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Electric Power Systems Research 123 (2015) 31–39

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Electric Power Systems Research

j o ur na l ho mepage: www.elsev ier .com/ locate /epsr

High performance operation for a four-leg NPC inverter withtwo-sample-ahead predictive control strategy

V. Yaramasua, M. Riverab,∗, M. Narimania, B. Wua, J. Rodriguezc

a Dep. of Electrical and Computer Eng., Ryerson University, Toronto, ON, Canadab Dep. of Industrial Technologies, Universidad de Talca, Curicó, Chilec Dep. of Electronics Eng., Universidad Técnica Federico Santa María, Valparaíso, Chile

a r t i c l e i n f o

Article history:Received 18 September 2014Received in revised form 20 January 2015Accepted 22 January 2015

Keywords:Dc–ac power conversionDistributed generationFinite control-set model predictive control(FCS-MPC)Multilevel invertersNeutral-point-clamped (NPC) inverterUninterruptible power supply (UPS)

a b s t r a c t

In this paper is proposed a finite control-set model predictive control (FCS-MPC) strategy which uses atwo-sample-ahead prediction horizon to achieve high-performance operation for a three-phase four-legneutral-point-clamped (NPC) inverter with an output LC filter. The control strategy is proposed in orderto minimize the error between the output voltages and their references, maintain equal voltage amongthe dc-link capacitors, and reduce the overall switching frequency of the inverter. One-sample-aheadand two-sample-ahead prediction horizon are evaluated and compared in terms of reference trackingerror and THD, under steady-state and transient operating conditions with linear and non-linear loads.The experimental results demonstrate that the proposed two-sample-ahead prediction horizon is moresuitable for high power applications where lower switching frequency operation is mandatory.

© 2015 Elsevier B.V. All rights reserved.

1. Introduction

The three-level neutral-point-clamped (NPC) inverter is themost widely used configuration in many medium voltage (MV)(from 2.3 to 4.16 kV) industrial applications [1,2]. This power con-verter has several advantages: (1) high voltage capability, (2)reduced common mode voltages, (3) nearly sinusoidal outputvoltage, (4) low dv/dt’s, which can reduce the electromagneticinterference, and (5) small or even no output filter [3]. Some appli-cations in which an NPC inverter with an output LC filter can be usedare uninterruptible power supplies (UPS), off-grid (stand-alone)distributed generation (DG) systems, dynamic voltage restorers(DVRs) and universal power quality conditioners (UPQCs) [4].

Most of the practical UPS, DG, DVR and UPQC systems need tofeed unbalanced/nonlinear loads in four-wire systems, and the con-ventional three-phase NPC is not suitable for this purpose becauseof: (1) insufficient dc-bus utilization, (2) high ripple on dc-linkcapacitors, and (3) difficulties in balancing the dc-link capacitor vol-tages due to low-frequency neutral-point voltage oscillations [5]. Afour-leg NPC inverter has been shown to be an effective solution for

∗ Corresponding author. Tel.: +56 995442860.E-mail addresses: vyaramas@ee.ryerson.ca (V. Yaramasu), marcoriv@utalca.cl

(M. Rivera), mnariman@ee.ryerson.ca (M. Narimani), bwu@ee.ryerson.ca (B. Wu),jrp@usm.cl (J. Rodriguez).

three-phase four-wire systems because it offers full utilization ofthe dc-link voltage and reduces the stress on the dc-link capacitors.

Nowadays, with technological advances, the implementationof new and more complex modulation and control strategies ispossible. One of the new control schemes for power converters isfinite control-set model predictive control (FCS-MPC) as describedin [6]. The classical control schemes with PI regulators and pulsewidth modulation (PWM)/space vector modulation (SVM) assumethe power converter as a linear system [7–9], while the FCS-MPCstrategy treats the system as nonlinear. The nonlinear nature ofthe power converter becomes more predominant at lower switch-ing frequency operation, and during such conditions the FCS-MPCstrategy provides better steady-state results and a fast transientresponse. Although predictive control requires a higher amount ofcalculations than a classic control scheme, with the development offast microprocessors, its implementation is possible, and this con-trol technique has been applied to wide range of power convertersand applications [10–13]. This predictive control technique usesthe model of the system, as the name implies, and this require-ment has prompted many investigations of the system model usedin different applications.

The predictive voltage control with an output LC filter isanalyzed for three-leg two-level [14] and four-leg two-levelconverters [15,16]. This concept has been extended by simulationstudies to four-leg NPC converter [17] using the same load modelintroduced in [14] for the three-wire applications. The predictive

http://dx.doi.org/10.1016/j.epsr.2015.01.0170378-7796/© 2015 Elsevier B.V. All rights reserved.

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Fig. 1. Four-leg NPC inverter topology with an output LC filter and three-phase arbitrary load.

current control of four-leg two-level converters with output Lfilter is analyzed in [4,18] considering the grid-connected/activepower filter application. The work in [19] extended this conceptto four-leg NPC converter. The previously mentioned FCS-MPCstrategies were based on one-sample-ahead prediction to simplifythe modeling and analysis. The works in [20–22] proposed longerprediction horizons to improve the control performance in athree phase converter. The questions about the complexity of thecontroller, the increase in the number of calculations, the compu-tational burden, and potential improvements in the performanceof the converter are still a research topic in the field of FCS-MPC.

In this paper, two-sample-ahead predictive control strategy ispresented and experimentally verified for a four-leg NPC inverterwith an output LC filter which can be used in UPS, DG, DVR andUPQC applications. To reduce the number of calculations, switch-ing frequency, and computational burden, a modification to thetwo-sample-ahead prediction is proposed. The performance of theproposed two-sample-ahead predictive control is compared withthe standard one-sample-ahead FCS-MPC in terms of referencetracking, load voltage quality, transient response and ability tooperate at lower switching frequencies. At difference of previousworks related to predictive control in four-leg converters, in thispaper a novel discrete-time model that considers the LC filter andthe neutral inductor Ln is proposed for the four-wire applications.In [28], a predictive current control strategy has been proposed forthe four-leg NPC converter. In this paper, a different topology whichconsiders an output LC filter with a different and more accuratemathematical model is extended for the regulation of output (load)voltages and dc-link capacitor voltages which are defined as thecontrol objectives in the cost function. During each sampling inter-val, the best one among all the possible switching states is selectedbased on the cost function minimization criteria. The experimentalresults are presented using a dSPACE DS1103 based rapid proto-typing platform for single-/three-phase, balanced/unbalanced, andlinear/nonlinear loads.

2. Continuous- and discrete-time model of the system

In this section, the continuous- and discrete-time mathematicalmodeling of the four-leg NPC inverter with an output LC filter anda neutral inductor Ln is presented. The load zero sequence voltageis controlled by the fourth-leg [23], and in doing so it operatesat a higher switching frequency than those found in the otherthree-phases [4]. This scenario leads to higher switching lossesin the fourth-leg, and this is undesirable in the operation of afour-leg inverter. To overcome this issue, a neutral inductor Ln can

Table 1Possible switching states of the four-leg NPC inverter.

S1x S2x S3x S4x vxN Px

1 1 0 0 vdc1 + vdc2 10 1 1 0 vdc2 00 0 1 1 0 −1

Notes: x = phase of the inverter, u, v, w, n; Lx = level of voltage vector.

be connected between the load neutral (o) and mid-point of thefourth-leg (n) as shown in Fig. 1. However, the inclusion of Ln leadsto higher-order modeling, and this is not addressed in the previousworks on predictive voltage control of four-leg NPC inverter.

2.1. Four-leg NPC inverter topology

The topology of the three-phase four-leg NPC inverter with anoutput LC filter is shown in Fig. 1. The main objective of the outputfilter is to provide sinusoidal voltages to the arbitrary/unknownloads.

Referring to Table 1, the voltage in any leg x of the NPCinverter with respect to the negative point of the dc-link (N) canbe expressed in terms of switching states and dc-link capacitorvoltages as follows [19]:

vxN = vdc1S1x + vdc2S2x, x = u, v, w, n, (1)

where vdc1 and vdc2 are dc-link capacitor voltages.The load-side ac voltages can be obtained from the above

inverter voltages as:

vyn = vyN − vnN, y = u, v, w, (2)

where vnN is the load neutral voltage.The switching states to achieve three voltage levels are summa-

rized in Table 1. For a four-leg NPC inverter, the total number ofpossible switching states is 81(= 34). The switch signal pairs (S1x,S3x) and (S2x, S4x) operate in a complementary manner.

2.2. Model of DC-link capacitor voltages

The nominal voltages of both capacitors are directly related tothe current idc1 and idc2 as [24]:

vdc1(t) = vdc1(0) + 1Cdc1

∫ t

0+idc1(�) d�,

vdc2(t) = vdc2(0) + 1Cdc2

∫ t

0+idc2(�) d�,

(3)

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Fig. 10. Comparison of performances with one-sample-ahead and two-sample-ahead prediction methods during switching frequency minimization: (a) THD versus fsw and(b) evo versus fsw .

Fig. 11. Experimental results for dc-link capacitor voltages balancing with perturbations in the system model: Ch1: dc-link capacitor-1 voltage (100 V/div), Ch2: dc-linkcapacitor-2 voltage (100 V/div), Ch3: difference between dc-link capacitor voltages (200 V/div), Ch4: weighting factor �vdc (0.5 V/div). Time scale: 500 ms/div.

voltages. To create a perturbation in the system model, a resistorRx (100 �) is connected across the bottom dc-link capacitor Cdc2.As shown in Fig. 11a, with this perturbation, the one-sample-aheadmethod shows a steady-state error between the dc-link capacitorvoltages. Fig. 11b demonstrates that the two-step method givesvery good balancing for capacitor voltages. The reason is that thesystem response is predicted two-samples ahead, and the bestswitching state which gives minimal value for the cost functionis selected despite the changes in system model.

At t = 1 s, the weighting factor associated with the capacitor vol-tages balancing is disabled meaning that the �vdc is changed from0.5 to 0. When the controller is disabled, the voltage in the bottomcapacitor is discharged through Rx. Since the total dc-supply voltagemust be shared by the two dc-link capacitors, the voltage across thetop capacitor vdc1 starts to increase in proportion to the drop in vdc2.With two-step method, the capacitor voltages diverge in slow ratecompared to the one-sample-ahead method. The weighting factoris enabled at t = 4 s (means �vdc changes from 0 to 0.5), the capacitorvoltages converge at a fast rate and finally become balanced evenwith Rx in the circuit. After convergence, the two-step method givesbetter balancing compared to the one-sample-ahead method. Thistest verifies that the two-step method is more robust in balancingthe dc-link capacitor voltages compared to the one-sample-aheadmethod.

5. Conclusions

In this paper, a model predictive voltage control strategy withtwo-sample-ahead prediction horizon has been proposed for thecontrol of a three-phase four-leg NPC inverter with an outputLC filter. The results demonstrate that the proposed two-sample-ahead method performs better in terms of (a) reference tracking,(b) load voltage quality, (c) dc-link capacitor voltages balanc-ing, and (d) dynamic response during step-change in reference

voltages while operating at a much lower switching frequencythan that seen in the one-sample-ahead method. These featurespromote the proposed methodology as a high-performance toolto control the high-power converters. The trade-off is given bythe higher computational capacity needed to perform the 81additional calculations during each sampling interval. However,it has been demonstrated that the current digital control plat-forms can facilitate the extra calculations without involving anyadditional software reconfiguration. The three-sample-ahead, andlonger horizons can also be realized, but it is beyond the scope ofthis paper. A detailed study on the performance improvement andcomputational burden with longer prediction horizons is consid-ered as a future work.

Acknowledgements

This work was supported in part by the Natural Sciences andEngineering Research Council of Canada through Wind EnergyStrategic Network Project 3.1, in part by the Fondecyt Initiation intoResearch under Grant 11121492, in part by CONICYT PCCI 12048Project and in part by the NPRP under Grant 4-077-2-028 throughthe Qatar National Research Fund. The statements made herein aresolely the responsibility of the authors.

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