Optimal Compensation of Harmonic Propagation in a Multi-Bus Microgrid

Transcription

1 Internatonal Conference on Renewable Energes and Power Qualty (ICREPQ 16) Madrd (Span), 4 th to 6 th May, 2016 Renewable Energy and Power Qualty Journal (RE&PQJ) ISSN X, No.14 May 2016 Optmal Compensaton of Harmonc Propagaton n a Mult-Bus Mcrogrd E. Skjong 1,3,4, J. A. Suul 2,5, M. Molnas 1 and T.A. Johansen 1,3 1 Department of Engneerng Cybernetcs 2 Department of Electrc Power Engneerng Norwegan Unversty of Scence and Technology O. S. Bragstads plass, 7034 Trondhem, Norway E-mal: espen.skjong@ulsten.com, jon.are.suul@ntnu.no, marta.molnas@ntnu.no, tor.arne.johansen@tk.ntnu.no 3 Centre for Autonomous Marne Operatons and Systems, 7491 Trondhem, Norway 4 Ulsten Power & Control AS, 6018 Ålesund, Norway 5 SINTEF Energy Research, 7465 Trondhem, Norway Abstract: Ths per dscusses how an Actve Power Flter (APF) can be utlzed for system-wde harmonc mtgaton n a mcrogrd wth multple sources of harmonc dstorton located at dfferent buses. A two-bus mcrogrd system wth ndependent nonlnear loads at both buses s frst nvestgated analytcally, and t s demonstrated that t s possble to derve a harmonc current njecton from the APF that wll mnmze the harmonc dstorton at both buses. However, analytcal optmzaton of the APF current wll be senstve to parameter varatons, wll deterorate when the APF reaches current saturaton and cannot be easly extended to larger systems wth many loads at dfferent buses. A more practcally plcable method for calculatng the APF current references, by usng the framework of Model Predctve Control (MPC) s nstead proposed for the nvestgated system. Under realstc operatng conons, ths proach can obtan further mprovement n the system-level harmonc mtgaton. The characterstcs and performances that are obtaned wth the analytcal soluton and the MPC-based control are assessed by tme doman smulatons n the Matlab/Smulnk envronment. The results clearly ndcate how an MPC-based system-orented compensaton can maxmze the utlzaton of a sngle APF n a mult-bus Mcrogrd. Keywords Actve Power Flter, Harmonc Mtgaton, Mcrogrd, Optmal Control, Power Qualty 1. Introducton Technques for analyzng and mtgatng harmonc dstortons of voltage and current waveforms have been nvestgated snce the early advents of electrc power systems [1]. Durng the last decades, the mpact of harmonc dstortons has become more crtcal n ndustral power systems due to the prolferaton of Varable Speed Drves (VSDs) wth dode- or thyrstor-based rectfers as grd nterfaces. The domnant harmoncs from varous rectfer loads can be compensated by varous passve flterng solutons, but such nstallatons have lmtatons wth respect to compensaton of harmoncs from dynamc loads and for operaton n systems wth tme-varyng resonance frequences due to changes n the system confguraton. However, the recent advances n swtchng converters have made Actve Power Flters (APFs) a vable soluton for real-tme harmonc compensaton under such conons. As a result of extensve research actvtes, the converter desgn and the local control strateges of APFs for selectve or broadband harmonc mtgaton are also well establshed n lterature [2], [3]. Today, APFs are commonly utlzed for compensatng the harmonc currents from a sngle load or for mtgatng voltage dstortons at a specfc pont n the power system. Thus, the real-tme control methods for APFs are usually desgned and developed on bass of only local consderatons and local measurements. However, n systems wth multple sources of harmonc dstortons, an APF has the potental to mprove the system-level harmonc mtgaton beyond what can be acheved based on only local consderatons. The potental for system-orented optmzaton of APF operaton was realzed n the early phase of research on power cononng devces as analyzed n [4], but ths aspect has not receved sgnfcant attenton n the development of APF control strateges. A frst proach for system-level harmonc mtgaton by usng Model Predctve Control (MPC) for on-lne optmzaton of the APF current references was recently proposed n [5]-[7]. Consderng the potental for system-wde harmonc mtgaton by a sngle APF, ths per analyzes a two-bus Mcrogrd system wth ndependent nonlnear loads at both buses. For ths system, t s shown that an explct soluton of the optmal APF compensaton current for each harmonc component can be found analytcally. The operaton of the MPC-based proach from [5]-[7] s then compared to the performance that can be obtaned wth the analytcal soluton by tme-doman smulatons. The presented results demonstrate how the MPC-based operaton acheves smlar or better results than the analytcal optmzaton, especally under the conons when the APF reaches current saturaton. The results are also benchmarked aganst traonal local control and the control method from [8]. The results demonstrate how the

2 Fg. 1. Smplfed shpboard power system (slanded mcrogrd) under nvestgaton: Two generators, two buses wth propulson loads (Varable Speed Drve (VSD) wth 12-pulse rectfers), an Actve Power Flter (APF) for harmonc mtgaton, an LCL flter to suppress swtchng nose from the APF and RC-shunts to model parastc shunt cactance of cables and bus-bars. system sgnfcantly benefts from control methods that are desgned for system-wde harmonc mtgaton. 2. Investgated Mcrogrd Confguraton The three-phase three-wre mcrogrd under nvestgaton n ths work s shown n Fg. 1. Ths system confguraton can be consdered to represent a two-splt shpboard power system, wth an Integrated Power System (IPS) confguraton [9]. Ths system s n many aspects smlar to other commercal slanded mcrogrds. The power system s two buses represent swtchboards where one propulson load and one generator are connected. The propulson loads are realzed as Varable Speed Drves (VSD) wth 12-pulse rectfers. The man bus connecton between the two swtchboards has an equvalent seres-mpedance gven by R and L. Parastc shunt cactances of the system are represented by C S1 and C S2 wth equvalent resstances gven by R S1 and R S2. The 12-pulse rectfer loads are known to produce current harmoncs wth the 11 th, 13 th, 23 th, 25 th as the domnant components. Thus, n ths work selectve harmonc mtgaton wth the APF wll be employed to mtgate the frst four characterstc harmonc components generated by the 12-pulse rectfers. The APF s nterfaced to bus 2 wth an LCL flter as ndcated to the rght n Fg Analyss of Optmal APF Currents Based on the power system showcased n Fg. 1, an analytcal expresson for the optmal APF current reference can be derved as a functon of the harmonc load current. A. Dervaton of Optmal APF Currents Usng Krchhoff s laws and assumng neglgble harmonc dstorton n the generator voltages, the quas-statonary voltage and current components for each ndvdual harmonc component n the system can be expressed by: v1,2 G1,2 (1) R j hl G1,2 G1,2 1,2 (2) R v 1 j hc v v 1 2 (3) R j hl v v 3 2 C2 (4) RL2 j hll2 1 v3 RC C1 RDD (5) j hcc (6) AF C1 C2 D (7) G2 L2 S2 C2 (8) G1 S1 L1 The current and voltage components n these equatons are defned n Fg. 1. The equatons are expressed on phasor form where j s the magnary operator and h s the harmonc order. The system s expressed by 11 equatons (wth 11 unknowns) for each harmonc component. Ths set of equatons can be solved analytcally for the harmonc currents flowng n the generators as a functon of the harmonc load currents and the current from the APF. Symbolc mathematcal software, such as Mle 1, can be used to fnd a soluton for the system gven as 2 : h,, (9) The 11 unknown varables are: L1 L2 AF,,,,,,,, v, v, v (10) G1 G2 S1 S 2 C1 C2 D whle the power system parameters collected n the vector ρ are gven by (11). LG 1, RG1, LG 2, RG 2, L, R, CS1, RS1, (11) C, R, L, R, L, R, C, R, R S 2 S 2 L1 L1 L2 L2 C C D The purpose of the harmonc mtgaton should be to mnmze the harmonc components n bus voltages and the generator currents. In ths case, an objectve functon for mnmzng the currents n the generators for a general harmonc order h s selected as gven by (12): 2 2 mn J,, h,,, (12) AF L1 L2 AF G1 G The detaled soluton s too large to show n ths per.

3 (a) (b) Fg. 2. Magntude (a) and angle (b) of k1 and k2 plotted for eght frst harmoncs (5 th, 7 th, 11 th, 13 th, 17 th, 19 th, 23 rd, 25 th ) as a functon of the man bus nductance L. The analyss s assumng that the optmal APF current s gven on the form: c re m j (13) AF af af consderng both magntude and phase nformaton. Substtutng (13) for AF n the soluton of G1 and G2 resultng from (12), the mnmzaton problem can be solved by dfferentaton wth respect to the real and magnary part of c AF: dj c,, h, L 1, L2, AF 0 re daf (14) dj c,, h, L 1, L2, AF 0 m d af Ths yelds a soluton on the form o h h k k AF 1 L1 2 L2 k (,, h) e h 1 L1 k (,, h) e h 2 L2 j 1 (,, h) j 2 (,, h) (15) where θ 1 = k 1, θ 2 = k 2, and h L1, h L2 are the load currents for harmonc h. Thus, the constants k 1 and k 2 are defnng the optmal APF current gven as a functon of h L1, h L2 and the system parameters ρ. B. Analyss of Optmal AFP Currents To llustrate the results from the analytcal optmzaton, the system confguraton from Fg. 1 s analyzed wth the parameters n Table I. Fg. 2 shows the magntude and angles of k 1 and k 2 plotted as functons of L. As can be seen, both the angle and the magntude of k 1 are dependent on L whle the angle and the magntude of k 2 are ndependent on L. Ths s as expected snce current njecton at bus 2 for mtgatng harmoncs n G1 must be corrected for the voltage drop and phase shfts ntroduced by the man bus mpedance and the shunt cactances of the system. The presented curves also ndcate how the optmzaton balances the dstorton n the two buses dependng on the mpedance between them. In case the bus mpedance s small, the APF can compensate for the harmoncs of both loads, whle the compensaton of the harmoncs from load 1 has to be reduced when the bus mpedance ncreases to avod ncreased dstorton n G2. However, the result from ths optmzaton s only vald as Table I: Power System Parameters (pu rel. generator ratng) Parameter Value Unt Nomnal voltage Vrms 690 V Nomnal frequency f 50 Hz Generator power ratng 1 MVA LG1 and LG2 0.2 [pu] RG1 0.1 LG1 ω [pu] RG2 0.1 LG2 ω [pu] L 0.04 [pu] R 0.1 L ω [pu] CS1 and CS2 2 µf RS1 and RS2 2 Ω LL1 and LL2 0.3 mh RL1 and RL Ω CC 30 µf RC 10 Ω RD 160 Ω long as the system parameters are accurately known and the current ratng of the APF s not exceeded. 4. MPC Generated APF Reference Another opton for generatng an optmal APF current reference n a mult-bus system confguraton was proposed n [5]-[7], utlzng an onlne optmzaton scheme based on Model Predctve Control (MPC). Fg. 3 llustrates the man concept of MPC, where measurements from the process are ntalzng a model of the system whch s used to obtan the control acton at each samplng nterval by solvng a fnte horzon optmal control problem [10]. The objectve of the optmzaton s formulated as a cost functon whch s gven to an optmzer together wth constrants reflectng lmtatons of the physcal process. The control actons are optmzed accordng to a predefned reference r(t k) (wth dscretzed tme step t k) reflectng the desred process behavor. The model output s gven by y (t k), and a closedloop feedback provdes the necessary model correctons ε(t k) calculated as model msmatch between the outputs of the model, y (t k) and the process, y(t k). The total MPC formulaton can be expressed on a standardzed form gven by (16). In ths equaton the dynamc state vector of the process s gven by x(t), the algebrac state vector s z(t), and the optmal control vector s u(t). The scalar functon V( ) s the objectve functon (wth l( ) as stage cost). The dfferental states are gven by

4 f( ), the algebrac states and equalty constrants are gven by g( ). Inequalty constrants are gven by h( ). The length of the dscrete control horzon s defned by T, where t 0 s the ntal tme nstance, and the optmal soluton s feasble regon s gven by. The power system s measurements (y(t k) n Fg. 3) are used to ntalze the MPC,.e. x(t 0) and z(t 0). t0 T mn ( x( ), z( ), u( )) ( ), ( ), ( ) x( t), z( t), u( t) x z u t0 s.t. Fg. 3. General llustraton of a Model Predctve Controller. V t t t l t t t x( t) f x( t), z( t), u( t) g x( t), z( t), u( t) 0 h x( t), z( t), u( t) 0 t [ t, t T ] x( t ), z( t ), (16) The smplfed power system model used n the dervaton of the MPC s llustrated n Fg. 4. Compared to the system model n Fg. 1, the LCL flter has been gnored and the RC-shunt elements are replaced by smple C-shunts. The pled MPC formulaton, based on [5]-[7], s brefly addressed n the followng. A. Model Formulaton Usng Krchhoff s laws, the dynamcs of the power system represented n Fg. 4 can be expressed as dg1,2 LG 1,2 RG1,2G 1,2 v (17) dvs1 C (18) S1 G1 L1 dvs 2 CS 2 G2 L2 AF (19) d L vs1 vs 2 R (20) In these equatons, three-phase currents and voltages are gven by bold symbols,.e. and v. As the MPC formulaton s only consderng the harmonc currents and voltages, the generator voltages are not ncluded n the model snce they are assumed to have no harmonc voltage components. The load currents can be wrtten as Fourer seres accordng to (21), wth ampltudes I L,, phases ϕ L, and harmonc orders to be mtgated gven by. Note that the fundamental frequency load current components are not ncluded snce only the harmonc currents are object of mtgaton. Fg. 4. Smplfed shpboard power system model for the dervaton of the MPC. IL, sn t L, La, () t 2 L ( t) L, b ( t) I L, sn t L,, 3 Lc, () t 2 IL, sn t L, 3 harmonc orders (21) The APF reference currents, AF, are kept as free varables and decded by the optmzaton scheme. Wth regards to MPC standard form, the dynamc and algebrac state vectors (x and z), along wth the control vector (u) can be wrtten as x,,, v, v G1 G2 S1 S 2 z v, v,, G1 G2 L1 L2 uaf AF, a, AF, b, AF, c (22) B. Cost Functon A sutable stage cost functon for harmonc mtgaton n the two swtchboards can be stated as: l x, z, u G1Q1 G1 G2Q2G2 u Quu (23) ( ) Q ( ), AF, a AF, b AF, c abc AF, a AF, b AF, c wth weghts gven by Q dag( q, q, q ), Q dag( q, q, q ), q q q Q q q q Q dag(,, ), dag(,, ). u u u u abc abc abc abc (24) The frst two parts of the stage cost functon gven by (23) s related to harmonc mtgaton and penalzes harmonc currents not equal to zero. The two last parts penalzes for hgh APF current ampltude and zero sequence components. C. Constrants The MPC s constrants should reflect the propertes and lmtatons of the physcal process, and n ths work the constrants are related to the APF current lmtatons. The blue hexagon n Fg. 5 llustrates the phase current lmtatons of the APF [11]. Assumng a balanced flter, the lmts wll be the same for all phases as expressed by. AF AF, a AF AF AF, b AF AF AF, c AF (25) The constrants are added to the functon h( ) n the MPC formulaton on standard form.

5 Table II: MPC mplementaton detals. Parameter Value Tme horzon T 12.5ms MPC run cycle 100Hz Dscretzaton N 220 Integrator RK4 Hessan Exact Hessan proxmaton Solver qpoases Iteratons 5 Stage cost weghts q1 q2 1000, qu 1, qabc 0 APF current lmt F 1 [pu] (APF pu model) Fg. 5. Actve power flter current lmtaton for three-phase three-wre system represented n the abc and αβ frames [11] 5. Smulaton study The power system from Fg. 1 has been modelled n the Matlab/Smulnk envronment usng the SmPower- Systems lbrary. For smplcty, the generators are assumed to be deal voltage sources and the frequency s assumed to be constant. The APF s operated wth nner loop hysteress current controllers wth 15% hysteress band and swtchng frequency of proxmately 20kHz. The APF s power ratng s set to 15% of the ratng of the generators. The smulaton step sze s set to 2 µs. The MPC s mplemented usng the ACADO (Automatc Control and Dynamc Optmzaton) toolkt [12], whch comes wth a code generaton tool [13] for generatng hghly effectve C code. The MPC was cross-compled to Matlab (as a mexfuncton), and ncluded n the Smulnk mplementaton of the power grd. Detals regardng the MPC mplementaton are lsted n Table II. Two dfferent cases are smulated to llustrate the performance of the MPC compared to results when operatng the APF wth current reference accordng to (15) wth constants k 1 and k 2 obtaned from analytcal optmzaton (labelled "Analytcal"). A thrd proach of calculatng the APF current references accordng to [8], has also been used as a benchmark case, and s referred to as BM2. Ths proach does not explctly consder the mpedance between the busses and calculates the current references to the APF by summng the harmonc load currents,.e. AF = h L1 + h L2, whch corresponds to k 1 and k 2 equal to 1.0 n (15). Furthermore, results from traonal local selectve harmonc flterng of load 2 are used as a reference for the THDs n the system, and s labelled as BM1. The harmoncs to be mtgated are the 11 th, 13 th, 23 th and 25 th components. For each case two plots are gven; the APF current measured after the LCL flter, and the deal APF reference from the controllers. A. Case 1 Table III lsts the confguraton of Case 1 and the results from the smulaton. The load demand from both propulson loads are set to 0.22 pu. The resultng THDs ndcate that the MPC s able to acheve the most effectve Table III: Confguraton and results from Case 1. MPC Analytcal BM2 BM1 THD v1 1.5% 1.6% 2.0% 2.6% THD v2 1.7% 2.5% 2.2% 2.3% Power load 1 Power load [pu] 0.22 [pu] Table IV: Confguraton and results from Case 2. MPC Analytcal BM2 BM1 THD v1 3.9% 4.7% 4.7% 6.4% THD v2 4.1% 5.2% 4.9% 5.6% Power load 1 Power load [pu] 1.0 [pu] harmonc mtgaton at both buses. The analytcal controller s better than BM2 for v 1, however, results n worse THD for v 2. Ths s a result of the balanced optmzaton of the generator current harmoncs, and the analytcal controller s n total slghtly better than BM2. All these three control proaches are ensurng a sgnfcantly mproved THD at bus 1 compared to BM1. Fg. 6 shows the resultng APF reference and output current for the MPC, the analytcal optmzaton and BM2. As can be seen, the phase and ampltudes for all three controllers are dfferent, and the MPC generates an APF reference current wth lower ampltude compared to the two other controllers. The current reference wth the analytcal optmzaton has hgher ampltude and a dfferent phase compared to BM2, snce the shunt and seres mpedances n the system are accounted for. Snce the MPC s re-ntalzed before every new cycle, t s able to compensate for model/process msmatch, and ths s causng the THD dfference between the MPC and the analytcal controller. The analytcal controller does not have any closed-loop feedback and s not able to compensate for model/process msmatch. BM2 does not have any nformaton about the power system, as the APF reference s constructed drectly from the sum of the harmoncs to be mtgated from both loads. B. Case 2 Table IV lsts the confguraton and the results from Case 2. The load demand from both propulson loads are now set to 1.0 [pu]. As can be seen, the MPC clearly results n the lowest THDs at both buses. In ths case, the analytcal current reference calculaton s resultng n poorer harmonc mtgaton at bus 2 than BM2 whle the conventonal BM1 control provdes the worst results.

6 Fg. 6. APF reference and output current (phase a) for Case 1 Fg. 7. APF reference and output current (phase a) for Case 2 Fg. 7 shows the resultng APF reference and output current for the MPC, the analytcal optmzaton and BM2. The same as dscussed for Case 1 also yelds for ths case, however now the APF currents are saturated. As the MPC s model ncludes the APF s current lmts as constrants, t s able to optmze the APF performance wthn the saturaton lmt. The analytcal controller does not have any nformaton regardng the APF s current lmts. Hence, the saturaton deterorates the controller s optmalty, whch n ths case results n worse THD for v 2 compared to BM2. As the analytcal controller employs a hgher ampltude and a phase shft compared to BM2, the saturaton effects are more severe. It should be noted t s the harmonc current references for the APF that are lmted wthn 1.0 pu. Thus, the actual current njected nto bus 2 s slghtly exceedng ths lmt due to the fundamental frequency current needed to compensate for losses and balance the dc-bus voltage of the APF. 6. Concluson Ths work has analyzed two conceptual methods for optmzed system-wde harmonc mtgaton of a two-bus power system by an APF. Frst, t has been shown how an analytcal expresson for the APF current that wll mnmze each harmonc component at the two buses can be calculated as a functon of the load current harmoncs and the system parameters. Ths serves to demonstrate how the APF can be controlled to beneft the overall system and not only the local pont where t s connected. However, the purely analytcal proach s senstve to system parameter varatons and does not take nto account practcal constrants lke the current ratng of the APF. An MPCbased controller s shown to be able to optmze the APF performance wthn such constrants. Thus, the MPC demonstrated clear advantages over the analytcally obtaned current references, related to robustness and adtve behavor, resultng n lower THDs at both bus voltages n the presented smulatons. Acknowledgement Ths work has been carred out at the Centre for Autonomous Marne Operatons and Systems (AMOS), sponsored by the Norwegan Research Councl. The work was supported by Ulsten Power & Control AS and the Research Councl of Norway, Project number References [1] G. K. Sngh, "Power system harmoncs research: a survey," n European Transactons on Electrcal Power, vol. 19, no. 2, March 2009, pp [2] P. Mattavell, "A Closed-Loop Selectve Harmonc Compensaton for Actve Flters," n IEEE Trans. on Ind. Appl., vol. 37, no. 1, January/February 2001, pp [3] H. Akag, E. Watanabe, and M. Aredes, "Instantaneous Power Theory and Applcatons to Power Cononng," Wley/IEEE Press Seres on Power Engneerng, 2007 [4] W. M. Grady, M. J. Samotyj, A. H. Noyola, "Mnmzng Network Harmonc Voltage Dstorton wth an Actve Power Lne Cononer," n IEEE Transactons on Power Delvery, vol. 6, no. 4, October 1991, pp [5] E. Skjong, M. Molnas, T. A. Johansen, "Optmzed Current Reference Generaton for System-level Harmonc Mtgaton n a Desel-Electrc Shp," n Proc. of the 2015 IEEE Int. Conf. on Industral Technology, ICIT 2015, Sevlle, Span, March 2015, pp [6] E. Skjong, M. Molnas, T. A. Johansen, R. Volden, "Shng the Current Waveform of an Actve Flter for Optmzed System Level Harmonc Cononng," n Proc. of the 1 st Int. Conf. on Vehcle Technology and Intellgent Transportaton Systems, VEHITS 2015, Lsbon, Portugal, May 2015, pp [7] E Skjong, M. Ochoa-Gmenez, M. Molnas, T. A. Johansen, "Management of harmonc propagaton n a marne vessel by use of optmzaton," n Proc. of the 2015 IEEE Transportaton Electrfcaton Conf. and Expo, ITEC 2015, Dearborn, Mchgan, USA, June 2015, 8 pp. [8] A. R. Årdal, E. Skjong, M. Molnas, "Handlng System Harmonc Propagaton n a Desel-Electrc Shp wth an Actve Flter," n Proc. of the 2015 Int. Conf. on El. Syst. for Arcraft, Ralway, Shp Propulson and Road Vehcles, ESARS 2015, Aachen, Germany, 3-5 March 2015, 6 pp. [9] M. R. Patel, "Shpboard Electrcal Power Systems," Taylor & Francs, 2011 [10] J. Rawlngs, D. Mayne, "Model Predctve Control: Theory and Desgn," Nob Hll Pub [11] J. A. Suul, "Control of Grd Integrated Voltage Source Converter under Unbalanced Conons," PhD Thess, Norwegan Unversty of Scence and Technology, 2012 [12] B. Houska, H. J. Ferreau, M. Dehl, "ACADO Toolkt An Open Source Framework for Automatc Control and Dynamc Optmzaton," n Optmal Control Applcatons and Methods, vol. 32, no. 3, May/June 2011, pp [13] B. Houska, H. J. Ferreau, M. Dehl, "An Auto-Generated Real-Tme Iteraton Algorthm for Nonlnear MPC n the Mcrosecond Range," n Automatca, vol. 47, no. 10. October 2011, pp