Active and Reactive Power Control Strategy for Grid-Connected Six-PhaseGenerator by using Multi-Modular Matrix Converters

David CABALLERO*, Federico GAVILAN*, Edgar MAQUEDA*,Raul GREGOR*, Jorge RODAS*, Derlis GREGOR†

*Laboratory of Power and Control Systems, †Laboratory of Distributed SystemsFacultad de Ingenierıa, Universidad Nacional de Asuncion

Luque, CP 2060, ParaguayE-mail: dcaballero, fgavilan, emaqueda, rgregor, jrodas & dgregor@ing.una.py

and

Sergio TOLEDO††, Marco RIVERA††

††Faculty of Engineering, Universidad de TalcaTalca, CP 747 - 721, Chile

E-mail: stoledo & marcoriv@utalca.cl

ABSTRACT

This paper proposes an active and reactive power control stra-tegy based on predictive control approaches applied to grid-connected renewable energy systems. To accomplish this amulti-modular matrix converter topologies are used in combi-nation with a simple but efficient grid synchronization strategy.The theoretical performance analysis is performed consideringa six-phase wind energy generator system interconnected withthe grid. Results based on a MATLAB/Simulink simulationenvironment are discussed and the most relevant characteristicsof the proposed control technique are highlighted consideringthe total harmonic distortion and the mean squared error as aparameters of performance.

Keywords: Predictive control, matrix converters, renewableenergy systems, multiphase induction generator.

1. INTRODUCCION

In the last years the interest in power generation from re-newable energy sources has experienced a significant growth,mainly justified by the reduced environmental impact generated.Renewable energy systems (RES), such as solar photovoltaic(PV), micro-hydraulic and wind energy systems are widelyused as an alternative to the traditional systems. A very activeresearch area in the field of RES are focused in the multiphasewind energy generator (MWEG) systems [1], [2]. In particular,MWEG systems with multiple three-phase windings are veryconvenient for wind turbine (WT) applications, due to importantaspects especially for high-power safety-critical applicationssuch as performance, reliability, smooth torque and partitionof power [3]. In MWEG, the six-phase wind energy generator(SpWEG) with two sets of three-phase stator windings spatiallyshifted by 30 electrical degrees and isolated neutral pointsis probably one of the most widely discussed topology withfully rated back-to-back converter system to grid-connectedapplications [4]-[6]. Consequently with the development ofmultiphase topologies and drives, recent research efforts have

been focused in the development of a flexible power interfacebased on a modular architecture capable to interconnectingdifferent renewable energy sources and load, including energystorage systems to the electrical grid. These efforts converge inthe multi-modular matrix converter (MMC) topologies whosethe main feature is the ability to provide a three-phase sinusoidalvoltages with variable amplitude and frequency using fullycontrolled bi-directional electronic switches without the useof energy storage elements [7]. These characteristics makesplausible the use of MMC in applications where are requiredhigh power density and compact converters such as SpWEGsystems, constituting an attractive alternative if it is comparedwith conventional converter topologies [8], [9].

The main contribution of this paper comparing with the previousworks will focus on a theoretical performance analysis of aMMC combined with a SpWEG scheme in order to ensure anefficient active and reactive power control from the generatorside to the grid side. Each module of the MMC architecture areconnected in cascade to the independent three-phase windings ofthe SpWEG. A model-based predictive control (MPC) techniqueis used to predict the effects of future control actions in orderto minimize a defined cost function. The control criterion willbe the active and reactive power control.

This paper is organized as follows: Section 2 describes themathematical model of the MMC. Section 3 presents a detaileddescription of the MPC control strategy. Section 4 discusses thesimulation results and a performance analysis of the proposedpredictive control technique using the total harmonic distortion(THD) and the mean square error (MSE) as a parametersof performance. Finally, the main remarks are summarized inSection 5.

2. POWER CONVERSION MODEL

The proposed topology consists of two three-phase matrixconverter (MC) modules connected to the SpWEG by usinga passive (LC) input filter and then connected to the gridby an output filter, as it was shown in Fig. 1. Each one of

ISSN: 1690-4524 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 14 - NUMBER 6 - YEAR 2016 57

Fig. 1. Proposed multi-modular matrix converter and power control topology applied to the six-phase wind energy generator.

these modules is represented by the power electronic schemeof Fig. 2. In this case, generated voltages by the SpWEG areindicated as Vuj , Vvj and Vwj where j ∈ 1, 2 dependingof the corresponding module. In the same way, the generatedcurrents are indicated as Iuj , Ivj and Iwj . The output currentsof the input filter are indicated as Ieu, Iev and Iew, respectively.Input voltages of the MC are Veuj , Vevj and Vewj . The outputvoltages of the MC respect to the corresponding SpWEG neutralpoint (N1 or N2) are VaNj , VbNj and VcNj . Moreover, outputcurrents are Ioaj , Iobj and Iocj , respectively. Finally, the outputfilter voltages (that are connected to the grid) are VoaNj , VobNjand VocNj .

The MC power topology is composed of nine bi-directionalpower switches, which can generate 27 switching states [10].If the three-phase vectors of voltages and currents are definedas:

Vsj =

VujVvjVwj

Vij =

VeujVevjVewj

Voj =

VaNjVbNjVcNj

(1)

Isj =

IujIvjIwj

Iij =

IeujIevjIewj

Ioj =

IoajIobjIocj

(2)

then the following vectorial equations relate the input and outputvoltages or currents in terms of the switching states of the MC:

Voj = S · Vij , Iij = ST · Ioj (3)

being S the instantaneous transfer matrix, defined as:

S =

Sua Sub SucSva Svb SvcSwa Swb Swc

(4)

where the Sxy element has a binary value, corresponding to thestate of the single switch.

In order to avoid short circuits on the input side and ensure anuninterrupted current flow on the load side, the switching signals

Fig. 2. Model of the power systems.

Sxy must satisfy the following condition:

Suy + Svy + Swy = 1 y ∈ a, b, c. (5)

The dynamic model of the passive output filter is defined as:

Voj − VoNj = LfodIojdt

+RfoIoj (6)

where:

VoNj =

VoaNjVocNjVocNj

(7)

is the voltage vector measured from the end of the output filterto the corresponding neutral point Nj of the SpWEG.

In the case of the input filter, the dynamic behavior can be di-rectly modeled by using the space-state representation approachas:

d

dt

[VijIsj

]= Ac

[VijIsj

]+Bc

[VsjIij

](8)

58 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 14 - NUMBER 6 - YEAR 2016 ISSN: 1690-4524

where:

Ac =

[0 1

Cf

− 1Lf

−Rf

Lf

]Bc =

[0 − 1

Cf1Lf

0

](9)

being Lf and Cf the filter inductance and capacitance, respec-tively, and Rf is the leakage resistance of Lf .

3. PROPOSED CONTROL METHOD

A. Predictive model

The MPC technique uses a model of the real system to predictthe future behavior of the variables to be controlled. Theinherent discrete nature of power converters simplifies the MPCoptimization algorithm to the prediction of the system behavioronly for the set of feasible switching states. This approach isknown as finite control set MPC, and it has been successfullyused in several power converter applications and topologies [11].

The discrete model of the system using the forward Eulerdiscretization is defined as follows [12]:

Ioj(k+1) =

(1− RfoTm

Lfo

)Ioj(k)+

TmLfo

(Voj(k)− VoNj(k))

(10)where Tm is the sampling time, Ioj(k) and VoNj(k) aremeasured, and Voj(k) is calculated for all switch combinationsto predict the next value of the output currents and evaluate thecost function in order to select the optimum solution.

B. References generation

Active and reactive power references in currents terms aredefined by the following equations [13]:

i∗α =2

3

vsαv2sα + v2sβ

P ∗s +2

3

vsβv2sα + v2sβ

Q∗s (11)

andi∗β =

2

3

vsβv2sα + v2sβ

P ∗s −2

3

vsαv2sα + v2sβ

Q∗s (12)

where P ∗s and Q∗s denote the active and reactive power refe-rences, respectively, while vsα and vsβ are the grid voltages instationary reference frame (α− β).

C. Cost function

The cost function can be defined as a deviation between thereferences and predicted currents and is normally defined asfollows:

J =‖ eid(k + 1) ‖2 + ‖ eiq(k + 1) ‖2 (13)

where

‖ eid(k + 1) ‖ =‖ i∗d(k + 1)− ipd(k + 1) ‖‖ eiq(k + 1) ‖ =‖ i∗q(k + 1)− ipq(k + 1) ‖

‖ . ‖ denotes vector magnitude, and i∗dq(k + 1) and ipdq(k + 1)are vectors which contain the reference and prediction currents,respectively in the dynamic reference frame (d − q). Thepredictions are based on the current states and control efforts.

Fig. 3. Block diagram of a PLL with special design of the compensator.

D. Digital PLL implementation

The dynamic performance of the proposed PLL is highly in-fluenced by the compensator G(z), Fig. 3 shows the proposedPLL diagram block. Considering that the reference signal isthe grid voltage in d axis, and since the loop gain includesan integral term, θ must track the constant component of thereference signal with zero steady-state error. However, to ensurezero steady-state error, the loop gain must include at least twointegrators. Therefore, G(z) must include at least one integralterm, that is, one pole at z = 1. The other poles and zerosof G(z) are determined mainly by the closed-loop bandwidthrequirements of the PLL and stability indices such as phasemargin and gain margin, according with the procedure describedin [14]. Due to the fact that G(z) is controllable, the transferfunction can be expressed into controllable canonical form asfollows:

x(k + 1) = [F]5×5 [x(k)]5×1 + [D]5×1 [e(k)]5×1 (14)

ω∗(k) = [C]1×5 [x(k)]5×1 (15)

where the matrix [F]5×5; and the vectors [D]5×1, and [C]1×5

define the dynamics of the PLL compensator [G(z)]. The set ofstate variables are defined as follows:

[F]5×5 =

2.5 −2.2 0.9 −0.2 0.011 0 0 0 00 1 0 0 00 0 1 0 00 0 0 1 0

(16)

[D]5×1 =[

1 0 0 0 0]T (17)

[C]1×5 =[

1.7 −5.7 8.1 −5.8 1.6]. (18)

This state-space realization is called controllable canonical formbecause the resulting model is guaranteed to be controllable.

E. Optimizer

The optimization process is performed by evaluating the costfunction for each valid switching state. The search space givenby the set of possible vectors can be defined as ε = φφo

i ,where φi and φo are the number of the matrix converter inputand output phases, respectively. For the particular case of athree-phase grid-connected system, the search space is definedby 27 possible vectors for performing the control law. Theoptimization algorithm selects the optimum vector Sopt whichminimizes the cost function J, as detailed in Algorithm 1.

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Algorithm 1 Optimization algorithm

1. Initialize J1o :=∞, J2

o :=∞2. Compute MMC input voltages (Eqn. 2)3. while i ≤ ε do4. Compute MMC output voltages (Eqn. 3)5. Compute the prediction of the states (Eqn. 10)6. Compute the cost function (Eqn. 13)7. if J1 < J1

o then8. J1

o ← J1, Sopt1 ← Si9. end if10. if J2 < J2

o then11. J2

o ← J2, Sopt2 ← Si12. end if13. i = i+ 114. end while15. Apply the optimum vector Sopt ∈ Sopt1 , Sopt2

4. SIMULATION RESULTS

The MMC has been modeled in MATLAB/Simulink in order tovalidate the proposed control scheme, considering the electricalparameters that are shown in Table I. Simulations have been per-formed to show the accuracy of the MPC technique. Numericalintegration by means of the first order Euler algorithm has beenapplied to obtain the evolution of the controlled variables. Fig. 4shows the accuracy of the proposed method and the voltage andcurrent behavior at the point of common coupling (PCC). Fig. 4(upper) shows the instantaneous active power reference change.The active power reference was initially set to 4,000 W andafter t = 0.06 s, the value of the power reference was changedto 2,000 W. It can be seen that the output power follows itsreference value, similar results are obtained at t = 0.12 s andt = 0.18 s. On the other hand, Fig. 4 (middle), shows thetracking current dynamic performance for a step of the activepower reference. As can be seen the dynamic response duringthe transient is very fast and the steady-state error is near to zero.Finally, Fig. 4 (bottom) shows the current and voltage behaviorin the PCC. When the reference power decreases, the currentamplitude decreases, keeping constant the voltage value.

To evaluate the proposed control performance the THD,Eqn. (19), and the MSE, Eqn. (20), are used as a figures ofmerit.

TABLE IELECTRICAL PARAMETERS

SpWEG MPC Power Control

PARAMETER SYMBOL VALUE UNIT

Electrical signal frequency fs 50 HzGrid voltage signal amplitude Vs 380 VInput filter resistance Rf 0.5 ΩInput filter inductance Lf 0.4 mHInput filter capacitance Cf 25 uFOutput filter resistance Rfo 4.7 ΩOutput filter inductance Lfo 3 mHSwitching period Tm 20 µsActive power reference P ∗ 4,000 WReactive power reference Q∗ 0 VAR

0 0.05 0.1 0.15 0.2 0.25-2,000

-1,000

0

1,000

2,000

3,000

4,000

5,000

0 0.05 0.1 0.15 0.2 0.25-2

0

2

4

6

8

10

12

0 0.05 0.1 0.15 0.2 0.25-1

-0.5

0

0.5

1

Fig. 4. Performance analysis: (upper) active power evolution, (middle)tracking current in dynamic reference frame and (bottom) PCC voltageand current behavior.

0 0.05 0.1 0.15 0.2 0.25-10

0

10

0 200 400 600 800 10000

0.2

0.4

Time (s)

Frequency (Hz)

Fundamental (50Hz) = 9.93 , THD = 4.80%

Mag

(%

of

Fund

amen

tal)

(A)

Selected signal: 12.5 cycles. FFT window (in red): 9 cycles

Fig. 5. Performance analysis: (upper) grid current, (bottom) grid currentTHD.

THD =

√√√√ 1

i21

N∑i=2

i2i (19)

MSE(Ψ) =

√√√√ 1

N

N∑j=1

Ψ2j (20)

60 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 14 - NUMBER 6 - YEAR 2016 ISSN: 1690-4524

where N is the number of vector elements, i1 is the amplitudeof the fundamental frequency of the analyzed current, ii arethe current harmonics and Ψ represents the difference betweenthe measured value and reference value of the analyzed signal.In Fig. 4 (middle) it can be also appreciated that the currentsfluctuate slightly due to the switching electronic components ofthe MMC, generating a small harmonic distortion. For an activepower of P ∗ = 4,000 W and a switching period of 20 µs. Itcan be seen that the THD is always below 5 %. Similar resultsare obtained for B and C phases. MSE was quantified on steadystate, between the reference and measurement currents in (d−q)reference frame, and the obtained value is 0.0952.

5. CONCLUSION

In this paper an active and reactive power control strategybased on the predictive control approaches applied to grid-connected SpWEG systems has been proposed. To achieve theinstantaneous power control, a MMC architecture has beenused in combination with the predictive control. The simulationresults confirm the capability of the proposed predictive controltechnique mainly in terms of low harmonic distortion, andalso showing an acceptable dynamic response when a multi-step power references is applied. Finally, the proposed controltechnique has proved to be viable providing an unity powerfactor allowing independently active power control.

Acknowledgment

The authors would like to thank the Paraguayan Governmentfor their encouragement and kind financial support providedthrough the CONACYT grant project (14-INV-097) and theLinking Program of Scientists and Technologists (PVCT16-187). This work was also funded by FONDECYT RegularProject No. 1160690. In addition, they wish to express theirgratitude to the anonymous reviewers for their helpful commentsand suggestions.

6. REFERENCES

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