J Electr Eng Technol Vol. 9, No. 5: 1746-175, 014 htt://dx.do.org/10.5370/jeet.014.9.5.1746 ISSN(Prnt) 1975-010 ISSN(Onlne) 093-743 An Alcaton of Proortonal-Resonant Controller n MMC-HVDC System under Unbalanced Voltage Condtons Ngoc-Thnh Quach, J-Han Ko, Dong-Wan Km and Eel-Hwan Km Abstract Ths aer resents an alcaton of roortonal-resonant (PR) current controllers n modular multleel conerter-hgh oltage drect current (MMC-HVDC) system under unbalanced oltage condtons. The ac currents are transformed and controlled n the statonary reference frame (αβ-frame). Thus, the comlex analyss of the oste and negate sequence comonents n the synchronous rotatng reference frame (dq-frame) s not necessary. Wth ths control method, the ac currents are et balanced and the dc-ln oltage s constant under the unbalanced oltage fault condtons. The smulaton results based on a detaled PSCAD/EMTDC model confrm the effecteness of the roosed control method. Keywords: Integral-roortonal controller, Modular multleel conerter-hgh oltage drect current system, Negate sequence comonent, Proortonal-resonant controller, Unbalanced oltage condtons 1. Introducton The modular multleel conerter (MMC)-based hgh oltage drect current (HVDC) system s a new tye of oltage source conerter (VSC) for medum or hgh oltage drect current ower transmsson. Recently, t has become more comette because t has adantages oer normal VSC-HVDC system such as low total harmonc dstorton, hgh effcency, and hgh caacty [1, ]. The oeraton of the MMC-HVDC system has been nestgated by many authors oer the world. In [3-5], the authors resented the control strateges for elmnatng the crculatng currents and mantanng the caactor oltage balancng of the MMC. The dynamc erformances of the MMC-HVDC system hae been analyzed n [6]. Smlar to other HVDC systems, the stable and relable oeraton of the system must be researched carefully, esecally when the system oerates under fault condtons. In [6-8], the authors showed out the control methods of the MMC-HVDC system under the unbalanced oltage condtons. Almost all of them only focus on the use of roortonal-ntegral (PI) current controllers n the synchronous rotatng reference frame (dq-frame) for enforcng steady-state error to zero. Howeer, the use of these PI current controllers wll be dffcult under the unbalanced oltage condtons because of the comlex control of the oste and negate sequence comonents of the currents [6-8]. Recently, the smle roortonal-resonant (PR) current controllers n the statonary reference frame (αβ-frame) hae been deeloed Corresondng Author: Det. of Electrcal Engneerng, Jeju Natonal Unersty, S. Korea. (ehm@jejunu.ac.r) Det. of Electrcal Engneerng, Jeju Natonal Unersty, S. Korea. (ngoct1984@yahoo.com) Multdsclnary Graduate School Program for Wnd Energy, Jeju Natonal Unersty, S. Korea. ({Jhon-e, seg305}@naer.com) Receed: October 4, 013; Acceted: Arl 7, 014 to oercome ths roblem [10]. The most mortant erformance of the PR current controllers s that the currents are controlled drectly n the αβ-frame. Therefore, the comlcated analyss of the oste and negate sequence comonents of the currents s gnored. Ths aer resents an alcaton of the PR current controllers n the MMC-HVDC system under the unbalanced oltage condtons. The comlcated analyss of the oste and negate sequence comonents n the dq-frame s not necessary because the currents are controlled drectly n the αβ-frame. The uroses are to ee a balance on the ac currents and a constant on the dc-ln oltage. The rest of ths aer s organzed as follows. Secton s the confguraton of the MMC-HVDC system. The roosed control method of the MMC-HVDC system s resented n Secton 3. Secton 4 s the smulaton results. Fnally, Secton 5 draws the conclusons.. Confguraton of the MMC-HVDC System The confguraton of the MMC-HVDC system s dected n Fg. 1. A MMC-HVDC system conssts of two bac-tobac-connected MMC unts. Each MMC s structured by sx arms as shown n Fg. 1. Each arm has a total of N sub-modules (SM) connected n seres and a seres nductor whch rodes current control wthn the hase arms and lmts fault currents. Two arms n the same leg comrse a hase unt. A SM s a half-brdge cell whch conssts of two IGBTs, two ant-arallel dodes, and a caactor. The acsde of each MMC s connected to a unty grd through a seres-connected resstance and nductance and a wye-delta three-hase transformer. The outut oltage of each SM, sm, has two alues: () sm = c f T 1 s swtched on and T s swtched off, () sm 1746
Ngoc-Thnh Quach, J-Han Ko, Dong-Wan Km and Eel-Hwan Km P 1, Q 1 g1 s1 t1 R L P, Q t L R s g Source 1 1 Source Fault SM1 SM1 SM1 uer arm SM SM SM hase unt ua ub uc R R R L L L a b c L 0 L 0 L 0 ta tb tc V dc L 0 L 0 L 0 lower arm la lb lc SM1 SM1 SM1 SM SM SM sm - T 1 T - c Sub-module Fg. 1. Confguraton of the MMC-HVDC system: sngle-lne dagram; crcut confguraton = 0 f T 1 s swtched off and T s swtched on. The chargng or dschargng of the caactor deends on the drecton of the current. If the current flows nto the SM, the caactor s charged. If the current flows out of the SM, the caactor s dscharged. 3. The Proosed Control Method of the MMC-HVDC System 3.1 Proortonal-resonant controller The PR controller has been analyzed n [10]. A PR controller s consttuted by the roortonal regulator and resonant controller. The transfer functon of the deal PR controller wth an nfnte gan at the ac frequency of ω s gen by Ks G = K (1) s ω The K s the roortonal gan that s adjusted as the same way for a PI controller. The K can be tuned for shftng the magntude resonse ertcally. Bode lots of the PR controller are shown n Fg.. As mentoned before, the magntude s nfnte at the resonant frequency, ths s necessary to enforce the steady-state error to zero. The magntude resonse of the PR controller s ncreasng wth the ncrease of the alue of K (Fg. ). A small K ges a low resonant ea, whereas a large K ges a hgher resonant ea (Fg. ). The adantage of the PR controller s that t can control drectly sgnals n the αβ-frame. Hence, a transformaton nto the dq-frame s not necessary. Ths s ery mortant n case of the unbalanced oltage condtons. Because the sgnals n the αβ-frame only hae one comonent wth the frequency of ω, the analyss of the oste and negate comonents under the unbalanced oltages s thus gnored. As a result, the control system wth the PR controller wll be more smle than that wth the PI controller. 3. The current controllers Under the unbalanced oltage condtons, the conentonal method s to analyze the oste and negate sequence comonents n the dq-frame [6-9]. The transformaton between the oste (dq), negate (dq) - and αβ-frames are gen by [9]. 1747
An Alcaton of Proortonal-Resonant Controller n MMC-HVDC System under Unbalanced Voltage Condtons Fg.. Bode lots of the PR controller: Changng K and Fxng K ; Fxng K and Changng K F dq jθ F dq = Fαβ. e Fdq = Fαβ. jθ jθ Fdq = Fdq. e e jθ = F. e (3) dq where θ=ωt. F denotes the ector of the oltage and current. Suerscrts and - refer to the oste (dq) and negate (dq) - -frames, resectely. Howeer, ths control method s comlcated and t requres more current controllers due to the negate sequence comonents. A more smle method s to analyze the oeraton of the system n the αβ-frame because there s only one comonent wth the frequency of ω n the αβframe under the unbalanced oltage condtons. From Fg. 1, the ac-sde hase oltages are calculated by d = (4) t _ j _ j s _ j _ jr L where j s the three-hase comonents of the oltages or currents, j = a, b, c. denotes to the MMC-1 and MMC-, = 1,. s_j, t_j, and _j are the three-hase oltages and currents of the MMC-. R and L are the resstance and nductance of the system, resectely. These oltages can be rewrtten n the αβ-frame as d _ α s _ α = _ α R L t _ α (5) d s = R L t (6) where s_α, s_β, t_α, t_β, _α and _β are the αβ-axs comonents of the three-hase oltages and currents of the MMC-. From (5) and (6), the PWM oltages can be calculated as () d t = R L (8) s The PWM oltages wll deend on the control of the ac currents. The current controllers used n ths aer are the PR current controllers. The α-axs current s used to control the reacte ower, meanwhle the β-axs current s emloyed to control the acte ower or the dc-ln oltage. The current controllers can be descrbed as ( _ α _ α ) s _ α ( ) s Ks t _ α = K s ω (9) Ks t = K s ω (10) where the suerscrt denotes the reference alues of the sgnals. Assumng that the three-hase currents are et n balance under the unbalanced oltage condtons wth the PR current controllers. Therefore, the negate sequence comonent of the currents s zero. The nstantaneous ower at the ac-sde can be exressed by P Q ( s _ d. _ d s _ q. _ q ) (. ) 3 = (11) 3 s _ d _ q s _ q. _ d = (1) where P and Q are the acte and reacte owers at the acsde, resectely. s _ d and s _ q are the dq-axs comonents of the oltages n the oste (dq) -frame. Because s _ d = 0, the reference currents n dq-frame can be rewrtten as d _ α t _ α = _ α R L (7) s _ α _ q = 3 P s _ q (13) 1748
Ngoc-Thnh Quach, J-Han Ko, Dong-Wan Km and Eel-Hwan Km roosed control method for the MMC-HVDC system under the same fault as the frst case. The arameters of the MMC-HVDC system are shown n Table 1. The MMC-1 s used to control the dc-ln oltage and the reacte ower, meanwhle the MMC- s used to control the acte and reacte owers. In the case of study, the command acte ower s set at 00 MW and t s flowng from the MMC-1 to the MMC-. The command reacte ower s zero at Fg. 3. Oerall control dagram of the MMC-HVDC system _ d = 3 Q s _ q (14) If the MMC- s used to control the dc-ln oltage, the q-axs comonent of the reference current s modfed by [6, 7] _ q K s ( V V ) = K dc dc (15) where V dc s the dc-ln oltage. The band sto flter can be used to flter the double frequency oscllaton comonent n the dc-ln oltage. Fnally, these current comonents are transformed nto the αβ-frame by usng () to get the reference currents for (9) and (10). The oerall control dagram of the MMC-HVDC system s shown n Fg. 3. The outer control loo s emloyed to control the acte ower, the reacte ower and dc-ln oltage wth the PI controllers. The outut sgnals of the outer control loo are the reference currents n the dqframe, and these currents are then transformed nto the αβframe. The nner control loo s used to control the currents wth the PR current controllers. The outut sgnals of the nner control loo are the reference oltages that are aled to the PWM method and the caactor oltage balancng method to get the gatng sgnals for IGBTs. The q-axs current comonent of the MMC- n Fg. 3 wll be relaced by the Fg. 3 f the MMC- s used to control the dc-ln oltage. 4. Smulaton results To ealuate the effecteness of the roosed control methods, the smulaton results are carred out n two cases wth the suort of the PSCAD/EMTDC model. The frst case s the control of the MMC-HVDC system under sngle hase-to-ground (SPG) fault wth the PI current controllers and wthout comensatng the negate sequence comonent of the currents. Another case s the use of the (c) (d) (e) (f) (g) (h) () Fg. 4. The oeraton of the MMC-HVDC system wth the PI current controllers and wthout comensatng the negate sequence comonent of the currents under the sngle hase-to-ground fault: MMC- threehase oltages; MMC- three-hase currents; (c) MMC- acte and reacte owers; (d) dc-ln oltage; (e) MMC- caactor oltages; (f) MMC-1 three-hase oltages; (g) MMC-1 three-hase currents; (h) MMC-1 acte and reacte owers; () MMC-1 caactor oltages. 1749
An Alcaton of Proortonal-Resonant Controller n MMC-HVDC System under Unbalanced Voltage Condtons both MMC. The SPG fault on the ac-sde of the MMC- occurs at t = 0.4 s and remoes at t = 0.6 s. The smulaton results n two cases are descrbed n Fg. 4 and Fg. 5, resectely. From t = 0. s to t = 0.4 s, the oeraton of the MMC- HVDC system n the steady-state n two cases are almost the same. Howeer, t s qute dfferent when the system oerates under the SPG fault. Fgs. 4 and Fg. 5 show the three-hase oltages of the MMC-. The threehase currents of the MMC- are resented n Fg. 4 and Fg. 5. It can be seen that the currents are not balanced wthout comensatng the negate sequence comonent of the currents (Fg. 4). Wth the PR controller, t comensates both oste and negate sequence comonents. Therefore, the three-hase currents are balanced as dected n Fg. 5. In ths case, the currents are controlled u to the ratng alue to achee the maxmum ower. Because the fault occurs at the ac-sde of the MMC-, the acte ower receed at the MMC- decreases and there s no oscllaton n the ower wth the PR current controllers (Fg. 5(c)). Meanwhle, there s a large oscllaton n the ower wth the PI current controllers (Fg. 4(c)). By usng the roosed control method, the dc-ln oltage s almost controlled at the reference alue as shown n Fg. 5(d). Fgs. 4(e) and Fg. 5(e) dect the caactor oltages of the uer arm of hase-a n two cases, resectely. Besdes, the three-hase oltages and currents of the MMC-1 are also shown n Fgs. 4(f)-(g) and Fgs. 5(f)-(g). The acte and reacte owers of the MMC-1 are dected n Fg. 4(h) and Fg. 5(h). Because the acte ower receed at the MMC- decreases, the acte ower transferred from the MMC-1 also decreases at the same tme to mae a ower balancng of the system (Fg. 5(h)). Fnally, Fgs. 4() and Fg. 5() resent the caactor oltages of the MMC-1. () (e) (h) (d) (g) (c) (d) (c) (f) (e) Fg. 5. The oeraton of the MMC-HVDC system wth the PR current controllers under the sngle hase-toground fault: MMC- three-hase oltages; MMC- three-hase currents; (c) MMC- acte and reacte owers, (d) dc-ln oltage; (e) MMC- caactor oltages; (f) MMC-1 three-hase oltages; (g) MMC-1 three-hase currents; (h) MMC-1 acte and reacte owers; () MMC-1 caactor oltages. (f) Fg. 6. The adjustng ablty of the PR current controllers: MMC- three-hase oltages; MMC- threehase currents; (c) MMC- acte and reacte owers; (d) dc-ln oltage; (e) MMC-1 three-hase currents; (f) MMC-1 acte and reacte owers. 1750
Ngoc-Thnh Quach, J-Han Ko, Dong-Wan Km and Eel-Hwan Km Table 1. Parameters of the MMC-HVDC system Quantty Acte ower AC system oltage Nomnal frequency Transformer rato dc-ln oltage Number of SMs er arm MMC swtchng frequency Sub-module caactor Value 00 MW 154 V 60 Hz 154 V/55.1135 V ±50 V 10 5 Hz 3300 μf To ealuate a more conncngly the control ablty of the PR current controllers under the unbalanced oltage condtons, another smulaton s set u. In ths case, the command acte ower s set at 100 MW. The smulaton results are shown n Fg. 6. The SPG fault occurs at 0.4 s and restores at 0.6 s as shown n Fg. 6. Durng faults, the PR current controllers control the currents to the reference alue to get the command ower or at least to get the maxmum net ower as dected n Fgs. 6-(c). As seen n Fg. 6(c), the acte ower reaches ts command alue durng the SPG fault. Fg. 6(d) shows the dc-ln oltage, t has a ery small oscllaton. The three-hase currents and the acte and reacte owers of the MMC-1 are exressed n Fgs. 6(e)-(f). 5. Conclusons Ths aer resents an alcaton of the PR controller n the MMC-HVDC system under the unbalanced oltage condtons. Wth the PR controller, the comlcated analyss of the oste and negate sequence comonents n the dq-frame s not necessary. The currents are controlled drectly n the αβ-frame. The smulaton results hae demonstrated that the ac currents are et balanced and the dc-ln oltage s constant under the unbalanced oltage condtons. Besdes, the adjustng ablty of the PR current controllers to get the command ower or the maxmum ower has been also confrmed. Acnowledgements Ths wor was suorted by the Deeloment of 0MW VSC HVDC for offshore wnd-farm nterconnecton of the Korea Insttute of Energy Technology Ealuaton and Plannng (KETEP), granted fnancal resource from the Mnstry of Trade, Industry & Energy, Reublc of Korea. (No. 01T10001551). Ths wor was suorted by the Exanson of the Tye Testng Ste for Wnd Turbnes (NO.01T10001731) of the Korea Insttute of Energy Technology Ealuaton and Plannng (KETEP) grant funded by the Korea goernment Mnstry of Trade, Industry and Energy. References [1] S. Allebrod, R. Hamers, and R. Marquar, New Transformerless, Scalable Modular Multleel Conerters for HVDC-Transmsson, IEEE Power Electroncs Secalsts Conference, PESC 008,. 174-179, 008. [] S. Rohner, S. Bernet, M. Hller, and R. Sommer, Modulaton, Losses, and Semconductor Requrements of Modular Multleel Conerters, IEEE Transactons on Industral Electroncs, ol. 57, no. 8,. 633-64, Aug. 010. [3] M. Hagwara and H. Aag, Control and Exerment of Pulsewh-Modulated Modular Multleel Conerters, IEEE Transactons on Power Electroncs, ol. 4, no. 7,. 1737-1746, July 009. [4] Jangchao Qn and Maryam Saeedfard, Predcte Control of a Modular Multleel Conerter for a Bac-to-Bac HVDC System, IEEE Transacton on Power Delery, ol. 7, no. 3,. 1538-1547, July 01. [5] Qngru Tu, Zheng Xu, and Le Xu, Reduced Swtchng-Frequency Modulaton and Crculatng Current Suresson for Modular Multleel Conerters, IEEE Transactons on Power Delery, ol. 6, no. 3,. 009-017, July 011. [6] M. Saeedfard and R. Iraan, Dynamc Performance of a Modular Multleel Bac-to-Bac HVDC System, IEEE Transactons on Power Delery, ol. 5, no. 4,. 903-91, Oct. 010. [7] Mnyuan Guan and Zheng Xu, Modelng and Control of a Modular Multleel Conerter-Based HVDC System under Unbalanced Grd Condtons, IEEE Transactons on Power Electroncs, ol. 7, no. 1,. 4858-4867, Dec. 01. [8] Qngru Tu, Zheng Xu, Young Chang, and L Guan, Suressng DC Voltage Rles of MMC-HVDC under Unbalanced Grd Condtons, IEEE Transactons on Power Delery, ol. 7, no. 3,. 133-1338, July 01. [9] Qngru Tu, Zheng Xu, Young Chang, and L Guan, Suressng DC Voltage Rles of MMC-HVDC System under Unbalanced Grd Condtons, IEEE Transactons on Power Delery, ol. 7, no. 3,. 133-1338, July 01. [10] Le Xu and Y Yang, Dynamc Modelng and Control of DFIG-Based Wnd Turbnes under Unbalanced Networ Condtons, IEEE Transactons on Power Systems, ol., no. 1,. 314-33, Feb. 007. [11] R. Teodorescu, F. Blaabjerg, M. Lserre, and P. C. Loh, Proortonal-Resonant Controllers and Flters for Grd-Connected Voltage-Source Conerters, n IEE Proceedngs Electrc Power Alcatons, ol. 153, no. 5,. 750-76, 006. 1751
An Alcaton of Proortonal-Resonant Controller n MMC-HVDC System under Unbalanced Voltage Condtons Ngoc-Thnh Quach He receed a B.S. degree n Electrcal Engneerng from Can Tho Unersty, Vetnam, n 007 and a M.S. degree n Electrcal Engneerng from Jeju Natonal Unersty, S. Korea, n 01. He s currently a PhD canddate n the Deartment of Electrcal Engneerng, Jeju Natonal Unersty, S. Korea. Hs research nterests nclude wnd energy systems, HVDC systems, and ower system stablty. J-Han Ko He receed a B.S. degree n Electrcal Engneerng from Jeju Natonal Unersty, S. Korea, n 01. He s currently a M.S. student n the Multdsclnary Graduate School Program for Wnd Energy, Jeju Natonal Unersty, S. Korea. Hs research nterests nclude wnd energy systems, HVDC system, and ower electroncs. Dong-Wan Km He receed a B.S. degree n Electrcal Engneerng from Jeju Natonal Unersty, S. Korea, n 01. He s currently a M.S. student n the Multdsclnary Graduate School Program for Wnd Energy, Jeju Natonal Unersty, S. Korea. Hs research nterests nclude wnd energy systems, mcro grd, and ower electroncs. Eel-Hwan Km He receed hs B.S., M.S. and Ph.D. degrees n Electrcal Engneerng from Chung-Ang Unersty, Seoul, Korea, n 1985, 1987 and 1991, resectely. Snce 1991, he has been wth the Deartment of Electrcal Engneerng, Jeju Natonal Unersty n Jeju, Korea, where he s currently a rofessor. He was a Vstng Scholar at the Oho State Unersty n 1995 and Unersty of Washngton n 004. Hs research acttes are n the area of ower electroncs and control, whch ncludes the dre system, renewable energy control alcatons, and ower qualty. He s a member of KIEE, KIPE, and IEEE. 175