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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Modulation and control for cascaded multilevel converters Marco Liserre liserre@poliba.it

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org active rectifier inverter H-bridge multilevel converters

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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 voltage unbalance of the dc link capacitors

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org H-bridge multilevel converters How does it work ? if V C1 =V C2 =Vo V ao = V o T1 1 and T4 1 ON V ao = -V o T2 1 and T3 1 ON V ao = 0 T1 1 and T3 1 ON or T2 1 and T4 1 ON The lower bridge produces the same voltage levels by turning on/off the corresponding switches

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org H-bridge multilevel converters How does it work ?

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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.

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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.

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org reduced line current harmonic distortion reduced weight and encumbrance voltage regulation Active rectifier in traction systems Applications

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org reduced EMI Many dc-links by one source no step-down transformer Applications

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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.

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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.

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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 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.

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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 independent H-bridges would be expected in order to manage distinct power transfers and different voltage levels on each structure. REF A. DellAquila, M. Liserre, V.G: Monopoli, P. Rotondo, Overview of PI-based solutions for the control of the dc-buses of a single- phase H-bridge multilevel active rectifier, IEEE Transactions on Industry Applications, May/June 2008.

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org First control scheme of the multilevel rectifier A. One voltage PI and one current P for each H-bridge to control them independently v c1 * v c1 +_ i*i* e e S1S1 P1P1 P2P2 i 1/E PWM _ + _ + 1/V d v c2 * v c2 +_ i*i* e S2S2 i 1/E _ + 1/V d 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.

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Second control scheme of the multilevel rectifier B. Two PIs for the two dc-links and one P for the current S 2 ·i S2S2 v c1 * v c1 +_ i*i* e vlvl S 1 +S 2 P1P1 P2P2 i PWM _ + v c2 * v c2 +_ _ + +_ 1/V d S2S2 S1S1 e 1/E + i + ÷ error The idea is to control the dc current in order to charge or discharge the dc-link. However the non-linear relation i 02 =S 2 ·i can not be used to calculate the switching function S 2 simply dividing by i. Thus the division leads to instability problems both at start-up and when the two reference voltages for the dc-links are different.

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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 S2S2 v c1 * +v c2 * I * max v c1 +v c2 +_ i*i* e e vlvl S 1 +S 2 P1P1 P2P2 i 1/E PW M _ + v c2 * S 2,max v c2 +_ e 1/E _ + +_ 1/V d S2S2 S1S1 The sum of the v C1 and v C2 is controlled through the choice of the grid current amplitude i. Then the grid current is controlled calculating the voltage generated by the multilevel converter on the ac side. The control of the voltage v C2 is made through another controller that directly selects the switching function amplitude S 2,max This control scheme works with different reference voltages and loads

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Simulation for reference and load steps: scheme 1 start-up dc-bus 1 load step ERROR !

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Simulation for reference and load steps: scheme 2 start-up dc-bus 2 reference step ERROR !

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Simulation for reference and load steps: scheme 3

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org V c1 +V c2 voltage controller Current loop System plant V c1 * (s)+V c2 * (s) I * max (s) V c1 (s)+V c2 (s) +_ I max (s) Tuning procedure: voltage loop V c2 voltage controller System plant V c2 * (s) S 2,max (s) V c2 (s) +_ The two voltage control loop have different plants and they are designed following the optimum symmetrical criteria

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Indipendent load transients

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Indipendent load transients

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Indipendent voltage steps

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Indipendent voltage steps

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Loads unbalance condition dc-link 1 voltage load step on the dc-link load step on the other dc-link

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Different dc voltages condition dc-link 1 voltage reference step on the dc-link reference step on the other dc-link

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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.

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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)

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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 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 carrier shifting

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Carrier shifting cascaded PWM techniques

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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. DellAquila, 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.

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Proposed generalized hybrid modulation Low voltage converter High voltage converter

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Proposed generalized hybrid modulation Example: v*(k)>V 1 (k) Variations in V 1 (k) and V 2 (k) must be at a lower frequency than f sw =1/T C LV converter must be centered on T C for a minimum final THD and hence: 0 V 2 (k) V 1 (k) V 1 (k)+V 2 (k) v*(k) TCTC t 2 (k) kk+1 D 1 (k)

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Proposed generalized hybrid modulation 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

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Proposed generalized hybrid modulation The fundamental frequency harmonics compensate, as in the hybrid modulation technique, the higher voltage converter harmonics.

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Comparison in terms of modulation signals

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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 (V 2 ) is varied in [0.51,0.99] (step = 0.05) Equal switching losses => m f = 40 for HM and GHM m f = 20 for CSM Evaluation parameters: - Amplitude of the output voltage fundamental frequency component - Weighted Harmonic Content (WHC) - Weighted Total Harmonic Distortion (WTHD) WTHD

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Simulation results: generalized hybrid modulation technique overall output voltage waveform High voltage converter output waveform Low voltage converter output waveform M =1.2, V 1 =1 V (p.u.), V 2 =0.61 V (p.u.), m f hybrid =40

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Simulation results: time-domain comparison GHM HM CSM Expects equal DC voltages LV converter uses only its DC voltage to establish duty cycles M =1.2, V 1 =1 V (p.u.), V 2 =0.61 V (p.u.), m f hybrid =40, m f shifting =20

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Simulation results: spectra comparison GHM HM CSM M =1.2, V 1 =1 V (p.u.), V 2 =0.61 V (p.u.), m f hybrid =40, m f shifting =20 I 1 =0.96 V (p.u.) WHC=1.19 10 -2 I 1 =1.2 V (p.u.) WHC=7.17 10 -4 I 1 =1.2 V (p.u.) WHC=5.1 10 -3

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Simulation results: overall comparison M in [0.6,1.4], V 2 /V 1 in [0.51,0.99], m f hybrid =40, m f shifting =20 Techniqueminimumaveragemaximum GHM6.2 10 -4 0.120.5 HM10 -2 23.661.3 CSM10 -3 0.140.5 % error in the output signal at the fundamental frequency WHC Techniqueminimumaveragemaximum GHM3.9 10 -4 8.7 10 -4 1.6 10 -3 HM5.5 10 -4 3.5 10 -2 0.13 CSM8.6 10 -4 3.6 10 -3 6.6 10 -3 GHM - There is not a clear dependency on dc-link voltage values CSM – WHC improves when arriving to equal DC voltages

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Experimental results 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) Hybrid Modulation. 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) Generalised Hybrid Modulation. 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)

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Discussion on the drawbacks of hybrid techniques M =1.2, V 1 =1 V (p.u.), V 2 =0.61 V (p.u.), m f hybrid =40 Both converters introduce low frequency current harmonics

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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. DellAquila, A. Pigazo, V. Moreno, Multilevel Phase-Shifting Carrier PWM Technique in Case of Non-Equal DC-Link Voltages, IECON 2006, Paris (France), November 2006.

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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 each converter must be shifted rad. The phasorial representation for the carrier signals is: Inv 1 Inv 2 Inv 3 Inv 4 N=4 Inv 3 Inv 1 Inv 2 N=3 Inv 2 N=2

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Principles of the PSC-PWM technique The overall output voltage: where: N is the number of cascaded converters, M is the amplitude modulation coefficient, is the pulsation of the modulating signal, is the pulsation of the carrier signal, is the Bessel function of order 2n-1 and is the relative phase of the carrier signal applied to the leg A of each converter It can be reduced by applying

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Proposed PSC-PWM technique The overall output voltage with non-equal dc-link voltages: A reduced WTHD can be obtained if: And, hence: which depend on the considered m and can not be verified for all m and

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Proposed PSC-PWM technique The mathematical expression of the WTHD is the minimum WTHD will be reached for m=1: Reduced WTHD condition: The dc-link voltage phasors generate a polygon in the complex plane whose center should match the system origin. is a phasor with amplitude matching the converter dc-link voltage and phase

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Original and proposed PSC-PWM. N=3 The original PSC-PWM angles can be obtained as a particular solution Asymmetrical PWM angles can be obtained dividing the obtained results by 2 original V dc 1 =3.2 pu, V dc 2 =1.4 pu and V dc 3 =4.4 pu Shifting angles =0º, 120º and 240º modified Shifting angles =0º, 36º and 191º

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Comparison of PSC-PWM techniques (N=3) 0.7248% 0.5928% original modified V 1 dc +V 2 dc +V 3 dc = 360V V 1 dc

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Comparison of PSC-PWM techniques (N=3) improvement Evaluation errors -> worst behaviour (-13.6%) Improvement region -> Up to 50.6% Limit of the reduced WTHD condition The reduced WTHD condition can not be verified. Improvement around 20% V 1 dc +V 2 dc +V 3 dc = 360V V 1 dc

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org Comparison of PSC-PWM techniques (N=3) V 1 dc =70V V 2 dc =120V V 3 dc =170V f 0 =50 Hz f c =1.6 kHz Low M. The original technique operates better. In average, a 3% At medium M values the proposed method improves the WTHD At high M values the proposed method improves the WTHD around a 20%

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Modulation and control for cascaded multilevel converters Marco Liserre liserre@ieee.org 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

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