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Modulation and control for cascaded multilevel converters Modulation and control for cascaded multilevel converters Marco Liserre [email protected] Marco Liserre [email protected] Modulation and control for cascaded multilevel converters A glance at the lecture content • Cascaded multilevel converters: • hybrid solution • applications • PI-based control • Multilevel modulations in case of time-varying dc voltages: • generalized hybrid modulation • generalized phase-shifting carrier modulation Marco Liserre [email protected] Modulation and control for cascaded multilevel converters A glance at the lecture content • Cascaded multilevel converters: • hybrid solution • applications • PI-based control • Multilevel modulations in case of time-varying dc voltages: • generalized hybrid modulation • generalized phase-shifting carrier modulation Marco Liserre [email protected] Modulation and control for cascaded multilevel converters H-bridge multilevel converters n 1 x1 (e Rx1 ) Pi x2i L i 1 x2i active rectifier Marco Liserre 1 Pi x1 i x2i Ci x1 n 1 ( e Rx ) Pi x2i 1 L i 1 inverter [email protected] Modulation and control for cascaded multilevel converters H-bridge multilevel converters • • Advantages • high voltage and high power • modularity and simple layout • reduced number of components compared to other multilevel topologies • phase voltage redundancy • reduced stress for each component • small filters Disadvantages • Marco Liserre voltage unbalance of the dc link capacitors [email protected] Modulation and control for cascaded multilevel converters H-bridge multilevel converters How does it work ? • io1 T31 T11 R L iL1 iC1 a C1 if VC1=VC2=Vo + vc1 R1 - i T41 T21 Vao = -Vo T21 and T31 ON e io2 T12 iL2 T32 iC2 C2 + vc2 b T22 T42 Vao = Vo T11 and T41 ON R2 Vao = 0 T11 and T31 ON or T21 and T41 ON The lower bridge produces the same voltage levels by turning on/off the corresponding switches Marco Liserre [email protected] Modulation and control for cascaded multilevel converters H-bridge multilevel converters How does it work ? • Voltage Levels and Switching Configurations io1 T31 T11 R L iL1 iC1 a C1 + vc1 R1 - i T41 T21 e io2 T12 iL2 T32 iC2 C2 + vc2 b T22 Marco Liserre T42 R2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Vab +2 Vo Vo Vo Vo Vo 0 0 0 0 0 0 -Vo -Vo -Vo -Vo -2 Vo T11 1 1 1 0 1 0 0 1 1 1 0 0 1 0 0 0 T31 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 T12 1 0 1 1 1 0 1 0 1 0 1 0 0 0 1 0 T32 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 1 S1 1 1 1 0 0 0 0 0 0 1 -1 0 0 -1 -1 -1 S2 1 0 0 1 1 0 0 0 0 -1 1 -1 -1 0 0 -1 [email protected] Modulation and control for cascaded multilevel converters Hybrid multilevel converter Multilevel converters based on the use of hybrid cell of converters subjected to different dc voltage levels. The basic idea is to use a converter switching at low frequency hence employing Gate-Turn Off thyristors or IGCTs (as a quasi-square wave modulation technique is used) and one switching at higher frequency. the fact that the dc-link voltage levels are in an integer relation among them allow to have (for subtraction) more voltage levels. Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Hybrid multilevel converter • The converter working at low switching frequency is the greatest contributor to the fundamental component of the overall output voltage and generates a considerable and well known harmonic content (typical of quasi-square waveform), and the PWM converter is generating an opposite harmonic content and the required additional fundamental component to obtain the desired voltage. • The principle is very similar to that one of active filters. The positive consequence is that the low frequency converter (that is the converter with the higher dc-link voltage level) can be designed as an high voltage converter while the other ones can be designed as low voltage converters. REF M. D. Manjrekar, P. K. Steimer, and T. A. Lipo, ” Hybrid Multilevel Power Conversion System: A Competitive Solution for High-Power Applications,” IEEE Transactions On Industry Applications, Vol. 36, No. 3, May/June 2000. Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Applications Active rectifier in traction systems reduced line current harmonic distortion reduced weight and encumbrance voltage regulation Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Applications reduced EMI Many dc-links by one source no step-down transformer Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Applications • Hybrid electric vehicles with different electric storages REF L. M. Tolbert, F. Z. Peng, T. Cunnyngham and J. N. Chiasson, ”Charge balance control schemes for cascade multilevel converter in hybrid electric vehicles,” IEEE Trans. on Industrial Electronics, vol. 49, n. 5, October 2002. pp. 1058 - 1064. Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Applications • Distributed generation multilevel converters: photovoltaic system REF F.-S. Kang, S.-J. Park, S.-E. Cho, C.-U. Kim and T. Ise, ”Multilevel PWM inverters suitable for the use of stand-alone photovoltaic power systems,” IEEE Transactions on Energy Conversion, vol. 20, n. 4, December 2005. pp. 906-915. Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Applications • In Unified Power Flow Controller , employing multilevel converters, the regulation of the dc voltage levels can be used to meet different design requirements in terms of harmonic compensation and losses reduction Lg Iload Ig VDVR E Ic shunt DVR REF T. Gopalarathnam, M. D. Manjrekar and P. K. Steimer, ”Investigations on a unified controller for a practical hybrid multilevel power converter,” in APEC 2002, vol. 2, March 2002, pp. 1024-1030. Marco Liserre [email protected] Modulation and control for cascaded multilevel converters A glance at the lecture content • Cascaded multilevel converters: • hybrid solution • applications • PI-based control • Multilevel modulations in case of time-varying dc voltages: • generalized hybrid modulation • generalized phase-shifting carrier modulation Marco Liserre [email protected] Modulation and control for cascaded multilevel converters PI control of cascaded multilevel converters In order to fulfil the control requirements above mentioned different schemes based on PI controllers can be considered. In ideal conditions completely i i T3 T1 independent H-bridges i L R + a would be expected in order to v R C manage i T2 T4 distinct power transfers and e i i different voltage levels T1 T3 i on each structure. + o1 L1 1 1 C1 1 1 c1 1 1 o2 2 L2 2 C2 C2 REF A. Dell’Aquila, M. Liserre, V.G: Monopoli, P. Rotondo, “Overview of PI-based solutions for the control of the dc-buses of a singlephase H-bridge multilevel active rectifier”, IEEE Transactions on Industry Applications, May/June 2008. Marco Liserre vc2 R2 b T22 T42 [email protected] Modulation and control for cascaded multilevel converters First control scheme of the multilevel rectifier A. One voltage PI and one current P for each H-bridge to control them independently i vc1* +_ K pv ,1 K iv ,1 i* _ + s K pi ,1 vc1 _ + 1/Vd S1 P1 e e PWM 1/E P2 i vc2* +_ K pv ,1 vc2 K iv ,1 s i* _ + K pi ,2 _ + 1/Vd S2 e e 1/E error This results in ineffective control of the grid current leading the system to the instability. Instability is caused by the attempt at independently controlling the same current through two controllers. Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Second control scheme of the multilevel rectifier B. Two PI’s for the two dc-links and one P for the current The idea is to control the dc current in order to charge or discharge the dc-link. e 1/E i vc1* +_ K pv ,1 K iv ,1 i* ++ s _ + vc1 vc2* +_ vc2 K pi vl _ + e K pv ,2 K iv ,2 1/Vd S1+S2 +_ P1 S1 PWM S2 P2 S2 S2·i ÷ s i error However the non-linear relation i02=S2·i can not be used to the leads switching function Sproblems 2 simply both dividing by i. and Thus calculate the division to instability at start-up when the two reference voltages for the dc-links are different. Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Third control scheme of the multilevel rectifier C. One PI for the overall voltage, one PI for a dc-bus and a P for the current vc1*+vc2* +_ K pv ,1 K iv ,1 I*max i* i _ + s K pi vc1+vc2 vl + e e S1+S2 _ 1/Vd S1 +_ S2 PW M P1 P2 1/E vc2* +_ K pv ,2 K iv ,2 S2,max S2 s vc2 e 1/E The control thevcurrent voltage vcontrolled iscontrolled made calculating through another controller The sum ofof the and visC2 the voltage choice of Then the grid the C2is C1 This control scheme works with differentthrough reference voltages thatgenerated directly selects the switching functionon S2,max current amplitude i.amplitude bythe thegrid multilevel converter the ac side. and loads Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Simulation for reference and load steps: scheme 1 ERROR ! start-up Marco Liserre dc-bus 1 load step [email protected] Modulation and control for cascaded multilevel converters Simulation for reference and load steps: scheme 2 Marco Liserre ERROR ! ERROR ! start-up dc-bus 2 reference step [email protected] Modulation and control for cascaded multilevel converters Simulation for reference and load steps: scheme 3 Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Tuning procedure: voltage loop Vc1*(s)+Vc2*(s) +_ K pv ,1 K iv ,1 I*max(s) s Vc1+Vc2 voltage controller Vc2*(s) +_ K pv ,2 1 1 m Ts s Current loop K iv ,2 s Vc2 voltage controller S2,max(s) Imax(s) S 1,max S 2 ,max Vc1(s)+Vc2(s) 2C s System plant I max 2C s Vc2(s) System plant The two voltage control loop have different plants and they are designed following the “optimum symmetrical” criteria Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Indipendent load transients vC1 [150 V/div] vC2 dc-bus1 load step dc-bus2 load step [150 V/div] i [10 A/div] Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Indipendent load transients vvC1 C1 [150 [150V/div] V/div] vvC2C2 [150 [150V/div] V/div] dc-bus1 dc-bus l o a d s t e1 p load step dc-bus2 dc-bus l o a d s t2e p load step ii [10 [10A/div] A/div] Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Indipendent voltage steps dc-bus1 ref. step vC1 [150 V/div] vC2 [150 V/div] d c -b u s 2 ref. step i [10 A/div] Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Indipendent voltage steps ddcc--bbuuss1 1 rreeff.. sstteepp C1 vvC1 [150 V/div] [150 V/div] vC2 vC2 [150 V/div] [150 V/div] d c -b u s 2 dc-bus r e f . s t e p2 ref. step i i [10 A/div] [10 A/div] Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Loads unbalance condition dc-link 1 voltage load step on the dc-link Marco Liserre load step on the other dc-link [email protected] Modulation and control for cascaded multilevel converters Different dc voltages condition dc-link 1 voltage reference step on the dc-link Marco Liserre reference step on the other dc-link [email protected] Modulation and control for cascaded multilevel converters A glance at the lecture content • Cascaded multilevel converters: • hybrid solution • applications • PI-based control • Multilevel modulations in case of time-varying dc voltages: • generalized hybrid modulation • generalized phase-shifting carrier modulation Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Hybrid modulation techniques These techniques have been developed in order to optimize the harmonic content of the voltage generated by multilevel converters with different dc-voltage levels The basic principle can be easily explained in case two bridges are adopted: One converter switches at low frequency (semi-square waveform). It carries all the fundamental power but it produces also low frequency harmonics The other converter switches at high frequency (PWM), it works as an active filter compensating the harmonics generated by the first bridge REF M. D. Manjrekar, P. K. Steimer and T. A. Lipo, ”Hybrid multilevel power conversion system: a competitive solution for high-power applications,” IEEE Trans. on Industry Applications, vol. 36, n. 3, May-June 2000. pp. 834-841. C. Rech, H. A. Grundling, H. L. Hey, H. Pinheiro and J. R. Pinheiro, ”A generalized design methodology for hybrid multilevel inverters,” in IECON 02, vol. 1, November 2002. pp. 834-839. Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Hybrid modulation techniques More voltage levels are obtained as subtraction of the different dc-link voltages Hence four of the multilevel states that, in case of equal dc-link voltages, generate zero voltage on the ac side, in case of hybrid modulation, and non-equal dc-link voltages, generate one voltage level more both positive and negative Major drawbacks: It is difficult to control the dc-link voltages in case of active rectifier application The dc-link currents have an heavy harmonic content (that is compensated on the ac-side and not on the dc-side) Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Carrier shifting cascaded PWM techniques These techniques have been developed in order to obtain optimum harmonic cancellation Asymmetric PWM allows harmonic cancellation up to the 2n-th carrier multiple v(t ) NVdc M cos0t N 1 J 2 n1 mM cosm n 1 cos2mc t 2n 10t 2m i m1 n 2m i 1 4Vdc (i 1) m kN , k 1, 2,3... N These techniques allow different power transfers and different voltage levels for each bridge • carrier shifting Marco Liserre i However in case of different voltage levels for each bridge the harmonic cancellation is not perfect [email protected] Modulation and control for cascaded multilevel converters v ,V tri Carrier shifting cascaded PWM techniques 1 ref 0 -1 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 t [s] 0 v ab [V] 100 -100 ref v ,V tri 0.02 0.03 0.035 0.04 t [s] 0.045 0.05 0.055 0.06 0.025 0.03 0.035 0.04 t [s] 0.045 0.05 0.055 0.06 0.025 0.03 0.035 0.04 t [s] 0.045 0.05 0.055 0.06 0.025 0.03 0.035 0.04 t [s] 0.045 0.05 0.055 0.06 1 0 -1 0.02 100 0 v cd [V] 0.025 -100 200 0 v ad [V] 0.02 -200 A [pu] 0.02 1 0.5 0 Marco Liserre 0 10 20 30 h 40 50 60 [email protected] Modulation and control for cascaded multilevel converters Carrier shifting and hybrid modulation Carrier Shifting and Hybrid modulation (CSM and HM) techniques performances rely on time-invariant dc-voltages However many applications such as traction, distributed generation and active filter could take advantage by using time-variant dc-link voltages In this case both the techniques are not adequate: CSM fails in obtaining optimum harmonic cancellation while preserving fundamental voltage control HM cannot preserve fundamental voltage control, even if optimal harmonic cancellation could be possible Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Proposed generalized hybrid modulation The proposed Generalized Hybrid Modulation (GHM) technique considers non-integer relationships between dc-link voltages which can be time-dependent Then, switching signals will depend on the instantaneous values of the dc-link voltages and can not be evaluated independently for each PWM converter, it means that independent power management is lost in case two bridges are adopted: One converter switches at low frequency (semi-square waveform). It carries all the fundamental power but it produces also low frequency harmonics The other converter switches at high frequency (PWM), adjusting switching signals to compensate the effect of time-variant dc-link levels and the absence of an integer ratio among them. The final objective is to minimize the output voltage THD REF M. Liserre, A. Pigazo,V. G. Monopoli, A. Dell’Aquila, V. M. Moreno, “A Generalised Hybrid Multilevel Modulation Technique Developed in Case of Non-Integer Ratio Among the dc-Link Voltages” ISIE 2005, Dubrovnik (Croatia), June 2005. Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Proposed generalized hybrid modulation Low voltage converter High voltage converter Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Proposed generalized hybrid modulation Example: v*(k)>V1(k) k Variations in V1(k) and V2(k) must be at a lower frequency than fsw=1/TC LV converter must be centered on TC for a minimum final THD and v * k TC V1 k TC V2 (k )t2 (k ) hence: t 2 (k ) v * (k ) V1 (k ) D2 (k ) TC V2 (k ) t2(k) k+1 V1(k)+V2(k) v*(k) V1(k) V2(k) 0 TC D1D(k) 2 (k ) 1 Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Proposed generalized hybrid modulation Marco Liserre Switching plane 4 regions more respect to the traditional hybrid modulation The proposed modulation has 9 regions in order to obtain optimum harmonic content and exact fundamental voltage also in case of time-varying dc-link voltages [email protected] Modulation and control for cascaded multilevel converters Proposed generalized hybrid modulation The fundamental frequency harmonics compensate, as in the hybrid modulation technique, the higher voltage converter harmonics. Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Comparison in terms of modulation signals Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Simulation results: conditions and parameters Analyzed modulation techniques: CSM, HM, GHM Linear region Modulation index (M) has been chosen in [0.6, 1.4] (step = 0.1) LV converter dc-voltage (V2) is varied in [0.51,0.99] (step = 0.05) Equal switching losses => mf = 40 for HM and GHM mf = 20 for CSM Evaluation parameters: - Amplitude of the output voltage fundamental frequency component - Weighted Harmonic Content (WHC) - Weighted Total Harmonic Distortion (WTHD) max(v *( k )) M V1 Marco Liserre V WHC n n2 n 2 WHC WTHD WHC V1 [email protected] Modulation and control for cascaded multilevel converters Simulation results: generalized hybrid modulation technique overall output voltage waveform High voltage converter output waveform Low voltage converter output waveform M =1.2, V1 =1 V (p.u.), V2 =0.61 V (p.u.), mfhybrid =40 Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Simulation results: time-domain comparison GHM HM LV converter uses only its DC voltage to establish duty cycles CSM Expects equal DC voltages M =1.2, V1 =1 V (p.u.), V2 =0.61 V (p.u.), mfhybrid =40, mfshifting=20 Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Simulation results: spectra comparison GHM I1=1.2 V (p.u.) WHC=7.17 10-4 HM I1=0.96 V (p.u.) WHC=1.19 10-2 CSM I1=1.2 V (p.u.) WHC=5.1 10-3 M =1.2, V1 =1 V (p.u.), V2 =0.61 V (p.u.), mfhybrid =40, mfshifting=20 Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Simulation results: overall comparison % error in the output signal at the fundamental frequency Technique minimum average maximum GHM 6.2 10-4 0.12 0.5 23.6 61.3 0.14 0.5 CSM – WHC improves when arriving HM to equal DC 10-2 voltages -3 CSM 10 WHC GHM - There Technique is not a clearminimum dependency on GHM dc-link 3.9 10-4 voltage values -4 average maximum 8.7 10-4 1.6 10-3 HM 5.5 10 3.5 10-2 0.13 CSM 8.6 10-4 3.6 10-3 6.6 10-3 M in [0.6,1.4], V2/V1 in [0.51,0.99], mfhybrid =40, mfshifting=20 Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Experimental results Hybrid Modulation. Generalised Hybrid Modulation. Time and frequency domains overall Time and frequency domains overall output voltage using output voltage using V1 = 100 V (V1 = 1.0 pu), V2 = V1 = 100 V (V1 = 1.0 pu), V2 = 61 V (V2 = 0.61 pu) and M = 120 V 61 V (V2 = 0.61 pu) and M = 120 V (M = 1.2 pu) (M = 1.2 pu) Marco Liserre Carrier shifting technique. Time and frequency domains overall output voltage using V1 = 100 V (V1 = 1.0 pu), V2 = 61 V (V2 = 0.61 pu) and M = 120 V (M = 1.2 pu) [email protected] Modulation and control for cascaded multilevel converters Discussion on the drawbacks of hybrid techniques Both converters introduce low frequency current harmonics M =1.2, V1 =1 V (p.u.), V2 =0.61 V (p.u.), mfhybrid =40 Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Discussion on the drawbacks of hybrid techniques The major drawback is the fact that is very difficult to control directly the different converters to have full control on the voltage generated by each of them. In other words it is only possible to decide the overall multilevel modulation signal and not the modulation signal of each converter independently The direct consequence is that it is difficult to control the dc-link voltages separately in an active rectifier application unless the phase of the converter ac voltages is controlled Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Carrier shifting cascaded PWM techniques These techniques have been developed in order to obtain optimum harmonic cancellation A suitable phase-shifting among the carrier signals relevant to n different bridges has to be introduced: (i-1)/n, (for i=1, 2, …, n) Asymmetric PWM allows harmonic cancellation up to the 2n-th carrier multiple These techniques allow different power transfers and different voltage levels for each bridge However in case of different voltage levels for each bridge the harmonic cancellation is not perfect REF M. Liserre, V. G. Monopoli, A. Dell’Aquila, A. Pigazo, V. Moreno, “Multilevel Phase-Shifting Carrier PWM Technique in Case of Non-Equal DC-Link Voltages”, IECON 2006, Paris (France), November 2006. Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Principles of the PSC-PWM technique 2 converters: The weighted total harmonic distortion (WTHD) of the output signal can be reduced if the carriers of leg A and B are shifted rad N cascaded converters: Using symmetrical PWM, the carrier of leg A in 2 each converter must be shifted N i 1 rad. The phasorial representation for the carrier signals is: Inv 1 Inv 3 Inv 1 Inv 2 Inv 1 Inv 2 N=2 N=3 Marco Liserre Inv 2 Inv 3 N=4 Inv 4 [email protected] Modulation and control for cascaded multilevel converters Principles of the PSC-PWM technique The overall output voltage: N 1 v(t ) NVdc M cos0t cos2mc t 2n 10t 2m i J 2n1 mM cosm n 1 m 1 n 2m i 1 4Vdc It can be reduced by applying where: Marco Liserre (i 1) N is the number of cascaded converters, i N M is the amplitude modulation coefficient, m kN , k 1,2,3... is the pulsation of the modulating signal, 0 cis the pulsation of the carrier signal, J 2 n1 is the Bessel function of order 2n-1 and i is the relative phase of the carrier signal applied to the leg A of each converter [email protected] Modulation and control for cascaded multilevel converters Proposed PSC-PWM technique The overall output voltage with non-equal dc-link voltages: N N 1 v(t ) M Vi cos0t J 2 n 1 mM cosm n 1 Vi dc cos2mct 2n 10t 2m i m1 n 2m i 1 i 1 dc 4 A reduced WTHD can be obtained if: N V And, hence: i 1 i dc cos2mc t 2n 10t 2m i 0 N dc Vi cos2m i 0 i 1 N Vi dc sin 2m i 0 i 1 which depend on the considered m and can not be verified for all m and i Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Proposed PSC-PWM technique The mathematical expression of the WTHD is Vn2 2 n2 n WTHD V1 the minimum WTHD will be reached for m=1: N dc Vi cos2 i 0 i 1 N Vi dc sin 2 i 0 i 1 dc Vi 0 N i 1 Vi dc is a phasor with amplitude matching the i th converter dc-link voltage and phase i Reduced WTHD condition: The dc-link voltage phasors generate a polygon in the complex plane whose center should match the system origin. Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Original and proposed PSC-PWM. N=3 Vdc1=3.2 pu, Vdc2=1.4 pu and Vdc3=4.4 pu original Shifting angles =0º, 120º and 240º modified Shifting angles =0º, 36º and 191º The original PSC-PWM angles can be obtained as a particular solution Asymmetrical PWM angles can be obtained dividing the obtained results by 2 Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Comparison of PSC-PWM techniques (N=3) 0.7248% original V1dc+V2dc+V3dc= 360V V1dc<V2dc<V3dc M=0.6 V1dc=60V…120V V2dc=60V…120V f0=50 Hz fc=1.6 kHz 0.5928% modified Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Comparison of PSC-PWM techniques (N=3) improvement V1dc+V2dc+V3dc= 360V V1dc<V2dc<V3dc M=0.6 The reduced WTHD condition can not be verified. Improvement around 20% Limit of the reduced WTHD condition Improvement region -> Up to 50.6% Evaluation errors -> worst behaviour (-13.6%) Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Comparison of PSC-PWM techniques (N=3) At medium M values the proposed method improves the WTHD V1dc=70V V2dc=120V V3dc=170V f0=50 Hz fc=1.6 kHz At high M values the proposed method improves the WTHD around a 20% Low M. The original technique operates better. In average, a 3% Marco Liserre [email protected] Modulation and control for cascaded multilevel converters Conclusions • It is possible to control independently the dc buses of a cascaded multilevel converter both with a linear controller (PI-based control) both with a non-linear controller (Passivity-based control) • Multilevel modulators should be adapted in case of time-varying dc voltages: • • generalized hybrid modulation • generalized phase-shifting carrier modulation A well design controller and a well designed modulation technique are indispensable in order to do not loose the harmonic advantages of the multilevel converter and do not lead the system to instability Marco Liserre [email protected]