Optimal Energy Management Using Sequential Quadratic Programming Algorithm for Stand Alone PV System

Transcription

1 Optmal Energy Management Usng Sequental Quadratc Programmng Algorthm for Stand Alone PV System S. Angalaeswar 1 and 2 Dr. K. Jamuna 1,2 School of Electrcal Engneerng, Vellore nsttute of echnology, Chenna, amlnadu, nda. 1,2 Orcd: , Abstract he operaton of the standalone photovoltac (SAPV) system predomnantly depends on solar generatng unts and battery storage systems (BSS). hs paper proposes the utlzaton of Sequental Quadratc Programmng (SQP) algorthm for achevng optmal energy management and also for supplyng energy contnuously to crtcal loads. he stand-alone PV system s modeled and the SQP algorthm s mplemented on the same. Dfferent test cases are evaluated and valdated. Keywords SQP Algorthm; Stand-Alone PV; Energy Management Nomenclature: L photo generated current 0 R s R p V mpp V ocg K 1 Q tme C 10 B dark current seres resstance shunt resstance maxmum power pont voltage open crcut voltage of PV generator model constant based on materal amount of current stored by the battery at a gven battery capacty requred current for dschargng battery bank n 10h battery current Δ temperature dfference between battery temperature and 25C η B DC AC V DC V AC η nv a 1 a 2 Battery Faraday Effcency Drect current Alternatng current Drect voltage Alternatng voltage nverter Effcency logc sgnal from prorty control algorthm logc sgnal from load schedule NRODUCON Mcro grds operate n two modes: Grd connected and slanded mode[1]. n slanded mode, alternatve energy sources are employed to meet the load demands n the network. Photovoltac (PV) Solar energy s the most commonly used energy source n the mcrogrd [2-5]. he SAPV acts only n slanded mode and demands an energy storage devce whch nvolves sgnfcant cost. he szng of solar generatng unt and BSS are crtcal for any SAPV system [6-8]. A better energy management along wth the effcency may be acheved by optmal control of BSS and the loads n the network. he loads are classfed based on prorty as: emergency, crtcal, essental and convenent loads [9-11]. he BSS may be allotted a varable prorty based on state of charge (SOC) of the battery. hs problem s formulated mathematcally by consderng the specfed prortes of the loads. Dynamc programmng s utlzed to dentfy the optmal soluton for the same. n ths paper, Secton provdes detals of SAPV specfcaton and modelng. Secton elaborates the SQP Algorthm. Secton V consders sutable test cases that valdate the operaton of SQP Algorthm on the SAPV system. Secton V presents the concluson of the paper. SAPV Specfcaton And Modellng he SAPV system s modeled n Matlab/Smulnk software. hs stand-alone PV system s havng PV panel, Battery, regulator, nverter and the load. he modelng of all the components s explaned. he dfferent models nclude: ) PV Generator Model he PV generator model s based on the equvalent crcut of a solar cell and s gven as (1). he smulaton consders solar radaton and temperature data. e( V R s exp( 1) L o mk ) V R Rp s (1) 12250

2 Maxmum Power Pont rackng (MPP) Model f MPP s not avalable n SPVA system, then usually the system behavor s nfluenced by the battery behavor. n ths paper a MPP model s consdered so as to decouple the PV generator and the battery bank, thereby provdng MPP voltage to the PV generator. An Open Crcut Voltage PV generator model s consdered for analyss as ndcated n (2). Vmpp K1V OCG (2) ) Battery Storage Model Prmary equatons are ntally defned for dscharge, charge and overcharge condtons of batteres. he state of charge, amount of currents stored by the battery, battery capacty and faraday effcency are gven by (3), (4) and (5) respectvely. Q SOC (3) C Q BBt (4) 1.67C C 10 ( ) (5) ( B ) 10 hs model ads n protectng the batteres from over dscharge and also enables n reconnectng the recovered batteres nto the network. And also the regulator s used to protect the battery from beng over charged when t s connected to the solar panel. Based on the State of Charge (SOC) of the battery level, the dsconnecton from the solar and reconnecton occurs. v) nverter Model he output of ths model s a constant rms voltage sgnal. he AC load extracts DC current ndcated as (6). V AC AC DC (7) nvv DC v) Load Model n ths work, a smple resstor s consdered as load.he equaton (8) whch governs ohm s law explans the current taken from load: [11] VAC AC ( a1* a2) (8) RL Where a1 and a2 are known as the sgnals from the algorthm and the load schedule. he loads are classfed based on ts prorty requrement as follows: battery based on ts SOC, emergency loads, crtcal loads, essental loads and the convenent or sophstcated loads ( SOC 1) b 1 exp[ ] (6) B ) Regulator Model Fgure 1: Smulnk model of Solar panel 12251

3 he optmzaton functon can be expressed as:[12] Maxmze n m R X j 1 1 R B X B (9) Subject to the nequalty constrant n m P X 1 j 1 t P X t B B E UCL E PV E ( SOC B B SOCmn ) (10) Fgure 2: Smulnk model of battery For all,j 0 X 1, 0 X B 1 (11) where R =r P t & R B=r BE B(1-SOC), r B=5(1-SOC) SQP Algorthm he Sequental Quadratc Programmng s wdely used to solve any nonlnear problem of optmzaton. hs algorthm manly depends on a fundamental theoretcal bass and gves potental algorthmc rules to preval optmal soluton for large scale engneerng problems. Fgure 3: Smulnk model of regulator Load control technque Due to the ntermttent nature of the renewable energy sources, the use of energy storage devces such as battery s mostly needed to store the excess energy. But stll the batteres may get over charged or over dscharged when t s connected wth the sources and loads. Many researches are gong n the controller development that can do the proper energy management, load sheddng etc. he load management also called as the Demand Sde Management (DSM) s also the effcent way of controllng the power from the sources. he loads can be prortzed based on the mportance of the loads on ts applcaton. hs categorzaton s manly done to protect the battery beng over charged or over dscharged. he algorthm followed n ths paper s based on the work from Groumpous and Khouzam [13, 14]. he loads are classfed as convenent, essental, crtcal and emergency loads [12]. he soluton s gven as the maxmzaton of the objectve functon that depends on the prorty of the load and the avalablty of energy supply. he basc dea of sequental quadratc programmng s to model the nonlnear programmng problem at a gven approxmate soluton, say x (k), by a quadratc programmng sub problem, and then to use the soluton to ths sub problem to construct a better approxmaton x (k+1). hs process s terated to create a sequence of approxmatons that wll converge to the optmal soluton x *. he prncpal dea of sequental quadratc programmng s the formulaton of a quadratc programmng sub problem based on a quadratc approxmaton of the Lagrangan functon of ( x, ) and by lnearzng the nonlnear constrants of the proposed system. he optmzaton problem can be expressed as Mnmzef (x) Subject to h ( x) 0, 1,..., me, h ( x) 0, me 1,..., m, (12) Where x can be defned as the vector of n desgn parameters, f(x) s the objectve functon to be optmzed, me s the total number of equalty constrants, m-me s the number of nequalty constrants

4 1 Mnmze f (s) 2 Subjected to g ( x s ). s g ( x. H.. s f ( x ) 0, ). s 1,..., m (13) e, (14) programmng sub problems of (13) to (15) s then used to form a new approxmaton as follows: x ( k1) x. s (16) g ( x ). s g ( x ) 0, m 1,..., m, e (15) (k) where s the step length parameter, whch s determned by the lne search procedure. n ths work, the x s taken wth the parameters of the current from the PV module, Voltage from the battery, state of charge of battery and the battery capacty. he optmum values of all the above parameters are determned from ths SQP algorthm and based on the load prorty and the SOC of the battery. Fgure 4: Smulnk model of nverter and the load he quadratc programmng sub problem (16) to (18) s solved usng the actve set method. he soluton of the quadratc Fgure 5: Smulnk dagram for the stand alone PV system n order to valdate the SQP algorthm n the system, two scenaros were consdered. n both scenaros, the ratngs of the solar panel, the capacty of the battery are taken dfferent. Only the ntal SoC of the battery s assumed to be same n both cases. For a 24 hour load profle wth constant and varable loads, the smulaton s carred out usng SQP and the prorty load control algorthm. he results were dscussed n the next chapter. RESULS AND DSCUSSON he smulaton has been done for 24 hours tme perod. he base load s taken as 150W n the system. he constant load value s taken as 545W. he varable load pattern for 24 hours s shown n the fgure

5 Power (W) Load profle Constant load profle Varable load profle CONCLUSON he stand-alone PV system s consdered as the test system. he prortzaton of the load s done based on the mportance of the load n the applcaton. he constant load and varable load s consdered for the valdty of the algorthm n the test system. wo scenaros are consdered and the prorty control algorthm and SQP algorthm have been mplemented n the system. From the results, t s understood that the gven Sequental Quadratc Programmng algorthm s gvng the optmum soluton for the objectve functon. State of charge (SOC) me (hour) Fgure 6: Load profle of the system SOC evoluton n Scenaro A SQP based control Prorty Load Control Algorthm me (hour) Fgure 7: Evaluaton of battery SoC for constant load profle he evaluaton of the objectve functon mentoned has been done for both the scenaros usng prorty control algorthm and SQP algorthm. he fgure 7 and 8 are showng the results for the cases consdered. t s observed that the proposed SQP algorthm n ths system s gvng better results for the objectve functon consdered. State of charge (SOC) SOC evoluton n Scenaro B SQP based control Prorty Load Control Algorthm me (hour) Fgure 8: Evaluaton of battery SoC for varable load profle REFERENCES [1] S.Angalaeswar, K.Jamuna. Constraned Power Loss Mnmzaton of DC Mcro grd Usng Partcle Swarm Optmzaton: nternatonal Conference on Data Engneerng and Communcaton echnology, Advances n ntellgent Systems and Computng 468, Sprnger (2015) pp.no [2] M. Marzband, A. Sumper, A. Ruz-Álvarez, J.L. Domínguez-García, and B. omoaga Expermental evaluaton of a real tme energy management system for standalone mcrogrds n day-ahead markets, Appl Energy, vol.106, no.0, pp , [3] X. Wang, A. Palazoglu, and N.H. El-Farra. Operatonal optmzaton and demand response of hybrd renewable energy systems, Appl Energy, vol.143, no.1, pp , [4] X. Ma, Y. Wang, and J. Qn. Generc model of a communty-based mcrogrd ntegratng wnd turbnes, photovoltacs and CHP generatons, Appl Energy, vol. 112, pp , [5] X. Xu, H. Ja, D.Wang, D.C. Yu, and H. Chang. Herarchcal energy management system for multsource mult-product mcrogrds, Renew Energy, vol.78, pp , [6] H. Xn, Y. Lu, Z. Wang, D. Gan and. Yang. A new frequency regulaton strategy for photovoltac systems wthout energy storage, EEE rans Sustan Energy, vol. 4, no.4, pp , [7] K. Bandara,. Sweet, J. Ekanayake. Photovoltac applcatons for off-grd electrfcaton usng novel mult-level technology wth energy storage, Renew Energy, vol. 37, pp.82-88, [8] F. Kenzle, P. Ahcn and G. Andersson, Valung nvestments n mult-energy converson, storage, and demand-sde management systems under uncertanty, Sustan Energy EEE rans, vol.2, no.2, pp , [9] A. Gupta, R. San, and M. Sharma. Modellng of 12254

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