System-Wide Harmonic Mitigation in a Diesel Electric Ship by Model Predictive Control

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS System-Wide Hrmonic Mitigtion in Diesel Electric Ship by Model Predictive Control Espen Skjong, Jon Are Suul, Member, IEEE, Atle Rygg, Tor Arne Johnsen, Senior Member, IEEE, nd Mrt Molins, Member, IEEE Abstrct This pper proposes system-oriented pproch for mitigting hrmonic distortions by utilizing single Active Power Filter (APF) in n electricl grid with multiple buses. Common prctice for control of APFs is to loclly compenste the lod current hrmonics or to mitigte voltge hrmonics t single bus. However, the opertion of n APF in multi-bus system will influence the voltges t neighboring buses. It is therefore possible to optimize the APF opertion from system perspective insted of considering only conventionl locl filtering strtegies. For such purposes, Model Predictive Control () is proposed in this pper s frmework for generting APF current references tht will minimize the hrmonic distortions of the overll system within given APF rting. A diesel-electric ship, with two buses supplying seprte hrmonic lods, with n APF locted t one of the buses, is used s study cse. The opertion with on-line bsed optimiztion of the APF current references is compred to two benchmrk methods bsed on conventionl pproches for APF control. The results demonstrte tht the genertes current references tht better utilize the APF current cpbility for system-wide hrmonic mitigtion. Index Terms Active Power Filter (APF), Optimiztion, Model Predictive Control (), System-Wide Hrmonic Mitigtion, Totl Hrmonic Distortion (THD) Mnuscript received July 3, 5; revised December, 5; ccepted Jnury 5, 6. Dte of publiction: 6; dte of current version: Jnury 9, 6 Copyright (c) 6 IEEE. Personl use of this mteril is permitted. However, permission to use this mteril for ny other purposes must be obtined from the IEEE by sending request to pubs-permissions@ieee.org This work hs been crried out t the Centre for Autonomous Mrine Opertions nd Systems (AMOS). The Norwegin Reserch Council is cknowledged s the min sponsor of AMOS. This work ws supported by Ulstein Power & Control AS nd the Reserch Council of Norwy, Project number 45. E. Skjong is with the Deprtment of Engineering Cybernetics, Norwegin University of Science nd Technology, 734 Trondheim, Norwy, with the Centre for Autonomous Mrine Opertions nd Systems (AMOS), Norwegin University of Science nd Technology, 75 Trondheim, Norwy, nd lso with Ulstein Power & Control AS, 68 Ålesund, Norwy (e-mil: espen.skjong@ulstein.com) J. A. Suul is with the Deprtment of Electric Power Engineering, Norwegin University of Science nd Technology, 7495 Trondheim, Norwy, nd lso with SINTEF Energy Reserch, 7465 Trondheim, Norwy (e-mil: jon.re.suul@ntnu.no) A. Rygg is with the Deprtment of Engineering Cybernetics, Norwegin University of Science nd Technology, 734 Trondheim, Norwy, (e-mil: tle.rygg@itk.ntnu.no) T. A. Johnsen is is with the Deprtment of Engineering Cybernetics, Norwegin University of Science nd Technology, 734 Trondheim, Norwy, nd lso with the Centre for Autonomous Mrine Opertions nd Systems (AMOS), Norwegin University of Science nd Technology, 75 Trondheim, Norwy, (e-mil: tor.rne.johnsen@itk.ntnu.no) M. Molins is with the Deprtment of Engineering Cybernetics, Norwegin University of Science nd Technology, 734 Trondheim, (e-mil: mrt.molins@ntnu.no) Color versions of one or more of the figures in this pper re vilble online t http://ieeexplore.ieee.org. Digitl Object Identifier... I. INTRODUCTION Hrmonics re ny devition from the pure sinusoidl voltge or current wveform typiclly generted by n idel voltge source with liner lods []. In diesel-electric ship power system, the min source of hrmonics is usully the diode rectifier stges of Vrible Frequency Drives (VFDs) for controlling the propulsion motors. A wide vriety of VFDs re in use tody depending on the power level, the pulse-number of the rectifiers nd the system design, ech of them generting different hrmonic distortion levels [] [4]. Hrmonic distortions in power system cn be mitigted by instlling pssive filter solutions (i.e. inductive nd cpcitive filters) tht will reduce the impct of hrmonic lod currents on the rest of the system. For lrge nonliner lods with known hrmonic spectr, tuned hrmonic filters for dominnt low-order components re commonly pplied [5], [6]. Such configurtions cn lso include high-pss filters for mitigting wider rnge of higher order hrmonics. However, pssive filters must be crefully designed to void resonnces cusing mplifiction of other hrmonic components, especilly when the instlltion is exposed to prmeter vritions or frequent chnges in system configurtion [7]. Furthermore, the mplitude of the hrmonic current components generted by diode rectifier will depend on the ctive power needed by the lods. Thus, set of shunt-connected pssive filters cnnot be effectively dpted to the wide rnge of vritions in propulsion lods on-bord n electricl ship. Another lterntive for pssive hrmonic mitigtion is to pply series connected wide spectrum filters [3]. However, such filters must be instlled in ech of the propulsion lods, nd will not mitigte hrmonics generted by smller VFD lods in the system. High hrmonic distortion levels in system with dominnt VFD lods cn lso be voided by pplying Active Rectifiers (ARs) insted of diode rectifiers. However, this solution is still more costly nd hs lso higher losses thn pssive rectifiers. Another option to del with hrmonics without resorting to pssive filters or diode rectifiers with high pulse numbers nd complex multi-winding trnsformers for ll VFD lods, is the use of Active Power Filters (APFs). The common prctice in ctive filtering is to use the APF for locl compenstion by pplying current reference equl to the hrmonic nd rective current components of the non-liner lod []. However, when there re multiple non-liner lods distributed on multiple buses in system, like in mrine vessel grid, minimizing the totl hrmonic distortion in the system will no longer be possible with the locl filtering pproch. In such grid configurtions, with severl nd dispersed sources of hrmonics,

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS pproches for controlling APFs with the objective of systemwide hrmonic mitigtion represents n interesting option tht hs not yet been systemticlly pursued. Optimiztion techniques cn provide generl frmework for generting optiml current reference wveforms for n APF with the objective of minimizing the overll totl hrmonic distortion (THD) in system. Significnt reserch efforts hve recently been directed towrds ppliction of Model Predictive Control () to the locl control of power electronic converters, including APFs [8], [9]. However, the potentil for utilizing in system-wide hrmonic mitigtion with n APF still remins to be exploited. In this pper, ppliction of is thoroughly investigted for system-wide hrmonic conditioning with shuntconnected Voltge Source Converter (VSC), controlled s n APF, bsed on the originl ide presented in [] []. The previously presented studies on this topic were preliminry explortions of the cpbility of the for minimizing the totl hrmonic voltge distortion (THD V ) in the lod buses of mrine vessel power grid, bsed on simplified models with idel current sources. Although the results in [] [] indicted tht APF current references generted by systemwide -bsed pproch cn improve the THD V t the min buses compred to locl filtering pproches, the impct of ccurte lod models nd the implementtion of the APF were not tken into ccount. A revised nd improved closed-loop implementtion of for optiml hrmonic mitigtion is presented in this pper, nd demonstrted in model of mrine vessel power grid implemented in MATLAB/Simulink with detiled models of VFD rectifiers nd the APF. The APF performnce with the proposed system-wide control pproch is compred to the results with trditionl locl filtering nd n d-hoc solution proposed in [3]. The sme trend s observed in the previous works is confirmed, with consistently improved system-level THD V when the pproch is used to clculte the APF current references. Furthermore, the results highlight the dvntges of the compred to the solution from [3], nmely the higher degree of freedom nd flexibility, the bility to impose APF current sturtion (constrints) nd the bility to find n optiml current reference for n APF in complex power grid with more thn two buses. II. MARINE VESSEL S POWER GRID Diesel-electric power genertion nd propulsion for mrine vessels ws commercilized nd fully dopted by the offshore industry in the mid 99s, with industry prtners for power solutions t the helm. For n offshore opertion vessel, the power demnd, i.e. the vessel s power profile, is given by the vessel s momentrily ssignment, e.g. trnsit, sttion keeping with Dynmic Positioning (DP) or nchorhndling. Diesel-electric vessels hve introduced flexibility of power genertion when needed, compred to mechnicl drive vessels where the prime mover is directly connected to the propeller vi mechnicl gers nd long shfts. Therefore, diesel-electric opertion hs contributed to cultivting green environment philosophy where the fuel consumption, nd thus the exhust emission, is in line with the power demnd []. Diesel-electric power genertion hs lso introduced dvnced redundnt power grid designs, e.g. ring bus designs, which stisfy requirements set by clssifiction entities, such s ABS, Lloyd s Register nd DNV GL [4]. This fvors n incresed number of instlled genertors with lower power rtings, fcilitting more step-less power genertion compred to vessels with redundnt mechnicl drives. The power grid under investigtion in this work is bsed on simplified equivlent of mrine Pltform Supply Vessel (PSV) power system with two buses nd two propulsion lods, operting with closed bus-tie breker. The simplifiction is justified from the fct tht these lods re typiclly responsible for the dominnt prt of the power consumption nd the dominnt hrmonic distortions. A single-line digrm of the ssumed power grid configurtion is shown in Fig.. In the investigted operting conditions, the vessel hs only two genertors in opertion, one connected to ech bus, Bus nd Bus, respectively, since this is ssumed to be the worst cse for voltge distortions in the system. One propulsion motor supplied through VFD is connected to ech bus. The VFD hs either 6-pulse or -pulse diode rectifier interfced to the bus, nd voltge source inverter for controlling the motor driving the propeller. A trnsformer is included to provide glvnic isoltion nd for phse shifting in cse of - pulse rectifier. A series impednce is included between the two buses. Finlly, the ctive filter is connected to bus s seen in the Fig.. Tble I lists the most importnt detils of the power grid under investigtion, where the dopted pu bse vlues re referred to the genertor rtings. GEN RS LS Bus Bus LMB Lod = MOT RMB = MOT LS Lod RS GEN = Active Power Filter (APF) Fig.. Simplified digrm of the power grid under investigtion, including two genertors, two lods nd n ctive power filter. TABLE I POWER GRID PARAMETERS, WITH GENERATOR RATING AS PU-BASE. Prmeter Vlue L S % [pu] Genertor MVA L S % [pu] Genertor MVA L MB 4% [pu] Motor MVA R S % L S ω [pu] Motor MVA R S % L S ω [pu] Active filter kva R MB % L MB ω [pu] Voltge (RMS) 69V, 5Hz The mximum llowed totl hrmonic distortion in mrine vessel s power system is regulted by clssifiction entities. DNV GL follows IEC 6--4 Clss, which implies tht the totl hrmonic voltge distortion (THD V ) shll not

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 3 exceed 8% [5]. In ddition, DNV GL requires tht no single order hrmonic voltge component shll exceed 5%. Similrly, Lloyd s Register requires tht the THD V t ny c switchbord or section bord is below 8% (unless specified otherwise) of the fundmentl, considering ll frequencies up to 5 times the supply frequency. Within this requirement, no voltge component t frequency bove 5 times the supply frequency should exceed.5% of the fundmentl of the supply voltge [6]. Americn Bureu of Shipping (ABS) recommends tht the THD V should not exceed 5%, s mesured t ny point of common coupling (PCC), with ny individul hrmonic voltge not exceeding 3% of the fundmentl voltge vlue. The rnge of hrmonics to be tken into ccount should be up to the 5th hrmonic [7]. Bureu Verits (BV) hs similr rules nd regultions [8]. However, the clssifiction entities do not provide cler set of requirements regrding totl hrmonic current distortion (THD I ) t ny specific points, s hrmonic current distortions do not propgte the power grid s esily s hrmonic voltge distortions due to impednces in the system. Thus, this work will focus on hrmonic voltge distortions t the min buses of the system, intending to comply with the clssifiction requirements ccording to ABS. III. MODEL PREDICTIVE CONTROL In this pper, Model Predictive Control () is utilized to chieve optiml APF control for system-wide selective hrmonic mitigtion in power grid, by generting APF current references optimized within the APFs current rting [] []. The min ide of is to clculte the control ction for process/system using (usully simplified) model to predict the system s future behvior. The model is initilized by mesurements of the system s current stte, nd t ech smpling intervl the control ction is obtined by solving online constrined finite horizon optiml control problem [9]. The control ction is extrcted from the resulting finite control sequence yielded from the optimiztion nd given to the system to close the control loop. Depending on the s computtionl costs, there might be non-negligible time dely between the initiliztion of the model nd the resulting clculted control sequence, which must lso be tken into ccount in the implementtion. The s ccurcy nd computtionl costs re dependent on the model of the system nd the vilbility nd ccurcy of rel-time mesurements. To model system perfectly is in most cses n impossible tsk. In ddition, modelling ll dynmics, if possible, usully result in lrge nd complex model with high computtionl costs, tht often requires more mesurements. Therefore, compromise between ccurcy nd computtionl costs must be mde when designing schemes. In generl, the model pplied for should be s simple s possible while contining ll dynmics needed to stisfy the control objective within the control horizon nd the level of discretiztion. The horizon s length is dependent on the control objective, nd the level of discretiztion should be chosen with respect to the fstest dynmics tht should be controlled. A thorough overview of dependble embedded s is given in []. In the literture it hs been reported implementtions with good rel-time properties [] [3], nd some reserch hs lso been conducted to explore the use of optimiztion nd in the field of electricl engineering [9], [4], [5]. The formultion described in this section is bsed on the models nd pproches from [], [] nd []. However, the implementtion nd the formultion of the objective function re further improved to benefit from the s flexibility in the serch for the optiml filter current injection. In the following, the power grid model nd the ctive filter constrints used in the development of the re discussed before the formultion is presented on stndrdized form. A. Power Grid Model As mentioned, depends on model of the system for clculting the optiml control ctions. The min 69V busbrs nd lods in diesel-electric ships re usully threephse three-wire systems. Thus, there will be no pth for zero-sequence currents nd the system could be modelled in the αβ frme (by using the Clrke trnsform) while ignoring zero sequence components []. This would imply reduced dimension of the problem formultion for the compred to modelling in the bc frme, nd could be beneficil for reducing computtionl costs (for rel-time implementtion). However, representtion in the αβ frme implies tht the current limit of the APF in the α-xis will depend on the current in the β-xis nd vice vers. Since functionlity for such limittions re not included in the softwre used in this work, the formultion will be bsed on the bc frme. In the following, subscript, b nd c re used to denote the bc phses of ech voltge nd current component. The vectors v nd i re used to represent the voltges nd currents, respectively, given in the bc frme. V S R S L S LS i C - V C + i S i L i MB R MB L MB i S C Lod Lod C i L i C R S i F - V C + APF Fig.. Simplified power grid model used to design the for hrmonic mitigtion. Fig. shows simplified power grid model pproximting the mrine vessel s power grid discussed in section II, with prmeters dopted from Tble I. The shunt cpcitors indicted in the figure re included to decouple the sttes representing currents in the inductnces, but cn lso be considered s n equivlent representtion of the cble nd busbr cpcitnces. The cpcitor voltge sttes will represent the busbr voltges used for ssessing the THD V in the system. In this work, simplified genertor model with fixed voltge mplitude behind n impednce is used for the modelling nd simultions. The per unit genertor impednce is selected to V S

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 4 be within the norml rnge for sub-trnsient rectnces of synchronous mchines, ccording to [6]. A constnt fundmentl frequency model is lso ssumed, i.e. ω := πf(t) = πf where f is the nominl fundmentl frequency. In relity, the frequency of ship power system will not be constnt nd the synchronous genertors will hve voltge controller dynmics s well s smll internl voltge distortions due to the physicl construction. However, the pplied simplified model cn be considered sufficient to demonstrte the stedy stte systemwide optimiztion chieved with the without depending on simultions with lrge mechnicl nd electromechnicl time constnts. The is lso prtly ble to reject unmodelled disturbnces since the internl system model will be continuously updted through closed-loop feedbck. Furthermore, the cn esily hndle frequency vritions s long s the hrmonic nlysis in the control system is frequencydptive. If necessry, simple dynmic frequency model, cn lso be embedded in the, s proposed in []. Assuming 6-pulse rectifiers re prt of the mrine vessel s propulsion system, the lods will introduce non-liner conditions drwing hrmonic current of order 5, 7,, 3, etc. from the genertors []. Hence, the lod model used in the cn be modeled s idel current sources, i L, (t) i I L,i sin (i (ωt + φ L,i )) i L (t) = i L,b (t) = i I L,i sin ( i ( )) ωt + φ L,i π 3 i L,c (t) i I L,i sin ( i ( )), ωt + φ L,i + π 3 i {6k ± k =,,...}, () which includes the ssumed hrmonic components, i, to be mitigted, with phse shifts φ L,i nd mplitudes I L,i. Note tht the lod model, (), does not include the fundmentl current components. If the mrine vessel s power grid includes elements tht generte other dominnt hrmonic components, the lod models nd the hrmonics to be mitigted by the cn be chnged ccordingly. The APF in Fig. should be controlled to suppress the hrmonic content of the genertor currents in order to minimize the voltge hrmonics t the min buses. The APF currents in ll three phses, i F,, i F,b nd i F,c, re kept s free vribles nd re optimlly clculted by the. This decision gives totl uthority to the, llowing the to phse shift nd lter the different hrmonic components of the filter currents in ny possible wy to chieve the best possible hrmonic mitigtion. This is n importnt property when the APF is reching its pek current limits. The power grid s dynmics cn be derived using Kirchhoff s lws nd be stted s L S di S dt C dv C dt L MB di MB dt C dv C dt L S di S dt = R S i S v C () = i S i MB i L (b) = v C v C R MB i MB (c) = i MB + i S i L + i F (d) = R S i S v C. (e) Three-phse current limittions i b i min i mx b i c i p F i mx c i β 3 i min c i lim F i min b i mx Fig. 3. Active power filter constrints: Three-phse three-wire system represented in the αβ nd bc frmes [7]. As seen from these equtions, the bus voltges re provided in the model by the cpcitnces, nd the differences between the two bus voltges determine the current flowing in the min bus impednce (i MB ). For the implementtion, () does not include the fundmentl components since the only regrds hrmonic components. It should lso be mentioned tht potentil voltge distortions originting from the genertors or from other components in the systems tht re difficult to mesure, will ffect the hrmonic genertor currents. Thus, the will indirectly ttenute the effect of such disturbnces since they will be contined by the feedbck signls used to initilize the internl model of the. B. Active Power Filter Constrints The APF s current nd voltge limits re determined by its physicl components. In generl, the semiconductor devices, usully IGBT modules contining nti-prllel diodes, determine the current rting, while the voltge rting of the dc-side cpcitor limits the mximum voltge vilble to inject current hrmonics into the grid. The current limittions will be the sme for ll three phses, s illustrted in the bc frme by the blue hexgon in Fig. 3 [7]. These limits should be included in the formultion to void unwnted effects from sturtion of filter current references (i.e. current clipping). Inclusion of the current limits in the will lso ensure tht the utiliztion of the current cpbility will be optimized. By this, the will be ble to optimlly clculte APF currents close to the APF s limits without sturtion effects impiring the hrmonic conditioning. The current constrints given by the hexgon in Fig. 3 cn be formulted in the bc frme s i min i j i mx, j {, b, c}, (3) i i α

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 5 where i min = i mx. The constrints given in αβ form cn be found in [] []. As mentioned, the model could be developed in the αβ frme for more effective implementtion of the system model. However, the implementtion of the current constrins re more complicted in the αβ frme. Therefore, it is preferred in this cse to implement the in the bc frme. For nottionl simplicity the set of fesible filter currents given by the constrints defined in (3) is in the following denoted S. C. Formulting the on Stndrd Form With the formultion of the model nd the APF s constrints, which ws discussed in section III-A nd III-B, the t time t with control horizon of length T cn be written on stndrd form s min x(t),z(t),u(t) s.t. V (x(t), z(t), u(t)) = t+t t l (x(t), z(t), u(t)) dt ẋ(t) = f (x(t), z(t), u(t)), g (x(t), z(t), u(t)) =, h (x(t), z(t), u(t)), t [t, t + T ] x(t ), z(t ) i F (t ) S, (4) where V ( ) is the objective function defining the objective of the optimiztion, l( ) is the stge cost function nd f( ) represents the power grid s dynmics given by (). g( ) represents the s equlity constrints, in which includes lgebric equtions such s the lod models given by (). h( ) represents the s inequlity constrints, which includes the filter s current limits given by (3). The dynmic stte vector, x, is given by the power grid s dynmic equtions, nd by omitting the time nottion (t), it cn be stted s x = [ i S, i S, i MB, v C, v C], (5) where i S nd i S re the hrmonic genertor (source) currents to be compensted, i MB is the min bus current nd v C nd v C re the bus voltges in Fig.. The lod currents i L nd i L cn be expressed by the lgebric stte vector z, z = [ i L, i L]. (6) The control vector, u, which consists of the filter currents, is given by u = i F = [i F,, i F,b, i F,c ]. (7) The objective of the is to conduct selective hrmonic mitigtion in the power grid. Hrmonic pollution my induce vibrtions nd torque chnges in the genertor shfts, depending on the genertors inductnce. To reduce wer nd ter on the genertors, the hrmonics in the genertor currents (source currents i S nd i S ) should be compensted. A convex stge cost function which ddresses the hrmonic pollution in the genertor currents cn be stted s l (x, z, u) = i SQ i S + i SQ i S + (i F, + i F,b + i F,c ) Q bc (i F, + i F,b + i F,c ) + u Q u u, with digonl weight mtrices given by Q = dig([q, q, q ]), Q = dig([q, q, q ]), Q u = dig([q u, q u, q u ]), Q bc = dig([q bc, q bc, q bc ]). The lst prt in (8) is dded to punish utiliztion of lrge filter currents (mplitudes), which will mke it esier for the to use phse shifting in the serch of the optiml hrmonic mitigtion []. The third prt is dded to void solutions tht relies on zero-sequence filter currents. Becuse punishment of lrge filter currents is of lesser importnce thn minimiztion of the hrmonic pollution nd voiding optiml solutions tht rely on zero-sequence filter currents, the weights should be selected so tht q bc > q, q > q u. Since the lod model in () s used by the does not include the fundmentl components, the objective is to minimize the source current, where perfect hrmonic cncelltion would yield i S = i S = 3. The weighting of the hrmonics from the different buses, q nd q, could be modified to lso include weighting reltive the mount of hrmonics originting from ech lod, i.e. q = k i I L,i q = k I L,i, i (8) (9) () where k nd k re weighting constnts nd i re the hrmonics to be mitigted. In this wy, the could be designed for prioritizing hrmonic mitigtion on the most polluted bus, or ccording to ny other criteri suitble for specific system. However, further discussions or nlysis of such possibilities re outside the scope of this work. IV. IMPLEMENTATION With references to section II nd section III, where the power grid nd the formultion were presented, respectively, the implementtion of the simultion environment will be discussed in this section. Before discussing the closedloop interction between the nd the power grid, the power grid simultion model nd the implementtion re seprtely ddressed. A. Power Grid Implementtion The power grid, which ws presented in Fig. with properties given in Tble I, is implemented in MATLAB/Simulink using the SimPowerSystems librry. For ensuring fst nd robust current reference trcking in simple wy, the APF control is bsed on trditionl phse current hysteresis controller [8], [9]. The hysteresis bnd is in this cse set

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 6 GEN R S L S L S R S GEN Bus Bus L MB C R MB C L LL R LL L LL R LL Lod R R Lod R D C LC R LC = Active Power Filter (APF) Fig. 4. Power grid implementtion in MATLAB/Simulink, with prmeters given in Tble I nd Tble II. to.5 [pu] (reltive the APF s rting), nd the resulting verge switching frequency is pproximtely 7.5kHz. The ctive filter s DC link voltge reference is set to pproximtely 4V (. 3 69V ), nd PI controller is used to control the DC link towrd its reference []. An LCL filter with pssive dmping is inserted between the ctive filter nd bus to suppress switching noise from the ctive filter. To void unrelistic high frequency oscilltions in the system, the prsitic bus cpcitnces re modelled s shunt RC elements plced on ech side of the bus-tie connection. An illustrtion of the power grid implementtion is given in Fig. 4, with the most importnt prmeters listed in Tble I nd Tble II. TABLE II POWER GRID IMPLEMENTATION DETAILS. Prmeter Vlue AF DC link 4V AF DC cpcitor 36µF AF hysteresis frequency 7.5kHz AF hysteresis bnd.5 [pu] (reltive APF rting) Shunt RC R = Ω, C = µf LCL filter L LL = L LL =.4mH, R LL = R LL =.Ω, C LC = 4µF, R D = Ω, R LC = Ω B. Implementtion The formultion ddressed in this work is implemented using the softwre environment ACADO (Automtic Control nd Dynmic Optimiztion) [3], which is higherlevel toolkit thn the CsADi frmework [3] used in [] []. Using ACADO, the formultions re implemented in stndrd form, nd the toolkit builds the using userspecified shooting techniques, e.g. single shooting, multiple shooting or colloction [3], nd solvers such s qpoases [33]. The ACADO toolkit lso provides code-genertion tool for generting efficient -implementtions in C nd MATLAB [34]. The min reson why ACADO is used in this work to relize the is the toolkit s fst prototyping properties nd the code-genertion feture, which cn generte n efficient MATLAB implementtion of the nd mke the integrtion with the power-grid implementtion in MAT- LAB/Simulink less cumbersome. The min detils of the implementtion re listed in Tble III. As indicted in Tble III, the s optimiztion horizon is set to.5ms, which is slightly longer thn hlf period for the TABLE III IMPLEMENTATION DETAILS. Prmeter Vlue Time horizon T.5ms Discretiztion N Discretiztion type Multiple Shooting Integrtor Runge-Kutt 4 (RK4) Hessin Approximtion ( x f( )) Exct Hessin Solver qpoases Number of itertions 5 Stge cost weights q = q =, q u =, q bc = AF current limit i p F = [pu] (of APF rting) fundmentl frequency of 5Hz. Even though the fundmentl period is ms, the is set to run every th ms to chieve fster closed-loop feedbck nd be ble to correct for model/process mismtches. Thus, only the first ms of the s resulting control horizon will be used to provide n optiml APF current reference. The dditionl.5ms re included to keep future chnges in ccount, nd provide n overlp between the control horizons. This is n importnt property for chieving continuous optimlity between ech cycle [9]. The filter currents in the model re kept s free vribles, s ws described in section III-A, giving the full flexibility nd uthority when serching for the optiml hrmonic mitigtion. Hence, the qulity of the hrmonic mitigtion is dependent on the s discretiztion. In ddition, the level of discretiztion hs significnt influence on the s rel-time properties. However, detils regrding reltime implementtion of the on suitble industril control pltforms is outside the scope of this study. In the following, the discretiztion is chosen to be smples for ech.5ms, which gives discretiztion step-size tht llows for resonbly ccurte nlysis up to bout the 37th hrmonics. C. Closing the Control Loop Using the nd the power grid model, closed loop APF control for system-wide hrmonic mitigtion cn be obtined. A block digrm illustrting the simulted system is given in Fig. 5. Instntneous mesurements re used to initilize the s internl model before ech new cycle. The FFT (moving horizon) block is used to extrct mesurements, i.e. mplitudes nd phse ngles, from the lod currents,

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 7 i ( t), v ( t) F dc i ( t), i ( t), i ( t), i ( t), i ( t) G G MB L L t t = t i ( t ), i ( t ), i ( t ) G G MB I ɶ ( t ), I ɶ ( t ), ɶ φ ( t ) L, i L, i L, i τ t, t,..., t, t N [ ] t + T N i ( t F ) [ t t T ] i ( τ), τ, + F [ t t t ] i ( τ), τ,,..., F N i ( τ), τ,,..., F [ t t t ] N Fig. 5. Functionl overview of the closed-loop implementtion in MATLAB/Simulink. originting from the Power Grid block. The output from the FFT block nd the instntneous mesurements re smpled with the sme clock signl s the rest of the system in the Smple & Hold block, which synchronizes the mesurements with the. The output from the block is discrete filter currents (vectors) in the bc frme. These vectors re sent to the Evlution block which ensures tht the filter currents re within the APF s constrints. As filter current references contining zero-sequence components cnnot be trcked by the APF, ny zero-sequence components re removed from the current references before they re provided to the APF s hysteresis controllers. As n lterntive to use the zero-sequence penlty in the s objective function, which ws given s the third term of (8), the Evlution block is equipped with dditionl functionlity tht trnsforms the filter current references to the αβ frme, where the zero-sequence current components re removed. The APF s constrints, which were shown in Fig. 3, re imposed before trnsforming the resulting filter current references bck to bc form. Since zero-sequence current components re equl for ll three-phse [], the elimintion of zero-sequence currents will not destroy the optimlity of the filter current reference clculted by the. TABLE IV CLOSED LOOP IMPLEMENTATION DETAILS. Prmeter Vlue cycle Hz Power grid simultion step-size µs After evluting the filter currents, the Evlution block extrcts subset of the filter currents to be used. The length of the extrcted subset is reltive the s run cycle. The subset of the filter current vector is then sent to the Interpoltion block, which interpoltes the points in the filter current vectors to get the sme discretiztion s used in the simultion environment. The resulting filter current vectors re sent to the Feeder block, which feeds the APF control block with one point (one for ech phse) t the time. The APF control block includes the locl control loops used to operte the APF in the power grid, including phse current hysteresis controllers nd dc-voltge PI controller providing the fundmentl frequency ctive current reference. A globl clock is used in the simultion to synchronize ll time dependent blocks, including the electricl system. The s run cycle nd the simultion step-size re given in Tble IV. V. RESULTS To vlidte the selective hrmonic conditioning using the formultion discussed in section III, two methods for ctive filter current reference genertion re pplied s benchmrk cses: BM: i F = i h L : i F = i h L + ih L, where i h L nd ih L re the selected hrmonic currents from lod nd lod in the bc frme, respectively, to be suppressed by the ctive filter. As cn be seen, BM, which is nmed locl filtering in [] [], only considers the lod connected to the sme bus s the APF. This pproch is considered s stndrd strtegy for hrmonic mitigtion. The second benchmrk cse,, is n d-hoc method for hrmonic mitigtion in two-bus system proposed in [3]. This pproch ttempts to mitigte the hrmonics in the system by using the sum of the hrmonic content from both lods s the current reference for the APF. Thus, the grid impednces re not considered, nd this pproch will only obtin direct compenstion of the lod hrmonics if the bus impednce is zero. It should be noted tht this pproch is not estblished or commonly pplied for APF control in multi-bus systems but it is included s reference cse for providing more fir

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 8 bsis of comprison for the thn wht is chieved with BM. Three different study cses re simulted for the two benchmrk models nd the proposed : ) Bus : 6-pulse rectifier lod. Bus : 6-pulse rectifier lod. The lods hve equl power demnd. ) Bus : -pulse rectifier lod. Bus : 6-pulse rectifier lod. The lod t bus hs higher power demnd thn the lod t bus. 3) Bus : -pulse rectifier lod in prllel to singlephse rectifier lod. Bus : 6-pulse rectifier lod. The ggregted lods t bus hs higher power demnd thn the lod t bus. The configurtion of the power grid used in the simultions ws given in Tble I, nd the hrmonic components to be mitigted re the 5th, 7th, th nd 3th. The 5th nd 7th hrmonic components will be the dominnt hrmonics in lod with 6-pulse rectifier while the th nd 3th hrmonic components re dominnt in lod consisting of -pulse rectifier. The filter current limits for hrmonic current injection re set to [pu] in ll phses (referred to the APF rting), s mentioned in Tble III. For ech cse the resulting THD V vlues verged for ll three phses of ech bus nd key informtion bout the system configurtion re summrized in tbles, nd two figures re presented: The first two plots in the first figure showing the filter output current (mesured fter the LCL filter) nd its reference, while the two lst plots show the resulting genertor currents. All results re plotted only for phse. The second figure shows the frequency spectr of the bus voltges nd genertor currents for phse up to the 5th hrmonic - ll hrmonics given in percentge of the fundmentl component. The results from ech cse re discussed in the following. A. Study Cse The first study cse is scenrio where both lods re equl, both with 6-pulse rectifiers, nd connected to the grid. As shown in Tble V, the power demnds from ech lod re set to 5% of their power rtings. As expected, the THD V s presented in Tble V for BM nd re not equl s BM only considers hrmonic mitigtion for bus while considers both buses. As BM only considers the locl lod connected to bus, hrmonic currents from lod will be unsuppressed nd flow through the grid, from one bus to the other, resulting in higher THD V s thn nd the. is in this cse better thn BM due to its considertion of the selected hrmonics to be suppressed from both lods. However, due to the lck of informtion of the power grid s configurtion, is not ble to mtch the THD V s resulting from the optiml hrmonic mitigtion using the. The reson why cn be seen from the two upper plots in Fig. 6, where the APF current with is slightly phse shifted nd hs slightly lower mplitude compred to the APF current with. This is minly becuse the is explicitly considering the impednces in the system. The resulting APF current from BM hs lower hrmonic mplitudes compred TABLE V STUDY CASE : CONFIGURATION AND RESULTING THD V. BM THD V L.4%.9%.6% THD V L.4%.6%.8% Lod element 6-pulse Lod element 6-pulse Power lod.5 [pu] Power lod.5 [pu] to the nd, since it is only compensting for the hrmonic currents generted by lod. The two lower plots in Fig. 6 show the genertor currents with hrmonic conditioning ccording to ll three methods. As shown, the genertor currents re quite similr for nd the, while they re significntly more distorted with BM. This is s expected, since the BM is not compensting for the hrmonic lod currents t bus. The two upper plots in Fig. 6b show the frequency spectr of the bus voltges while the two lower plots show the frequency spectr of the genertor currents up to the 5th hrmonic component. For the bus voltge, the is better thn BM for lmost ll the hrmonics. Compred to, the gives slightly higher mgnitude for the 5th, 7th nd 3th hrmonic, however, results in lower mgnitudes for ll other dominting hrmonic components. This is due to the fct tht the penlizes filter currents which introduce hrmonics tht is not prt of the hrmonic suppression in the grid. This cn be seen from (8), where ll filter currents corresponding to non-zero genertor hrmonics re penlized. For the bus voltge the seems to result in lower mgnitudes thn BM nd for ll dominting hrmonic components. As evident, BM hs the highest mgnitudes in both voltge spectr, indicting higher THD V thn both the nd. As the lod demnds from both lods re quite smll, the THD I is quite high for the genertor currents, which cn be observed from the two lower plots in Fig. 6b. B. Study Cse The second study cse is scenrio where lod hs -pulse diode rectifier nd lod hs 6-pulse rectifier. The power demnd from lod is set higher thn the power demnd from lod, s indicted in Tble VI, with power demnds of 8% nd 3% of rted lod, respectively. The THD V s presented in Tble VI show tht lso in this cse the is providing superior performnce compred to BM, since the hrmonic components in lod hve significnt impct on the bus voltges. However, the is ble to improve the hrmonic mitigtion beyond wht is chievble with, further decresing the THD V s t both buses. It cn be noticed tht in this cse BM violtes the ABS clssifiction requirement of THD V below 5%, nd the individul hrmonic limits re lso exceeded for the th nd the 3th hrmonic voltge components t bus, see Fig. 7b. As in the previous cse, the filter current resulting from BM devites from nd the due to the locl filtering pproch, which cn be seen from Fig. 7. The difference between the filter currents from nd the is lso in

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 9 i AF ref i AF i G i G -.38.385.39.395.4 -.38.385.39.395.4. -..38.385.39.395.4. -..38.385.39.395.4 () Filter nd genertor currents. Fig. 6. Study cse : Two lods with 6-pulse rectifiers nd equl power demnd, one lod connected to ech bus. BM BM BM BM v, [%] of fund. v, [%] of fund., [%] of fund. i G, [%] of fund. i G BM v v v 5 5 5 3 35 4 45 5 BM v v v 5 5 5 3 35 4 45 5 3 BM i G i G i G 5 5 5 3 35 4 45 5 3 BM i G i G i G 5 5 5 3 35 4 45 5 (b) Lod voltge nd genertor current frequency spectr. i AF ref i AF i G i G -.38.385.39.395.4 -.38.385.39.395.4 -.38.385.39.395.4 -.38.385.39.395.4 () Filter nd genertor currents. BM BM BM BM v, [%] of fund. v, [%] of fund., [%] of fund. i G, [%] of fund. i G 4 BM v v v 5 5 5 3 35 4 45 5 4 BM v v v 5 5 5 3 35 4 45 5 3 BM i G i G i G 5 5 5 3 35 4 45 5 3 BM i G i G i G 5 5 5 3 35 4 45 5 (b) Lod voltge nd genertor current frequency spectr. Fig. 7. Study cse : One lod with -pulse rectifier connected to bus nd one lod with 6-pulse rectifier connected to bus. The power demnd from lod is higher thn the power demnd from lod. this cse given by smll phse shift nd smll difference in mplitude. From the two upper plots in Fig. 7b it is seen tht the hs lower mgnitudes for ll dominting hrmonic components in the bus voltge compred to, except the th nd 37th hrmonic components. Hence, the compromises nd scrifies the th hrmonic component in the bus voltge to decrese the THD V in bus beyond the bilities of. This is seen in the spectr for the bus voltge, where the mgnitude of lmost ll dominting hrmonic components re lower for the compred to. The spectr for the genertor currents in the lower two plots in Fig. 7b show some of the sme behvior, resulting in lower THD I s for both genertor currents when using the for hrmonic mitigtion compred to BM nd.

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS i AF ref i AF i G i G -.38.385.39.395.4 -.38.385.39.395.4 -.38.385.39.395.4 -.38.385.39.395.4 () Filter nd genertor currents. BM BM BM BM v, [%] of fund. v, [%] of fund., [%] of fund. i G, [%] of fund. i G 4 BM v v v 5 5 5 3 35 4 45 5 4 BM v v v 5 5 5 3 35 4 45 5 4 BM i G i G i G 5 5 5 3 35 4 45 5 4 BM i G i G i G 5 5 5 3 35 4 45 5 (b) Lod voltge nd genertor current frequency spectr. Fig. 8. Study cse 3: A three-phse lod with -pulse rectifier nd single-phse lod with -pulse rectifier connected to bus. One three-phse lod with 6-pulse rectifier connected to bus. The ggregted power demnd from lod is higher thn the power demnd from lod. TABLE VI STUDY CASE : CONFIGURATION AND RESULTING THD V. BM THD V L.8% 5.3% 3.% THD V L.8% 4.5% 3.4% Lod element -pulse Lod element 6-pulse Power lod.8 [pu] Power lod.3 [pu] TABLE VII STUDY CASE 3: CONFIGURATION AND RESULTING THD V. BM THD V L 3.9% 6.% 4.% THD V L 3.5% 5.% 4.% Lod element -pulse + single-phse -pulse Lod element 6-pulse Power lod.8 [pu] +. [pu] Power lod.5 [pu] C. Study Cse 3 The third study cse illustrtes the performnce of the three different hrmonic mitigtion pproches with n dditionl ggregtion of single-phse lods on bus, resulting in unblnced conditions. The power demnds from bus re 8% for the three-phse -pulse lod nd in totl % for ggregted single-phse diode rectifier lods (phse nd b). This results in lod current unblnce of bout 6% on bus. The power demnd from the three-phse 6-pulse lod in bus is 5%. The resulting THD V s for the three different hrmonic mitigtion methods re given in Tble VII, nd lso in this cse there re cler distinctions between the methods. As in the previous study cses the conducts the best hrmonic mitigtion while BM conducts the worst. Evidently, BM violtes lso in this cse the clssifiction requirement of THD V below 5%. Compred to the previous study cses, the difference between the APF reference currents generted by the three methods re now esier to recognize, s illustrted in the two upper plots in Fig. 8. Differences between the three APF reference currents in both phse ngles nd mplitudes re esily recognized from the plot, indicting different results from the hrmonic mitigtion, which is supported by the resulting THD V s in Tble VII. The frequency spectr in Fig. 8b show the presence of zerosequence hrmonics, e.g. 3rd nd 9th, which is result of the unblnced conditions cused by the single-phse diode rectifier lod connected to bus. From the spectr of bus voltge, the results in lower mgnitudes compred to for ll dominting hrmonic components, except for the 5th nd th component. Also from the spectr of bus voltge, the hs lower dominting hrmonic mgnitudes thn, except for the 5th hrmonic component. From both voltge spectr it is esy to see tht BM results in the worst hrmonic mitigtion, where the th nd 3th components re mjor contributors to the incresed THD V compred to the nd. Also in this cse the 3% single hrmonic voltge limit set by some of the clssifiction entities is violted by BM. The results in this section indicte tht the use of cn provide better system-level hrmonic mitigtion thn both BM nd. The results lso demonstrte tht, which is used in this work s reference for comprison, is not

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS n optiml solution, especilly when there is non-negligible impednces between the buses in the system nd when the APF current sturtion is reched. Furthermore, the results demonstrte tht the cn chieve better utiliztion of n APF within its current limittions. VI. CONCLUSION An pproch for system-wide hrmonic mitigtion using Model Predictive Control () to generte the current reference for n ctive power filter (APF) hs been presented nd implemented in this pper. Three cse-studies of non-liner lod conditions in ship power system with two seprte buses hve been implemented in MATLAB/Simulink model, nd the compenstion performnce obtined with the bsed control is compred to two control techniques bsed on conventionl filtering strtegies. The THD V s obtined with system-oriented on-line optimiztion with the re the lowest mong the three cses investigted. The presented results highlight the dvntges of the over conventionl pproches; nmely its higher degree of freedom when dynmiclly serching the optiml vlues by treting ll selected hrmonics t once without restricting the APF current references by direct mthemticl reltion to the lod currents, nd the bility to optimize within APF current limits (constrints). In prticulr, the hs dvntges when the vilble current from the APF is constrined by the current rting of the converter. Although the results presented in this pper re obtined in system with only two seprte buses, the lgorithm cn esily be extended to ccount for lrger system configurtion. Thus, the use of the or nother forml optimiztion technique for online system-wide hrmonic mitigtion cn be clerly beneficil compred to conventionl pproches for generting APF current references. This will especilly be the cse when the complexity of the electricl grid increses, nd when the APF opertion is constrined by its current rtings. The pproch presented in this mnuscript cn lso be pplied to other APF topologies, or it cn be included in ctive rectifiers or inverters with multi-functionl control cpbilities. REFERENCES [] H. Akgi, E. Wtnbe, nd M. Aredes, Instntneous Power Theory nd Applictions to Power Conditioning. Wiley, 7. [] M. Ptel, Shipbord Electricl Power Systems. Tylor & Frncis,. [3] I. Evns, A. Hoevenrs, nd P. Eng, Meeting hrmonic limits on mrine vessels, in Electric Ship Technologies Symposium, 7. ESTS 7. IEEE, My 7, pp. 5. [4] S. Gleves nd G. Perl, Electric propulsion, it s time to get onbord, Mritime Reporter nd Engineering News, 9. [5] R. P. Strtford, Hrmonic Pollution on Power Systems - A Chnge in Philosophy, IEEE Trnsctions on Industry Applictions, vol. IA-6, no. 5, pp. 67 63, September/October 98. [6] S. M. Peern nd C. W. P. Cscdden, Appliction, Design, nd Specifiction of Hrmonic Filters for Vrible Frequency Drives, IEEE Trnsctions on Industry Applictions, vol. 3, no. 4, pp. 84 847, July/August 995. [7] C.-J. Wu, J.-C. Ching, S.-S. Yen, C.-J. Lio, J.-S. Yng, nd T.-Y. Guo, Investigtion nd Mitigtion of Hrmonic Amplifiction Problems Cused by Single-tuned Filters, IEEE Trnsctions on Power Delivery, vol. 3, no. 3, pp. 8 86, July 998. [8] P. Cortés, M. P. Kzmierkowski, R. M. Kennel, D. E. Quevedo, nd J. Rodríguez, Predictive control in power electronics nd drives, IEEE Trnsctions on Industril Electronics, vol. 55, no., pp. 43 434, December 8. [9] T. Geyer, G. Ppfotiou, nd M. Morri, Model predictive control in power electronics: A hybrid systems pproch, in 44th IEEE Conference on Decision nd Control 5, nd 5 Europen Control Conference. CDC-ECC 5., Dec 5, pp. 566 56. [] E. Skjong, M. Molins, nd T. A. Johnsen, Optimized current reference genertion for system-level hrmonic mitigtion in diesel-electric ship using non-liner model predictive control, in IEEE ICIT 5 Interntionl Conference on Industril Technology, Mrch 5. [] E. Skjong, M. Molins, T. A. Johnsen, nd R. Volden, Shping the current wveform of n ctive filter for optimized system level hrmonic conditioning, in VEHITS 5 Interntionl Conference on Vehicle Technology nd Intelligent Trnsport Systems, My 5. [] E. Skjong, M. Ocho-Gimenez, M. Molins, nd T. A. Johnsen, Mngement of hrmonic propgtion in mrine vessel by use of optimiztion, in 5 IEEE Trnsporttion Electrifiction Conference nd Expo 5 (ITEC 5), Mrch 5. [3] A. Rygg Ardl, E. Skjong, nd M. Molins, Hndling system hrmonic propgtion in diesel-electric ship with n ctive filter, in ESARS 5 Conference on Electricl Systems for Aircrft, Rilwy, Ship Propulsion nd Rod Vehicles, Mrch 5. [4] DNVGL-OS-D: Offshore stndrds, Electricl Instlltions, July 5. [5] DNV-RU-SHIP-Pt4Ch8: Prt 4 Systems nd components, Chpter 8 Electricl instlltions, October 5. [6] Lloyd s Register: Generl Informtion for the Rules nd Regultions for the Clssifiction of Ships, July 4. [7] ABS: Guidnce Notes on Control of Hrmonics in Electricl Power Systems, My 6. [8] Bureu Verits: Rules for the Clssifiction of Steel Ships: Prt C - Mchinery, Electricity, Automtion nd Fire Protection, July 4. [9] J. Rwlings nd D. Myne, Model Predictive Control: Theory nd Design. Nob Hill Pub., 9. [] T. Johnsen, Towrd dependble embedded model predictive control, IEEE Systems Journl, vol. in press, no. 99, pp., 4. [] K. Ling, S. Yue, nd J. Mciejowski, A FPGA implementtion of model predictive control, in Americn Control Conference, 6, June 6, pp. 6 pp.. [] F. Xu, H. Chen, W. Jin, nd Y. Xu, FPGA implementtion of nonliner model predictive control, in The 6th Chinese Control nd Decision Conference (4 CCDC),, My 4, pp. 8 3. [3] G. Frison, D. Kwme Minde Kufolor, L. Imslnd, nd J. Jørgensen, Efficient implementtion of solvers for liner model predictive control on embedded devices, in Proceedings of 4 IEEE Interntionl Conference on Control Applictions (CCA), 4, pp. 954 959. [4] P. Lezn, R. Aguiler, nd D. Quevedo, Model predictive control of n symmetric flying cpcitor converter, IEEE Trnsctions on Industril Electronics, vol. 56, no. 6, pp. 839 846, June 9. [5] A. Grces, M. Molins, nd P. Rodriguez, A generlized compenstion theory for ctive filters bsed on mthemticl optimiztion in ABC frme, Electric Power Systems Reserch, Elsevier Journl, vol. 9, no., pp.,. [6] N.-Q. Dinh nd J. Arrilg, A Slient-Pole Genertor Model for Hrmonic Anlysis, IEEE Trnsctions on Power Systems, vol. 6, no. 4, pp. 69 65, November. [7] J. A. Suul, Control of Grid Integrted Voltge Source Converters under Unblnced Conditions, PhD thesis, Norwegin University of Science nd Technology, Deprtment of Electricl Power Engineering, Mrch. [8] D. M. Brod nd A. W. Novotny, Current Control of VSI-PWM Inverters, IEEE Trnsctions on Industry Applictions, vol. IA-, no. 4, pp. 56 57, My/June 985. [9] M. P. Kźmierkowski nd L. Mlesni, Current Control Techniques for Three-Phse Voltge Source PWM Converters: A Survey, IEEE Trnsctions on Industril Electronics, vol. 45, no. 5, pp. 69 73, October 998. [3] B. Housk, H. Ferreu, nd M. Diehl, ACADO Toolkit An Open Source Frmework for Automtic Control nd Dynmic Optimiztion, Optiml Control Applictions nd Methods, vol. 3, no. 3, pp. 98 3,. [3] J. Andersson, A Generl-Purpose Softwre Frmework for Dynmic Optimiztion, PhD thesis, Arenberg Doctorl School, KU Leuven, Deprtment of Electricl Engineering (ESAT/SCD) nd Optimiztion in

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Engineering Center, Ksteelprk Arenberg, 3-Heverlee, Belgium, October 3. [3] L. Biegler, Nonliner Progrmming: Concepts, Algorithms, nd Applictions to Chemicl Processes. Society for Industril nd Applied Mthemtics (SIAM, 36 Mrket Street, Floor 6, Phildelphi, PA 94),. [33] H. Ferreu, C. Kirches, A. Potschk, H. Bock, nd M. Diehl, qpoases: A prmetric ctive-set lgorithm for qudrtic progrmming, Mthemticl Progrmming Computtion, vol. 6, no. 4, pp. 37 363, 4. [34] B. Housk, H. Ferreu, nd M. Diehl, An Auto-Generted Rel-Time Itertion Algorithm for Nonliner in the Microsecond Rnge, Automtic, vol. 47, no., pp. 79 85,. Atle Rygg received his MSc from the Deprtment of Electricl Power Engineering t the Norwegin University of Science nd Technology (NTNU), Trondheim, Norwy, in. From August to December 4, he ws with SINTEF Energy Reserch, Trondheim, Norwy. He is currently employed s PhD-cndidte with the Deprtment of Engineering Cybernetics t NTNU. His min field of reserch is rel-time monitoring of stbility in power electronic dominted systems. This includes detection of hrmonic resonnces s well s interctions between different subsystems. Espen Skjong received his MSc degree in Engineering Cybernetics t the Norwegin University of Science nd Technology (NTNU), Trondheim, Norwy, in 4, specilizing in model predictive control () for utonomous control of UAVs. He is currently employed in Ulstein Power & Control AS (A lesund, Norwy) s n industril PhD cndidte. His reserch topic is optimiztion in power mngement systems for mrine vessels. His industril PhD fellowship is within the Center of Excellence on Autonomous Mrine Opertions nd Systems (AMOS) t NTNU. Tor Arne Johnsen (M 98, SM ) received the MSc degree in 989 nd the PhD degree in 994, both in electricl nd computer engineering, from the Norwegin University of Science nd Technology (NTNU), Trondheim, Norwy. From 995 to 997, he worked t SINTEF s resercher before he ws ppointed Associted Professor t NTNU in Trondheim in 997 nd Professor in. He hs published severl hundred rticles in the res of control, estimtion nd optimiztion with pplictions in the mrine, utomotive, biomedicl nd process industries. In Johnsen co-founded the compny Mrine Cybernetics AS where he ws Vice President until 8. Prof. Johnsen received the 6 Arch T. Colwell Merit Awrd of the SAE, nd is currently principl resercher within the Center of Excellence on Autonomous Mrine Opertions nd Systems (AMOS) nd director of the Unmnned Aeril Vehicle Lbortory t NTNU. Jon Are Wold Suul (M ) received the MSc nd PhD degrees from the Deprtment of Electric Power Engineering t the Norwegin University of Science nd Technology (NTNU), Trondheim, Norwy, in 6 nd, respectively. From 6 to 7, he ws with SINTEF Energy Reserch, Trondheim, where he ws working with simultion of power electronic converters nd mrine propulsion systems, until strting his PhD studies. In 8, he ws guest PhD student for two months with the Energy Technology Reserch Institute of the Ntionl Institute of Advnced Industril Science nd Technology (AIST), Tsukub, Jpn. He ws lso visiting PhD student for two months with the Reserch Center on Renewble Electricl Energy Systems, within the Deprtment of Electricl Engineering, Technicl University of Ctloni (UPC), Terrss, Spin, during. Since, he hs resumed prt-time position s Reserch Scientist t SINTEF Energy Reserch while lso working s prt-time postdoctorl resercher t the Deprtment of Electric Power Engineering of NTNU. His reserch interests re minly relted to control of power electronic converters in power systems nd for renewble energy pplictions. Mrt Molins (M 94) received the Diplom degree in electromechnicl engineering from the Ntionl University of Asuncion, Asuncion, Prguy, in 99; the Mster of Engineering degree from Ryukyu University, Jpn, in 997; nd the Doctor of Engineering degree from the Tokyo Institute of Technology, Tokyo, Jpn, in. She ws Guest Resercher with the University of Pdov, Pdov, Itly, during 998. From 4 to 7, she ws Postdoctorl Resercher with the Norwegin University of Science nd Technology (NTNU) nd from 8-4 she hs been professor t the Deprtment of Electric Power Engineering t the sme university. From 8 to 9, she ws Jpn Society for the Promotion of Science (JSPS) Reserch Fellow with the Energy Technology Reserch Institute, Ntionl Institute of Advnced Industril Science nd Technology, Tsukub, Jpn. In 4, she ws Visiting Professor t Columbi University nd Invited Fellow by the Kingdom of Bhutn working with renewble energy microgrids for developing regions. She is currently Professor t the Deprtment of Engineering Cybernetics, NTNU. Her reserch interests include stbility of power electronics systems, hrmonics, oscilltory phenomen, nd non-sttionry signls from the humn nd the mchine. Dr. Molins hs been n AdCom Member of the IEEE Power Electronics Society. She is Associte Editor nd Reviewer for IEEE Trnsctions on Power Electronics nd PELS Letters.