Aalborg Unverstet Prncple and Desgn of a Sngle-phase Inverter-Based Groundng System for Neutralto-ground Voltage Compensaton n Dstrbuton Networks Wang, Wen; Yan, Lngje; Zeng, Xangjun; Fan, Bshuang; Guerrero, Josep M. Publshed n: I E E E Transactons on Industral Electroncs DOI (lnk to publcaton from Publsher): 1.119/TIE.216.261218 Publcaton date: 217 Document Verson Early verson, also known as pre-prnt Lnk to publcaton from Aalborg Unversty Ctaton for publshed verson (APA): Wang, W., Yan, L., Zeng, X., Fan, B., & Guerrero, J. M. (217). Prncple and Desgn of a Sngle-phase Inverter- Based Groundng System for Neutral-to-ground Voltage Compensaton n Dstrbuton Networks. I E E E Transactons on Industral Electroncs, 64(2), 124-1213. https://do.org/1.119/tie.216.261218 General rghts Copyrght and moral rghts for the publcatons made accessble n the publc portal are retaned by the authors and/or other copyrght owners and t s a condton of accessng publcatons that users recognse and abde by the legal requrements assocated wth these rghts.? Users may download and prnt one copy of any publcaton from the publc portal for the purpose of prvate study or research.? You may not further dstrbute the materal or use t for any proft-makng actvty or commercal gan? You may freely dstrbute the URL dentfyng the publcaton n the publc portal? Take down polcy If you beleve that ths document breaches copyrght please contact us at vbn@aub.aau.dk provdng detals, and we wll remove access to the work mmedately and nvestgate your clam.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 1 Prncple and Desgn of a Sngle-phase Inverter Based Groundng System for Neutral-to-ground Voltage Compensaton n Dstrbuton Networks Wen Wang, Member, IEEE, Lngje Yan, Xangjun Zeng, Member, IEEE Bshuang Fan and Josep M. Guerrero, Fellow, IEEE Abstract Neutral-to-ground overvoltage may occur n non-effectvely grounded power systems because of the dstrbuted parameters asymmetry and resonance between Petersen col and dstrbuted capactances. Thus, the constrant of neutral-to-ground voltage s crtcal for the safety of dstrbuton networks. In ths paper, an actve groundng system based on sngle-phase nverter and ts control parameter desgn method s proposed to acheve ths objectve. Relatonshp between ts output current and neutral-to-ground voltage s derved to explan the prncple of neutral-to-ground voltage compensaton. Then, a practcal current detecton method s proposed to specfy the reference of compensated current. A current control method consstng of proportonal resonant (PR) and proportonal ntegral (PI) wth capactve current feedback s then proposed to guarantee suffcent output current accuracy and stablty margn subjectng to large range of load change. The PI method s taken as the comparatve method and the performances of both control methods are presented n detal. Expermental results prove the effectveness and novelty of the proposed groundng system and control method. Index Terms Current control, dstrbuton networks, flexble groundng method, neutral voltage compensaton. I. INTRODUCTION ITHER n theory or practce, the major objectve of Egroundng system n dstrbuton networks s to constran the ground current to extngush the arcs caused by the snglelne-to-ground (SLG) fault. However, the other purpose of groundng system s commonly dsregarded,.e., to control the neutral-to-ground voltage wthn certan lmt [1]. Ths s crtcal for the safety of the power system especally when the Manuscrpt receved March 24, 216; revsed June 6, 216 and July 25, 216; accepted August 19, 216. Date of publcaton Month xx, 21x; date of current verson August 19, 216. Ths work was supported n part by the Natonal Natural Scence Foundaton of Chna under Award 514714 and 5142571, n part by the Hunan Provncal Natural Scence Foundaton of Chna under Award 215JJ39, and n part by the Project Funded by the Hunan Provncal Department of Educaton under Award 15B7. W. Wang, L. Yan, X. Zeng, and B. Fan are wth the Hunan Provncal Key Laboratory of Smart Grds Operaton and Control, School of Electrcal and nherent asymmetry s hgh. Inherent asymmetry drectly determnes the neutral-toground voltage n ungrounded system or hgh resstance grounded (HRG) system [2]. It s caused by the asymmetry of the dstrbuted parameters,.e., phase-to-ground capactances and leakage resstances. Several reasons may cause the asymmetry, ncludng napproprate transposton n overhead lnes, sngle- or two- phase open-crcut, medum voltage (MV) sngle phase load [3], etc. Moreover, the neutral-to-ground voltage closely relates to the groundng method. Obvously, t s lmted to a small value n an effectvely grounded system. Whereas, n resonant grounded (RG) system, t may even exceed the lne-to-neutral voltage as resonance happens between Peterson col and dstrbuted capactances [4]. For the purpose of mantanng power supply relablty and extngushng fault arcs, most MV dstrbuton networks adopt HRG or RG method, whch makes the problem of hgh neutralto-ground voltage unavodable. Several measures are taken to lmt the neutral-to-ground voltage n non-effectvely grounded systems [3]. Transposton enhancement s a common method for overhead lnes to decrease the asymmetrcal voltage. However, ths method needs huge amount of work and s complcated to mplement. Three phase couplng capactances are used to balance the dstrbuted capactances. Nevertheless, t s not flexble enough to adapt the change of operaton modes n power system. Improvement of detunng and dampng rato n RG systems can decrease the neutral-to-ground voltage caused by the aforementoned resonance [4]. However, ths method s not able to elmnate the neutral-to-ground voltage caused by the asymmetry of dstrbuted parameters. For the purpose of elmnatng the neutral-to-ground overvoltage, an actve groundng system s needed wth the Informaton Engneerng, Changsha Unversty of Scence and Technology, Changsha 41, Chna (e-mal: ww_csust@126.com; 9175764@qq.com; eexjzeng@hotmal.com; fanbshuang@126.com). J. M. Guerrero s wth the Department of Energy Technology, Aalborg Unversty, 922 Aalborg, Denmark (e-mal: joz@et.aau.dk). Color versons of one or more of the fgures n ths paper are avalable onlne at http://eeexplore.eee.org.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2 characterstcs of njectng certan currents to the neutral pont and make t seem lke short-crcuted to the ground. Obvously, ths system cannot be realzed by passve components lke resstor, reactor or capactor. Thus, a sngle-phase nverter based groundng system s adopted n ths paper. The current detecton and control methods are essental to the control system of an nverter. These two aspects are great challenges for the desgn and mplementaton of the actve groundng system. Regardng to current detecton methods, lteratures [5]-[1] have ntroduced several chargng current detecton methods. In [5], the dstrbuted capactances are detected by twce changng the Petersen col nductance and measurng the correspondng neutral-to-ground voltage and Petersen col current. The chargng current can be easly calculated then wth the measured parameters and the lne-toneutral voltage. However, ths method reles on the exstence of Petersen col, thus cannot be adopted n the actve groundng system. Lterature [7] has ntroduced a chargng current detecton method by the phase voltage of the faulty feeder and the varaton of three-phase currents. Ths method can be easly mplemented by feeder termnal unts. However, the method employs too many sensors, thus the accuracy s hard to be guaranteed. Bolted connecton of one phase to the ground wth a fxed resstor and a contactor s ntroduced n [1] to detect the chargng current. Ths method can easly guarantee the current accuracy. However, t stll needs a groundng resstor and the detecton procedure s too complcated for the control of actve groundng system. Addtonally, these methods cannot be used drectly to compensate the neutral-to-ground voltage as the current for voltage compensaton s not dentcal to the chargng current. The dstrbuton transformer s always n delta/wye connecton, thus the three-phase load of the feeder lne has no nfluence on the zero sequence mpedance. As the neutral-toground voltage only depends on the zero sequence crcut, the real load of the groundng system s thus the dstrbuted mpedance. Obvously, the load s manly capactve and s lkely to be resonant wth the LC flter of the groundng system at around fundamental frequency. Ths may brng about steady state error and undermne stablty margn of the control system. These features complcate the topology and parameter desgn of the actve groundng system controller. Several lteratures have addressed the load effect and resonance phenomena, and many effectve measures have been proposed [11]-[14]. Lterature [11] has proposed a mxed controller of proportonal ntegral dfferental (PID) and Resonant plus load current feedback, to reduce the steady state error and mprove the dynamc response whle dealng wth dfferent load types. However, the desgn of the controller parameters are not dscussed n detal. Lterature [12] has dscussed the nherent nstablty of LCL flter n actve power flter and ntroduced the actve dampng method of capactve current feedback (CCF) to mprove the stablty margn. Degradaton method can smplfy the desgn of control system for LCL flter [14]. However, as the load types of the groundng system are dfferent from that of the LCL flter, these methods cannot be adopted wthout modfcaton. In ths paper, a new groundng system based on sngle-phase nverter s proposed to flexbly control the neutral-to-ground voltage. The relatonshp between njected current of the groundng system and the neutral-to-ground voltage s frstly derved. Then, a practcal current detecton method for compensatng the neutral-to-ground voltage s ntroduced by analyzng that relatonshp. Furthermore, the load effect and resonance phenomena are addressed n detal, followed by a current control strategy. The controller desgn method s then presented to fulfll the requrements of the control system. Expermental results for valdaton of the proposed control topology and desgn method are subsequently provded. II. PRINCIPLE OF ACTIVE GROUNDING SYSTEM A. Prncple of Neutral-to-ground voltage compensaton A typcal 1kV non-effectvely grounded dstrbuton network [15] wth one feeder s studed n ths paper. Fg. 1 shows the topology of the dstrbuton network wth the proposed actve groundng system. Snce the 1kV busbar s suppled from the 11kV system va a wye/delta transformer T d, there s no actual neutral pont. Thus, a zgzag/wye transformer T z s appled to vrtualze one, and the groundng system s connected between the pont and the ground. Fg. 2 shows the smplfed dstrbuton network, where E A, E B, E C are three phase voltages. The dstrbuted capactance and resstance of phase X (X=A, B or C) are C X and R X, respectvely. The groundng system s composed of a sngle-phase full-brdge nverter, a LC-type output flter and a couplng transformer T. The DC bus of the nverter s suppled by a three phase uncontrolled rectfer whch connects to the secondary wndngs of T z. The output current of the system s controlled by the PWM pulses of IGBT to execute compensated current reference detecton and neutral-to-ground voltage compensaton. The transformer s used to regulate the nverter output voltage and solate the nverter from the dstrbuton network. Assume that the nverter output current s totally under control, then the groundng system can be treated as an deal 11kV T d T T z 1kV busbar Load Fg. 1. Topology of dstrbuton network and actve groundng system (n dashed box). v d u o L o C o o N E A EB G Fg. 2. Smplfed dstrbuton network. N E C CC RC CB RB CA RA
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 3 N N G Fg. 3. Smplfed crcut of the dstrbuton network. current source. Accordng to electrc crcut theores, the partton of dstrbuton network can be smplfed to a voltage source n seres wth an mpedance. Therefore, the crcut of the whole system can be smplfed to Fg. 3, where E eq and G denote the equvalent voltage source and mpedance of the dstrbuton network, respectvely. They are shown n (1) and (2), where Y X s the phase-to-ground admttance,.e., Y X =jω C X + 1/R X, and ω denotes the fundamental angular frequency. Eeq G( EAYA EBYB E CYC ) (1) 1 1 G (2) Y YA YB YC Therefore, the relatonshp between the output current of the groundng system N and the neutral-to-ground voltage u N s NGEeq G( NEAYAEBYBE CYC). (3) Obvously, f N can be controlled to the value n (4), the neutral-to-ground voltage wll be zero, whch means the asymmetry of dstrbuton network s fully compensated. EAYAEBYBE CYC (4) It can be further concluded that the compensated current reference also meets (4) whle an nductor or resstor s parallel connected to the groundng system. Ths ndcates the groundng system s sutable for dstrbuton network wth both HRG and RG groundng. However, as the dstrbuted parameters of the dstrbuton network are complcated to be precsely detected, drect calculaton of s not practcal. As the lne-to-neutral voltages are balanced and postvesequenced, E B and E C can be substtuted by expressons of E A. Take the ntal phase angle of E A as the zero phase base,.e., E A =E A, then (3) can be rewrtten to j j u N G ( Ne e ). (5) In (5), θ and θ denote the phase angle of N and, respectvely. Therefore, the magntude of neutral-to-ground voltage can be obtaned. 2 2 ( N, ) G N 2Ncos( ) (6) Take the frst-order partal dervatve operaton of u N, then the change rate of u N wth the magntude and phase angle of N can be observed. ( N, ) N cos( ) G (7) 2 2 N N 2Ncos( ) ( N, ) Nsn( ) G (8) 2 2 N 2 N cos( ) It can be seen from (4) that and θ are fxed n a specfc u N E eq G dstrbuton network. From (7), when we set θ to certan value θ *, u N has an nflecton pont n * N cos( ). (9) The trend of u N needs to be dscussed under several condtons. If π/2 θ * θ < π/2, u N wll frst decrease then ncrease when N ncreases from to nfnte. The break pont s determned by (9). Ths means u N has a mnmal value at the pont. If π/2 θ * θ < 3π/2, u N wll be monotoncally ncreasng. Therefore, u N has a mnmal value at the pont determned by (9) as well. From (8), when we set N to certan value of *, u N has another nflecton pont n. (1) B. Compensaton Current Detecton Method Comparng (9) wth (1), nterestng conclusons can be found. Frstly, the nflecton pont determned by (9) s related to θ *, whch means t changes wth the set value of θ. However, the nflecton pont determned by (1) s ndependent to N. That s to say, whatever value N s chosen, the nflecton pont wll not vary. Secondly, θ must be chosen to θ to make the nflecton pont n (9) equal to the magntude of, whch s the compensated current reference; whereas, the nflecton pont n (1) s rght the phase angle of. These features can be used to quckly locate the magntude and phase of. From the analyss above, t can be seen that f snusodal currents wth any fxed magntude and changng phases are njected to the neutral, the phase of can be located just by detectng the mnmal u N. Comparatvely, only when the phase of the njected current s set to θ could the magntude of be located n the same way, whch s almost mpossble as s unknown. Ths can be seen more drectly from the vector dagrams n Fg. 4 and Fg. 5. In these fgures, the magntude of u N s dvded by the magntude of G to smplfy the analyss. Fg. 4 shows the varaton of u N when dfferent magntudes of N are chosen. Two typcal values are chosen, that s, N1 and N2. The frst one s smaller than, and the second s larger. Assumng the two groups of N wth fxed magntudes are u N2 u N1 u NM2 u NM1 N2 N1 O N1 NM1 NM2 N2 NM1 NM2 Fg. 4. Vector dagram of when N vares. u NM1 θ θ 1 M2 NM1 O NM2 θ 4 u NM4 u NM3 NM3 NM4 θ 2 θ 3 Fg. 5. Vector dagram of when θ vares.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 4 njected to the neutral, the correspondng groups of vector u N can be drawn accordng to (5). Obvously, the ntal ponts of them are fxed to the tal of, and the termnal ponts of them follow the crcles n dash lne, as u N1 and u N2 llustrate. By the laws of geometry, the vector n radal drecton has the mnmal magntude n both groups, shown by u NM1 and u NM2. The correspondng njected current vectors are shown by NM1 and NM2. Obvously, they have the same phase angle wth θ, thus the concluson can be drawn that no matter how much the njected current magntude s chosen, the phase angle of the current correspondng to the mnmal magntude of u N s just the same wth θ. Fg. 5 shows the varaton of u N when dfferent phase angles of N are chosen. θ 1 to θ 4 are chosen for comparson; two of them have less than π/2 angle dfference to (θ 1 and θ 2 ), and the others larger (θ 3 and θ 4 ). Assumng that four groups of N wth these phase angles are njected to the neutral, the correspondng groups of u N can be drawn accordng to (5). For the frst two groups of u N, t s obvous that the mnmal magntude occurs when u N s vertcal to N, as shown by u NM1 and u NM2. The njected current vectors correspondng to them are NM1 and NM2, respectvely. For the other two angles of N, the mnmal u N occurs only when N comes to zero, as u NM3 and u NM4 show. It can be seen that none of the current magntudes correspondng to the mnmal u N s dentcal to θ. It can be concluded that when the magntude of N s preset and fxed to certan value large enough for precse detecton, the angle of can be located va detectng mnmal u N ; whereas, f the angle of N s preset and fxed to certan value, the magntude of can hardly be located by detectng mnmal u N. Therefore, a convenent way to detect the magntude and phase of can be drawn. Frstly, preset the magntude of N to certan value; search the mnmal magntude of u N by changng the angles of N and njectng them to the neutral; the phase angle correspondng to mnmal u N s namely θ r. Then, fx the angle of N to θ r; search the mnmal magntude of u N agan by changng the magntudes of N and njectng them to the neutral; the correspondng magntude s namely r. Fnally, the current reference for compensatng the dstrbuton network asymmetry s wth the magntude of r and the angle of θ r. v m L o C o u c v d u o C S R S H c G (s) Fg. 6. Smplfed man crcut. o o r r III. CURRENT CONTROL STRATEGY A. Control model As the lne-to-neutral voltages rarely change, we consder them to be zero durng the control analyss. Thus, the voltage source E eq n Fg. 3 can be treated as short-crcuted. By convertng the equvalent mpedance G to the converter sde of the couplng transformer as C S and R S, the man crcut s thus smplfed to Fg. 6. Whle conductng the current control, a typcal method s to use output current feedback. Fg. 7 shows the feedback control dagram of the system, where Δ o s the output current error. From ths dagram, the relatonshp between modulaton sgnal v m and nverter output current o s presented by G 1. o ( s) Kpwm ( src s s 1) G1( s) (11) 2 vm() s s RsLo( Co Cs) slo Rs As L o, the nductance of LC flter, s usually set to be small, resonance occurs when the frequency comes to ω r. r 1 L ( C C ) o o s (12) Fg. 8 shows Bode dagram of G 1 wth typcal parameters lsted n TABLE I. The parameters of dstrbuton network are the same as a real one wth 5A chargng current. In Fg. 8, resonance n ω r can be obvously observed. Ths resonance brngs about phase shft to G 1. The resonant frequency s related to C s, whch vares wth the dstrbuton network parameters. If the frequency locates n the low frequency band, * (s) Δ o(s) v m(s) G (s) Magntude(dB) Phase(deg) 8 7 6 5 4 9 45 45 9 K pwm o(s) c(s) 1/(sL o) 1/(sC o) u c(s) 1/R s Fg. 7. Control dagram wth only output current feedback. sold: nomnal load dash-dot: 6% nomnal load dot: 3% nomnal load Frequency(rad/s) Fg. 8. Bode dagrams of G1(s) when Cs vares. Dstrbuton Network Groundng system ω TABLE I SYSTEM PARAMETERS Parameters sc s Values Dampng rato d.8 Phase-to-ground capactance CA, CB 8.76 uf Phase-to-ground capactance CC 14 uf Fundamental frequency f 5 Hz Phase-to-neutral voltage EX 1.5/ 3 kv Transformer rato 1.5/ 3:.32 Output nductance Lo.5 mh Output capactance Co 5 uf Inverter gan Kpwm 3 DC voltage 6 V o(s)
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 5 Magntude(dB) Phase(deg) sold: G 1(s) 1 dash-dot: G PR(s) 5 5 dot: G C(s) 18 9 9 18 Frequency(rad/s) Fg. 9. Bode dagrams of G1(s), GPR(s) and GC(s). the steady state error mght ncrease. Fg. 8 also shows Bode dagrams as C s vares n nomnal, 6%, and 3% of nomnal. Magntude n fundamental angular frequency decreases from 67.7 db to 47.1 db as C s decreases, whch means sgnfcant ncrease of steady state error at fundamental frequency. Moreover, f the resonant frequency locates n the medum band, the phase margn of the control system mght decrease. In order to guarantee mnmal steady state error n fundamental frequency, the proportonal resonance controller s usually adopted [16]. However, the controller also brngs about phase shft, as the Bode dagrams n Fg. 9 show. Snce the crossover frequency ω c s always n the medum band, whch s probably larger than ω r and ω, the phase margn of the whole control system G C (s) = G PR (s)g 1 (s) approaches zero, whch makes the system easly unstable. B. Capactve current feedback From the analyss above, the resonance should be carefully damped to meet control performance requrements [17]-[19]. Ths paper presents an actve dampng method that flexbly damps the resonance wthout any loss as llustrated n Fg. 1. In ths method, the current of C o s feedback to the control loop wth a rato of H. Therefore, the transfer functon from current regulator output v r to output current o s o ( s) Kpwm ( src s s 1) G2 ( s). 2 vr( s) s RsLo( Co Cs) s( Lo KpwmHRC s o) Rs (13) Obvously, the capactve current feedback (CCF) ntroduces a rato of K pwmh R sc o to the s term of the denomnator. As a result, the magntude of G 2 decrease sgnfcantly at the orgnal resonant frequency ω r, whch effectvely damps the control system. Fg. 11 shows both Bode dagrams of the orgnal system and damped system. It s clear that CCF damps the magntude at the resonant frequency and enhances the phase margn of the system. The dampng degree rses as the feedback rato H ncreases, whch means smaller magntude n resonant frequency and larger phase margn. Meanwhle, the CCF also brngs smaller magntude at fundamental frequency, whch 1/Rs * (s) Δo(s) vr(s) vm(s) G(s) Kpwm c(s) 1/(sLo) 1/(sCo) uc(s) scs H c(s) o(s) Fg. 1. Control dagram wth proposed CCF. o(s) Magntude(dB) Phase(deg) sold: H 8 dash-dot: H.6 dot: H1 6 4 2 9 45 145 Frequency(rad/s) Fg. 11. Bode dagrams comparson of G1(s) and G2(s) wth varous H. undermnes the steady state performance. Therefore, the current regulator must have sgnfcant magntude at fundamental frequency to acheve mnmal steady state error. C. Current Regulator PR controller wth damped form s used n current regulator to enhance the steady state performance and adapt to the power system frequency varaton. 2krs GPR () s kp_pr (14) 2 2 s 2 s The magntude of PR controller n both low and hgh frequency band s determned only by the proportonal rato k p_pr. To avod the hgh order harmonc nterference, the crossover frequency of the whole control system s always set n the medum band, typcally 1/1 of the swtchng frequency [2]. In order to fulfll ths requrement, k p_pr should not be too large. However, the lmted k p_pr may not ensure the system stablty as shown later. Therefore, PR controller can hardly meet both the requrements of ant-nterference and control system stablty. Thus, an addtonal PI controller s ntroduced. k GPI () s kp_pi (15) s The compound controller has the advantage of nfnte gan at zero frequency and fxed gan n hgh frequency. Thus, t s easy to enlarge the system gan n low band and avod ts nfluence to the crossover frequency. The ntegral rato k should also be carefully chosen to prevent the phase shft n low frequency from undermnng phase margn. Consequently, the current regulator and the open-loop transfer functon of the whole system can be descrbed as follows. G () s GPR () s GPI() s (16) G () s G () s G () s G () s (17) t PR PI 2 IV. CONTROL PARAMETER DESIGN A. PWM constrant The PWM constrant s frstly descrbed so that the concluson can be used n the followng analyss. For a realzable pulse wdth modulaton, the modulaton waveform should only cross the carrer waveform once n a swtchng perod. That s to say, the maxmum frequency of modulaton waveform should not exceed the swtchng frequency [21]. Therefore, the followng expresson stands.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 6 B. PI controller H 4 f L sw o (18) Kpwm As the PI controller has phase shft n low frequency band, whch mght decrease the phase margn of the control system, the corner frequency of the controller should be much smaller than the crossover frequency. That s k. (19) c kp_pi The proportonal rato k p_pi can be adjusted to slghtly modfy the performance of the whole system. In order to smplfy parameter desgn, k p_pi s set to one, so that n the medum frequency band and above, the effect of PI controller s neglgble. Therefore, the followng expresson of ntegral rato stands. (2) k C. Crossover frequency To prevent phase shft of PR controller from decreasng the phase margn, the crossover frequency ω c s always set to be n the medum band far away from the fundamental frequency. Thus, the PR controller can be smplfed to a pure amplfer loop at crossover frequency determned by the proportonal rato. As analyzed above, the PI controller at the crossover frequency can be treated as a proportonal loop wth the gan of k p_pi. Thus, the gan of current controller at the crossover frequency s G ( jc) GPR( jc) GPI( jc) kp_pr. (21) As the magntude of open-loop gan at the crossover frequency s unty, the relatonshp of ω c, k p_pr and H can be obtaned by the followng equaton. Gt ( jc ) 1 (22) Usng (13) to (21), followng equaton can be drawn. kp_prkpwm (1 jc RC s s) 1 2 (23) Rs[1 clo( Co Cs)] jc( Lo KpwmH RC s o) Notce that the dstrbuton network dampng rato d =1/ (ω or sc s) has typcal values of.3 to.8. It s reasonably neglgble comparng to one. The capactance of LC flter C o s always set to be much smaller than the dstrbuted capactance C s. Thus, (23) can be rewrtten to kp_pr (1 jd ) c o o 1 1 pwm s pwm c s c 1. (24) d L C H j ( clo) K C K C Consderng the reactance of C s at the crossover frequency s far less than that of L o, thus, (24) can be further smplfed to 2 2 Co 2 clo 2 k H ( ) ( ). (25) C K p_pr s It can be observed from (18) that H s lmted to a small value. Furthermore, C o s much smaller than C s, thus the followng expresson stands. pwm k L c o p_pr (26) K pwm As the zero-frequency gan of G 2(s) s K pwm/r s from (13), f sngle PR controller wth certan proportonal rato of (26) s used, the whole system gan at zero-frequency wll be cl K o pwm clo. (27) K pwm Rs Rs Wth the typcal values lsted n TABLE I, t can be seen that ω c L o / R s s less than one. Thus, the gan of the control system wth sngle PR controller n zero frequency s below db lne, whch means the whole control system s margnally unstable as shown n Fg. 12. It also shows the stablzed control system after addng PI controller. D. Steady state error and stablty margn constrant The magntude of output current error at fundamental frequency s used to descrbe the steady state error. * ( j) o( j) E (28) * ( j ) Assumng that unty feedback of output current s appled, the equaton above can be descrbed by open-loop transfer functon Gt ( j ) 1 E 1. (29) 1 Gt ( j ) 1 Gt ( j ) As the magntude of PR controller s k p_pr + k r at the fundamental frequency, usng expressons from (13) to (17), (29) can be transformed to 1 ( kp_pr kr ) Kpwm 1. E dlo KpwmHCo / Cs j(1/ Cs Lo) (3) At fundamental frequency, the reactance of L o s neglgble. Also, H C o C s s neglgble comparng to k p_pr + k r. The reactance of C s at fundamental frequency s also neglected to smplfy the analyss. As a result, the steady state error constrant can be descrbed as kp_pr kr Co. (31) H CE s Obvously, the gan of current controller at fundamental frequency s nversely proportonal to the steady state error. Increasng the gan can obtan better steady state performance. However, the CCF rato H s proportonal to the error, whch Magntude(dB) Phase(deg) 8 6 4 2 2 18 9 18 sold: PR plus PI controller wth CCF dash-dot: Sngle PR controller wth CCF db Frequency(rad/s) Fg. 12. Bode dagrams of open-loop transfer functon wth sngle PR controller and PR plus PI controller.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 7 means better dampng of load resonance brngs larger steady state error. It can be seen from Fg. 12 that, wth careful selecton of controller parameters, the phase of the open-loop transfer functon wll not exceed the lne. These selecton tps nclude that the corner frequency of PI controller should be far away from the crossover frequency, and the resonant cutoff frequency of PR controller should be as small as possble. Consequently, nfnte gan margn can be acheved. Whle dealng wth phase margn constrant, t s necessary to consder the effect of resonant rato to phase shft. Consder the PR controller at crossover frequency, GPR ( jc ) kp_pr 2 kr / s. (32) As s analyzed above, the PI controller can be treated as a pure amplfer loop at the crossover frequency. Therefore, phase margn (PM) can be expressed as follows. PM 18 GPR ( jc ) G2 ( jc ) (33) Usng (13) and (32), consderng that the reactance of C s at crossover frequency s neglgble, the constrant of phase margn s derved n the Appendx and s expressed as follows. k c( r clc o s KpwmCoH tan PM) (34) k 2 ( L C tan PM K C H ) p_pr c o s pwm o V. PARAMETER DESIGN AND EXPERIMENTAL RESULTS In order to valdate the theoretcal analyss, comparatve nvestgatons are carred out on two control methods of PI and PR plus PI (compound controller) wth or wthout CCF. As stablty margn s not easy to be observed n expermental results, Bode dagrams are used to llustrate t. Experment analyss focuses on the dynamc and steady state performance. A. Parameter desgn Accordng to the theoretcal analyss, the parameters of PI and PR controller are constrant by expressons (2), (26), (31) and (34). Thus, the crossover frequency, steady state error and phase margn need to be set forward. As the swtchng frequency s fxed to 1 khz, the crossover frequency s set to 1 khz. The steady state error s set to.5% to guarantee good steady state performance. The phase margn s set to 6 to ensure suffcent stablty margn. The corner frequency of PI controller s set to 3 Hz to avod nterference of steady state accuracy and stablty margn. Therefore, the parameters of the two controllers can be obtaned as n TABLE II. The Bode dagram of the regulated open-loop transfer functon s shown n Fg. 13. It can be seen that the crossover frequency of the control system s 7.13 1 3 rad/s, slghtly over the set value. The gan at fundamental frequency s 83.3 db, whch means a steady state error of 6.45 1-5, a far smaller TABLE II CONTROL PARAMETERS Parameters Values PI controller Proportonal rato kp_pi 1 Integral rato k 189 Proportonal rato kp_pr.1 PR controller Resonant rato kr 6.4 Dampng rato ω 3.14 CCF Feedback rato H.6 value than the set value. Ths s because the resonant rato k r s not only determned by the steady state error constrant expresson (31), but also PM constrant expresson (34). The larger k r s chosen here to meet both requrements. The phase of open-loop functon does not exceed the lne, valdatng that the gan margn s nfnte. Addtonally, the phase margn s 61.3, whch s close to the set value. Comparatve Bode dagrams of PI and compound controller are also shown n Fg. 13, both wthout CCF. Obvously, the former has greater crossover frequency and phase margn, ndcatng qucker response and better stablty than the proposed one. However, t s not able to effectvely suppress the harmoncs of the output currents. The compound controller wthout CCF suffers from the 18 phase shft of load resonance thus s not stable because of negatve gan margn. The voltage and current ratngs of the proposed groundng system also need to be dscussed. From the system topology, the voltage ratng relates to the neutral-to-ground voltage llustrated n (1) and (2). The compensated current of the groundng system s determned by the asymmetry of the dstrbuted parameters, whch s llustrated n (4). From these expressons, t can be observed that the worst case occurs n two-phase open-crcut condton. In ths condton, the neutral voltage rses to lne-to-neutral voltage and the compensated current reference reaches 1/3 of the system chargng current. Therefore, the nomnal voltage s dentcal to the lne-to-neutral voltage and the nomnal current s set to 1/3 of the system chargng current. Please note that t s not the objectve of the proposed groundng system to compensate the ground current n SLG fault. Actually, parallel connected Petersen Col s needed to provde large reactve power to compensate the ground current whch s manly capactve. B. Expermental results To verfy the proposed actve groundng system practcally, a 1kVA prototype s bult n laboratory, based on the topology n Fg. 1 and parameters n TABLE I. Slght change has been made to the topology that a step-up transformer s used to convert a 38V power supply to 1kV, substtutng the 11kV supply and transformer T d. The nverter of the groundng system manly conssts of two parallel connected sngle-phase IPM modules FF45R12ME4 from Infneon. The capacty of couplng transformer T s 1kVA. The nherent phase-to-ground capactance and resstance s realzed by two groups of capactors and resstors correspondng to nomnal Magntude(dB) Phase(deg) 8 6 4 2 2 18 9 18 27 sold:compound controller wth CCF dash-dot: PI controller wthout CCF dot: Compound controller wthout CCF Frequency(rad/s) Fg. 13. Bode dagrams of open-loop transfer functon wth compound controller and CCF.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 8 value n TABLE I and 3% of them to represent two dfferent load levels. The control methods dscussed above are executed n a dgtal sgnal processor TMS32F28335 development platform wth carrer waveform frequency of 1 khz. In the expermental process, a step-up of load from to 3% nomnal load s frstly carred out, followed by another step-up from 3% nomnal load to 1%. The controller of PI wthout CCF s taken as the comparatve controller to the proposed compound controller wth CCF. The reference values of output current are detected by the compensaton current detecton method proposed n Secton II. Dynamc waveforms subjectng to the two step-ups wth dfferent controllers are shown n Fg. 14 to Fg. 17. The error of the output current Δ o (see Fg. 7) s shown for explct observaton of the control performance. From the dynamc waveforms of output currents, t can be seen that both methods can reach stable system output. The adjustng tme of PI controller s slghtly smaller than the proposed method because of larger bandwdth of PI control system as shown n Fg. 13. However, Fg. 14 and Fg. 15 ndcate that PI method suffers from larger overshoot than the proposed method wth almost twce the value of output current and neutral-to-ground voltage, whch s harmful for the safety of power supply apparatus. It can be seen from Fg. 16 that wth PI method the percentage error of output current s smaller subjectng to 1% nomnal load than 3% of nomnal load, whch can be explaned by the load effect n secton III. Comparatvely, as shown n Fg. 17, wth the proposed controller, the percentage errors of output current before and after load change are relatvely closer than that of PI method, whch ndcates the proposed controller s more sutable for load change than PI controller. It should be notced that the dynamc process of neutral-to-ground voltage after load change are longer than that of output current, due to the large tme constant of the load. Fg. 18 and Fg. 19 show steady state waveforms of the two control methods subjectng to 1% nomnal load. Greater error n the fundamental components of output current error and neutral-to-ground voltage can be observed wth PI controller than the proposed method. Spectrum analyss ndcates that the neutral-to-ground voltage subjectng to the proposed method manly contan harmoncs wth ntegrally multple orders of the swtchng frequency. The neutral-to-ground voltage waveform n Fg. 18 shows a reduced voltage of around 42V subjectng to PI method. Spectrum analyss ndcates the total harmonc dstorton (THD) of the output current as 5.1%. From the output current and current error waveform n Fg. 19, t can be seen that the steady state error of the proposed method reaches 3%. The neutral-to-ground voltage s reduced by the groundng system wth the proposed method to around 21V, better than PI method. The THD of the output current wth the proposed method reaches 3.%, also better than that of PI method. Both (1kV/dv) (12kV/dv) u AG u BG u CG o (15A/dv) u AG u BG u CG Δo (15A/dv) o (3A/dv) (2kV/dv) t(1ms/dv) Fg. 14. Dynamc waveforms subjectng to load step-up from to 3% nomnal load wth PI controller. (2kV/dv) (1kV/dv) o (1A/dv) u AG u BG u CG Δo (2A/dv) Δo (1A/dv) t(1ms/dv) Fg. 16. Dynamc waveforms subjectng to load step-up from 3% nomnal load to 1% wth PI controller. (12kV/dv) o (3A/dv) u AG u BG u CG Δo (1A/dv) (1.5kV/dv) t(1ms/dv) Fg. 15. Dynamc waveforms subjectng to load step-up from to 3% nomnal load wth proposed method. (1.5kV/dv) t(1ms/dv) Fg. 17. Dynamc waveforms subjectng to load step-up from 3% nomnal load to 1% wth proposed method.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 9 (1kV/dv) o (3A/dv) Δo (5A/dv) (3V/dv) u CG u AG u BG t(1ms/dv) Fg. 18. Steady state waveforms subjectng to 1% nomnal load wth PI controller. (1kV/dv) o (3A/dv) u BG u CG u AG 1/(ω R s C s ), t yelds K G2( jc) L K H RC pwm (1 jd ) c. (A.1) 1 j( L ) o pwm s o c o RC s s ccs As the reactance of C s at crossover frequency s much smaller than that of L o and dω / ω c << 1, (A.1) can be rewrtten as clrc o s s G2( jc)= arctan. (A.2) L K H RC o pwm s o Usng (A.2) and (32), (33) can be rewrtten as 2kr clorc s s PM 18 arctan arctan k L K H RC p_pr c o pwm s o. (A.3) Equaton (A.3) can be rewrtten by an nequalty as 2kr clorc s s arctan arctan 18 PM. (A.4) k K H RC p_pr c pwm s o Applyng the tangent functon operaton to both sdes of (A.4), followng expresson can be obtaned. k c( r clc o s KpwmCoH tan PM) (A.5) k 2 ( L C tan PM K C H ) p_pr c o s pwm o Δo (2A/dv) (1V/dv) t(1ms/dv) Fg. 19. Steady state waveforms subjectng to 1% nomnal load wth proposed method. of the neutral-to-ground voltage and output current THD ndcate a better steady state performance of the proposed method than PI method. VI. CONCLUSION The proposed actve groundng system s able to effectvely constran the neutral-to-ground voltage to avod possble overvoltage caused by asymmetrcal dstrbuted parameters or resonance between Petersen col and phase-to-ground capactance. A practcal compensaton current detecton method s proposed whch frstly specfes the phase angle, and then the magntude of the current reference. Current control method s also presented whch conssts of a PR plus PI controller and capactve current feedback. The proposed control method s sutable for large range of load change and s mmune to possble resonance between load capactance and output LC flter nductance. Expermental results show that the proposed control method has better performance n dynamc and steady state than PI method. APPENDIX The lmt of k r /k p_pr constrant by phase margn (PM) s derved here. The expresson of G 2(jɷ c) can be easly obtaned from (13). Dvdng both the nomnator and denomnator by jω cr sc s, and consderng that C o<<c s and substtutng d for REFERENCES [1] IEEE Recommended Practce for Groundng of Industral and Commercal Power Systems, IEEE Std. 142-27, 27. [2] L. J. Kngrey, R. D. Panter, and A. S. Locker, Applyng Hgh-Resstance Neutral Groundng n Medum-Voltage Systems, IEEE Trans. Ind. App., vol. 47, no. 3, pp. 122 1231, May 211. [3] X. Zeng, Y. Xu, and Y. Wang, Some novel technques for nsulaton parameters measurement and Petersen-col control n dstrbuton networks, IEEE Trans. Ind. Electron., vol. 57, no. 4, pp. 1445 1451, Apr. 21. [4] A. Kalyuzhny, Analyss of Temporary Overvoltages Durng Open-Phase Faults n Dstrbuton Networks Wth Resonant Groundng, IEEE Trans. Power Del., vol.3, no.1, pp.42-427, Feb. 215. [5] X. Ln, J. Huang, and S. Ke, Faulty Feeder Detecton and Fault Self- Extngushng by Adaptve Petersen Col Control, IEEE Trans. Power Del., vol.26, no.2, pp.129-1291, Apr. 211. [6] M. Brenna, E. D. Berardns, L. D. Carpn, P. Paulon, P. Petron, G. Sapenza, G. Scrosat, and D. Zannell, "Petersen Col Regulators Analyss Usng a Real-Tme Dgtal Smulator," IEEE Trans. Power Del., vol.26, no.3, pp.1479-1488, July 211. [7] X. Zeng, K. K. L, W. L. Chan, S. Su, and Y. Wang, Ground-Fault Feeder Detecton Wth Fault-Current and Fault-Resstance Measurement n Mne Power Systems, IEEE Trans. Ind. App., vol. 44, no. 2, pp. 424 429, Mar. 28. [8] J. Tan, Q. Chen, L. Cheng, and Y. Zhang, "Arc-suppresson col based on transformer wth controlled load," IET Elect. Power App., vol.5, no.8, pp.644-653, September 211. [9] X. Chen, B. Chen, C. Tan, J. Yuan, and Y. Lu, "Modelng and Harmonc Optmzaton of a Two-Stage Saturable Magnetcally Controlled Reactor for an Arc Suppresson Col," IEEE Trans. Ind. Electron., vol.59, no.7, pp.2824-2831, July 212 [1] D. Paul, P. E. Sutherland, and S. A. R. Panetta, A Novel Method of Measurng Inherent Power System Chargng Current, IEEE Trans. Ind. App., vol. 47, no. 6, pp. 323 324, Nov. 211. [11] D. Dong, T. Thacker, R. Burgos, F. Wang, and D. Boroyevch, On zero steady-state error voltage control of sngle-phase PWM nverters wth dfferent load types, IEEE Trans. Power Electron., vol. 26, no. 11, pp. 3285 3297, Nov. 211. [12] Y. Tang, P. C. Loh, P. Wang, F. H. Choo, F. Gao, and F. Blaabjerg, Generalzed desgn of hgh performance shunt actve power flter wth output LCL flter, IEEE Trans. Ind. Electron., vol. 59, no. 3, pp. 1443 1452, Mar. 212.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 1 [13] F. Lu, Y. Zhou, S. Duan, J. Yn, B. Lu, and F. Lu, Parameter Desgn of a Two-Current-Loop Controller Used n a Grd-Connected Inverter System Wth LCL Flter, IEEE Trans. Ind. Electron., vol. 56, no. 11, pp. 4483 4491, Nov. 29. [14] G. Shen, X. Zhu, J. Zhang, and D. Xu, A New Feedback Method for PR Current Control of LCL-Flter-Based Grd-Connected Inverter, IEEE Trans. Ind. Electron., vol. 57, no. 6, pp. 233 241, Jun. 21. [15] X. Dong and S. Sh, "Identfyng Sngle-Phase-to-Ground Fault Feeder n Neutral Noneffectvely Grounded Dstrbuton System Usng Wavelet Transform," IEEE Trans. Power Del., vol. 23, no. 4, pp. 1829-1837, Oct. 28. [16] A. Kuperman, Proportonal-Resonant Current Controllers Desgn Based on Desred Transent Performance, IEEE Trans. Power Electron., vol. 3, no. 1, pp. 5341 5345, Oct. 215. [17] R. Peña-Alzola, M. Lserre, F. Blaabjerg, R. Sebastán, J. Dannehl, and F. W. Fuchs, Analyss of the Passve Dampng Losses n LCL-Flter-Based Grd Converters, IEEE Trans. Power Electron., vol. 28, no. 6, pp. 2642 2646, Jun. 213. [18] W. Wu, Y. He, T. Tang, and F. Blaabjerg, A New Desgn Method for the Passve Damped LCL and LLCL Flter-Based Sngle-Phase Grd-Ted Inverter, IEEE Trans. Ind. Electron., vol. 6, no. 1, pp. 4339 435, Oct. 213. [19] M. Lserre, R. Teodorescu, and F. Blaabjerg, Stablty of photovoltac and wnd turbne grd-connected nverters for a large set of grd mpedance values, IEEE Trans. Power Electron., vol. 21, no. 1, pp. 263 272, Jan. 26. [2] Erckson and D. Maksmovc, Fundamentals of Power Electroncs, 2nd ed. Norwell, MA, USA: Kluwer, 21, pp. 331 48. [21] C. Bao, X. Ruan, X. Wang, W. L, D. Pan, and K. Weng, Step-by-Step Controller Desgn for LCL-Type Grd-Connected Inverter wth Capactor Current-Feedback Actve-Dampng, IEEE Trans. Power Electron., vol. 29, no. 3, pp. 1239-1253, Mar. 214. Wen Wang (M 14) receved the B.S. and Ph.D. degrees n electrcal engneerng from Hunan Unversty, Changsha, Chna, n 28 and 213, respectvely. Snce 213, he has been an Assstant Professor wth the School of Electrcal and Informaton Engneerng, Changsha Unversty of Scence and Technology, Changsha, Chna. In 216, he s a Guest Researcher n the Department of Energy Technology, Aalborg Unversty, Aalborg, Denmark. Hs current research nterests nclude power electroncs, groundng methods n dstrbuton networks. Lngje Yan was born n Hube Provnce, Chna, n 199. He receved the B.S. degree n electrcal engneerng and automaton from Huazhong Unversty of Scence and Technology, Wuhan, Chna, n 21. He s currently workng toward hs M.S. degree n electrcal engneerng at Changsha Unversty of Scence and Technology, Changsha, Chna. Hs research nterests nclude power electronc technology n flexble groundng system. Xangjun Zeng (M 3) receved the B.S. degree from Hunan Unversty, Changsha, Chna, n 1993, the M.S. degree from Wuhan Unversty, Wuhan, Chna, n 1996, and the Ph.D. degree from Huazhong Unversty of Scence and Technology, Wuhan, Chna, n 21, all n electrcal engneerng. He worked as post-doctoral fellow n Xuj Relay Company and the HongKong Polytechnc Unversty and a Vstng Professor at Nanyang Technologcal Unversty, Sngapore, Sngapore. He s now a Professor and Dean of the School of Electrcal and Informaton Engneerng, Changsha Unversty of Scence and Technology, Changsha, Chna. Hs research nterests nclude real-tme computer applcaton n power systems control and protecton. Bshuang Fan receved the B.S. degree n automaton control n 22, and the M.S. degree n automaton of electrc power system n 27, both from Changsha Unversty of Scence and Technology, Changsha, Chna, and the Ph.D. degree n control scence and engneerng from Central South Unversty, Changsha, Chna, n 214. Snce 215, he has been an Assocate Professor wth the School of Electrcal and Informaton Engneerng, Changsha Unversty of Scence and Technology, Changsha, Chna. In 216, he s a Vstng Scholar at the power electroncs laboratory n the Department of Electrcal Engneerng and Computer Scence, Unversty of Tennessee, Tennessee, USA. Hs current research nterests nclude power converson technologes. Josep M. Guerrero (S 1-M 4-SM 8-FM 15) receved the B.S. degree n telecommuncatons engneerng, the M.S. degree n electroncs engneerng, and the Ph.D. degree n power electroncs from the Techncal Unversty of Catalona, Barcelona, n 1997, 2 and 23, respectvely. Snce 211, he has been a Full Professor wth the Department of Energy Technology, Aalborg Unversty, Denmark, where he s responsble for the Mcrogrd Research Program (www.mcrogrds.et.aau.dk). From 212 he s a guest Professor at the Chnese Academy of Scence and the Nanjng Unversty of Aeronautcs and Astronautcs; from 214 he s char Professor n Shandong Unversty; from 215 he s a dstngushed guest Professor n Hunan Unversty; and from 216 he s a vstng professor fellow at Aston Unversty, UK, and a guest Professor at the Nanjng Unversty of Posts and Telecommuncatons. Hs research nterests s orented to dfferent mcrogrd aspects, ncludng power electroncs, dstrbuted energy-storage systems, herarchcal and cooperatve control, energy management systems, smart meterng and the nternet of thngs for AC/DC mcrogrd clusters and slanded mngrds; recently specally focused on martme mcrogrds for electrcal shps, vessels, ferres and seaports. Prof. Guerrero s an Assocate Edtor for the IEEE TRANSACTIONS ON POWER ELECTRONICS, the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, and the IEEE Industral Electroncs Magazne, and an Edtor for the IEEE TRANSACTIONS on SMART GRID and IEEE TRANSACTIONS on ENERGY CONVERSION. He has been Guest Edtor of the IEEE TRANSACTIONS ON POWER ELECTRONICS Specal Issues: Power Electroncs for Wnd Energy Converson and Power Electroncs for Mcrogrds; the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Specal Sectons: Unnterruptble Power Supples systems, Renewable Energy Systems, Dstrbuted Generaton and Mcrogrds, and Industral Applcatons and Implementaton Issues of the Kalman Flter; the IEEE TRANSACTIONS on SMART GRID Specal Issues: Smart DC Dstrbuton Systems and Power Qualty n Smart Grds; the IEEE TRANSACTIONS on ENERGY CONVERSION Specal Issue on Energy Converson n Next-generaton Electrc Shps. He was the char of the Renewable Energy Systems Techncal Commttee of the IEEE Industral Electroncs Socety. He receved the best paper award of the IEEE Transactons on Energy Converson for the perod 214-215, and the best paper prze of IEEE- PES n 215. In 214 and 215 he was awarded by Thomson Reuters as Hghly Cted Researcher, and n 215 he was elevated as IEEE Fellow for hs contrbutons on dstrbuted power systems and mcrogrds.