A Method for the Realization of an Interruption Generator Based on Voltage Source Converters

Transcription

1 energies Artile A Method for Realization an Interruption Generator Based on Voltage Soure Converters Junhui i, *, Tianyang Zhang, ei Qi 2 Gangui Yan Shool Eletrial Engineering, Norast Eletri Power University, Jilin 3202, China; wonder35260@63.om (T.Z.); yangg@neepu.edu.n (G.Y.) 2 iaoning Aademy Safety Siene, Shenyang 079, China; qileinedu@26.om * Correspondene: lijunhui@neepu.edu.n; Tel.: Reeived: 9 August 207; Aepted: Otober 207; Published: 9 Otober 207 Abstrat: In this paper we desribed struture working priniple an interruption generator based on soure onverters (VSCs). main iruit parameters VSCs are determined aording to target power transfer apability, harmoni suppression, dynami response apability. A state feedbak linearization method in nonlinear differential geometry ory used for dq axis urrent deoupling, based on mamatial model used in dq oordinate system VSCs. diret urrent ontrol strategy adopted to ahieve independent regulation ative power reative power. proportional integral (PI) link used to optimize dynami performane ontroller, PI parameters were adjusted. Disturbane waves were generated by regular sampling method. PSCAD/EMTDC simulation results physial prototype experiments showed that devie ould generate various disturbane waveforms steadily, had good dynami steady-state performane. Keywords: power quality; interruption; soure onverter; power ontrol. Introdution With rapid development tehnology, load struture power system has hanged a lot in reent years. A large number non-linear loads have resulted in power quality problems suh as flutuations, distortions, unbalaned onnetions to power system [ 4]. With improvement China s industrial automation, preise automati equipment used is very sensitive to power quality, power quality problems might ause equipment stoppages. Problems power quality monitoring, analysis, management have thus beome important issues in eletri power supply utilization [5]. In view this, a power interruption generator an be used to provide disturbane signal soures to test orretness power quality analysis ory, or examine power quality ontrol devies. In addition, a power interruption generator an also be used to test operation harateristis eletri power equipment under disturbane onditions. Researh on se interruption generators has been foused on trying to ahieve flexibility, regulation, high preision [6]. At present, most power quality interruption generators are designed based on power eletronis [7]. Shanxi Eletri Power Researh Institute has ome up with a power quality interruption devie that an simulate urrent disturbane a power system. devie has harateristis good waveform, large power, high grade, an waveforms sag, flutuation fliker, harmoni, urrent harmoni, unbalaned 3-phase urrent [8]. A series hybrid power quality interruption generator developed by State Key aboratory Alternate Eletrial Power System with Renewable Energy Soures North China Eletrial University, it based on arrier phase shifting sinusoidal pulse width modulation [9]. In [0], a bak to bak 2 H bridge Energies 207, 0, 642; doi:0.3390/en

2 Energies 207, 0, Energies 207, 0, shifting sinusoidal pulse width modulation [9]. In [0], a bak to bak 2 H bridge is used in main iruit struture a multi-level asade is used in soure inverter. Both se devies have is used advantages in main flexibility iruit struture diversity. a However, multi-levelir asade strutures is usedare in omplex soure []. In inverter. [2], it proposed Both sea devies new design have power advantages eletroni flexibility interruption diversity. generator. However, It adopts irunontrollable strutures are retifier omplex []. booster In [2], iruit. it proposed It an only a newsimulate design power swell eletroni sag, but its interruption duration, depth, generator. startstop It adopts phase unontrollable type an retifier all be adjusted booster smoothly. iruit. It an only simulate swell sag, but its duration, method depth, start-stop using phase phase shift type iruit an all to be regulate adjusted transformer smoothly. taps to produe disturbanes has been method used in many using or phase devies. se iruit devies to regulate are less transformer expensive taps to stable produe in operation, disturbanes but have has been potential used in problems many or suh devies. as inonvenient se devies settings, are less a single expensive disturbane stable wave, in operation, so on. A but devie have potential developed problems by University suh as inonvenient Arizona provides settings, a single disturbane disturbane signal soure wave, by means so on. Aa devie iruit swith developed by transformer University tap ontrolled Arizona by provides a simulated phase-shift disturbaneiruit signal[3]; soure however, by means devie a iruit an only swith realize transformer tap sag ontrolled waveform by a simulated is unable to phase-shift adjust ontinuously. iruit however, In [4], a sheme devie based an only interleaved realize paralleled sag H-bridges waveformtopology is unable proposed. to adjustit ontinuously. presented a ontrol In [4], method a shemeomposed based on interleaved DC paralleled feed forward H-bridges ontrol topology a phase proposed. shifting PWM It presented method. a ontrol sheme method redues omposed load regulation DC feed forward large apaity ontrol a phase interruption shiftinggenerator; PWM method. however, sheme design redues load impedane regulation parameters large apaity is inonvenient for interruption small apaity generator; one. however, synhronous designompensator is onvenient impedane in parameters realizing power is inonvenient disturbanes, but small its sope apaity appliation one. is synhronous limited by its weight volume. is onvenient in realizing power disturbanes, but its sope appliation is limited by its weight volume. In this paper, we presented idea applying soure onverters (VSCs) to interruption In this paper, generator we to presented deal with ir ideashortomings. applying Compared soure with onverters urrent (VSCs) devies, to interruption generator based to deal on VSCs with ir has a simpler main iruit, Compared but it still withhas good urrent dynami devies, steady-state interruption performane generator based it an ongenerate VSCs has various a simpler disturbane main iruit, but waveforms it still hasompared good dynami with devies steady-state that performane use phase shift it an iruit generate to regulate varioustransformer disturbanetaps. waveforms rest this ompared paper is with organized devies as follows: that use Setion phase 2 gives shift a mamatial iruit to regulate model interruption taps. generator rest thisbased paperon is VSCs organized in an as ab follows: oordinate Setion system. 2 gives ainfluene mamatial on model system interruption seletion priniple generator based main on VSCs iruit inparameters an ab oordinate are also system. analyzed. Setion influene 3 disusses on system ontrol objetives; seletion priniple grid onverter main provides iruit parameters a stable are DC also analyzed. while Setion load 3 disusses onverter ontrol provides objetives; disturbane grid waveform onverter provides aording ato stable speified DC modulation while wave. load power onverter deoupling provides ontroller disturbane designed waveform based on aording nonlinear to feedbak speified linearization modulation wave. ory, power deoupling dynami performane ontroller is designed ontroller based is optimized nonlinear feedbak based on linearization lassial ory, ontrol ory. dynami In Setion performane 4, dynami ontroller is steady-state optimized performane based on lassial ontroller ory. is verified In Setion by 4, PSCAD/EMTDC dynami (Version steady-state 4.2.0, performane Manitoba HVDC Researh ontrollercentre, is verified Winnipeg, by PSCAD/EMTDC MB, Canada) (Version simulation 4.2.0, results. Manitoba n, HVDC in Setion Researh 5, a physial Centre, Winnipeg, prototype is MB, designed Canada) to simulation prove simulation results. n, results in in Setion Setion 5, 4. a physial Finally, Setion prototype 6 presents is designed our onlusions. to prove simulation results in Setion 4. Finally, Setion 6 presents our onlusions. 2. Struture Main Ciruit in VSCs 2. Struture Main Ciruit in VSCs struture diagram an interruption generator based on VSC is given in. struture diagram an interruption generator based on VSC is given in. ontrolled retifier transforms AC into a high preision DC. inverter is used ontrolled retifier transforms AC into a high preision DC. inverter is to generate a speified disturbane for load. used to generate a speified disturbane for load. Three-phase AC input Retifier Inverter Filter oad Controller Controller 2 Disturbane instrution. Struture diagram proposed system.. Struture diagram proposed system.

3 Energies Energies 207, 207, 0, 642 0, Mamatial Models in an ab Coordinate System 2.. Mamatial Models in an ab Coordinate System To simplify To simplify study, study, we wemade madetwo assumptions: assumptions: () () A 3-phase A 3-phase infinite infinite power power supply supplyis ial ideal symmetrial. symmetrial. (2) (2) swith swith is ideal, is ideal, its its swithing-delay swithing-delay is is ignored. ignored. single single topology topology VSC is is shown shown in in 2. E2. sa Esa,, E Esb, sb, Es E s are are AC AC s; s; i a, i b, ia, ib, i are i AC are AC input input urrents; Ua, U a Ub,, U b, U U are AC s s onverter; onverter; i is i is load load urrent; urrent; R is R is equivalent resistane; is AC filter reatane; C is C is DC DC apaitor. apaitor. Esa R ia g g3 g5 Ua id Esb R ib Ub Ud + _ C Es R i U AC system g4 g6 g Struture Struture diagram diagram topology. topology. mamatial model onverter an be expressed as follows: mamatial model onverter an be expressed as follows: dia di a = sa a dt = E dt sa Ri a U a di b dt di= E sb Ri b U b b = sb Rib b di () dt dt = E s Ri U C du d () di dt = i s i = Es Ri U dt 2.2. Design AC Side Indutane du d C = is i Aording to Equation (), equivalent dt iruit AC is shown in 3. Sine filter indutane has a restraining effet on high frequeny urrent omponent, fundamental omponent frequeny urrent is only omponent that should be onred. In addition, filter 2.2. indutane Design also AC stores Side Indutane reative power, whih flows in 3-phase iruits. When apaity devie Aording is fixed, to Equation a large reative (), power equivalent will redue iruit transmission AC apability is shown in ative 3. power, Sine filter thus indutane reduing has effiieny a restraining effet devie. on As a high result, frequeny re is an urrent upper limit omponent, on seletion fundamental indutane. Meanwhile, filter indutor also plays a role in restraining sudden hange in urrent. omponent frequeny urrent is only omponent that should be onred. In addition, filter refore, re is also a lower limit on seletion indutane [5,6]. indutane also stores reative power, whih flows in 3-phase iruits. When apaity devie is fixed, a large reative power will redue transmission apability ative power, thus reduing effiieny devie. As a result, re is an upper limit on seletion indutane. Meanwhile, filter indutor also plays a role in restraining sudden hange in urrent. refore, re is also a lower limit on seletion indutane [5,6].

4 Energies 207, 0, Energies 207, 0, Esa R ia Ua Esb R ib Ub Es R i U 3. Struture diagram AC equivalent iruit. 3. Struture diagram AC equivalent iruit. Three indies are defined as follows for limits indutane: Three indies are defined as follows for limits indutane: () steady-state ative transmission apaity index: indutane should not be greater () than steady-state 20% AC ative rated transmission. apaity index: indutane should not be greater (2) Transient than 20% operation ACperformane: rated. urrent variation in a ontrol yle should be less than 0% (2) Transient AC operation rated urrent. performane: It reflets urrent transient variation ondition in aonstraints. ontrol yle should be less than 0% (3) Filtering ACperformane: rated urrent. It reflets total harmoni transient distortion ondition urrent onstraints. should be less than or equal to (3) 5%. Filtering performane: total harmoni distortion urrent should be less than or equal to 5%. Aording to above indies, whih are related to devie apaity, AC, DC apaitor, ontrol yle, or or parameters [7,8], [7,8], expression expression indutane indutane seletion seletion is shown is shown in Equation in Equation (2): (2): (2u 2 (2 d + 3E ud + 3 sa )E Esa ) T EsaT s os ϕ s osϕ 3 3E2 sa os ϕ Esa osϕ (2) 0.4P 0ωP (2) 0. 4P 0ω P 2.3. Design DC Side Capaitor 2.3. AsDesign shown indc Equation Side Capaitor (), inrease DC apaitor C an redue flutuation. Meanwhile, apaitor annot be too large onring size ost devie. As shown in Equation (), inrease DC apaitor C an redue main reason for ausing DC flutuation is differene instantaneous power flutuation. Meanwhile, apaitor annot be too large onring size ost devie. between retifier inverter [9]. During devie testing, maximum power hange ours main reason for ausing DC flutuation is differene instantaneous power at moment loading, when power DC apaitor suddenly hanges from 0 to P. between retifier inverter [9]. During devie testing, maximum power hange ours However, when devie is applied to power quality problems in a lab, re may be bakward power at moment loading, when power DC apaitor suddenly hanges from 0 to P. flow, that is to say, operation performane inverter hanges from absorbed power P to However, when devie is applied to power quality problems in a lab, re may be bakward feedbak power P, flutuation DC is most severe at this time [20,2]. power flow, that is to say, operation performane inverter hanges from absorbed DC flutuation rate is defined as 0% in a ontrol yle. Conring harateristi power P to feedbak power P, flutuation DC is most severe at this apaitor element, expression apaitane C is as follows: time [20,2]. DC flutuation rate is defined as 0% in a ontrol yle. Conring harateristi apaitor element, expression apaitane C is as follows: C 20P maxt s (3) u d 20 u Pmax dmax Ts C (3) 2.4. Constraint Disturbane oad u dδ u d max hoie disturbane load is limited when DC is stable [22]. If load 2.4. is very Constraint small, it will Disturbane inevitably oad lead to a larger load urrent power for load dem will be greater. hoie When power disturbane loadis exeeds limited when apaity DC devie, is stable DC [22]. If load will is novery longer small, be stable, it will inevitably lead drop to a will larger our. load In urrent addition, power urrentfor should load be less dem thanwill be maximum greater. allowable When power urrent load power exeeds devie, orwise apaity devie devie, will bedc burned out [23 25]. will refore, no longer be stable, minimum load is subjet drop to will our. two onstraints In addition, above, as urrent shownshould in Equation be less (4). than S max is maximum apaityallowable AC power, urrent I max is power maximum devie, orwise urrent through devie swithing will be burned devie. out [23 25]. refore, minimum load is subjet to two onstraints above, as shown in Equation (4). Smax is apaity AC power, Imax is Z > max( maximum u2 dre f urrent, u dre f ) through swithing devie. (4) S max I max

5 Energies 207, 0, Design Controller Devie 3.. Dynami Mamatial Model in dq Coordinate System For a 3-phase power supply, d axis is oinided with spae vetor, d axis is π/2 ahead q axis. E sd = U m, E sq = 0. Kirhhf equations power equations retifier in rotating dq oordinate system are shown in Equations (5) (6): di d dt di q dt C du d dt = E sd E sq 0 { R ω m d ω R m q m d m q 0 i d i q u d 0 0 i (5) P = E sd i d Q = E sd i q (6) funtion retifier is to stabilize DC, that is to say, essene retifier is to ontrol power supply to injet ative power into DC apaitor. design power ontroller is based on Equation (6). ative reative power AC power supply are respetively proportional to urrent d axis q axis. Based on above analysis, diret urrent ontrol strategy is determined [26] Deoupling Method Based on State Feedbak inearization Based on Equation (5), re is a oupling between i d i q. That is to say, re is a oupling between P Q, whih brings great inonveniene to design ontroller. nonlinear state feedbak linearization ory is a powerful tool for solving this kind problem. This ory makes non-linear systems linearized by non-linear oordinate transformation over a wide range. This enables multiple input system to be linearized deoupled at same time [27,28]. state equations equations deoupled ontrollable linear system by oordinate transformation state feedbak are shown in Equation (7): [ dz dt dz 2 dt [ Y Y 2 ] [ z ] [ υ ] = k + k z 2 υ ] [ ] 2 (7) z = z 2 state variables z z 2 are equal to i d i q, respetively. Aording to optimal ontrol ory, relations between new input variables, υ υ 2, state variables an be represented as: [ ] ( )[ ] υ υ 2 = 0 0 Based on Equations (7) (8), a set variables i d i q orresponds to a set referene values i dref i qref dq axis urrents. Thus, diret urrent ontrol is ahieved. power swith funtion, whih is applied in power swith by sinusoidal pulse width modulation (SPWM) is dedued as in Equation (9): ( m d m q ) ( = u d z z 2 Rx + ωx 2 z + E sd ωx Rx 2 z ) (8) (9)

6 funtion, whih is applied in power swith by sinusoidal pulse width modulation (SPWM) is dedued as in Equation (9): m d 2 Rx + ωx z + Esd = mq u (9) d ωx Rx2 z Energies 207, 0, Optimization Controller Dynami Performane 3.3. Optimization Controller Dynami Performane losed-loop transfer funtion urrent shown in Equation (0) is derived from aplae transform losed-loop Equation transfer(7): funtion urrent shown in Equation (0) is derived from aplae transform Equation (7): id () s k Φ Φ id () s id (s) = i d(s) = f (s) s+k idref () s s+ k Φ iq (s) i q(s) i qre f (s) = s+k k (0) (0) iq () s k Φ iq () s = = iqref () s s+ k Aording to Equations (7) (0), losed-loop transfer funtion urrent is a first-order inertial element. Aording to lassial Equations ontrol (7) ory (0), shows losed-loop that transfer first-order funtion inertial urrent element is a provides first-order good dynami inertial properties element. lassial re isontrol no overshoot, ory shows statithat error or first-order osillation inertial element system. provides stability good system dynami is determined properties byre proportionality is no overshoot, stati oeffiient error or k. osillation Aording in to system. Routh riterion, stability if k > 0, system is determined by proportionality oeffiient k. Aording to Routh riterion, if k > system is stable, that is to say, losed-loop poles should be in left half plane s domain. 0, system is stable, that is to say, losed-loop poles should be in left half plane s And response speed an be regulated by adjusting k. domain. And response speed an be regulated by adjusting k. devie devie is ontrolled is ontrolled by by digital digital signal signal proessors. proessors. In In digital digital ontrol ontrol systems, systems, sampling sampling delay delay swithing swithing delay delay are are related to ontrol yle yle T. T. sampling sampling delay delay time is time equal isto equal to ontrol yle. And swith has two states: turn-on turn-f turn-f in one in one ontrol ontrol yle, yle, so so swithing swithing delay delay yle yle is half is half ontrol yle. dynami blok diagram urrent urrent loop loop is is shown shown in in i dref + - Ts+ k 0.5Ts+ s i d Dynami blok diagram urrent loop. loop. frequeny eletroni power swith is high. s 2 term oeffiient is muh smaller than s frequeny term oeffiient after eletroni ombination power swith is delay high. link. refore, s 2 term oeffiient s 2 term is an muh be negleted, smaller than s term oeffiient open-loop after transfer funtion ombination is expressed as: delay link. refore, s 2 term an be negleted, open-loop transfer funtion is expressed as: k Gi () s = () s(.5tk s+ ) G i (s) = () s(.5t where k is proportionality oeffiient T is s + ) ontrol yle. Equation (2) is losed-loop where harateristi k is proportionality equation oeffiient urrent loop system: T is ontrol yle. Equation (2) is losed-loop harateristi equation urrent loop 2system: k s + s 0.5T +.5T = (2) angular frequeny damping s 2 + ratio s + k.5t system = is 0 expressed as: (2).5T angular frequeny damping ratio system is expressed as: ω n = k.5t ξ = 2.5kT (3) overshoot adjusting time system are shown in Equation (4). In this paper, we defined urrent traking index as overshoot σ% < 0% adjusting time t s < 5 ms. proportionality oeffiient k an be alulated aording to Equations (2) (3): { σ% = e πξ/ ξ 2 00% t s = 4.5 ξω n (4)

7 ξ = 2.5kT overshoot adjusting time system are shown in Equation (4). In this paper, we defined urrent traking index as overshoot σ % < 0% adjusting time ts < 5 ms. proportionality oeffiient k an be alulated aording to Equations (2) (3): Energies 207, 0, πξ / ξ σ % = e 00% Equations (0) (4) express rapidity 4.5 (4) t = s stability urrent traking. However, re is a ξωn ondition that indutane equivalent resistane R be ompletely determined. In atual engineering, Equations reators (0) (4) are usually express installed rapidity on grid stability, urrent traking. indutane However, on re transmission a line is ondition very small that ompared indutane with reators. equivalent refore, resistane R be transmission ompletely determined. line indutane In atual an be engineering, reators are usually installed on grid, indutane on transmission negleted indutane system an be onred as aurate. equivalent resistane line is very small ompared with reators. refore, transmission line indutane an be R is grid equivalent loss resistane devie is not easy to determine. It is related negleted indutane system an be onred as aurate. equivalent resistane to line loss, swithing loss, temperature [29]. Based on Equation (9), power swith R is grid equivalent loss resistane devie is not easy to determine. It is related to funtion line onring loss, swithing disturbane loss, resistane temperature R is[29]. expressed Based on as: Equation (9), power swith funtion onring ( disturbane ) ( resistane Δ R is expressed as: m d = (R + R)x + ωx 2 z ) + E sd m q u d ωx (R + R)x 2 z (5) m d ( R+Δ R) x + ωx2 z + Esd = (5) m q u d ωx ( R R) x2 z Based on Equations (5) (5), +Δ open loop transfer funtion urrent-loop onring disturbane Based on resistane Equations R (5) is shown (5), inopen Equation loop transfer (6). funtion d axis urrent urrent-loop has same onring open-loop transfer disturbane funtion asresistane q axis Δ urrent, R is shown refore, in Equation we take (6). d axis urrent has an example: same open-loop transfer funtion as q axis urrent, refore, we take d axis urrent as an example: k G id (s) k G s + R, (6) id () s = s+δ R, (6) swithing swithing delay delay sampling sampling delay delay make order order system system transfer transfer funtion funtion higher. higher. PI link PI link is used is used to redue to redue order order improve its stability. In Inorder order to to simplify simplify design, design, k is k is set toset, to, dynami blok blok diagram urrent loop onring resistane disturbane system system delay delay is shown is shown in in i dref + k i id k p + s Ts+ 0.5Ts+ s +ΔR Dynami blok diagram urrent urrent loop onring loop onring resistane resistane disturbane disturbane system system delay. delay. open-loop transfer funtion is expressed as: open-loop transfer funtion is expressed as: kp( s+ Ti) Gid () s =, s.5ts + ΔR (7) G s+ id (s) = k p(s + T i ) s.5t s + s + R, (7) T i = k i k p, (8) Equation (7) is a three order osillation link. pole-zero anellation is used to redue order. Aording to automati ontrol ory, in s domain, poles far from imaginary axis have little influene on system. In general, poles aused by resistane disturbane are loser to imaginary axis than those aused by delay link. et T i = R. Based on pole-zero anellation, pole aused by resistane disturbane is eliminated by zero point PI orretion. This will fset influene pole. orreted open-loop transfer funtion is expressed as: G id (s) = k p s(.5t s + ) (9)

8 ΔR et Ti =. Based on pole-zero anellation, pole aused by resistane disturbane is eliminated by zero point PI orretion. This will fset influene pole. orreted open-loop transfer funtion is expressed as: Energies 207, 0, 642 k p G () 8 9 id s = (9) s(.5t s+ ) In this study, optimal damping ratio ξ set to Equations (20) (2) show PI In this study, optimal damping ratio set to Equations (20) (2) show PI orretion urrent loop: orretion urrent loop: k p k, (20) p =, (20) 3T T k i Δ R R k (2) i = 3T (2) 3T Substituting Equations (20) into Equation (9) negleting higher order terms, open-loop Substituting Equations (20) into Equation (9) negleting higher order terms, openloop transfer funtion is expressed as: transfer funtion is expressed as: G id (s) = 3T s, (22) Gid () s =, (22) losed-loop transfer funtion is expressed as: 3Ts losed-loop transfer funtion is expressed as: G id (s) = (23) 3T s + Gid () s = (23) 3Ts + Aording to Equations (22) (23), urrent loop is approximately equivalent to a first order inertial link, Aording to inertial Equations time (22) onstant (23), is 3Turrent. Based loop onis approximately step response equivalent property to a first order first order inertial inertial link, link, 98.2% referene inertial value time an onstant be reahed is 3T. after Based 2T on 5T step. When response property swithing frequeny first is order inertial link, 98.2% referene value an be reahed after 2T 5T. When swithing high, that is to say, ontrol yle is short, urrent traking has good rapidity. frequeny is high, that is to say, ontrol yle is short, urrent traking has good rapidity. DC apaitor relates to ative power injeted into VSC from AC power DC apaitor relates to ative power injeted into VSC from AC power supply. supply. Based Based on Equation on Equation (6), (6), DC DC loop loop with with PI PI orretion orretion is added is added onto onto d axis d axis urrent urrent loop. loop. It forms It forms a double a double losed losed loop loop system. dynami struture struture is shown is shown in in Ts+ m d 6. Dynami blok diagram loop. 6. Dynami blok diagram loop. Aording Aording to to harateristis harateristis swithing swithing funtion, funtion, m md is d is a nonlinear a nonlinear link, link, it is it is Energies 207, 0, inonvenient inonvenient for for system system design. Whenusing using SPWM SPWM modulation, modulation, maximum maximum value value md is. m d is. refore, refore, when when m d =, it has greatest impat on system. Combining delay terms md =, it has greatest impat on system. Combining delay terms negleting negleting higher higher order order terms, terms, simplified dynami struture is isshown in in Simplified dynami blok diagram loop. 7. Simplified dynami blok diagram loop. Aording to Mason Gain Formula, system transfer funtion is expressed as: Aording to Mason Gain Formula, system transfer funtion is expressed as: 2 kvps+ kvi 4Ts + s ud () s = u () () 3 2 dref s i 3 2 s (24) 4CTk s vp s + + Csk vi + kvps + kvi 4CTs + Cs 4T + s kvps + kvi u d (s) = 4CT s 3 + Cs 2 u + k vp s + k dre f (s) 2 + s vi 4CT s 3 + Cs 2 i + k vp s + (s) (24) k vi system onsists two responses: DC, disturbane urrent load. system error E(s) is expressed as: E() s = u () s u () s, (25) dref d is a: input is a unit step signal, disturbane urrent is also a step signal, but its amplitude udref () s =, (26) s

9 Energies 207, 0, system onsists two responses: DC, disturbane urrent load. system error E(s) is expressed as: E(s) = u dre f (s) u d (s), (25) is a: input is a unit step signal, disturbane urrent is also a step signal, but its amplitude u dre f (s) = s, (26) i (s) = a s, (27) Aording to final orem, steady-state error an be represented as: e ss = lim s 0 se(s) = 0, (28) steady-state error is not influened by disturbane urrent. re is no stati error during steady state. harateristi equation losed loop is as follows: s 3 + s 2 + k vp s + k vi = 0, (29) 4T 4CT 4CT To ahieve required dynami performane steady-state performane in higher order systems, usual treatment in engineering is to arrange two poles as a pair onjugate poles, onfigure or two poles far away from imaginary axis. harateristi equation is expressed as: (s 2 + 2ξω n s + ω 2 n)(s + nξω n ) = 0, (30) Comparing Equations (29) (30), parameters after PI orretion loop are as follows: { k vp = 4CT (2nξ 2 + )ωn 2 k vi = 4CT nξωn 3, (3) ω n = 4ξT (n + 2), (32) In summary, ontrol struture interruption generator based on VSCs is shown in 8. Energies 207, 0, g g3 g5 s s3 s5 Esa ia R oad o Esb Es ib i R R Ud + - oad 2 oad 3 P Q ref u dref θ 3s/2r ω E sd N D i q ω i - qref N/D N PI N/D D i d + i dref - PI N PI N/D u - d D 2r/3s g4 g6 g2 ma m b m g ~ g 6 SPWM N s4 s6 s2 SPWM s ~ s 6 Disturbane instrutions 4. Analysis Simulation Case 4.. Parameters Simulation Case Struture diagram ontrol system. system. simulation parameters main iruit ontroller are respetively shown in Tables 2. simulation platform based on PSCAD/EMTDC is shown in 9.

10 ref u dref N iqref N/D + - N PI N/D D i d + i dref - PI N PI N/D - D u d 2r/3s Energies 207, 0, m b m SPWM SPWM Disturbane instrutions 8. Struture diagram ontrol system. 4. Analysis Simulation Case 4. Analysis Simulation Case 4.. Parameters Simulation Case 4.. Parameters simulation Simulation parameters Case main iruit ontroller are respetively shown in Tables 2. simulation parameters platform based on PSCAD/EMTDC main iruit is shown ontroller in are 9. respetively shown in Tables 2. simulation platform based on PSCAD/EMTDC is shown in 9. Table. Parameters main iruit. Table. Parameters main iruit. Parameters Main Ciruit Values Parameters AC phase Main /V Ciruit 220 Values AC Grid- phase /V reator/mh Equivalent Grid- reator/mh loss resistane/ω Equivalent apaitane loss resistane/ω DC /µf Equivalent Operating apaitane DC DC /μf apaitor/v Operating Control DC yle/ms apaitor/v Equivalent Control disturbane yle/ms load/ω Equivalent disturbane load/ω 50 Table 2. Parameters ontroller. Table 2. Parameters ontroller. PI Parameters Current oop PI Parameters Voltage oop PI Parameters Current oop PI Parameters Voltage oop k p Ti k vp T kp Ti kvp Tvi vi s s s Verifiation Controller Performane Simulation platform based on on PSCAD/EMTDC. Aording to s 5 7, a dynami struture based on double losed loop ontrol onstruted in MATAB/Simulink (R204b, MathWorks, Natik, MA, USA), whih is shown in 0a,b; its unit step response is shown in a,b. urrent traking an be ompleted in 4 ms, whih is basially onsistent with oretial value. overshoot is very small, re is no stati error in steady state. DC reahes steady-state value 700 V in 00 ms with no stati error in steady state, overshoot is 7%. simulation results thus verified orretness ontroller design.

11 Energies 207, 0, 0, Aording to s 5 7, a dynami struture based on double losed loop ontrol onstruted in MATAB/Simulink (R204b, MathWorks, Natik, MA, USA), whih is is shown in 0a,b; its unit step response is is shown in a,b. Energies 207, 0, (a) (b) 0. (a) Dynami simulation model urrent loop; (b) dynami simulation model 0. (a) Dynami simulation model urrent loop; (b) dynami simulation model loop. loop. (a) (b). (a) Unit step response urrent loop; (b) unit step response loop.. (a) Unit step response urrent loop; (b) unit step response loop. urrent traking an be ompleted in 4 ms, whih is is basially onsistent with oretial 4.3. Simulation Researh value. overshoot is is very small, re is is no stati error in steady state. DC reahes performane steady-state value retifier 700 is V in verified 00 ms inwith no 2. stati Aterror 0.2 s, in steady reative state, power overshoot AC flowing is is 7%. into simulation retifier results inreased thus verified from 0 to 20orretness kvar, that is to say, ontroller Q ref = 20design. kvar, under no-load operating ondition. power traking done in about 5 ms, as shown in 2a. In 2b, 4.3. reative Simulation power Researh jump did not affet stability DC. 2 shows waveforms AC urrent, whose phase differene 90 performane retifier is is verified in 2. At. 2d is urrent spetrum 0.2 s, s, reative power AC AC, shows that re no low-order harmoni whih will ause pollution to grid. flowing into retifier inreased from 0 to 20 kvar, that is is to say, Qref Qref = 20 kvar, under no- 2e is waveform DC sudden inrease load. DC reovered load operating ondition. power traking done in about 5 ms, as shown in 2a. In after one yle, maximum hange rate 2%. Furrmore, performane ontroller 2b, reative power jump did not affet stability DC. 2 against shows waveforms external disturbanes AC good. In urrent, 2f, whose when phase equivalent differene resistane 90. AC 2d is is inreased urrent by spetrum 0. Ω, DC AC, shows almost that unhanged, re whih no low-order shows that harmoni ontroller whih will had good ause performane pollution to against grid. internal 2e disturbanes. is is waveform DC sudden inrease load. DC reovered after one yle, maximum hange rate 2%. Furrmore, performane ontroller against external disturbanes good. In 2f, when equivalent resistane AC inreased by 0. Ω, DC almost unhanged, whih shows that ontroller had good performane against internal disturbanes.

12 Energies 207, 0, 642 Energies 207, 0, (a) (b) () (d) (e) (f) 2. (a) Jump reative power; (b) DC ; () urrent AC ; 2. (a) Jump reative power; (b) DC ; () urrent AC ; (d) urrent urrent spetrum; spetrum; (e) (e) DC DC with with external external disturbanes; disturbanes; (f) (f) DC DC with with (d) internal disturbanes. internal disturbanes. In 3, feasibility method interruption generator verified by several In 3, feasibility method interruption generator verified by several typial disturbane waveforms produed by SPWM waves based on regular sampling method. typial disturbane waveforms produed by SPWM waves based on regular sampling method. 3a is sag waveform. dropped by 0%, sag lasted for 3a is sag waveform. dropped by 0%, sag lasted for four yles. 3b is swell waveform. inreased by 2.5%, four yles. 3b is swell waveform. inreased by 2.5%, swell lasted for four yles. 3 is interruption waveform, whih lasted four yles. swell lasted for four yles. 3 is interruption waveform, whih lasted four yles. 3d,e are frequeny fset waveforms. frequenies modulation wave were 49 Hz 3d,e are frequeny fset waveforms. frequenies modulation wave were 49 Hz 5 Hz. 3f is fundamental waveform with 0.5 times third harmoni injetion. 5 Hz. 3f is fundamental waveform with 0.5 times third harmoni injetion. 3g is 3g is 3-phase unbalaned waveform with a degree unbalane 32.5%. 3h is 3-phase unbalaned waveform with a degree unbalane 32.5%. 3h is flik flik waveform. modulation wave obtained by superposition fundamental waveform. modulation wave obtained by superposition fundamental waveform waveform wave whose amplitude 0% fundamental waveform frequeny wave whose amplitude 0% fundamental waveform frequeny 5 Hz. 5 Hz.

13 Energies 207, 0, 642 Energies 207, 0, (a) (b) () (d) (e) (f) (g) (h) 3. (a) Voltage sag; (b) swell; () interruption; (d) waveform 49 Hz; (e) 3. (a) Voltage sag; (b) swell; () interruption; (d) waveform 49 Hz; waveform 5 Hz; (f) harmoni injetion; (g) 3-phase unbalaned waveform; (h) flik. (e) waveform 5 Hz; (f) harmoni injetion; (g) 3-phase unbalaned waveform; (h) flik. 5. Experimental Results Analyses 5. Experimental Results Analyses A 30 kva VSC physial prototype shown in 4 designed to prove method above. Aontrol 30 kvahip VSCisphysial prototype shown in 4 designed to prove method above. TMS320F282 (Texas Instruments, Dallas, TX, USA). 5 gives struture diagram ontrol hip is TMS320F282 (Texas Instruments, Dallas, TX, USA). 5 gives struture physial prototype, whih onsists a grid- onverter, an isolation transformer, diagram physial prototype, onsists a grid- onverter, a DC unit, a load onverter, whih a line swith. Tehnial indies deviean areisolation shown intransformer, Table 3. a DC unit, a load onverter, a line swith. Tehnial indies devie are shown in Table 3.

14 Energies 207, 0, x 4 9 Energies 207, 0, 642 Energies 207, 0, Energies 207, 0, Physial prototype Physial Physial prototype. prototype. 4. Physial prototype. Current Currentlimiting limitingresistor resistor Transformer RR50/50W Transformer 50/50W Hall KM Halldevie devie KM Dynami Dynamisimulation simulation infinite infinitepower powersupply supply Dynami simulation infinite power supply KM2 KM2 Current limiting resistor Transformer R 50/50W Ciruit Contator Ciruitbreaker breaker Contator Hall devie KM 380V/380V Voltage 380V/380V Voltagesampling sampling Grid Grid Current Power supply ontroller Currentsampling sampling onverter Power supply ontroller onverter 380V/380V Voltage sampling Ciruit breaker Contator Current sampling Grid Ciruit KM2 Ciruitbreaker breaker oad oad Ciruit breaker onverter onverter oad oad oad oad Power supply ontroller onverter onverter 5. Struturediagram 5.Struture Struture diagram physial physialprototype. prototype. 5. Struture diagram physial prototype. Table Table Tehnialindies Table3.3.Tehnial indies devie. devie. Table 3. Tehnial indies devie. Eletrial EletrialParameters Parameters Eletrial Parameters Eletrial Parameters Capaity Capaity devie devie Capaity devie Capaity devie Capaity Capaity load load load Capaity Capaity load Error DC Error Error DC DC Error DC Range disturbane Range disturbane Range disturbane Range disturbane Maximum harmoni number Maximum harmoni number Maximum harmoni number Maximum harmoni number Tehnial TehnialIndexes Indexes Tehnial Indexes Tehnial Indexes 30 30kVA kva 3000 kva 30 kva 00AA 00 A00 A ±% ±% ±% ±% 00 2% 0 2% 2% 0 2% provides disturbane devie provides following disturbanewaveforms. waveforms. devie devie provides following following disturbane waveforms. 6 waveform sag: dropped by 2.4% from 220 VV to 73 6 shows waveform sag: dropped dropped 2.4% from 220 VV to 73 6shows shows waveform sag: droppedby by 2.4% from 220 to 73 waveform sag: by 2.4% from 220 to 73 V V for 00 ms. VV for 00 ms. 00 ms. forfor 00 ms. Waveform sag. 6.6.Waveform sag. 6. Waveform sag.

15 Energies 207, 0, 0, Energies 207, 0, shows waveform swell: inreased by 2.5% from 220 V to 248 V for 00 ms. 7 7 shows waveform swell: inreased by 2.5% from 220 V Vto to V V for for ms. ms. 7. Waveform swell. swell. 7. Waveform swell. Voltage interruption is most serious problem for power quality. 8 is waveform Voltage interruption is most serious problem for power quality. 8 is waveform Voltage interruption, showing is most an interruption serious problem for 20 for ms. power quality. 8 is waveform interruption, interruption, showing showing an interruption an interruption for for ms. ms. 8. Waveform interruption. 8. Waveform interruption. A 0.5 times third harmoni injeted into fundamental, as shown in A 0.5 times third harmoni injeted into fundamental, as shown in A times third harmoni injeted into fundamental, as shown in Waveform with third harmoni injetion Waveform with third harmoni injetion.

16 Energies 207, 0,0, 642 Energies 207, 642 Energies 207, 0, 642 Energies 207, 0, phase unbalaned waveform realized by differing amplitudes 3-phaseunbalaned unbalanedwaveform waveform realized by 3-phase by differing differing amplitudes amplitudes 3-phase wave. unbalaned 3-phase waveform with abydegree unbalane 32.5% modulation 3-phase waveform realized differing amplitudes is 3-phase modulation wave. 3-phase 3-phase waveform waveform with 3-phase modulation wave. with aa degree degree unbalane unbalane32.5% 32.5%is is shown 20. wave. 3-phase waveform with a degree unbalane 32.5% is 3-phaseinmodulation shown in shown in shown in Waveform 3-phase unbalaned Waveform Waveform 3-phase 3-phaseunbalaned unbalaned 20. Waveform 3-phase unbalaned. stability DC guarantees waveform. 2 2 shows shows error error stability DC guarantees waveform. stability DCDC guarantees waveform. 22shows error stability guarantees waveform. shows error DC under sag shown shown in in error error between between DC under ondition ondition sag DC under ondition sag shown in 6. error between DC under ondition sagse shown in errorindies. between 0.2% 6 V. V. results met6. devie 0.2% 0.6%, 0.6%, maximum maximum flutuation flutuation se results met devie indies. 0.2% V. se se resultsmet met devie devieindies. indies. 0.2% 0.6%, 0.6%, maximum maximum flutuation flutuation 66 V. results 2. 2.DC DC 2. DC error error sag. sag. 2. DC error sag. When load load onneted onneted to to grid grid for for When grid grid onneted onneted experiment, experiment, devie devie When load onneted toto When load onneted grid gridfor for grid gridonneted onnetedexperiment, experiment, devie is isworking workingin in state state unontrolled unontrolled retifier, retifier, phases phases grid is grid working in instate unontrolled retifier, phases grid shown is working state unontrolled retifier, phases grid shown in oinided. shownin in 22 oinided. oinided. in shown 22 oinided. 22. Voltage relation before grid onnetion. onnetion Voltage relationbefore beforegrid gridonnetion. onnetion. Voltagerelation relation before

17 Energies207, 207, 0, Energies Energies 207,0, 0, load load onneted onneted to to grid grid through through Ω Ω resistane. resistane provides provides load onneted to grid through 50 Ω resistane. 23 provides relationships between grid-, load, system relationships between grid-, load, system.. relationships between small, grid- load, system. flutuation thus proving load onneted to flutuation urrent urrent small, thus, proving that that load onneted to grid. grid. flutuation urrent small, thus proving that load onneted to grid. sag experiment after grid onnetion is shown in 24. Phases sag experiment after grid onnetion is shown in 24. Phases sag experiment after grid onnetion is shown in by Phases to were dropped 5.4% from V 00 grid grid were same. same. dropped by 5.4%24. from 280 V V to 265 V for for 00 ms, ms, grid were same. dropped by 5.4% from 280 V to 265 V for while devie remained stable. while devie remained stable. 00 ms, while devie remained stable. 23. Parameters in grid onnetion Parameters Parameters in in grid grid onnetion. onnetion. 24. Voltage sag experiment after grid onnetion Voltage Voltage sag sag experiment experiment after after grid grid onnetion. onnetion. 6. Conlusions Conlusions In this paper, we presented universal design method for main iruit ontroller based In In this this paper, paper, we we presented presented aaa universal universal design design method method for for main main iruit iruit ontroller ontroller based based on operation ondition power ontrol ory. A PSCAD/EMTDC simulation platform for an on ondition power powerontrol ontrolory. ory.aapscad/emtdc PSCAD/EMTDC simulation platform on operation ondition simulation platform forfor an interruption generator reated, n a 30 kva physial prototype established in an interruption generator reated, n a 30 kva physial prototype established in aa interruption generator reated, n a 30 kva physial prototype established a dynami simulation lab based on simulation. simulation experimental results showed dynami simulation. simulation experimental results showed that dynamisimulation simulationlab labbased basedonon simulation. simulation experimental results showed that generator VSC high auray, generator basedbased on on VSC has advantages high auray, various thatinterruption interruption interruption generator based on has VSC has advantages advantages high auray, various waves. We an platform for power quality disturbane waves. We provided an experimental platform for addressing power quality problems various disturbane disturbane waves. We provided provided an experimental experimental platform for addressing addressing power quality problems operating equipment under disturbane measuring operating harateristis ompensation equipment under disturbane problems measuring measuring operating harateristis harateristis ompensation ompensation equipment under onditions. disturbane onditions. onditions. Aknowledgments: This work is supported by speial fund for industrial innovation Jilin Provine Development Reform Commission (207C07-2), Sienefund Tehnology Projet State Grid Corporation Aknowledgments: This is by for innovation Jilin Aknowledgments: This work work is supported supported by speial speial fund Operation for industrial industrial innovation Jilin Provine Provine China (Key Tehnology Appliation Grid Conneted arge CapaityBattery Energy Development Reform Commission (207C07-2), Siene Projet Grid Development Reform (207C07-2), Tehnology Tehnology ProjetProjet State State Grid Corporation Corporation Storage Power Station), JilinCommission Provinial 3th Five-YearSiene Plan Siene Tehnology ([206]88), Jilin Appliation Grid Operation arge Provinial 2thTehnology Five-Year Plan Key Self-Help Projet (ZC3072). China China (Key (Key Tehnology Eduation Appliation Siene Grid Conneted Conneted Operation arge Capaity Capaity Battery Battery Energy Energy Storage Power Station), Jilin Provinial 3th Five-Year Plan Siene Tehnology Projet ([206]88), Storage Power Station), Jilin Provinial 3th Five-Year Plan Siene Tehnology Projet ([206]88), Author Contributions: Junhui i designed experiments wrote paper; Tianyang Zhang performed Jilin Provinial 2th Five-Year Plan Eduation Siene Key Self-Help Projet (ZC3072). Jilin Provinial 2th Yan Five-Year Plan Eduation Siene Key Self-Help reagents/materials/analysis Projet (ZC3072). experiments; Gangui provided important guidane; ei Qi ontributed tools.

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