Research on a Low-Harmonic Nearest Level Modulation Method for Modular Multilevel Converters Pengfei Hu1, a, Xi Wang1, Lun Tang1,

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1 6th International Conference on Machinery, Materials, Environment, Biotechnology an Computer (MMEBC 06) Research on a ow-harmonic Nearest evel Moulation Metho for Moular Multilevel Converters Pengfei Hu, a, Xi Wang, un Tang, Sichuan Electrical Power Research Institute, Chengu, 6007, China a hupengfei0@63.com Keywors: Moular Multilevel Converters; Moulation strategy; Control Strategy Abstract. Moular Multilevel Converters (MMC) have been wiely applie in meium- an high-voltage applications such as High Voltage Direct Current (HVDC) Transmission. Hence, the moulation metho which can generate low harmonic waves with low losses is quite suit for the HVDC conition. This paper proposes a new nearest level moulation (NM) metho for the MMC, with which can ecrease the harmonic components. sing this metho, the level number of the MMC is almost ouble an the height of the in the wave is halve. The performance of the propose metho is verifie by simulations with the PSCAD/EMTDC software. Introuction In recent years, the MMC has attracte much attention by acaemic scholars resulting in large numbers of research publications, which focus on mathematical moeling []-[], moulation methos [3]-[4], control strategies [5], capacitor-voltage balancing [6], an so on. As to the moulation methos for MMCs, there are mainly two types (i.e. pulse with moulations (PWMs) an wave moulations). Furthermore, PWM methos inclue the carrier-phase-shifte PWM (CPSPWM), the sub-moule unifie PWM (SPWM) an the improve SPWM, sharing some common features such as high switching frequency, large switching losses an complex implementation process. Among the PWM methos, the CPSPWM an improve SPWM can generate output voltages with N+ levels while the conventional SPWM can only generate output voltages with N+ levels. As for wave moulation methos, they mainly inclue selective harmonic elimination (SHE) metho [7] an nearest level moulation (NM) metho [8], which share some common characteristics such as low switching frequency an N+ levels. Compare to the SHE metho, the NM metho oes not nee a complex calculation of the trigger angles, making NM metho the simplest an most practical moulation metho for the MMC. However, in spite of the low switching frequency an simple implementation, the NM metho generates poorer quality waveforms than the CPSPWM an the improve SPWM methos in case of small numbers of sub-moules. Therefore, the NM metho is mainly applie in high voltage applications where the number is large enough to improve the output voltage. In orer to improve the performance of the NM metho in case of a small number of sub-moules, this paper proposes a moifie NM metho with which the maximum level number reaches N+ as the same as that with the CPSPWM an the improve SPWM methos. The outline of this paper is organize as follows: Principles of the MMC are briefly presente in section II. The propose NM metho is presente an analyze in section III. In section IV, simulation an results verify the propose metho. Principles of MMCs The topology of a single-phase MMC as shown in Fig. (a) consists of the upper an lower arms, each forme by N series-connecte ientical half-brige sub-moules as well as one arm inuctor. Applying Kirchhoff s Voltage aw (KV) an Kirchhoff s Current aw (KC) in Fig. (a) yiels 06. The authors - Publishe by Atlantis Press 7

2 i u u t i u u t () i i i () i u N R i u u R u ue i Fig. (a) Topology of the single-phase MMC; (b) equivalent circuit of the MMC The equivalent circuit of the MMC is shown in Fig. (b). From () an (), the output voltage can be expresse as i u ( u u ) (3) t It can be seen from (3) that the ac electromotive force (EMF) of the MMC is written as ue ( u u ) (4) In general, the reference value of ac EMF is expresse as ref m ue cos( t) (5) where m(0 m ) is the moulation inex an is the angular frequency. With the conventional NM metho, N sub-moules are inserte in the circuit. Therefore, the following equation is satisfie on the sie. u u (6) From (5) to (7), reference voltages of the upper an lower arms are etermine by ref u [mcos( t)] (7) ref u [mcos( t)] Without reunant sub-moules, the sub-moule capacitor voltage an the voltage satisfy the following equation. 8

3 N (8) ow Harmonic NM Metho Fig. illustrates the principle of the low harmonic NM metho. It is worth noting that the moments of changing in u an u are not exactly the same. The level numbers of arm voltages are N+, while the level number of output voltage is N+. Moreover, the height of the in u e ecreases to 0.5. This little ifference leas to substantially increase levels. Fig. Principles of the low harmonic NM metho To shift the moments of changing in the upper- an lower-arm voltages, the arm inserte sub-moule numbers shoul be moifie as expresse in (9). The roun function (roun0.5(x)) means that the real number x is roune to the nearest whole number accoring to the ecimal fraction of x. If the ecimal fraction of x is bigger than 0.5, x is roune up to the next whole number, otherwise roune own to the next whole number. The overall iagram of the moifie NM metho is illustrate in Fig.3. N roun0.5 [m cos( t)] (9) N roun0.5 [m cos( t)] Equation (7) N N D D roun ( x) 0.5 RSF voltage balancing algorithm Firing pulses Fig.3 Overall iagram of the moifie NM metho Simulation Results The simulation is carrie out in the PSCAD/EMTDC software with circuit parameters liste in Table. I. 9

4 Table.I Main circuit parameters for simulations Items Symbols Values Rate AC line-line voltage s 35 kv AC system inuctance ac 5 mh AC system resistance R ac 0.03 ohm Rate frequency f 50 Hz Rate irect voltage ±5 kv Arm inuctance 5 mh Total number of SMs per arm N 0 Capacitor voltage kv SM capacitance C 7000 uf Fig.4 - Fig.6 show the simulation results with both the conventional an low harmonic NM methos. When using the conventional NM metho, the three-phase ac voltages on the converter sie appear evient istortion an the total harmonic istortion (THD) reaches 5.90%. Since currents flow through the sub-moule capacitors, the s are smoothe by the fluctuation of sub-moule capacitor voltages. Anyway, it also can be seen levels in the ac voltages. Besies, the THD of three-phase ac currents reaches 4.86%, which is cause by the harmonics of the ac voltages. When using the low harmonic NM metho, THDs of the three-phase ac voltages an currents are reuce to.0% an 0.79%, respectively. The voltage s are too many an small to recognize. Moreover, the sub-moule capacitor voltages ecrease a little with the low harmonic NM metho as shown in Fig.5. This is because the total number of inserte sub-moules varies between N an N+ (i.e. equivalent number is greater than N) with the low harmonic NM metho. The variation of the total number of inserte sub-moule also leas to larger voltage across the upper an lower arm inuctors as shown in Fig.5. Fig.6 shows that the error in i is reuce with the low harmonic NM metho. Fig.4 Three-phase ac voltages an currents Fig.5 capacitor voltages an the upper an lower inuctor voltage Fig.6 The active current (i ) 30

5 Conclusion A low harmonic NM metho for moular multilevel converters, which can generate N+ level ac output voltage, is propose in this paper. The level number of ac output voltage with the low harmonic NM metho is almost ouble than that with the conventional NM metho. Compare to the improve SPWM an CPSPWM methos, which can both generate N+ level ac output voltage, the low harmonic NM metho has lower switching frequency. Principles of the low harmonic NM metho are presente. Simulation results valiate the effectiveness of the low harmonic NM metho. References [] Harnefors, l.; Antonopoulos, A.; Norrga, S.; Angquist,.; Nee, H.-P., "Dynamic Analysis of Moular Multilevel Converters," Inustrial Electronics, IEEE Transactions on, vol.60, no.7, pp.56,537, July 03 [] Antonopoulos, A.; Angquist,.; Harnefors,.; Ilves, K.; Nee, H.-P., "Global Asymptotic Stability of Moular Multilevel Converters," Inustrial Electronics, IEEE Transactions on, vol.6, no., pp.603,6, Feb. 04 [3] Ilves, K.; Antonopoulos, A.; Norrga, S.; Nee, H-.P.;, "A New Moulation Metho for the Moular Multilevel Converter Allowing Funamental Switching Frequency," Power Electronics, IEEE Transactions on, vol.7, no.8, pp , Aug. 0 [4] Zixin i; Ping Wang; Haibin Zhu; Zunfang Chu; Yaohua i, "An Improve Pulse With Moulation Metho for Chopper-Cell-Base Moular Multilevel Converters," Power Electronics, IEEE Transactions on, vol.7, no.8, pp.347,348, Aug. 0 [5] Jiangchao, Q. an M. Saeeifar, Preictive Control of a Moular Multilevel Converter for a Back-to-Back HVDC System. Power Delivery, IEEE Transactions on, 0. 7(3): p [6] Kui Wang; Yongong i; Zeong Zheng; ie Xu, "Voltage Balancing an Fluctuation-Suppression Methos of Floating Capacitors in a New Moular Multilevel Converter," Inustrial Electronics, IEEE Transactions on, vol.60, no.5, pp.943,954, May 03 [7] uois, D.C.; Venkataramanan, G., "Simplifie Terminal Behavioral Moel for a Moular Multilevel Converter," Power Electronics, IEEE Transactions on, vol.9, no.4, pp.6,63, April 04 [8] Minyuan Guan; Zheng Xu; Hairong Chen, "Control an moulation strategies for moular multilevel converter base HVDC system," IECON 0-37th Annual Conference on IEEE Inustrial Electronics Society, vol., no., pp.849,854, 7-0 Nov. 0 3