Comparison of finite control set and hysteresis

based model predictive control for NPC and T-Type

converter in case of low carrier ratio

Stefan Walz, Giampaolo Buticchi, Marco Liserre

University of Nottingham Ningbo China, 199 Taikang East Road, Ningbo,

315100, Zhejiang, China.

First published 2019

This work is made available under the terms of the Creative Commons

Attribution 4.0 International License:

http://creativecommons.org/licenses/by/4.0

The work is licenced to the University of Nottingham Ningbo China under the Global University Publication Licence: https://www.nottingham.edu.cn/en/library/documents/research-support/global-university-publications-licence.pdf

Comparison of Finite Control Set and HysteresisBased Model Predictive Control for NPC andT-Type Converter in case of low carrier ratio

Stefan WalzChair of Power Electronics

Christian-Albrechts-Universitat zu KielKiel, Germany

swa@tf.uni-kiel.de

Giampaolo ButicchiPEMC Group

University of Nottingham Ningbo ChinaNingbo, China

buticchi@ieee.org

Marco LiserreChair of Power Electronics

Christian-Albrechts-Universitat zu KielKiel, Germany

ml@tf.uni-kiel.de

Abstract—The control of machines in case of low carrier ratio(ratio of switching frequency to electrical frequency fsw/fel)is a challenging topic at the highly dynamic control of high-speed machines and high power converters. While common PIControllers face stability issues at low ratios, Model PredictiveControl (MPC) can be used to ensure stability. The cost functioncan be used, to reduce the Total Harmonic Distortion of themotor currents (THDi) or, keeping the THDi constant, reducingthe motor filter size. This paper presents a comparison of FiniteControl Set (FCS) and hysteresis based MPC algorithm for threelevel converter. The predictive control of the currents is providinggood dynamic performance. The Neutral Point Clamped (NPC)or T-Type converter are considered to optimize the harmonicdistortion of the permanent magnet synchronous motor (PMSM)currents. Simulation and experimental results prove the effec-tiveness of the analyzed control for 3-Level Converters.

Index Terms—Model Predictive Control, Hysteresis BasedControl, Multilevel Converter, PMSM.

I. INTRODUCTION

Low carrier ratio, meaning low ratio of switching frequencyto electrical frequency (fel/fS) is a challenging topic forapplications like high-speed drives, or high power drives [1].

In the industry, for electrical drive applications a cascadedfield-oriented control (FOC) is commonly used. Model pre-dictive control offers the possibility to reduce the effectiveswitching frequency of the converter while maintaining fastdynamic response, and good steady-state performance, whichis important assuming a cascaded control structure [2]. Thecost function can be used to optimize performance, losses,or increase robustness, but raises high computational require-ments, for example shown for FCS MPC in [3]. On theother hand, deadbeat predictive control can be used to nullthe control error after a predefined number of switchingperiods and obtains very good dynamic performance. In [4]modulation and predictive current control for low switchingfrequencies are shown. In [5] a comparison of MPC schemesis given for medium voltage induction machines.

For multilevel converter the computational effort rises ex-ponentially [6].

The paper structure is organized as follows: the systemdescription, including the analyzed three level converters andmotor equations is given in Section II. In Section III, the con-trol structure of the hysteresis based Model predictive controlis introduced and simulation results are given in Section IV.Experimental results are provided in Section V to validate thetheoretical analysis. Conclusions are drawn in Section VII.

II. SYSTEM DESCRIPTION

This section describes analyzed drive system with the twodifferent 3-Level topologies, the NPC and T-Type. In Fig. 1overview of the system configuration is given. The 3-LevelVoltage Source Converter (VSC) is represented by the voltagevector hexagon. Different to PI based structures with PWM,the MPC is directly calculating the six duty cycles (plus sixinverted) to control the IGBTs of the VCS. The processing andcalculation period takes one sampling period. In (1) and (2) themotor equations for a digital control are given. The voltagesare calculated based on the predicted currents and the outputvoltages based on the sampled values and are applied at the(k+2)-th period. The measured values in the k-th period areused for the calculations of the (k+1)-th period and i∗dq(k) isused as reference currents.

vd(k + 1) =Ld

TS(i∗d(k)− id(k + 1)) +Rsid(k + 1)−

− Lqωeliq(k + 1)(1)

vq(k + 1) =Lq

TS

(i∗q(k)− iq(k + 1)

)+Rsiq(k + 1)+

+ Ldωelid(k + 1) + ωelΨPM

(2)

The investigated NPC and T-Type converter are the mostcommonly used. Their schematic is given in Fig. 2 and Fig. 3.For the control of electrical machines, the PI Control isused since many decades in industry. With the use of digitalsystems, the Controller has to be discretized, for example usingthe Euler Methods. Using these methods, with lowering thepulse ratio, stability problems will occur. A way to overcomethis problem, is the direct design of the PI Controller in

1

the discrete time domain, as for example shown in [7]. Thismethod is used for the comparisons in this paper.

III. 3-LEVEL HYSTERESIS BASED MODEL PREDICTIVECONTROL

The hysteresis based MPC (or MPC with bounds) uses themotor equation to predict the motor currents in the next controlsteps. If the absolute value of the predicted current is higherthan the defined bounds, a new voltage vector will be applied,to keep the current trajectory inside the bounds. The currentbounds are directly influencing the motor current harmonics,THDi. The cost function is designed to choose the voltagevector with the best ratio of periods that the trajectory willstay inside the bounds, compared to the switching instancesneeded to apply this voltage vector.

For three-level Converters, a good knowledge of the systemparameters is required, to choose correctly of the 27 differentvoltage vectors. Parameters mismatches due to converter non-linearities, deadtimes, or saturation have to be taken intoaccount. Considering the low ratio of switching to electricalfrequency fsw,eff/fel, it is also very important, that theangular displacement is compensated.

Based on the known last applied voltage vector V indold ,the current at the end of the sampling period, idq,pred =idq(k + 1), can be predicted accurately based on the motorequations. Using the possible voltage vectors of the three-levelconverter, the current trajectories T i

x for the next samplingperiod are calculated. As there are redundant voltage vectors,these calculations have to be done 19 times, showing theincreased computational effort for the three-level converterscompared to the two-level with seven different voltage vectors.The current trajectories are predicted for example with analgorithm introduced by Bolognani, adapted here for the three-level converter [8].

iid(k + 2) = id(k + 1) +TSLd

(V id (k + 1)−Rsid(k + 1)

+ ωelLqiq(k + 1)(3)

iiq(k + 2) = iq(k + 1) +TSLq

(V iq (k + 1)−Rsiq(k + 1)

− ωelLdid(k + 1)− ωelΨPM

(4)

By calculating the error amplitude and change of the errorangle of each voltage vector, the trajectories are approximatedas linear current curve.

T ix = 2 · iBound·

·cos(π + arctan

iq(k+1)−iiq(k+2)

id(k+1)−iid(k+2)

− arctani∗q(k)−iq(k+1)

i∗d(k)−id(k+1)

)abs(idq(k + 1)− iidq(k + 2)

)(5)

These calculations are executed in every sampling period.To make sure the current stays inside the bound at all time,the absolute value of the d/q-current error with the currently

applied voltage vector is compared to the bound limit. In casethis current iindold(k + 2) is bigger than the bound, a newvoltage vector has to be applied. The cost function choosesthe new index by maximizing the cost function, (6). For thisthe trajectories T i

x are normalized by the sampling time TS .Additionally for redundant voltage vectors, the one with theleast commutations should be applied. This means, choosingthe voltage vector that will keep the trajectory inside thebounds the longest, but taking into account the number ofswitching instances ncom to reach this state.

ind = maxi=[1...27]

(floor(T i

x/TS)

ncom

)(6)

Even though the results can be fraction numbers, this termgives an idea of how many sampling periods per commutationthe current will stay inside the bounds. For example, it ispreferable to choose a voltage vector that keeps the currentinside the bounds for three sampling periods with only oneswitching operation, instead of a voltage vector that providesfive sampling periods but needs two commutations. Problemscan occur, if two vectors provide the same number of periods.To prevent that in this case always the first solution is chosen,the cost function is extended by an correction term ci. If twoor more solutions are providing the same number of periods,the solution with the lease mean error should be chosen. Forthat the accumulated error ei,accum is divided by the predictednumber of periods nip and added to the cost function (6). Thisensures the best initial position for the next optimization step.

ci =

∑||i∗dq − iidq(k + Tn)||

iBound · nip(7)

IV. FINITE CONTROL SET MODEL PREDICTIVE CONTROL

Similar to the hys. based MPC, the FCS MPC algorithmis using the motor equations. The cost function of the FCSMPC is minimizing the tracking error of the motor currents.The effective switching frequency can be set by and additionalterm, which is penalizing switching operations by using theparameter λ, eq. (8).

mini=[1...27]

Ji =

= (i∗d(k)− id(k + 1))2

+(i∗q(k)− iq(k + 1)

)2+ λ ·∆V (k)

(8)

For the cost function of the FCS MPC two terms, thetracking error and the penalty on switching are used. Oneadvantage of the FCS MPC is that also other objectives canbe included in the cost function, like temperature, power, ormany other.

V. SIMULATION RESULTS

The finite control set and hysteresis based MPC algorithmsfor NPC and T-Type are compared with a discrete-time currentregulator, e.g. shown in [7]. The machine and converterparameter are givenin I and II.

2

C1

VDC N

C2

(high-speed) PMSM

Loadmachine

Gate Signals

iabcvab,bc,ca

Encoder

ωM

Model Predictive Control with Bounds defined iBound

define number of steps delay compensation angle compensation

optional Filter

Lf Cf

Sensors

3-Level VSC

Fig. 1. Schematic of 3-Level Converter with MPC Control.

Sa1

Sa2

Sa3

Sa4

Da5

Da6

Db5

Sb1

Sb2

Sb3

Sb4

Db6

Dc5

Dc6

Sc1

Sc2

Sc3

Sc4

C2

Vdc

NP

iaibic

abc

C1

iNP

vC2

vC1

iinvidciC1

Fig. 2. 3-Level NPC with IGBTs.

Sa1

Sa2

abc

Sa3

Sa4

Sb1

Sb4

Sc1

Sc4

Sb2

Sb3

Sc2

Sc3

C2

Vdc

NP

C1

vC1

vC2

iaibic

idc iinviC1

iC2

iNP

Fig. 3. 3-Level T-Type with IGBTs.

Figure 9 shows the THDi over the (effective) switchingfrequency, comparing the hysteresis based MPC with a sam-pling frequency of fS = 20kHz, and the direct designedPI Control at nominal speed, (fel = 100Hz). The dashedlines shown the simulation results. It can be seen, that thehysteresis based MPC is advantageous compared to the finitecontrol set MPC. For the same switching frequency, both MPCalgorithms are providing better current distortion compared to

the PI Control, or, for the same THDi, the switching frequencycan be reduced. Especially for the region of fS

fel< 10,

where high-speed and high power machines are often operated,the improvement increases significantly. For higher switchingfrequencies, the THDi of the MPC algorithms is limited bythe control frequency, defining the minimum turn-on time ofthe semiconductors.

TABLE IMACHINE SETUP DATA

PPMSM,rated 22kW

nrated 2000rpm

fel 100Hz

pole pairs 3

Ls,dq 2.2µH

Rs 0.1Ω

TABLE IICONVERTER SETUP DATA

VDC 560V

fControl 20kHz

Tdeadtime 2µs

Another important aspect for MPC is the choice of thesampling frequency. In Figure 4 the THDi of the motor currentover the effective switching frequency at nominal speed isshown for different sampling frequencies fS . It can be seen,that for low carrier ratios, the outcome is very similar. Thischanges, when a ratio of sampling to effective switchingfrequency of approximately fsw,eff

fS= 15 is reached. The sam-

pling time limits the minimum pulse width. Thus, smaller andmore effective switching instances reducing the THDi are notpossible. Secondly, a small improvement at higher pulse ratioscan be seen for a higher switching frequency. In addition, thesmaller possible pulse widths are having an positive effect, aswell as the fact, that due to the higher sampling frequency, theprobability of finding effective trajectories is increased.

3

500 1000 1500 2000 2500 3000 3500

fsw,eff

[Hz]

5

10

15

20

25

30

TH

Di [

%]

fS

=10kHz

fS

=20kHz

fS

=40kHz

Fig. 4. Comparison of total harmonic motor current distortion THDi over(effective) switching frequency fsw(,eff).

0 0.2 0.4 0.6 0.8 1

Modulation Index

0

20

40

60

80

100

120

140

Losses [W

]

NPC Conduction Losses

NPC Switching Losses

T-Type Conduction Losses

T-Type Switching losses

Fig. 5. Comparison of switching and conduction losses for NPC and T-TypeConverter.

A. Power semiconductor rating

To compare the cost of different inverter topologies, thepower semiconductor design rating is chosen as criteria. Dis-crete Infineon IGBTs are used. The evaluation of the semi-conductor rating and losses are based on data sheet parameters.The comparison of the power semiconductor rating of the NPCand T-Type is shown in III. The procedures are shown forexample in [9] or [10]. It can be seen, that for the Converterand PMSM shown in I and II, the NPC has a lower rating,0.438MVA compared to 0.468MVA for the T-Type.

B. Losses

In Fig. 5 the conduction and switching losses for NPCand T-Type are compared. As the switching frequency is verysmall, the conduction losses are mainly defining the overalllosses. At an modulation index of 0.25, a break even pointcan be found. At higher modulation factors, the T-Type ishaving lower losses, while at small modulation factors orhigher switching frequencies, the NPC is providing betterefficiency. For a modulation factor of M = 1 and a pulseratio of fsw,eff

fel= 8, the loss distribution of NPC and T-Type

is shown in Fig. 6 and Fig. 7.

Sx1

Sx2

Sx3

Sx4

Dx5

Dx6

0

10

20

30

40

Losses [W

]

NPC, fel

= 100Hz, fsw,eff

= 800Hz

Fig. 6. Losses for NPC, M=1: Conduction losses (blue), switching losses(yellow).

Sx1

Sx2

Sx3

Sx4

0

10

20

30

40

Losses [W

]

T-Type, fel

= 100Hz, fsw,eff

= 800Hz

Fig. 7. Losses for T-Type, M=1: Conduction losses (blue), switching losses(yellow).

VI. EXPERIMENTAL RESULTS

The simulation results of the current controllers are vali-dated by experiments with a 22kW Siemens PMSM, connectedto a DC load machine. The DC link of the converter isconnected to a 10kW DC voltage source. The waveform ofthe output current is measured and recorded by a TektronixDPO3014 Oscilloscope with a Tektronix TCP0030 CurrentProbe. The inductance and resistance of the machine weremeasured with a Sourcetronic ST2826A LCR meter and aregiven in I. A DSpace MicroLabBox is used to control thesystem. The laboratory setup is shown Fig.8.

In Figure 9 the simulated and measured results are com-pared. All three control algorithms show good correlation ofsimulation and experimental results. For the MPC algorithms,

(a)

(b)

(d) (e)

(c)

Fig. 8. Experimental setup: (a) Siemens PMSM, (b) DC Load machine, (c)Oscilloscope, (d) DSpace MicroLabBox, (e) Converter.

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TABLE IIICOMPARISON OF POWER SEMICONDUCTOR RATING FOR DIFFERENT CONVERTER TOPOLOGIES

Semiconductor VCE [V] Irated [A] Number of IGBTs / Diodes Rating [MVA]

3-Level NPC Infineon IKW50N60T / Infineon IDW40G65C5 600 50 / 40 12 + 6 0.438

3-Level T-Type Infineon IKW40T120 / Infineon IKW50N60T 1200 / 600 40 / 50 6 + 6 0.468

300 400 500 600 700 800 900 1000 1100 1200

fsw,eff

[Hz]

15

20

25

30

35

40

45

TH

Di [

%]

3-Level VSI, fel

= 100Hz, fS = 20kHz

Hys. based MPC Simulation

Hys. based MPC Laboratory

FCS MPC Simulation

FCS MPC Laboratory

Direct Designed PI Control Simulation

Direct Designed PI Control Laboratory

Fig. 9. Comparison of (effective) switching frequency over THDi for simulation (dashed lines) and experimental results (solid lines) of hys. based MPC(blue), FCS MPC (green), and PI Control (black).

small deviations can occur due to saturation of the magnets,saliency of the machine, or other parameter uncertainties. Itcan be proven, that the hysteresis based MPC is providing thebest results.

FCS (green) and hys. based MPC (blue) are favorablecompared to PWM based PI Control (black). Only at very highswitching frequencies, where the THDi of the MPC algorithmsis limited by the control frequency, the PI Control is providingbetter results.

VII. CONCLUSION

In this paper finite control set and hysteresis based modelpredictive control for NPC and T-Type are presented andcompared for a PMSM in case of low carrier ratio. Whilethe T-Type is preferable for high modulation indexes, the NPCgets more advantageous for lower modulation indexes, or if theswitching frequency is increased. The NPC is having a smallerpower semiconductor rating. The hys. based MPC is providinga better THDi or lower switching frequency, compared to FCSMPC. Both MPC algorithms are favorable compared the PWMbased PI Control.

ACKNOWLEDGMENT

The research leading to these results has received fundingsfrom the European Union/Interreg V-A - Germany-Denmark,under the PE:Region Project.

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