An Optimal Dynamic Generation Scheduling for a Wind-Thermal Power System *

Transcription

1 Energy and Power Engineering, 2013, 5, doi: /epe b194 Published Online July 2013 (hp:// An Opimal Dynamic Generaion Scheduling for a Wind-Thermal Power Sysem * Xingyu Li, Dongmei Zhao School of Elecrical and Elecronic Engineering, orh China Elecric Power Universiy, Beijing, China lxylyxy123@ncepu.edu.cn Received March, 2013 ABSTRACT In his paper, a dynamic generaion scheduling model is formulaed, aiming a minimizing he coss of power generaion and aking ino accoun he consrains of hermal power unis and spinning reserve in wind power inegraed sysems. A dynamic solving mehod blended wih paricle swarm opimizaion algorihm is proposed. In his mehod, he soluion space of he saes of uni commimen is creaed and will be updaed when he saus of uni commimen changes in a period o mee he spinning reserve demand. The hermal uni operaion consrains are inspeced in adjacen ime inervals o ensure all he saes in he soluion space effecive. The paricle swarm algorihm is applied in he procedure o opimize he load disribuion of each uni commimen sae. A case sudy in a simulaion sysem is finally given o verify he feasibiliy and effeciveness of his dynamic opimizaion algorihm. Keywords: Generaion Scheduling; Dynamic Opimizaion; Wind Power; Paricle Swarm Opimizaion 1. Inroducion The proporion of wind energy in he paern of world energy has been increasing since he beginning of he weny-firs cenury. Since wind power plays a posiive role in energy saving and reducing emissions of polluans, power companies should ranspor and disribue wind power elecriciy as much as possible. However, when large-scale wind power accesses he power sysem, he generaion scheduling and reserve need o be re-arranged and adjused due o inermien and variable characerisic of wind power oupu. Currenly, researchers a home and abroad have done a lo of work. In he sudy of opimal scheduling model, in lieraure [1], a dynamic economic scheduling model is buil considering he random variaion of he wind speed; and in dynamic opimizaion model, he uni ramp rae mus be a consrain [2]. In he research of uni commimen for power sysems wih wind farms, he credible daa of wind speed and wind power oupu are needed, in [3], he wind speed is prediced by ime series mehod based on neural nework. The opimizaion of uni scheduling is a large-scale nonlinear mixed ineger model, and a variey of algorihms are used o solve he problem. Tradiional mehods like prioriy lis [4-5], LaGrange Relaxaion and dynamic programming have been applied o solve he * The aional High Technology Research and Developmen of China 863 Program (2012AA050201). model. Wih he developmen of arificial inelligence algorihms, a variey of inelligen algorihms, such as geneic algorihms [6], an colony algorihm [7], paricle swarm opimizaion [8-9] have also been used o deal wih opimizaion scheduling. In his paper, an opimal generaion scheduling model is esablished, aiming a he minimum cos of convenional fuel energy in a wind-hermal power sysem, and a dynamic soluion mehod combined wih paricle swarm opimizaion algorihm is proposed. In he soluion process, spinning reserve is firsly calculaed o ensure a uni commimen sae valid considering wind power inegraed. The load disribuion of hermal power unis is done using he Paricle Swarm Opimizaion (PSO) algorihm. Afer analyzing every uni commimen sae in each ime period, he ramp rae, operaion and ouage ime consrains are inspeced o make a refined arrangemen of generaion scheduling. Finally, a case in a es sysem is given wih an opimal scheduling plan o show he feasibiliy and effeciveness of his soluion mehod. 2. Objecive Funcion and Formulaion In a power sysem, he operaion saus and oupu power of he generaors should be regulaed as he sysem load changes. In he sudy of he power sysem operaion scheduling, a scheduling period is usually divided ino several ime inervals, and in each inerval, he load is consan. The opimizaion generaion scheduling prob- Copyrigh 2013 SciRes.

2 X. Y. LI, D. M. ZHAO 1017 lem is deermining a uni commimen and load dispaching plan o minimize he coss of power generaion and ensure operaion safey, power balance, reserve demand and oher consrains of generaors in a scheduling period. I can be formulaed as follows Objecive Funcion In he wind-hermal power sysem, wind urbines do no consume fossil fuels. The objecive of he opimal scheduling model is o minimize he sar consumpion and power generaion fuel coss of convenional hermal power unis in he sysem scheduling period. Thus he funcion is defined as min 1 T ui, f Pi, ui, ui, 1 S i, (1) 1 i1 where T is scheduling period, divided ino24 inervals, is number of hermal power unis, u i, is saus (on/off) of uni i in period, P i, is he acive oupu, S i is sarup cos of uni i. f (P i, ) is he cos of hermal power uni and can be approximaely described by quadraic funcion: 2 i, i i i, i i f P a bp c P, (2) where, a i, b i, c i are he coefficiens of consumpion characerisics. Sarup cos S i is a exponenial funcion of he uni ouage ime, he longer ouage ime, he greaer he sarup cos [10]. As he scheduling period is 24 hours, S i is regarded as a consan for each uni. And he objecive funcion is subjeced o following consrains Consrains 1) Sysem consrains a) Power balance Pi, PW PD 0 (3) i1 P W is he oupu of wind farm wihin he period ; P D is he load hermal power unis mus supply in he ime period. b) Spinning reserve requiremens Posiive spinning reserve capaciy: R min P P, U T1 ui, i,max i, Ri di, i, i,min RiT 1 ui, Rdi, wd% Pw,max Pw (7) (4) ui, Rui, RDwu% Pw (5) i1 egaive spinning reserve capaciy: R min P P, D (6) i1 where R D is load reserve, w u % and w d % are influence coefficiens caused by wind power predicion error; P w,max is he maximum oupu of he wind farm; T 1 represens one hour; D Ri and U Ri are respecively for he uni down ramp rae and upward ramp rae. 2) Thermal uni consrains a) Minimum operaion and ouage ime consrains on on Ti Ti ui ui off off Ti Ti ui ui (8), 1,min, 1, 0, 1,min,, 1 0 on off where T i, and T i, sands respecively for accumulaed coninuous operaion and ouage ime of uni i ill period. b) Ramp rae consrain D P P U (10) Ri i, i, 1 Ri (9) c) Maximum and minimum power limis P P P (11) i,min i, i,max 2.3. Wind Power Oupu Analysis The wind power oupu is random mainly caused by he random variaion of he primary energy wind iself. The wind urbines in he same wind farm have almos he same wind direcion and wind speed. Therefore, i is possible o simulae power oupu of a wind farm by an equivalen wind urbine [3]. A funcion of wind power oupu and wind speed can be described by an approximae piecewise funcion expression; and he equaion beween he cu-in speed and cu-ou wind fis a cubic funcion [3]. 0, v v or v v CI 3 3 v vci, w 3 3 R 3 3 R CI R v v v v R CI R CI P P P v v v P, v v v R R CO CO (12) where P R is he raed power of he wind urbine. The wind power oupu used in he opimal scheduling is deermined by he following mehod. Firs some sample values of wind speed are chosen from he hisorical saisics daa of wind speed randomly in ime order of a day. And hen, he wind speed values are prediced in he mehod based on ime series mehod and arificial neural nework [11]. The power oupu of a wind farm is he sum of he oupu of each urbine using Equaion (12) in every inerval. The oal power oupu wind farms generae can be approximaely aken as he sum of each wind farm oupu. 3. Mehod for Solving he Model 3.1. Creae he Se of Uni Commimen The mahemaical model in his paper is a cerain kind of Copyrigh 2013 SciRes.

3 1018 X. Y. LI, D. M. ZHAO dynamic programming problem, because in each period of he scheduling period, he load disribuion mus be deermined for he curren uni commimen saus and suiable resuls of uni commimen mus be recorded. In a pracical power sysem, he load curve wihin one day will increase o peak and hen decline in he rend, so in some differen periods of one day, he load command and he sae of uni commimen can be fully consisen wih ha of oher period; and he oupu of generaing unis could be differen due o he Increase and decrease of he load. Therefore, in he process of solving he generaing model, a se of saes of uni commimen can be se up and updaed from he firs inerval. In fac, he esablishmen of he se of saes of each uni is simple and feasible. The hermal uni can be sored in ascending order by comparing heir average fuel cos per hour. A sae of uni commimen is hen generaed o ensure ha all he insalled capaciy is larger han he sum of load and reserve for he sysem operaion. The elemen in he se can be described using a vecor. The vecors of all he inervals reflec a cerain uni commimen plan and i shows as follows T T T uu 1 2 u, uu 1 2 u,, u1u2 u WT1 WT 2 P min, W P P (14) W P w, j j1 (13) u i is eiher 0 or 1, and 0 or 1 indicaes ha a uni is OFF or O Deermine he Maximum Wind Power and Reserve The accuracy of wind power forecas is no exac and precise, so in he generaion scheduling he maximum of wind power sysems can accep should be deermined in order o adjus spinning reserve. In an inerval, when he curren saus of uni commimen does no mee he reserve demand, a new uni may sar up or an old one shus down o saisfy he consrains (3), (5) and (7). In [12], considering ha he oal ramp capaciy of convenional hermal unis is near he expeced wind power flucuaions, he larges wind power peneraion level can be expressed as. P WT1 (15) WT 2 P PD uipi,min /1 r% i1 (16) where W is he number of wind farms, r% is coefficien of addiional reserve proporion, and P w,j is described in secion Applicaion of Paricle Swarm Opimizaion The basic PSO algorihm is used here o complee he load dispaching for every uni commimen sae in each inerval. Define he uni oupu value a ime period as he posiion of he paricle, hen he paricle m a ime period can be expressed, X m PP 1 2 P (17) The algorihm begins where he uni oupu is near he raed capaciy or acive power a he minimum raio of consumpion, and in he researching he speed does no exceed 50 MW and he finess funcion is he operaion coss in an inerval, referring equaion (1). Paricle swarm opimizaion speed and posiion updae formula shows below: V V cr p X k1, k, k, m m 11 m m 2 2 m cr g X k, m k1, k, k1, m m m (18) X X V (19) where V k, m is he speed in period of he m-h paricle, X k, m sands for he posiion of he paricle, p m for he opimal posiion afer k ieraions, g m for he opimal posiion among all paricles afer k ieraions Overall Soluion Process Sep 1: Read he sysem daa and se values of algorihm parameers. Sep 2: The ime inerval = 1, creae he iniial se of saes of uni commimen; >1, begin nex-sage search. Sep 3: Deermine he maximum wind power and reserve of curren sae, and inspec wheher i is necessary o open a new uni or shu down one for meeing reserve consrains, minimum operaion and ouage ime consrains. If necessary, updae he sae and he se. Sep 4: Complee he load disribuion of his sae in he inerval using PSO. Sep 5: Inspec he boundary consrains (10) and (11). If neiher is me, give up he sae and delee i from he se. If only one is obeyed, adjus he power oupu o he boundary value. Sep 6: Sill anoher sae o be calculaed? Yes, urn back o sep 3; oherwise, go nex. Sep 7: Record all he saes ill curren inerval and sum up cumulaive objecive funcion values. Sep 8: Is his las inerval of he period? If no, se =+1, go back o sep 2. If rue, compare he objecive value of each scheduling plan consising of all sae from firs inerval o las. Oupu he bes one whose cos is lower han any oher. Copyrigh 2013 SciRes.

4 X. Y. LI, D. M. ZHAO 1019 Sep 9: Afer oupu generaion scheduling plan, he process is erminaed. 4. Simulaion Resuls In his paper, he es sysem conains en hermal unis and wo wind farms and his sysem is generalized from a cerain region power sysem in Souh China. The scheduling period is one day divided ino 24 inervals. The operaing parameers of hermal unis are lised in Table 1, and he load and he wind power oupu prediced are shown in Table 2. In PSO algorihm, consan ω = 1.2, learning facor C 1 = C 2 = 1.8. And he programming work is done on he program Visual Sudio When he whole procedure is compleed, here are wo resuls in soluion space of he uni commimen se. The resuls indicae differen scheduling plan. They are respecively shown in Table 3 and Table 4. These wo resuls boh mee he spinning reserve demand when he wind power accesses o power sysem and he consrains of sysem operaion. The operaing coss are $ 74,063.9, and lower han ha of plan2 whose coss are $ 75, I can be seen ha plan 1 is indeed slighly beer han plan 2. Therefore generaion scheduling plan 1 is he final resul his mehod proposes and he hisogram of uni power oupu is shown in Figure 1. In he resul, some power generaion unis, which show beer power economy and lower fuel consumpion, are operaing all he ime in he period. During he load peak period, some small and medium-sized hermal unis, which have beer performance in peaking regulaion, help rack he load change, while large unis keep seady oupus. So in his generaion scheduling, he regulaion abiliy of all he hermal generaors is sronger and can deal wih he possible flucuaion of wind power. Wih he opimized process running sep by sep, consrains are coninuously inspeced and power oupu of each uni keeps correced. In he soluion space, he number of he enire uni sae is conrolled wihin a reasonable range o ensure ha he algorihm coninues. The resuls mee he sysem power balance requiremens, and he coss of hermal power unis in each period can be conrolled by paricle swarm opimizaion and meanwhile he hermal power unis have sufficien spinning reserve capaciy. So he resuls of his case can verify he feasibiliy and raionaliy of he solving process proposed. Table 1. P parameers of he hermal unis. Uni1 Uni2 Uni3 Uni4 Uni5 P max (MW) P min (MW) a($/h) b($/mwh) c($/mw 2 h) Uni6 Uni7 Uni8 Uni9 Uni10 P max (MW) P min (MW) a($/h) b($/mwh) c($/mw 2 h) Table 2. Load and wind power. T Load (MW) Wind Power(MW) T Load (MW) Wind Power(MW) T Load (MW) Wind Power(MW) Copyrigh 2013 SciRes.

5 1020 X. Y. LI, D. M. ZHAO Uni Table 3. Scheduling Plan 1. Hours(1-24) Uni Table 4. Scheduling plan 2. Hours(1-24) Figure 1. Resul for load disribuion of hermal unis. 5. Conclusions This paper focuses on reducing he operaion coss in he wind-hermal sysem while he sysem spinning reserve consrains are me a various periods, in which wind power oupu keeps slighly changing. An opimizaion generaion scheduling model is buil considering power balance, reserve margin, and operaing limis of hermal unis. The model is cerainly a dynamic model mixed wih ineger variables, so a dynamic opimizaion mehod dealing wih changes of uni commimen saes is presened. In he searching process, he sae of uni commimen can be updaed for meeing he operaion balance and reserve. The PSO algorihm is used in load disribuion of each saus. The resuls in a es sysem obained by his mehod shows ha he generaion scheduling is reasonable. The uni commimen and load dispach can mee he power sysem demand and he dynamic opimizaion procedure works well. 6. Acknowledgemens The auhors would like o graefully acknowledge he conribuions of he co-workers o he programming work. REFERECES [1] H. Y. Chen, J. F. Chen and X. Z. Duan, Fuzzy Modeling and Opimizaion Algorihm on Dynamic Economic Dispach in Wind Power Inegraed Sysem, Auomaion of Elecric Power Sysems, Vol. 30, o. 2, 2010, pp [2] M. L. Wang, B. M. Zhang and Q. Xia, A ovel Economic Dispaching Algorihm wih Uni Ramp Rae and ework Securiy Consrains, Auomaion of Elecric Power Sysems, Vol. 24, o.10, 2000, pp [3] Y. Z. Sun, J. Wu, G. J. Li and J. He, Dynamic Economic Dispach Considering Wind Power Peneraion Based on Wind Speed Forecasing and Sochasic Programming, Proceedings of he CSEE, Vol. 29, o. 4, 2009, pp [4] T. Senjyu, A Fas Technique for Uni Commimen Problem by Exended Prioriy Lis, IEEE Transacions on Power Sysems, Vol. 18, o. 2, 2003, pp doi: /tpwrs [5] F.. Lee, The Applicaion of Commimen Uilizaion Facor (UFC) o he Thermal Uni Commimen, IEEE Transacions on Power Sysems, Vol. 6, 1991, pp doi: / [6] L. Y. Sun, Y. Zhang and C. W. Jiang, A Soluion o he Uni Commimen Problem Based on Marix Real-coded Geneic Algorihm, Proceedings of he CSEE, Vol. 26, o. 2, pp , Feb [7] S. Chusanapipu, D. ualhong and S. Janarang, Uni Commimen by Selecive Self-adapive ACO wih Relaiviy Pheromone Updaing Approach, Power Energy Conference, Vol. 13, o. 24, 2007, pp [8] K. Han, J. Zhao and J. X. Qian, A Closed-loop Paricle Swarm Opimizaion Algorihm for Power Sysem Uni Commimen, Auomaion of Elecric Power Sysems, Vol. 33, o. 1, 2009, pp [9] Y. W. Jiang, C. Chen and B. Y. Wen, Paricle Swarm Research of Sochasic Simulaion for Uni Commimen in Wind Farms Inegraed Power Sysem, Transacions Of China Elecro Technical Sociey, Vol. 24, o. 6, 2009, pp [10] R. Q. Li and Z. Qin, The Opimizaion Operaion of Uni Commimen by Considering Sysem Reliabiliy, Modern Elecric Power, Vol. 29, o. 2, 2012, pp Copyrigh 2013 SciRes.

6 X. Y. LI, D. M. ZHAO 1021 [11] Yang Xiuyuan, Xiao Yang and Chen Shuyong, Wind Speed and Generaed Power Forecasing in wind Farm, Proceedings of he CSEE, vol. 25, o.11, pp. 1-5, June [12] Chun-Lung Chen, Opimal Wind-Thermal Generaing Uni Commimen, IEEE Transacions on energy Conversion, vol. 23, o. 1, Mar doi: /TEC Copyrigh 2013 SciRes.