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Prediction-based Deadbeat Control for Grid-connectedInverter with L-filter and LCL-filterAbousoufiane Benyoucefa, Kamel Karaa, Aissa Chouderb & Santigo Silvestrec

a SET Laboratory, Department of Electronics, University of Blida, Blida, Algeriab Centre de Développement des Energies Renouvelables, Bouzaréah, Algiers, Algeriac Electronic Engineering Department, Universitat Politècnica de Catalunya, C/Jordi Girona1-3, Campus Nord UPC, Barcelona, SpainPublished online: 30 Jul 2014.

To cite this article: Abousoufiane Benyoucef, Kamel Kara, Aissa Chouder & Santigo Silvestre (2014) Prediction-basedDeadbeat Control for Grid-connected Inverter with L-filter and LCL-filter, Electric Power Components and Systems, 42:12,1266-1277, DOI: 10.1080/15325008.2014.927031

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Electric Power Components and Systems, 42:1266–1277, 2014Copyright C© Taylor & Francis Group, LLCISSN: 1532-5008 print / 1532-5016 onlineDOI: 10.1080/15325008.2014.927031

Prediction-based Deadbeat Controlfor Grid-connected Inverter with L-filter andLCL-filterAbousoufiane Benyoucef,1 Kamel Kara,1 Aissa Chouder,2 and Santigo Silvestre3

1SET Laboratory, Department of Electronics, University of Blida, Blida, Algeria2Centre de Developpement des Energies Renouvelables, Bouzareah, Algiers, Algeria3Electronic Engineering Department, Universitat Politecnica de Catalunya, C/Jordi Girona 1-3, Campus Nord UPC,Barcelona, Spain

CONTENTS

1. Introduction

2. System Description

3. Deadbeat Control Algorithm: “Classical Approach”

4. Drawbacks of the Traditional Deadbeat Control Algorithm

5. Improved Deadbeat Algorithm Controller

6. Simulation Results

7. Conclusion

References

Keywords: renewable energy, single-phase inverter, grid-connected,deadbeat algorithm, predictive control, L-filter, LCL-filter, unity powerfactor, lower total harmonic distortions, digital signal processor

Received 8 June 2013; accepted 19 May 2014

Address correspondence to Mr. Abousoufiane Benyoucef, SET Laboratory,Department of Electronics, University of Blida 1, P. O. Box 270, Blida,09000, Algeria. E-mail: benyoucefsoufiane@gmail.comColor versions of one or more of the figures in the article can be found onlineat www.tandfonline.com/uemp.

Abstract—In this article, an improved deadbeat control algorithmsuitable for digital signal processor-based circuit implementation isproposed. The control algorithm allows the derivation of a nearly sinewave output current with a fixed switching frequency of a current-controlled voltage source inverter. Two low-pass output filters con-figurations are considered in this study: a simple inductance filterand an LCL-filter. By taking advantage of prior knowledge of thestate variables’ shape, the improved deadbeat control algorithm isbased on a simple prediction model to derive the expected duty cy-cle needed to switch on and off the power switches. The controlstudy of the grid-connected inverter with L and LCL output filtershas been considered using a co-simulation approach with (PowersimInc., Rockville, Maryland, USA) and MATLAB software (The Math-Works, Natick, Massachusetts, USA). The obtained results show theimprovement of both shape quality and tracking accuracy of the out-put current quantified by low ripple content and a nearly unity powerfactor.

1. INTRODUCTION

Renewable energy sources are currently widely deployed toface the dependency on fossil fuels and to minimize green-house gas emissions. Additionally, renewable sources haveshown great benefits, especially in saving power at times ofpeak demand when production is large, leading to a reductionof losses in transmission and distribution lines [1]. Usually,inverters are used to interconnect distributed generation (DG)sources to the utility grid. These inverters are connected tothe grid via a low-pass filter. In grid-connected photovoltaicsystems, it is necessary to have low levels of total harmonicdistortion (THD) at the inverter output and a very good powerfactor (PF), close to unity, so it is imperative to design a high-performance controller for the inverter [2]. As for its flexi-bility and insensitivity to electromagnetic interference (EMI),full digital control algorithms are becoming the best choice toachieve highest levels of power quality and immunity to grid

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disturbances. Moreover, the availability of powerful digital sig-nal processors (DSPs) with high efficiency and low cost hasmade the implementation of robust and complex digital controlalgorithms an easy task [3]. Recently, many advanced controltechniques have been developed to improve the THD and to ob-tain a faster response for the output voltage and current. Thesetechniques, presented under various names, include deadbeatcontrollers [4–11], adaptive controllers [12–14], multi-loopfeedback controllers [15–17], controllers based on artificialintelligence tools [18, 19], and predictive techniques [20–22].Due to its good performance and simplicity, deadbeat controlappears as an attractive way for the control of power converters[23]. It has been applied in the control of inverters [4–11], rec-tifiers [24], active filters [25], uninterruptible power supplies(UPSs) [26, 27], etc.

However, conventional deadbeat controllers suffer from thepresence of two delays; the first is inherent to the deadbeatcontrol algorithm and causes a steady-state error, and the sec-ond arises when the algorithm is implemented in a DSP-basedplatform and has more serious consequences. It affects the sys-tem stability and leads to the appearance of ripples and phaseshift in the output current [4, 5, 7, 28, 29].

Much research has proposed several solutions to deal withthe aforementioned delays: using state observers, delay com-pensators, or prediction algorithms. In [6, 7], the authors in-troduced state observers to estimate the future samples of therequired variables for computing the pulse width of the nextcontrol cycle. The resulting algorithm becomes more compli-cated, and its performance depends on the accuracy of the usedobservers. To decrease the control delay of the deadbeat controlalgorithm, Zeng et al. presented a new solution that uses a dual-timer sampling scheme to properly arrange the sampling tim-ing [11]. This method requires a high-speed analog-to-digitalconverter (ADC) and an optimized code of the control algo-rithm. A control algorithm that allows computing the switchingduty cycle of photovoltaic grid-connected inverter in advancewas proposed by Yang et al. [8]. It combines the deadbeat tech-nique and the based Taylor formula prediction algorithm. Inthis algorithm, several equations with long regressors are usedto predict each state variable that can significantly increase thecomputation time and the required memory space. A methodthat can overcome the shortcoming of complicated dynamicphase angle compensation in a three-level grid-connected in-verter was proposed in [10]. This approach, based on a dual-timer sampling scheme, uses a prediction method to estimatethe future values of the required variables and requires a high-speed ADC. Other versions of deadbeat control that use neuralnetworks and fuzzy logic as sinusoidal predictors have alsobeen developed [29, 30]. Such prediction models are complexand require an excessive computation.

In this work, an improved and an efficient version of thewell-known deadbeat control algorithm suitable for DSP-basedplatform implementation is proposed to avoid both aforemen-tioned delays. It allows deriving a nearly sine wave outputcurrent by controlling power switches of a current controlledvoltage source inverter (VSI) linked to the utility grid by twolow-pass filter configurations. Contrary to the available meth-ods, this approach uses a simple prediction model, built onprior knowledge of the shape of the state variables, to computethe duty cycle of the power switches.

The control problem of an inverter with an output L-filterand an output LCL-filter is considered using co-simulationin PSIM (Powersim Inc., Rockville, Maryland, USA) andMATLAB (The MathWorks, Natick, Massachusetts, USA) en-vironments. Results obtained show the improvement of theshape quality of the output current and the tracking accuracy.

The outline of the article is as follows: In Section 2, abrief description of the grid-connected system, used as a studyplant, is given, whereas Sections 3 and 4 deal with the tra-ditional deadbeat control approach where its drawbacks arehighlighted. The design procedure of the improved algorithmis presented in Section 5. Efficiency and control performanceof the proposed algorithm are given in Section 6 by consid-ering the control of an inverter with an output L-filter and anoutput LCL-filter. Finally, conclusions are drawn in Section 7.

2. SYSTEM DESCRIPTION

The basic schematic of the grid-connected DC/AC pulse-widthmodulated (PWM) converter used in this study is shown inFigure 1 [2], which is a current-controlled voltage source con-verter (VSC). It is common to use a low-pass inductance fil-ter (Figure 2(a)) in low-power applications to cancel high-frequency ripples of current; while the LCL-filter (Figure 2(b))is used for low-frequency switching and high-power applica-tions [31].

Overall, the control loop intends to synchronize and syn-thesize a real sine wave current to be injected to the util-ity grid with a high-quality waveform and quasi-unity PF[32, 33].

FIGURE 1. Grid-connected system.

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FIGURE 2. (a). L-filter and (b) LCL-filter.

3. DEADBEAT CONTROL ALGORITHM:“CLASSICAL APPROACH”

Hereafter, the derivation procedures of the traditional deadbeatcontrol approach applied to the grid-connected inverter arepresented for both output filters.

3.1. Inductive Filter

According to Figures 1 and 2(a), the output current is relatedto the output voltage of the inverter and the utility grid voltageby the following equation:

Ld IL (t)

dt= U0(t) − Ugrid (t) , (1)

where L is the filter inductance, IL (t) is the current in induc-tance L (the injected current), Ugrid (t) is the grid voltage, andU0(t) is the inverter output voltage.

The discrete form of Eq. (1) is given by the following ex-pression:

IL (k + 1) = IL (k) + T

LU0(k) − T

LUgrid (k), (2)

where T is the sampling period.The pulse width of the DC voltage at the output terminals

of the H-bridge denoted by�T (k) is assumed to be centered ateach switching cycle, as shown in Figure 3.

When U0(t) is replaced by Ud ∗ �T (k), Eq. (2) can berewritten as follows:

IL (k + 1) = IL (k) + T

L�T (k)Ud − T

LUgrid (k). (3)

In the traditional deadbeat control, at each control pe-riod k, the current IL (k + 1) is replaced with the reference

FIGURE 3. Pulse-width pattern.

current I ∗L (k), then duty cycle �T (k), which allows bringing

the injected current IL to its reference I ∗L , is given by

�T (k) =LT (I ∗

L (k) − IL (k)) + Ugrid (k))

Ud. (4)

3.2. LCL-filter

Although the LCL-filter has higher filtering capability than thesimple L-filter, it does not allow a direct control of injectedcurrent. In this topology, a nearly sine wave current to beinjected into the utility grid is obtained by controlling thecapacitor voltage. So according to the circuit of Figure 2(b),the output current is given by

d IL2(t)

dt= Vc (t)

L2− Ugrid (t)

L2, (5)

where L2 is the interconnection inductance, IL2(t) is the cur-rent in inductance L2 (the injected current), and Vc(t) is thecapacitor voltage.

The discrete form of Eq. (5) is written as

IL2 (k + 1) = IL2(k) + T Vc(k)

L2− T Ugrid (k)

L2. (6)

As mentioned above, the current IL2(k + 1) in Eq. (6) isreplaced by the reference current I ∗

L2(k). The capacitor voltagereference V ∗

c (k) needed to let the injected current IL2(k) beequal to its reference current I ∗

L2(k) is then given by

V ∗C (k) = L2

T

(I ∗

L2(k) − IL2(k) + Ugrid (k)). (7)

To apply the deadbeat control algorithm allowing the calcu-lation of V ∗

c (k), the discrete-time state equations of the powerplant (Figures 1 and 2(b)) are described below:

d X (t)

dt= AX (t) + BU (t), (8)

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FIGURE 4. Time delay of traditional deadbeat algorithm.

where

A =

⎡⎢⎢⎢⎢⎢⎣

0−1

L10

1

C0

−1

C

01

L20

⎤⎥⎥⎥⎥⎥⎦

; X (t) =

⎡⎢⎣

IL1 (t)

Vc (t)

IL2(t)

⎤⎥⎦ ;

B =

⎡⎢⎢⎢⎢⎣

1

L10

0 0

0−1

L2

⎤⎥⎥⎥⎥⎦ ; u (t) =

[U0 (t)

Ugrid (t)

].

The discrete form of this representation can be obtainedusing the following equation:

X (k + 1) = ϕX (k) + γ u(k), (9)

where

ϕ = exp(AT ) = I + AT + A2T 2

2!+ . . . + AnT n

n!,

γ =[

I T + AT 2

2!+ . . . + An−1T n

n!

]× B,

X (k) =⎡⎣ IL1(k)

Vc(k)IL2(k)

⎤⎦ ; u(k) =

[U0(k)

Ugrid (k)

].

For n = 3, it can be written from Eq. (9)

Vc(k + 1) = ϕ21 IL1(k) + ϕ22Vc(k) + ϕ23 IL2(k)

+ γ21U0(k) + γ22Ugrid (k), (10)

when ϕ21, ϕ22, ϕ23 and γ21, γ22 are the second line elements ofthe matrix ϕ and γ , respectively.

In Eq. (10), replacing Vc(k + 1) by V ∗C (k) and U0(k) by

�T (k) ∗ Ud , the required pulse width �T (k) is obtained asfollows:

�T (k)

= V ∗C (k) − ϕ21 IL1(k) − ϕ22Vc(k) − ϕ23 IL2(k) − γ22Ugrid (k)

γ21Ud.

(11)

FIGURE 5. Time delay due to DSP implementation.

Equation (11) denotes the implicit maner of controlling theinjected current by direct control of the capacitor voltage Vc(k)using a deadbeat controller.

4. DRAWBACKS OF THE TRADITIONALDEADBEAT CONTROL ALGORITHM

In the traditional deadbeat control algorithm, besides the delayintroduced by the control law used to compute the duty cycle,another delay is introduced when implementing this algorithmin a DSP-based platform. These delays give rise to currentripples and phase shift between the injected current and thegrid voltage.

4.1. Phase Delay Caused by Control Algorithm

As is illustrated in Figure 4, the first delay of one controlperiod is created by the control algorithm itself and is due tothe fact that the current IL(k + 1) is replaced by the referencecurrent I ∗

L (k) (L-filter case), and the current IL2(k + 1) and thecapacitor voltage Vc(k + 1) are replaced by I ∗

L2(k) and V ∗

c (k),respectively (LCL-filter case). Thus, the injected current I (k)is phase shifted by one control period to its reference I ∗(k).

FIGURE 6. Correction of inherent deadbeat controller delay.

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FIGURE 7. Main difference between conventional and im-proved approaches.

4.2. Phase Delay Caused by DSP Implementation

The second delay is due to the internal architecture of DSP.Indeed, when using a DSP, the PWM signal is generated bycomparing the values of two specific registers. The content ofthe register containing the duty cycle value should not be mod-ified during the current control period. Since the pulse widthis limited by the time that the sampling and the computing

FIGURE 8. Procedure for parameters estimation.

FiltersReferencevariables

Controlledstate variables

Measured statevariables

L IL ∗ (k + 1)IL ∗ (k + 2)

IL (k + 1) Ugrid (k + 1)

LCL IL2 ∗ (k + 1) IL2(k + 1) Ugrid (k + 1)IL2 ∗ (k + 2) Vc(k + 1) IL1(k + 1)

TABLE 1. Variables categories

operations take, the obtained duty cycle cannot be applied atthe current control period. To overcome this difficulty, the dutycycle computed value is written to the shadow register of theDSP during the current control period, and it is automaticallywritten to the comparison register at the beginning of the nextcontrol period [8]. Hence, the duty cycle value computed atthe current control period will not be effective until the nextcontrol period, as shown in Figure 5. This leads to a shift ofone control period, and then much higher ripples will appearin the injected current.

5. IMPROVED DEADBEAT ALGORITHMCONTROLLER

As showed in the previous section, the conventional deadbeatcontroller suffers from the presence of two delays. In thissection, the based prediction algorithm that allows overcomingthis drawback is given.

To eliminate the delay caused by the control law used tocompute the duty cycle, the one-control-period-ahead pre-dicted values of I ∗(k) (i.e., I∗(k + 1)) are used as referencerather than the actual values of I ∗(k). Hence, the delay dueto the deadbeat control algorithm will be canceled, and theinjected current I (k) will be equal the actual reference I ∗(k),as shown in Figure 6.

FIGURE 9. Parameters evolution.

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FIGURE 10. Prediction of a purely sinusoidal signal.

On the other hand, to eliminate the delay created when im-plementing the algorithm in a DSP board, computing of theduty cycle �T of the (k + 1)th control period must be antici-pated within the kth control period. Hence, the state variablesvalues at the (k + 1)th sampling instant, upon which the dutycycle depends, must be predicted during the kth control period.Regarding the statement concerning the cancelation of the de-lay due to the deadbeat algorithm, the injected current mustfollow the two-control-period-ahead shifted reference currentI∗(k + 2).

As shown in Figure 7, the main difference between theconventional and improved approaches resides on the addedprediction block. This allows computing the duty cycle�T(k + 1) at the kth control period by using an appropri-ate reference current and applying it in its (k + 1)th controlperiod.

Unlike the already-proposed deadbeat control techniquesthat use complex and time-consuming prediction models[7–11, 29, 30], the strong point of the proposed approachis the simplicity of its prediction model, which is linear andits coefficients are estimated offline. These features are made

FIGURE 11. Prediction of a distorted sinusoidal signal(THD50 = 8.55%).

FIGURE 12. Simulink model of proposed controller (induc-tive filter case).

possible by exploiting prior knowledge of the shapes of thestate variables. In fact, these variables can be classified intothree categories.

• The reference variables are pure sinusoidal signals,which are real, centered, and stationary. So, theyare predictable signals with a second-order recurrence

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FIGURE 13. Simulink model of proposed controller (LCL-filter case).

relationship given in Eq. (12) [34]:

x(k + 1) = a0x(k) + a1x(k − 1), (12)

where a0 and a1 are the parameters to be estimated.

• The values of the controlled state variables at the (k +1)th sampling time are estimated by using their referencevalues and the resulting error of the previous estimation.Thus, it is assumed that the value of the state variable

FIGURE 14. Injected and reference currents for conventionaldeadbeat controller (inductive filter case).

at the (k + 1)th sampling instant will be equal to itsreference value in the same instant (x(k + 1) = x∗(k +1)), and then the prediction error in the previous samplinginstant k is compensated to avoid error accumulation.This is given by the following equations:

x(k + 1) = x∗(k + 1) − e(k),

e(k) = x∗(k) − x(k). (13)

• The measured state variables have a disturbed sinusoidalshape, such as the grid voltage; nevertheless, the val-ues of their next samples can be well considered as alinear combination of their previous values. Since, in agrid-connected system, the sampling frequency is usu-ally high enough, the state variables can be consideredas changing linearly. Consequently, a linear extrapolationfrom previous values can be used [29, 35]. Hence, theprediction model given by Eq. (12) is a good choice toestimate the future values of these state variables.

FIGURE 15. Injected and reference currents for proposedcontroller (inductive filter case).

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FIGURE 16. Comparison between conventional and proposedapproaches (inductive filter case).

Based on these points, a prediction model that uses a singleequation to predict the values of all the state variables neededin computing the duty cycle value that allows avoiding theaforementioned time delays is developed. The variables to bepredicted are gathered, according to their category, in Table 1.

The estimation procedure of the prediction model’s coeffi-cients given in Eq. (12) using the root least-square (RLS) al-gorithm is illustrated in Figure 8. Since all the state variable’sshapes are sine wave, the results of parameters estimation willbe the same as that seen in Figure 9, where

x(k) = sin(2 ∗ π ∗ 50 ∗ k). (14)

Simulation results of a pure and disturbed sine waves pre-diction have shown the good accuracy of the chosen model(Figures 10 and 11).

The developed algorithm of the improved deadbeat controlhas been tested on the two output filters of the grid connectedinverter—the L-filter and the LCL-filter.

FIGURE 17. Typical dynamic simulation performance (in-ductive filter case).

FIGURE 18. Injected and reference currents for conventionaldeadbeat controller (LCL-filter case).

5.1. Case of the Inductive Filter

Applying the methodology explained in Section 5 on the dead-beat controller when using an inductive filter, Eq. (4), whichgives the expected pulse width, becomes

�T (k + 1) =LT

(I ∗

L (k + 2) − IL (k + 1))

+ Ugrid (k + 1)

Ud,

(15)where the prediction of measured, controlled, and referencestate variables are given below:

Ugrid (k + 1) = a0Ugrid (k) + a1Ugrid (k − 1), (16)

IL (k + 1) = I ∗L (k + 1) + e(k),

e(k) = IL (k) − I ∗L (k), (17)

I ∗L (k + 1) = a0 I ∗

L (k) + a1 I ∗L (k − 1) , (18)

I ∗L (k + 2) = a0 I ∗

L (k + 1) + a1 I ∗L (k). (19)

The Simulink model of the proposed controller is given inFigure 12. In this model, the DSP behavior is simulated byadding a delay block of one control period.

FIGURE 19. Injected and reference currents for proposedcontroller (LCL-filter case).

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1274 Electric Power Components and Systems, Vol. 42 (2014), No. 12

Parameters Value Parameters Value

DC bus, Ud 400 V a0 2Grid voltage,

Vgrid (RMS)220 V a1 –1

Load rate 2.2 kW L 20 mHUtility

frequency50 Hz L1 10 mH

Samplingfrequency

10 kHz C 1 μF

Switchingfrequency

10 kHz L2 5 mH

TABLE 2. Simulation parameters

5.2. Case of the LCL-filter

When the aforementioned methodology is applied on the dead-beat controller in the LCL-filter case, Eq. (11) becomes

�T (k + 1)

= V ∗C (k + 1) − ϕ21 IL1(k + 1) − ϕ22 Vc(k + 1) − ϕ23 IL2(k + 1) − γ22Ugrid (k + 1)

γ21Ud,

(20)

where the prediction of measured, controlled, and referencestate variables are given below:

IL2(k + 1) = I ∗L2 (k + 1) + eIL2 (k)

eIL2 (k) = IL2(k) − I ∗L2(k), (21)

I ∗L2 (k + 1) = a0 I ∗

L2(k) + a1 I ∗L2 (k − 1) , (22)

VC (k + 1) = V ∗C (k + 1) + eV c(k),

eV c(k) = VC (k) − V ∗C (k). (23)

V ∗C (k + 1) is given by replacing Eqs. (16), (21), and (22) into

Eq. (7) :

V ∗C (k + 1) = L2

T{ I ∗

L2 (k + 1) − IL2 (k + 1) + Ugrid (k + 1)}.(24)

Since, to compensate the controller delay, the two-steps-aheadshifted prediction I ∗

L2 (k + 2) is used instead of I ∗L2(k + 1), Eq.

(24) becomes

V ∗C (k + 1) = L2

T

{I ∗

L2 (k + 2) − IL2 (k + 1) + Ugrid (k + 1)},

(25)

Approaches PF (%) THD50 (%)

Traditional 99.9003 2.73Proposed 99.9914 1.12

TABLE 3. Performance comparison (inductive filter case)

FIGURE 20. Comparison between conventional and proposedapproaches (LCL-filter case).

where

I ∗L2 (k + 2) = a0 I ∗

L2 (k + 1) + a1 I ∗L2(k). (26)

Finally, the current IL1(k + 1) can be computed as follows:

IL1(k + 1) = a0 IL1(k) + a1 IL1(k − 1). (27)

The Simulink model of the proposed controller, when usingan LCL-filter, is given in Figure 13.

6. SIMULATION RESULTS

The developed controllers are implemented using a co-simulation methodology by combining MATLAB/Simulinkand the PSIM software [36]. The single-phase inverter andits output filters are implemented in the PSIM environment,while the control algorithm is implemented in the MAT-LAB/Simulink environment. The values of all parameters usedin simulation are given in Table 2.

The simulation results of the conventional and proposedcontrollers when an inductive filter is used are given in Fig-ures 14–17. As is shown in Figure 14, there is a phase shiftbetween the grid-connected and reference currents; hence, thePF cannot be equal to 1. This phase shift is compensated, andthe current waveform is significantly improved when the pro-posed controller is used (Figure 15). A comparison betweenthe results of the two controllers is made in Figure 16. It ap-pears that the proposed controller is more efficient than the

Approaches PF (%) THD50 (%)

Traditional 99.7757 0.64Proposed 99.9995 0.29

TABLE 4. Performance comparison (LCL-filter case)

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FIGURE 21. Typical dynamic simulation performance.

conventional one. The PF and the THD values for the twocontrollers are given in Table 3.

Figure 17 shows a typical dynamic simulation performanceof the inverter system using the proposed controller. The sim-ulation results of the conventional and proposed controllerswhen using an LCL-filter are given in Figures 18–21. Forthe case of the conventional deadbeat controller, Figure 18shows that, in addition to the ripples that are present in theinjected current waveform, the reference and injected currentsare phase shifted. In the case of the improved deadbeat con-troller, these ripples and the phase shift are eliminated (Fig-ure 19). A comparison between the results of the two con-trollers is made in Figure 20. The proposed controller is moreefficient than the conventional one. Table 4 gives the PF andthe THD values for the two controllers. Figure 21 shows a dy-namic performance of the inverter system using the improvedcontroller.

7. CONCLUSION

A simple, efficient version of the deadbeat control algorithm isdeveloped in this article. It allows overcoming the main weak-ness of the conventional deadbeat control algorithm when it isimplemented in a DSP board. The proposed algorithm is givenand studied for both an output L-filter and an output LCL-filter.These configurations are the most used in grid-connected in-verters. In the design procedure of the developed controller, asimple linear prediction model is used to compute the futurevalues of all the state variables required for computing theexpected duty cycle. By using such a model, it is possible tocompute and apply the expected duty cycle within the samesampling cycle. This fact leads to overcoming the phase shiftproblem, and hence, the THD and the PF values are improved.The developed algorithm was used to control a grid-connectedinverter and the co-simulation results have shown the effec-tiveness of the developed approach. In particular, a nearly sine

wave current with a practically unity PF and low harmoniccontent was obtained.

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BIOGRAPHIES

Abousoufiane Benyoucef received his License and Masterdegrees in Electrical Engineering from the Saad Dahlab Uni-versity of Blida, Algeria, in 2009 and 2011 respectively. Cur-rently, he is an assistant researcher in Electrical Systems andRemote control Laboratory (LabSET), His research interestsinclude control of power converters, grid connected PV sys-tems, artificial intelligence and heuristic optimization.

Kamel Kara received the engineering diploma in electronicsfrom the University of Setif, Algeria, in 1992, and the magis-ter diploma in electronics from the University of Constantine,Algeria, in 1995, and the doctoral degree from the Univer-sity of Setif, Algeria, in 2006. He was an associate lecturer,from Sep. 1995 to Sep. 1996, at the higher institute of indus-try, Misurata, Lybia. Presently, he is an associate professorin signal processing and systems control at the Departmentof electronics, University of Blida, Algeria. His current re-search interests are focused on nonlinear systems identifica-tion and control, artificial intelligence, heuristic optimization,diagnostic and control of photovoltaic systems and embeddedsystems.

Aissa Chouder received The Ingenieur and Magister in Elec-tronics degrees from Ferhat Abbas University, Setif, Alge-ria in 1991 and 1999 respectively and the Ph.D degree inElectronic Engineering From the Polytechnic University ofCatalonia (UPC) in 2010. He is currently a senior researcher in

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the photovoltaic laboratory of Development Centre of Renew-able Energies (CDER), Algiers, Algeria. His research interestincludes power electronics, modeling and control of renewableenergy sources, fault detection and diagnosis in photovoltaicsystems.

Santigo Silvestre received the M.S. and Ph.D. degreesin Telecommunication Engineering from the UniversitatPolitecnica de Catalunya (UPC), Barcelona, Spain, in 1992 and1996, respectively. Associate Professor of the Electronic Engi-

neering Department at the UPC, were he has been Vice Deanof the Telecommunication Engineering School of Barcelonafrom June 2000 to April2006. He is a Senior Member of theIEEE from 2006 and Associate Editor of the Journal of SolarEnergy Engineering (ASME) from 2011.The main researchareas of work, where he has been involved are: Solar Cells(simulation, design, characterization and fabrication), Photo-voltaic systems (simulation, modeling, monitoring and designof automatic fault detection for PV systems), Grid connectedPV systems (simulation and modeling).

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