DC Voltage Control and Power-Sharing of Multi-Terminal DC Grids Based on Optimal DC Power Flow and Voltage Droop Strategy

Transcription

1 oltage Control and Power-Sharng of Mult-Termnal Grds Based on Optmal Power Flow and oltage Droop Strategy F. Azma* and H. Rajab Mashhad* (C.A.) Abstract: Ths paper develops an effectve control framework for voltage control and power-sharng of Mult-Termnal (MT) grds based on an Optmal Power Flow (OPF) procedure and the voltage-droop control. In the proposed approach, an OPF algorthm s executed at the secondary level to fnd optmal reference of voltages and actve powers of all voltage-regulatng converters. Then, the voltage droop characterstcs of voltage-regulatng converters, at the prmary level, are tuned based on the OPF results such that the operatng pont of the MT grd les on the voltage droop characterstcs. Consequently, the optmally-tuned voltage droop controller leads to the optmal operaton of the MT grd. In case of varaton n load or generaton of the grd, a new stable operatng pont s acheved based on the voltage droop characterstcs. By executon of a new OPF, the voltage droop characterstcs are re-tuned for optmal operaton of the MT grd after the occurrence of the load or generaton varatons. The results of smulaton on a grd nspred by CIGRE B4 grd test system demonstrate effcent grd performance under the proposed control strategy. Keywords: CIGRE B4 Grd Test System, Herarchcal Control, Mult-Termnal Grds, Optmal Power Flow, oltage Droop Control. 1 Introducton1 Recently, a lot of attentons have been focused, both from the ndustry poneers and academa, towards the concept of grds. From 1951 tll now, more than 180 manly two-termnal H projects have been put nto operaton around the world. Over the past 0 years some H applcatons have been expanded wth two or three termnals n order to obtan the frst functonal Mult-Termnal (MT) grds [1]. Wth the development and ncreasng avalablty from multple vendors of hgh power voltage source converters (SC), the prospect of a MT grd, composed of multple converters has become a realstc possblty []. umerous advantages and applcaton deas have been dentfed and proposed n the lterature wth regards to the MT concept. Accordng to [3], MT grds could be one of the most sutable solutons for ntegraton of wnd farm energy nto the manland AC grds. Furthermore, MT grds could facltate the development of the so-called European super grd [4], Iranan Journal of Electrcal & Electronc Engneerng, 015. Paper frst receved 16 Apr. 014 and n revsed form 0 Oct * The Authors are wth the Department of Electrcal Engneerng, Ferdows Unversty of Mashhad Mashhad, Iran. E-mals: F.Azma@eee.org and h_mashhad@um.ac.r. [5]. Ultmately ths large MT would nterconnect the orth Sea wnd farms wth Medterranean solar plants and Scandnavan hydropower. Besdes, MT applcatons can be found for nterconnectng multple non-synchronous AC areas [6]. The need for MT networks and the advantages they could brng for the modern grds are already wellestablshed. However, at the moment the knowledge on the subject s scarce. Several proposals for prmary control of voltage can be found n the lterature, as the ones n [1, 7, 8] and [9], all of them presentng varous advantages and dsadvantages. At the present moment, the concept of MT stll requres a lot of researches on the topcs related to herarchcal control, protecton, as well as markets and nteractng wth exstng AC networks. Ths paper provdes a control framework based on an optmal power flow algorthm and the voltage droop strategy for effcent control and power-sharng n MT grds. In the proposed control framework, the voltage droop characterstcs are tuned based on the optmal power flow results. Hence, the grd s effcently controlled under voltage-droop scheme n case of varatons n demand and generaton. Iranan Journal of Electrcal & Electronc Engneerng, ol. 11, o., June

2 The rest of ths paper s organzed as follows. Secton presents the optmal power flow algorthm. The proposed control framework, composed of optmal power flow and voltage droop control, s presented n Secton 3. The smulaton results on CIGRE B4 grd test system are reported n Secton 4. The paper conclusons are presented n Secton 5. Optmal Power Flow Algorthm.1 Optmal Power Flow: Problem Statement Consderng an MT grd wth termnals (or buses), the problem of optmal power flow (OPF) for a grd s formulated by Eqs. (1)-(5), stated below, mn f ( ) (1) subject to the followng constrants, ( ) g, P = 0 () <, <, = 1,, (3) mn P < P, = 1,, (4) I < I k = L (5), k, k, 1,, The objectve functon and constrants of the optmal power flow problem, outlned by Eqs. (1)-(5), are explaned below. In Eq. (1), f ndcates the grd losses, whch have to be mnmzed. Moreover, s the vector of grd s voltages, as stated below, T =,1,, (6) The mnmzaton functon f can be computed as, j j = 1 j = ( + 1) = 1 ( ) ( ) f = G + G (7) where, termnals and j whle G j ndcates the total conductance between G represents the sum of all conductances connected between the termnal and the ground. Constrant () ncludes msmatch between generaton and demand and mposes load flow equatons, as follows, (, ) = [ ] T g P g1 g g (8) where, T P = [ PP 1 P ] (9) s the vector of grd s powers, G L j j j = 1 g = P P + G (10) and, P G and P L represent the generaton and load at termnal. Constrants (3)-(5) ndcate the lmts on termnals voltages, the power flowng through converters and current through the transmsson lnes. In constrant (3), and mn ndcate the upper and lower lmts on voltages at grd s termnals, respectvely. In Eq. (4), P ndcates the mum permssble power of the converter staton. Fnally, I, k n Eq. (5) sets the upper lmt on the permssble current transmtted by lnk k. It s worth notng that two types of buses can be dentfed n a grd system, as expressed below, Load (generaton) or P-bus, whose net njected power s pre-determned. oltage or slack bus whose voltage s prespecfed.. Optmal Power Flow: Soluton Method The optmal power flow problem, stated by Eqs. (1)-(5), represents a nonlnear-constraned optmzaton problem whch wll be solved usng a gradent-based optmzaton technque. Ths s done by constructng the Lagrangan for the optmzaton problem, as stated below, T L ( P, ) = f ( ) + λ g(, P) + q(, P, I ) (11) where, λ s a vector contanng Lagrange multplers for the equalty constrant (), I s the vector of currents through grd lnks, q s the penalty functon for the nequalty constrants of (3)-(5), stated below, (,, ) = pf v, ( ) q P I = 1 = 1 = 1 L k = 1 mn, mn ( ) + pf mn ( ) + pf P P P, ( ) + pf I I I, k, k, (1) n whch pf, pf, pf v, v mn, P,, and pf I, denote the penalty factors for mum voltage lmts, mnmum voltage lmts, converters power lmts and lnks current lmts, respectvely. The soluton of the optmal power flow can be obtaned by settng the Lagrangan dervatve wth respect to the unknown varables to zero and then solvng the problem teratvely. 3 Proposed Control Framework The proposed control framework s based on the optmal power flow and the voltage droop strategy. To be more specfc, the voltage droop characterstcs of the voltage regulatng statons are tuned based on the optmal power flow results. Fg. 1 depcts the structure of the proposed control framework. The 138 Iranan Journal of Electrcal & Electronc Engneerng, ol. 11, o., June 015

3 llustrated structure ncludes a hgh-level sends approprate control sgnals (.e. α, β and γ ) to the control system of the secondary control center (SCC) whch converter statons at the prmary level. In fact, the optmal power flow s carred out n the secondary control level whle voltage-droop control for each converter staton s performed locally and at the prmary level. It s worth notng that the decoupled current control (or d-q control) strategy [10] s mplemented at the prmary level. 3.1 Optmal Power Flow-Based oltage Control and Power-Sharng The general structure of the proposed control framework, ncludng prmary and secondary levels, for the MT grds was presented and dscussed n Secton II. In the proposed herarchcal structure, the secondary level sets the reference power n the voltage-droop characterstcc and hence guarantees the desrable power exchange. At the prmary control level, however, voltage droop control strategy s employed. In ths strategy, the voltage-regulatng converters contrbute to the voltage control and power sharng n the grd based on ther voltage droop characterstcs. Fg. llustrates the general form of a voltage droop characterstc. Ths characterstcc can be expressed mathematcally by, α + β P + γ = 0 where, and P are voltage and power at the α, sde of the converter and the PCC, respectvely and β and γ are the coeffcents of the voltage droop characterstcs, determned by the secondary control level, as shown n Fg. 3.,1,, P P P1 oltage droop Controller 1 oltage droop Controller oltage droop Controller [α β γ] [α β γ] [α1 β1 γ1] ICC1 ICC ICC P 1 P P PWM PWM... PWM 1 (SCC) Secondary Control Center Grd data MT Grd generaton & demand (13) Fg. 1 The overall control structure for an MT grd wth prmary and secondary control levels wth voltage droop characterstcs P1 P... P Fg. The generalzed voltage droop characterstcs. Fg. 3 Adjustment of voltage droop characterstc coeffcents based on the optmal power flow soluton. The secondary control level adjusts thesee coeffcents for the voltage-regulatng converters based on the power exchange requrements and optmal power flow outputs. To be more specfc, the coeffcents of the voltage characterstcs are set usng optmal power flow outputs (, ref and P ref ). In other word, α, β and γ must be selected such that the and, ref P ref le on the voltage droop characterstcs of the voltage regulatng converters. Hence, for k voltage-regulatng converters, the and, ref P re ef soluton must obtaned from optmal power flow le on the correspondng voltage characterstcs, + β P + γ =, = 1,, k (14) α P, ref, where,, ref, and P ref, ndcate the reference voltage and power of the voltage-regulatng staton (derved from optmal power flow), respectvely, and α, β and γ are the voltage droop coeffcents of ref, 0 the voltage-regulatng staton.,0 P,,mn P Azma & Rajab Mashhad: oltage Control and Power-Sharng of Mult-Termnal Grds 139

4 There are three unknown parameters n Eq. (14) ( α, β and γ ). Hence, two more equatons must be added to solve for α, β and γ. In ths paper, the slope of voltage droop characterstcs, m, are assumed constant and pre-defned. Accordngly, β m =, = 1,, k (15) α Assumng α = 1, one can compute, β =, = 1,, k (16) m Based on Eqs. (15) and (17), the γ can be determned as, γ =, ref, mpref,, 1,, = k (17) By tunng the voltage droop coeffcents usng Eqs. (15)-(17), t s guaranteed that the grd wth voltagedroop control wll operate on the effcent operatngpont obtaned by the optmal power flow. The procedure of tunng the voltage droop characterstcs based on optmal power flow soluton s llustrated n Fg. 3. It must be noted that n the proposed approach, t s not necessary to nclude voltage-droop characterstcs drectly nto optmal power flow algorthm. The voltage droop coeffcents are tuned based on power flow results. 3. Frequency Support to the AC Grds In case of weak AC systems, the MT grd can be helpful to support the frequency of such a grd. Ths can be accomplshed by ncludng a frequency-regulatng block n the outer control loop of the d-q control strategy. Ths s depcted n Fg. 4. In fact, the reference power for the outer actve power controller s determned based on the voltage droop characterstc as well as the frequency controller acton. By applyng the frequency support acton, the MT grd would ad the weak AC system n balancng the generaton and consumpton through the tme. Based on Fg. 4, the change n reference power of frequency controllng SC, n Laplace doman, s governed by, Grd frequency devaton PI controller Reference power + Reference power correcton Fg. 4 Implementaton of frequency controller n the outer loop of d-q control strategy. + P ref B0 A0 Ba A0 Ba B0 Ba B Bb B4 Cb B Bb B Ba A1 Ba B1 Cb A1 Cb B1 Bb A1 Bb B1 Fg. 5 Schematc dagram of S3. Bb D1 Bb B1s Bb C Cb C Bo C Cb D1 Bo D1 Bb E1 C D1 bpole (± 400 k) AC onshore (380 k) AC offshore (145 k) Cable Overhead lne k f, I Δ Pref ( s) = m ( s) +Δ f ( s) k f, P + s (18) where, m s droop slope, Δ f represents frequency devaton of the AC system, and k f, P and k f, I ndcate proportonal and ntegral gan of the frequency support controller, respectvely, shown n Fg Smulaton Results The proposed control framework s evaluated by the recently released CIGRE B4 grd test system. The CIGRE test system has been developed by CIGRE s B4 workng group as a benchmark for conductng grds studes and analyss. The CIGRE B4 grd test system ncludes two onshore AC systems, four offshore AC systems, two nodes, wth no connecton to any AC system and three systems, namely S1, S, and S3. The overall system s comprsed of 11 SC statons. In ths paper the S3, a fve-termnal bpolar H meshed grd wth lnk voltage of ±400k, s employed for evaluatng the proposed control strategy. In ths test grd, shown n Fg. 5, two SCs are connected to offshore AC buses Bo-C and B0-D1, whle other three SCs serve as nterfaces between the grd and onshore AC buses,, and Ba- B (.e. are operated as grd connected SCs). In S3, the offshore systems are modeled as constant power sources and onshore systems are stff grds represented by deal voltage sources behnd the mpedance. It must be noted that two of the AC buses ( and Ba-B) are stff grds whle the thrd one () s consdered a weak AC system. lne and converter statons data are presented n Tables 1 and, respectvely. Table 1 overhead lne and cable data. Lne Data R [Ω/km] L [mh/km] C [µf/km] G [µs/km] OHL±400 k Cable±400 k AC OHL 380 k Iranan Journal of Electrcal & Electronc Engneerng, ol. 11, o., June 015

5 Table converter staton parameters. SC Staton R T (Ω) L T (mh) C (μf) Cb-A Cb-B Cb-B Cb-C Cb-D The control mode of SCs depends on whether they are connected to an offshore or an onshore AC grd. The grd-sde converters, Cb-B1 and Cb-B, control the voltage of the MT grd (or the actve power at the PCC) and reactve power at the PCC, as they are connected to stff grds. On the other hand, the SC Cb- A1, connected to the weak AC grd, supports the frequency of the AC grd and controls ampltude of the AC voltage at the PCC. Durng the smulatons, t s assumed that the onshore converter statons Cb-A1 and Cb-B demand fxed power whle Cb-B1 acts as the slack converter (.e. Bb-B1 s the slack bus). The voltage droop characterstcs of these three statons are adjusted by the optmal power flow such that the mentoned requrements (.e. fxed power demand by Cb-A1 and Cb-B) are met. More detaled data on the optmal power flow are presented n Table 3. ote that the base power s 500 MW and samplng tme for the SCC s assumed one second. Table 3 Base-Case power flow data. Bus Bus Type oltage et Injected Power Bb-A1 P Unknown -0.8 Bb-B1 Slack Unknown Unknown Bb-B1s ntermedate Unknown 0 Bb-B P Unknown -0.4 Bb-B4 ntermedate Unknown 0 Bb-C P Unknown 0.9 Bb-D1 P Unknown 1.9 Bb-E1 ntermedate Unknown 0 Table 4 Power Flow Results for the Base-Case. Bus Bus type oltage (pu) et Power (pu) Bb-A1 P Bb-B1 Slack Bb-B1s ntermedate Bb-B P Bb-B4 ntermedate Bb-C P Bb-D1 P Bb-E1 ntermedate Table 5 oltage Droop Parameters for the Base-Case. Converter Staton α β γ Bb-A Bb-B Bb-E Base-Case Smulaton The base-case smulaton s carred out based on the OPF data summarzed n Table 3. The smulaton starts by adjustng the voltage droop characterstcs of the grd-sde SCs based on the results of the optmal power flow, presented n Table 4. Moreover, the calculated droop coeffcents of the grd-sde SCs are also summarzed n Table 5. More detaled results of the OPF for the base case are shown n Fg. 6. ote that Cb-B1, as the slack converter, has lowest voltage droop slope and hence wll have the largest contrbuton to the power-sharng and voltage control of the grd. The voltage and actve power profles for all converter statons, obtaned by applyng OPF-tuned voltage droop characterstcs, are llustrated n Fgs. 7 and 8, respectvely. Moreover, to show the desrable effect of the proposed control technque on grd losses, a comparson between S3 s losses due to the OPF algorthm and a smple power flow (PF) algorthm s shown n Fg. 9. ote that n the PF algorthm, the voltage of the slack bus (.e. Bb-B1) s assumed 1 pu. B0 A0 Ba A0 Ba B0 Ba B Bb B4 Cb B Bb B Ba A1 Ba B1 Cb A1 Cb B Bb A Bb B1 Bb D1 1.4 Bb B1s 1.40 Bb C Cb C Bo C C Cb D1 Bo D1 1.9 Bb E1 D1 bpole (± 400 k) AC onshore (380 k) AC offshore (145 k) Cable Overhead lne Fg. 6 Detaled optmal power flow results for base case. voltage (pu) Ba-B Bo-C Tme (s) Fg. 7 voltages at converter statons for the base case. Azma & Rajab Mashhad: oltage Control and Power-Sharng of Mult-Termnal Grds 141

6 Actve power (pu) Ba-B Bo-C Besdes, as stated earler, the AC grd s assumed a weak grd equpped wth frequency support control. The frequency controller keeps the frequency of the at 50 Hz durng the varaton n the offshore generaton and as well as durng the modfcaton of the parameters of the voltage droop characterstcs by the SCC, as shown n Fg. 1. Moreover, transmsson losses durng ths smulaton are llustrated n Fg Tme (s) Fg. 8 Actve powers at converter statons for the base case. Transmsson losses (%) OPF PF Tme (s) Fg. 9 Transmsson losses n MT grd for the base-case. 4. aratons n Offshore Generaton The second smulaton case addresses varatons n offshore generatons. Ths smulaton s ntended to demonstrate how the proposed control approach deals wth varatons n offshore generaton and how new optmal operatng pont of the grd s acheved. In ths smulaton, generaton of offshore buses, Bb-C and Bb-D1 s accordng to Table 4, pror to t = 0.3 sec. However, at t = 0.3 sec. offshore generaton of Bb-D1 s reduced from 1.9 to 1.3 pu. Ths would results n an nstantaneous power mbalance wthn the grd and the control system must respond to t properly. The voltage and actve power profles for ths case are depcted n Fgs. 10 and 11, respectvely. Suddenly after ths change n the offshore generaton, the voltage droop control of the grd-sde converters (.e. prmary control acton) start to restore the power balance n the grd. Ths can be observed n Fg. 11. However, due to such prmary control actons, the power flow wthn the grd devates from the pre-specfed settngs. For nstance, the power absorbed by Bb-B devates from to -0.. ext, the SCC sends new parameters of the voltage droop characterstcs of the grd-sde SCs after about one second, whch s ts samplng perod. Ths secondary control acton restores the pre-specfed power flow n the grd. voltage (pu) Tme (s) Fg. 10 voltages at converter statons for varaton n offshore generaton. Actve power (pu) Ba-B Bo-C - Tme (s) Fg. 11 Actve powers at converter statons for varaton n offshore generaton. Frequency (Hz) Ba-B Bo-C Tme (s) Fg. 1 Frequency at durng varaton n offshore generaton. 14 Iranan Journal of Electrcal & Electronc Engneerng, ol. 11, o., June 015

7 Transmsson losses (%) Tme (s) Fg. 13 Transmsson losses n MT grd durng varaton n offshore generaton. 4.3 Lack of Generaton n Weak AC Grd In the thrd smulaton case, response of the proposed control system to the lack of generaton n the weak AC grd,.e. s nvestgated. Durng ths smulaton, the demand of s ncreased at t = 6 sec, resultng n generaton lack of about 0.6 pu. The voltages and actve powers of the SC statons durng ths smulaton are shown n Fgs. 14 and 15, respectvely. Suddenly after ths ncdent, the net power mport by the correspondng SC,.e. Cb-A1 s ncreased due to ts frequency support acton as well as the voltage droop control of Cb-B1 and Cb-B. However, the power flow wthn the grd changes due to these actons. After one second, the SCC sends new parameters of the voltage droop characterstcs at t = 7 sec and restores the power flow to the pre-specfed values, as shown n Fg. 15. The frequency of the durng these evolutons s shown n Fg. 16. Clearly, the frequency support acton has successfully mantans weak AC grd frequency at the reference level. Fnally, transmsson losses n ths case s shown n Fg. 17 and compared to the losses due to mplementaton of power flow algorthm. voltage (pu) OPF PF Ba-B Bo-C Tme (s) Fg. 14 voltages at converter statons durng lack of generaton n. Actve power (pu) Tme (s) Fg. 15 Actve powers at converter statons durng lack of generaton n. Frequency (Hz) Ba-B Bo-C Tme (s) Fg. 16 Frequency at durng lack of generaton n Ba- A1. Transmsson losses (%) OPF PF Tme (s) Fg. 17 Transmsson losses n MT grd durng lack of generaton n. 5 Concluson Ths paper proposed an optmal power flow-based voltage droop control for effcent control and powersharng n mult-termnal (MT) grds based on optmal power flow (OPF) procedure and voltage droop control. In the proposed approach, an OPF algorthm s Azma & Rajab Mashhad: oltage Control and Power-Sharng of Mult-Termnal Grds 143

8 executed at the secondary level to fnd optmal reference voltages and actve powers of all voltage-regulatng converters. Then, the parameters of the voltage droop characterstcs of voltage-regulatng converters, at the prmary level, are tuned based on the OPF results such that the operatng pont of the MT grd les on the voltage droop characterstcs. Consequently, the generalzed voltage droop controller leads to the optmal operaton of the MT grd. In case of varaton n load or generatonn of the grd, a new stable operatng pont s acheved based on the voltage characterstcs. By executon of a new OPF, the voltage characterstcs are re-tuned for optmal operaton of the MT grd after the occurrence of the load or generatonn varatons. The smulaton results of CIGRE B4 grd test system ndcated effcent grd performance under the proposed control strategy. It s worth notng that a low-bandwdth communcaton channel s necessary between the control levels. However, f the communcaton between the prmary and secondary control center s lost, the grd wll reman stable based on the prevous droop settngs, achevng a non-optmal pont of operaton. References [1] K. Meah and A. H. M. S. Ula, A new smplfed adaptve control scheme for mult-termnal H transmsson systems,, Internatonal Journal of Electrcal Power & Energy Systems, ol. 3, o. 4, pp , May 010. [] C. D. Barker and R. Whtehouse, Autonomous converter control n a mult-termnal H system, 9th IET Internatonal Conference on AC and Power Transmsson, 010. AC, pp. 1 5, 010. [3] L. Xu, B. W. Wllams and L. Yao, Mult- large offshore wnd farms, IEEE Power and termnal transmsson systems for connectng Energy Socety General Meetng-Converson and Delvery of Electrcal Energy n the 1st Century, pp. 1-7, 008. [4] R. da Slva, R. Teodorescu and P. Rodrguez, Multlnk transmsson system for supergrd future concepts and wnd power ntegraton, IET Conference on Renewable Power Generaton (RPG 011), pp. 1-6, 011. [5] L. Wemers, A European Super Grd-A Technology Provders ew, Power Systems- Coordnated prmary frequency control among non-synchronous systems connected by a mult- termnal hgh-voltage drect current grd, IET H, 011. [6] J. Da, Y. Phulpn, A. Sarlettee and D. Ernst, Generaton, Transmsson & Dstrbuton, ol. 6, o.. pp , 01. [7] C. Derckxsens, K. Srvastava, M. Reza, S. Cole, J. Beerten and R. Belmans, A dstrbuted voltage control method for SC MT systems, Electrc Power Systems Research, ol. 8, o. 1, pp , Jan. 01. [8] S.-Y. Ruan, G.-J. L, X.-H. Jao, Y.-Z. Sun and T. T. Le, Adaptve control desgn for SC-HC systems based on backsteppng method, Electrcc Power Systems Research, ol. 77, o. 5-6, pp , 007. [9] B. K. Johnson, R. H. Lasseter, F. L. Alvarado and R. Adapa, Expandable multtermnal systems based on voltage droop, IEEEE Transactons on Power Delvery, ol. 8, o. 4. pp , [10] R. da Slva, R. Teodorescu and P. Rodrguez, Multlnk transmsson system for supergrd future concepts and wnd power ntegraton, IET Conference on Renewable Power Generatonn (RPG 011), pp. 1 6, 011. Farborz Azma was born n Tehran, Iran, n He receved the B.Sc.. degree n electroncs engneerng from Sharf Unversty of Technology, Tehran, Iran, n 1989; and attended the M.Sc. program n electrcal engneerngg at Ferdows Unversty of Mashhad n He s currently pursung research assstance at the department of Electrcal Engneerng, Ferdows Unversty of Mashhad, Mashhad, Iran. Habb RajabMashhad was born n Mashhad, Iran, n He receved the B.Sc. and M.Sc. degrees wth honor from the Ferdows Unversty of Mashhad, both n electrcal engneerng, and the Ph.D. degree from the Department of Electrcal and Computer Engneerng of Tehran Unversty, Tehran, Iran, under jont cooperaton of Aachen Unversty of Technology, Germany, n 00. He s as Professor of electrcal engneerngg at Ferdows Unversty of Mashhad. Hs research nterests are power system operaton and plannng, power system economcs, and bologcal computaton. 144 Iranan Journal of Electrcal & Electroncc Engneerng, ol. 11, o., June 015