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**Modulation and control for cascaded multilevel converters**

Marco Liserre Marco Liserre

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**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

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**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

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**H-bridge multilevel converters**

active rectifier inverter Marco Liserre

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**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 Marco Liserre

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**H-bridge multilevel converters**

How does it work ? if VC1=VC2=Vo Vao = Vo T11 and T41 ON Vao = -Vo T21 and T31 ON 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

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**H-bridge multilevel converters**

How does it work ? Marco Liserre

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**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

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**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

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**Applications Active rectifier in traction systems**

reduced line current harmonic distortion Active rectifier in traction systems reduced weight and encumbrance voltage regulation Marco Liserre

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**Applications reduced EMI Many dc-links by one source**

no step-down transformer Marco Liserre

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**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 pp Marco Liserre

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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 pp Marco Liserre

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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 Marco Liserre

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**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

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**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. Dell’Aquila, 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. Marco Liserre

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**First control scheme of the multilevel rectifier**

One voltage PI and one current P for each H-bridge to control them independently vc1* vc1 +_ i* e S1 P1 P2 i 1/E PWM _ + 1/Vd vc2* vc2 S2 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

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**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. S2·i S2 vc1* vc1 +_ i* e vl S1+S2 P1 P2 i PWM _ + vc2* vc2 1/Vd S1 1/E ÷ error However the non-linear relation i02=S2·i can not be used to calculate the switching function S2 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. Marco Liserre

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**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 S2 vc1*+vc2* I*max vc1+vc2 +_ i* e vl S1+S2 P1 P2 i 1/E PWM _ + vc2* S2,max vc2 1/Vd S1 The control of the voltage vC2 is made through another controller that directly selects the switching function amplitude S2,max Then the grid current is controlled calculating the voltage generated by the multilevel converter on the ac side. The sum of the vC1 and vC2 is controlled through the choice of the grid current amplitude i. This control scheme works with different reference voltages and loads Marco Liserre

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**Simulation for reference and load steps: scheme 1**

ERROR ! start-up dc-bus 1 load step Marco Liserre

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**Simulation for reference and load steps: scheme 2**

ERROR ! ERROR ! start-up dc-bus 2 reference step Marco Liserre

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**Simulation for reference and load steps: scheme 3**

Marco Liserre

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**Tuning procedure: voltage loop**

Vc1+Vc2 voltage controller Current loop System plant Vc1*(s)+Vc2*(s) I*max(s) Vc1(s)+Vc2(s) +_ Imax(s) Vc2 voltage controller System plant Vc2*(s) S2,max(s) Vc2(s) +_ The two voltage control loop have different plants and they are designed following the “optimum symmetrical” criteria Marco Liserre

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**Indipendent load transients**

Marco Liserre

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**Indipendent load transients**

Marco Liserre

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**Indipendent voltage steps**

Marco Liserre

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**Indipendent voltage steps**

Marco Liserre

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**Loads unbalance condition**

dc-link 1 voltage load step on the other dc-link load step on the dc-link Marco Liserre

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**Different dc voltages condition**

dc-link 1 voltage reference step on the other dc-link reference step on the dc-link Marco Liserre

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**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

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**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 pp 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 pp Marco Liserre

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**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

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**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 carrier shifting 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 Marco Liserre

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**Carrier shifting cascaded PWM techniques**

Marco Liserre

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**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

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**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

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**Proposed generalized hybrid modulation**

Low voltage converter High voltage converter Marco Liserre

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**Proposed generalized hybrid modulation**

Example: v*(k)>V1(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 hence: k t2(k) k+1 V1(k)+V2(k) v*(k) V1(k) V2(k) TC D1(k) Marco Liserre

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**Proposed generalized hybrid modulation**

4 regions more respect to the traditional hybrid modulation Switching plane 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 Marco Liserre

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**Proposed generalized hybrid modulation**

The fundamental frequency harmonics compensate, as in the hybrid modulation technique, the higher voltage converter harmonics. Marco Liserre

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**Comparison in terms of modulation signals**

Marco Liserre

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**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) WTHD Marco Liserre

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**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

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**Simulation results: time-domain comparison**

GHM LV converter uses only its DC voltage to establish duty cycles HM Expects equal DC voltages CSM M =1.2, V1 =1 V (p.u.), V2 =0.61 V (p.u.), mfhybrid =40, mfshifting=20 Marco Liserre

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**Simulation results: spectra comparison**

I1=1.2 V (p.u.) WHC= GHM I1=0.96 V (p.u.) WHC= HM I1=1.2 V (p.u.) WHC= CSM M =1.2, V1 =1 V (p.u.), V2 =0.61 V (p.u.), mfhybrid =40, mfshifting=20 Marco Liserre

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**Simulation results: overall comparison**

% error in the output signal at the fundamental frequency GHM - There is not a clear dependency on dc-link voltage values CSM – WHC improves when arriving to equal DC voltages Technique minimum average maximum GHM 0.12 0.5 HM 10-2 23.6 61.3 CSM 10-3 0.14 WHC Technique minimum average maximum GHM HM 0.13 CSM M in [0.6,1.4], V2/V1 in [0.51,0.99], mfhybrid =40, mfshifting=20 Marco Liserre

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**Experimental results 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) 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) 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) Marco Liserre

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**Discussion on the drawbacks of hybrid techniques**

M =1.2, V1 =1 V (p.u.), V2 =0.61 V (p.u.), mfhybrid =40 Both converters introduce low frequency current harmonics Marco Liserre

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**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

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**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

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**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 3 Inv 1 Inv 2 N=3 Inv 1 Inv 2 Inv 3 Inv 4 N=4 Inv 1 Inv 2 N=2 Marco Liserre

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**Principles of the PSC-PWM technique**

The overall output voltage: It can be reduced by applying 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 Marco Liserre

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**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 Marco Liserre

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**Proposed PSC-PWM technique**

The mathematical expression of the WTHD is the minimum WTHD will be reached for m=1: is a phasor with amplitude matching the converter dc-link voltage and phase Reduced WTHD condition: The dc-link voltage phasors generate a polygon in the complex plane whose center should match the system origin. Marco Liserre

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**Original and proposed PSC-PWM. N=3**

Vdc1=3.2 pu, Vdc2=1.4 pu and Vdc3=4.4 pu original modified Shifting angles =0º, 120º and 240º 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

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**Comparison of PSC-PWM techniques (N=3)**

V1dc+V2dc+V3dc= 360V V1dc<V2dc<V3dc M=0.6 V1dc=60V…120V V2dc=60V…120V f0=50 Hz fc=1.6 kHz 0.7248% original 0.5928% modified Marco Liserre

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**Comparison of PSC-PWM techniques (N=3)**

V1dc+V2dc+V3dc= 360V V1dc<V2dc<V3dc M=0.6 Improvement region -> Up to 50.6% improvement Limit of the reduced WTHD condition The reduced WTHD condition can not be verified. Improvement around 20% Evaluation errors -> worst behaviour (-13.6%) Marco Liserre

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**Comparison of PSC-PWM techniques (N=3)**

V1dc=70V V2dc=120V V3dc=170V f0=50 Hz fc=1.6 kHz At medium M values the proposed method improves the WTHD 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

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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

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