mportant. As a mnmzaton functon, we smplfed the proft maxmzaton problem. Here, the transmsson constrants, the operatng lmts and the ISO market clearng functons are consdered wth no KKT optmalty condtons. A recently developed optmzaton algorthm Group Search Optmzer (GSO) has been used to solve the problem model. Ths paper nvestgated the role of populaton sze of the GSO on maxmzng the proft of the strategc producers. Fnally, the smulaton result produces the relatonshp between the populaton sze and the maxmzed proft. Keywords: bddng, strategc, GSO, proft, GENCO, market, deregulated. I. INTRODUCTION In worldwde the power markets have been rasng comprehensve because of the need of transformaton from regulaton to competton n power sectors. To allocate the power to many deregulated envronment they act as the most mportant meda [1] [2] [3]. The electrcty producers face great bddng challenge towards maxmzng ts

2 294 Naresh Kumar Yadav profts n these markets [4]. Generally, the bddng arse between the buyers and the producers. Here, the producers submt ts prce offers for the produced energy and the buyers submt the approprate amount of energy [11]. On the bass of the demand and the offerngs of several buyers and producers, the market operator processes the nformaton and defnes energy prce for specfc ntervals [5]. In electrcty market some popular bddng characterstcs are (a) at the ntersecton of aggregate offer curve remuneratng prce and aggregate demand curve, (b) at every aucton consder both the offers and the bds from the buyers and the sellers, (c) From the sellers and the buyers accept the multple offers and bds and fnally (d) hdng bds or offers of one buyer or seller to the rest of the sellers or the buyers [6]. For survvng n the market the development of optmal strategc bddng procedures has become a sgnfcant feld n research [5]. A producer must devse the problem accurately n order to obtan vgorous optmal bddng strateges [32, 33]. The several techno economc parameters, operatng constrants, generaton parameters that nclude the start up costs and the shut down costs, ramp constrants, etc needs to nclude n the problem model [4]. The b-level and complementary models have been developed recently to consder these market clearng problems and wde parameters [7]. For example, n the market equlbrum, a lnear complementarly problem (LCP) s derved n [8]. Addtonally, the optmalty condtons of the producers to the market clearng condtons. Both the proft maxmzaton constrants and the power flow constrants as separate searchng formulatons have consdered n the tradtonal b-level model [9]. To fnd the Nash equlbra n the market over the perod the model has been used [10]. In the lterature the same knd of b-level models have been reported by comprsng the power constrants as the mnmzaton/ maxmzaton functons [4] [10]. To handle the strategc bddng framework some other methodologes have adopted bnarzed encodng procedure for the problem model [12] [13] [14]. In the lterature the problem of self schedulng of a thermal electrcty producer n both day ahead energy market and reserve market have been reported. Here, several reserve constrants and market clearng parameters have been consdered [15]. The strategc bddng models have been developed n the perspectve of prce takers [15, 18, 19, 20, 21, 23, 24], prce makers [2, 6, 13, 14, 25-31] and both [12, 13, 34-38] n the lterature. The sngle level strategc bddng model from tradtonal b-level bddng model has been derved n ths paper. Our model s a unfed verson of proft maxmzaton model, ISO market clearng constrants and transmsson constrants. In the near- real envronment by consderng the transmsson constrants, the derved model resembles [1]. Then, to solve the derved model we ntroduce GSO, whch s a recent optmzaton algorthm [16]. II. BIDDING PROBLEM WITHOUT KKT CONDITIONS The eqn. (1) represents a typcal proft maxmsaton problem of the producer. Here, N and N ndcates the power producers and Tme perod, R S H t ndcates the revenue and C t ndcates the Cost parameters. Besdes, C t n eqn. (1) represents the quadratc

3 Impact of Populaton of Group Search Optmzer on Bddng Strateges 295 formulaton of cost ncurred by the generators to generate the quantty of power offered. It can be llustrated as below; P, N H N S Rt Ct Q t1 1 arg max (1) N N f f Ct a Q b Q c f 1 f 1 Where, Q represents the volume of power presented at the 2 th th f slot of t (2) hour by th th producer and a, b and c ndcates the cost effcency of the. The eqn. (4) llustrates the ISO marketng clearng problem and t s subjected to the lmtatons mn max stated n eqn. (4) and (5). In eq. (4), the Q and Q represents the mnmum and maxmum generaton capactes of the t th producer. P, NH Ns N f arg mn P Q (3) Q t 1 1 f 1 Q mn Q Q (4) max N f Q Q f 1 In ths secton, the strategc bddng problem s nterpreted as a mnmsaton functon that s llustrated as below; max arg mn up Q P,, Q l 1, P Q P Q Here, u ndcates the upper level problem, l ndcates the lower level problem and ndcates the operatng margn penalty. Besdes, the u and l are nothng but eqn. (1) and (3) and the contemplated as the transmsson constrants. The operatng margn penalty functon can be nterpreted as cost parameters whch assess the operatng margns of the transmsson system whle the system users deal wth the proffer curve of all the producers. It s llustrated n eqn. (7) whle consderng P, Q, the represents the resultant transmsson lne parameters. As an max mn example, could be the voltage stablty margn, here and ndcates the maxmum and mnmum operatng ranges of those parameters. When contemplatng the proffer curve parameters the wll be acqured from the load flow analyss. The xrepresents the step functon wth response. 1, (5) (6)

4 296 Naresh Kumar Yadav P Q mn, 1 exp mn 1 max exp max, f, t (7) Constraned soluton Generator Soluton qualty check GSO searchng Load flow analyss Soluton Evaluaton Fg. 1. Block dagram of GSO bddng strateges III. GSO- BASED BIDDING STRATEGIES Fg. 1 demonstrates the soluton encodng and t s used to create the soluton and so t can be processed wth GSO. Besdes, the offer curve has mportant constrants along wth eqn. (4) and (5) lke Q Q f 1t (8) Q 0 (9) The populaton based optmsaton algorthm s GSO. Here, the searchng behavour of the anmals s mathematcally modelled. To fnd the optmal bddng strateges the GSO method s used. The producng operaton s performed as follows. (a) (b) Scannng at zero degree and subsequently by three random angles the random lateral scannng s performed. If t fnds an enhanced soluton pont the producer wll move or else t wll wat n the smlar poston.

5 Impact of Populaton of Group Search Optmzer on Bddng Strateges 297 (c) (d) (e) In the smlar poston f the producer wats for long tme, subsequently t turn rear to zero degree. Produce an arbtrary head angle To move to the new soluton pont produce a Gaussan dstrbuted random dstance. Algorthm: GSO procedure Set k=0 Get Randomly X Intal solutons; offer curve Intalze head angles φ of all members; Determne Intal member ftness values by means of eqn. (6) whle For each and every member n the group In the group dentfy the producer Xp Do producng Do scroungng by means of randomly choosng 80% of rest of the members End for Increase K by 1 Do dsperson Compute new ftness f(x) End whle IV. SIMULATION RESULTS Ths secton wll present the results of the GENCOs and here, we use IEEE 14 bus system [37] to nvestgate the performance. The smulaton model s performed n MATLAB R-2015 a. Three GENCOs such as GENCO 1, 2 and 3 are chosen and the expermental results produced are shown n Fgs. 2, 3, 4 and 5. Fg. 2 llustrated the

6 298 Naresh Kumar Yadav proft analyss, Fg. 3 llustrates the MCP analyss, Fg. 4 llustrates the Generaton strategy and Fg. 5 llustrates the Computatonal Complexty of GENCOs. A. Proft Analyss Fg. 2 llustrates the proft analyss of GENCO (Generaton Company). Here, totally three GENCOs such as GENCO 1, GENCO 2 and GENCO 3 have been used. Here, the proft s plotted over the Populaton sze (10 to 50). The GENCO 1 has been acheved $ profts under varyng populaton sze. The GENCO 2 has been obtaned $ profts under varyng populaton sze. Smlarly, $ profts have been obtaned by the GENCO 3. Hence, Fg. 2 clearly states the maxmum proft s acheved by the GENCO 1 whle comparng wth the other GENCOs. Fg. 2. Proft analyss of GENCOs for IEEE 14 bus system Fg. 3. MCP analyss of GENCOs for IEEE 14 bus system

7 Impact of Populaton of Group Search Optmzer on Bddng Strateges 299 B. MCP Analyss Fg. 3 demonstrates the Market Clearng Prce (MCP) analyss of GENCO for IEEE 14 bus system. The MCP of dfferent GENCOs determnes the profts of bds. In Fg. 3 the MCP acheved by the GENCO 1 s $ durng the populaton sze 10 and decreased steadly durng the populaton sze 20 and 30. The GENCO 2 acheved $ MCP durng the populaton sze 10 and t reduced durng the populaton sze 2.9. At populaton sze 10 the GENCO 3 has attaned $ MCP and t steadly ncreased durng the populaton sze 20 and 30. From the Fg. 3 t s found that the GENCO 1 gves hgher MCP values than the GENCO 2 and GENCO 3. C. Impact on Generaton Strategy The graphcal llustraton of Fg. 4 demonstrates the Generaton strategy of GENCO for IEEE 14 bus system. Here, the Generaton strategy (2600 to 2900) s plotted over the Populaton sze (10 to 50). Durng the populaton sze 10 the GENCO 1 produced 2800 Generaton (MW) at populaton sze 20, the 2748 Generaton (MW) has been produced. The GENCO 2 have been produced 2695 Generaton (MW) and t remans tll the populaton sze 20. The GENCO 3 produced 2650 Generaton (MW) at populaton sze 10. From the Fg. 4 t s clear that the GENCO 1 have produced hgher GENERATION (MW) when comparng wth the GENCO 2 and GENCO 3. D. Computatonal Complexty Fg. 5 depcts the computatonal tme of GENCOs for IEEE 14 bus system. The computatonal tme of GENCO 1, 2 and 3 remans same at populaton sze 10 to 30. However, the computatonal tme of GENCO 1 s steadly ncreased durng the populaton sze 31 to 40. But at the populaton sze 50 the GENCO 1, 2 and 3 poses same computatonal tme. Fg. 4. Generaton strategy of GENCOs for IEEE 14 bus system

8 300 Naresh Kumar Yadav Fg. 5. Computatonal tme of GENCOs for IEEE 14 bus system V. CONCLUSION In ths paper, a unfed model for bddng strategy have been developed from the tradtonal b-level bddng model. The common bddng strategc process ams ncreasng the proft of the strategc producers whch s provded offer curve and t s used to resolve the ISO market clearng problem. Furthermore, a robust populaton based optmzaton algorthm the GSO s ntroduced to solve the derved model. The methodology s expermented n bus systems and the performance s compared aganst GENCO based strategc bddng. The smulaton results llustrate that the obtaned proft maxmzaton through GENCO1 based bddng strateges s hgher than the other two GENCOs. The results also notfed that the ncrease n populaton sze has an mpact on ncreasng the proft despte t consumed more computng effort. REFERENCES [1] J. B. Cardell, C. C. Htt, and W. W. Hogan, Market power and strategc nteracton n electrcty networks, Resource Energy Econo., vol. 19, no. 1 2, pp , Mar [2] Ln Xu ; Baldck, R. ; Sutjandra, Y., Bddng Into Electrcty Markets: A Transmsson-Constraned Resdual Demand Dervatve Approach, IEEE Transactons on Power Systems, Vol. 26, No. 3, Page(s): , [3] Roy H. Kwon, Danel Frances, Optmzaton-Based Bddng n Day-Ahead Electrcty Aucton Markets: A Revew of Models for Power Producers, Energy Systems, Handbook of Networks n Power Systems I, 2012, pp

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11 Impact of Populaton of Group Search Optmzer on Bddng Strateges 303 [30] H.M.I. Pousnho, J. Contreras, A.G. Bakrtzs, J.P.S. Catalao, Rskconstraned schedulng and offerng strateges of a prce-maker hydro producer under uncertanty, IEEE Trans. Power Syst. 28 (2012), pp [31] C.K. Smoglou, P.N. Bskas, A.G. Bakrtzs, Optmal self-schedulng of a domnant power company n electrcty markets, Int. J. Electr. Power Energy Syst,. 43(2013), pp [32] C.J. Day, B.F. Hobbs, J.S. Pang, Olgopolstc competton n power networks: a conjectured supply functon equlbrum approach, IEEE Trans. Power Syst. 17(2002), pp [33] V.P. Gounts, A.G. Bakrtzs, Effcent determnaton of Cournot equlbra n electrcty markets, IEEE Trans. Power Syst. 19 (2004) pp [34] C.A. Daz, J. Vllar, Electrcty market equlbrum based on conjectural varatons, Electrcal Power Systems Research, 80 (2010), pp [35] C. Ruz, A.J. Conejo, Y. Smeers, Equlbra n an olgopolstc electrcty pool wth stepwse offer curves, IEEE Trans. Power Syst. 27 (2012), pp [36] E.G. Kardakos, C.K. Smoglou, A.G. Bakrtzs, Short-term electrcty market smulaton for pool-based mult-perod auctons, IEEE Trans. Power Syst. 28 (2013) [37] Naresh Kumar Yadav, A hybrd optmzaton model for profcent bddng strateges wth no Karush Kuhn Tucker optmalty condtons, Internatonal Journal for Numercal Methods n Engneerng, [Int. J. Numer. Meth. Engng. (2015)], Publshed onlne on 27 th Aprl, 2015 n Wley Onlne Lbrary (wleyonlnelbrary.com). DOI: /nme [38] Naresh Kumar Yadav, Mukesh Kumar, S. K. Gupta, Group Search Optmzer based Optmal Bddng strateges wth No Karush-Kuhn-Tucker Optmalty Condtons, Journal of Expermental & Theoretcal Artfcal Intellgence, Vol. 29, No. 2, pp , [39] IEEE system data avalable at accessed on 25/11/2014.

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