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Model Predictive Control of H5 Inverter forTransformerless PV Systems with Maximum Power

Point Tracking and Leakage Current ReductionAbdulrahman J. Babqi∗, Zhehan Yi†, Di Shi†, Xiaoying Zhao†

∗Department of Electrical Engineering, Taif University, Taif, Saudi Arabia†GEIRI North America, San Jose, CA 95134

Emails: ajbabqi@tu.edu.sa, {zhehan.yi, di.shi, xiaoying.zhao}@geirina.net

Abstract—Transformerless grid-connected solar photovoltaic(PV) systems have given rise to more research and commercialinterests due to their multiple merits, e.g., low leakage currentand small size. In this paper, a model-predictive-control (MPC)-based strategy for controlling transformerless H5 inverter forsingle-phase PV distributed generation system is proposed. Themethod further reduces the PV leakage current in a cost-effectiveand safe manner and it shows a satisfactory fault-ride-throughcapability. Moreover, for the first of its kind, PV maximum powerpoint tracking is implemented in the single-stage H5 inverterusing MPC-based controllers. Various case studies are carriedout, which provide the result comparisons between the proposedand conventional control methods and verify the promisingperformance of the proposed method.

Index Terms—Solar PV System, H5 Inverter, distributed gen-eration, renewable integration, model predictive control, leakagecurrent, maximum power point tracking, fault ride through.

I. INTRODUCTION

Renewable distributed energy resources (DERs), such assolar photovoltaic (PV) and wind power systems, have beengetting more attentions recently to be used as alternatives offossil fuels [1]–[3]. PV power systems are considered as oneof the most attractive renewable DER technologies thanks tothe abundance of solar energy and the declining capital andoperational expenses [4], [5]. Generally, PV systems can beinterfaced with the utility grid through transformer-isolationor transformerless configurations. Since line frequency trans-formers are heavy, inefficient, and cost-ineffective for PVsystems, transformerless configurations are attracting more andmore interests from both research and commercial points ofview. However, the lack of galvanic isolation in the trans-formerless configurations will lead to a common-mode (CM)leakage current between the PV panels and the ground throughparasitic capacitors, which reduces the overall efficiency andgrid current quality and may cause serious electromagneticinterference and insecurity issues [6]. The parasitic capacitanceis approximately 60 nF to 110 nF every kilowatt of the PVarray [7]. Therefore, various inverter topologies with specificmodulation strategies have been introduced to suppress theleakage current, in which only a few topologies have been

This work is supported by the SGCC Science and Technology ProgramDistributed High-Speed Frequency Control under UHVDC Bipolar BlockingFault Scenario.

Ci Co

L1

L2

S5

S1

S2

S3

S4

Cp GNDLeaki

PVi

PVV

Li

+

-

1LV+ -

2LV+ -

Cii

gVoutV

+

-

Fig. 1. A typical configuration of the H5 transformerless inverter in a PVsystem.

developed into industrial products, e.g., H5, H6, and HERICinverters. The H5 structure is adopted by the SMA SolarTechnology due to its simple topology with the least numberof switches [8]. Fig. 1 illustrates a typical grid-connectedtransformerless PV system using a H5 inverter, where iLeak

stands for the CM leakage current, CP is the PV parasiticcapacitor mentioned previously.

In order to extract the maximum power of a PV array un-der different ambient conditions (irradiance and temperature),maximum power point tracking (MPPT) algorithms, such asPerturb & Observe (P&O) and Incremental Conductance (In-Cond), are employed to control the power-electronics stage.Although there are numerous existing methods to implementMPPT for grid-tied PV systems, most of them use two-stage cascaded DC/DC-DC/AC converting systems [9]–[11]or single-stage DC/AC inverters [12]–[15] with PI-based con-trollers or their variants. These methods may suffer from oneor multiple of the following major drawbacks:

• PI-based controllers require iterative tuning efforts whensystem parameters change;

• It is relatively difficult to find optimal gain and timeconstants for the controllers;

• Extra pulse width modulation (PWM) modules are re-quired;

• Some of the methods require multiple stages of costlyconverters, which reduces the converting efficiency; and

• CM leakage current is not considered in most methods.Furthermore, very few research has tried to control the PVMPPT using a transformerless single-stage H5 inverter.

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THIS WORK HAS BEEN ACCEPTED BY THE 44TH ANNUAL CONFERENCE OF THE IEEE INDUSTRIAL ELECTRONICS SOCIETY (IECON 2018). THIS IS A PREPRINT. 2

Ci Co

L1

L2

S5

S1

S2

S3

S4

Ci Co

L1

L2

S5

S1

S2

S3

S4

Ci Co

L1

L2

S5

S1

S2

S3

S4

Ci Co

L1

L2

S5

S1

S2

S3

S4

(a) (b)

(c) (d)

Fig. 2. The four operation modes of H5 inverter for grid-connected PV systems.

Model predictive control (MPC) is an optimal control ap-proach which uses the system model and measurements topredict the future behavior of the controlled states based onminimizing a cost function [16]–[18]. It is a fast, robust, andaccurate controller that requires little tuning efforts. Recently,MPC has been seen in the literature for controlling PV powersystems [19]–[22]. However, these works only design MPC tocontrol DC/DC converters. There is no existing work aimingat designing MPC for H5 inverters. To fill this gap and asan attempt to address the aforementioned issues, this paperproposes a MPC-based strategy for controlling the single-stage transformerless H5 inverter for PV distributed generationsystems. The control strategy further reduces the PV leakagecurrent comparing with conventional control methods. More-over, fast and accurate MPPT is implemented for the single-stage H5 transformerless inverter using MPC. Additionally, theproposed method improves the robustness and the fault-ride-through capability of transformerless PV systems. The restof the paper is organized as follows: Section II presents thedesign of H5 inverter and its operation modes; the proposedMPC for H5 inverters is descried in Section III; case studiesare carried out in Section IV to verify the control scheme;Section IV concludes the paper.

II. H5 INVERTER OPERATION MODES

The topology of a H5 inverter is similar to the single-phasefull-bridge inverter by adding an extra DC-bypass switch “S5”that disconnects the PV array from the utility grid during thecurrent-freewheeling periods. Fig. 1 shows the topology ofH5 inverter with the leakage current (iLeak) between the PVarray and ground. In general, there are four operation modesfor H5 inverters, which are depicted Fig. 2. The first operationmode (Fig. 2(a)) is the active mode which occurs during thepositive-half cycle, where the switches S1, S4, and S5 areconducting and the current flows through S1 and S5 and then

TABLE IH5 INVERTER SWITCHING STATES

Mode S1 S2 S3 S4 S5 Vout

1 1 0 0 1 1 VPV

2 1 0 0 0 0 03 0 1 1 0 1 −VPV

4 0 0 1 0 0 0

Fig. 3. H5 inverter space vector modulation (SVM).

returns to the cathode of the PV array through S4. The secondmode of operation shown in Fig. 2(b) is also referred to as thecurrent-freewheeling mode with the zero voltage vector. In thismode, S1 is triggered on, while S4 and S5 are turned-off. Thecurrent is conducting through the freewheeling diode of S3.Fig. 2(c) illustrates the third mode of operation of H5 inverter,which is the active mode that occurs during the negative-half cycle. During mode 3, switches S2, S3, and S5 conductand the current flows through the inductors L1 and L2 in theopposite direction of that in mode 1. The fourth mode is thefreewheeling mode during the zero voltage vector where S2and S5 are turned-off and S3 is on. Similar to S3 in mode2 (Fig. 2(b)), S1 works as a freewheeling diode in mode 4.Table I and Fig. 3 show the operation modes and space vectormodulation (SVM) of the H5 inverter.

III. THE PROPOSED MODEL PREDICTIVE CONTROL FORTRANSFORMERLESS H5 INVERTERS ENABLING PV MPPTA. State Predictions of H5 inverter

As is mentioned above, in the first mode of operation, S1,S4, and S5 are conducting. The system model can be derived

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by KCL and KVL, respectively:

iPV = iCi + iL (1)

VPV = VL1 + VL2 + Vg (2)

where iPV and VPV are the PV array output current andvoltage, respectively. iCi and iL are the currents throughcapacitor Ci and the inductor L1, respectively. VL1 and VL2

are the voltages across inductor L1 and L2 and Vg is the utilitygrid voltage.

In the second mode of operation where only S1 is turned-on,the system model is:

iPV = iCi, (3)

VPV = VCi. (4)

where VCi is the capacitor Ci voltage.In the third mode, S2, S3, and S5 are closed and the system

model can be written as:

iPV = iCi + iL, (5)

VPV = VL1 + VL2 + Vg. (6)

During the fourth mode, the only closed switch is S3 and thesystem model can be given as:

iPV = iCi, (7)

VPV = VCi. (8)

Additionally, the capacitor current and inductor voltages canbe expressed as:

iCi =dVPV

dt, VL1 =

diL1

dt, VL2 =

diL2

dt. (9)

For a PV system, the MPPT is realized by forcing thePV operating pointing to be around maximum power point,namely, to control VPV to track the MPPT reference voltageVref . Therefore, we have to predict the future values of PVarray voltage, VPV (k + 1) per horizon step. To this end, (1),(3), (5), and (7) must be discretized. Using the forward finitedifference formula for the derivative

dx

dt≈ x(k + 1)− x(k)

Ts, (10)

where Ts is the sampling period, the future values of the PVoutput voltage for the aforementioned four operation modesare predicted as:

VPV 1(k + 1) = VPV (k) +Ts

Ci[iPV (k)− iL(k)] (11)

VPV 2(k + 1) = VPV (k) +Ts

CiiPV (k) (12)

VPV 3(k + 1) = VPV (k) +Ts

Ci[iPV (k)− iL(k)] (13)

VPV 4(k + 1) = VPV (k) +Ts

CiiPV (k) (14)

It is noteworthy that for the PV array voltage, the predictionsof mode 1 and 3 are identical, so are mode 2 and 4. Thiswill reduce the mode switching frequency and thus the CMleakage current, which will be seen in the verification in thecase studies (Section IV).

Start

( ) ( ) ( 1)PV PV PVdV k V k V k

( ) ( ) ( 1)PV PV PVdi k i k i k

( ) 0?PVdV k

( ) ( )?

( ) ( )PV PV

PV PV

di k i k

dV k V k

N

( ) 0?PVdi k

Y

( ) ( )?

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PV PV

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Y

Y

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PV PV

V k V k

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Predict PV voltage in 4 modes:

1

2

3

4

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( 1) ( ) ( )

( 1) ( ) [ ( ) ( )]

( 1) ( ) ( )

SPV PV PV L

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SPV PV PV L

SPV PV PV

TV k V k i k i k

CiT

V k V k i kCiT

V k V k i k i kCiT

V k V k i kCi

2min [ ( 1)]ref PViJ V V k

H5 Inverter Space Vector Modulation

End

Fig. 4. The proposed MPC-based PV MPPT control for transformerless H5inverters.

B. Maximum Point Point Control of H5 Inverter Using MPC

The proposed method is modified from one of the most pop-ular MPPT algorithms, the Incremental Conductance method[23], for extracting the maximum power output of the trans-formerless PV array with H5 inverter under varying irra-diance and temperature. Fig. 4 depicts the process of theproposed algorithm in detail. At every sampling period Ts,the controller samples the values of VPV , iPV , and iL fromthe transformerless PV system and follows the proceduresof the flowchart to determine the optimal control inputs.After predicting the future value of the PV output voltage,a quadratic cost function:

J = [Vref − VPV (K + 1)]2 (15)

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is designed to quantify the difference between the MPPT refer-ence voltage Vref and the future PV array voltage VPV (k+1).The control process is then transferred into a optimizationproblem, which minimizes the quadratic function (15), i.e.,the error between the reference and predicted value, and selectthe optimal control inputs with the least cost. This is achievedby evaluating each possible scenario (i.e., the four modesof operation) and selecting the best operation mode at everysampling step. Once the optimal operation mode is determined,appropriate gating signals are sent to the H5 inverter switches.

Via optimization, the controller will automatically selectthe switch signals that lead to a minimum error between thecontrolling states and references, which eliminates the tuningefforts that required by conventional controllers. Moreover, theswitching signals will be directly applied to the H5 inverterwithout the needs for an extra PWM module, which lowersthe cost and complexity of the control system.

IV. CASE STUDIES

To examine the performance of the proposed control strat-egy for H5 inverters, multiple case studies are carried out inthis section. The transformerless PV system with the sameconfiguration in Fig. 1 is modeled in the PSCAD/EMTDCplatform, while the proposed algorithm is implemented usingFortran. The numerical values of the tested system parametersare provided in Table II. The parameters of the PV arrayare measured under standard testing condition (STC, irradi-ance=1000 W/m2, temperature=25°C) It is noteworthy that,although the proposed method is verified in a testbed withcertain parameters, it is scalable to work for different trans-formerless PV systems. For systems with other configurations,similar approach can be used to design the controller. Thetested cases are elaborated below.

Case Study 1

This case verifies the MPPT capability of the proposedcontrol method, which aims at extracting the maximum powerof the PV array under varying irradiance situations. Fig. 5shows the PV array instantaneous output voltage (VPV ) andcurrent (IPV ) as well as the MPPT voltage reference (Vref ).At the beginning, the irradiance is set to 1000 W/m2 and thetemperature is 25◦C. At t = 2 s, the irradiance drops from1000 W/m2 to 800 W/m2. It can be seen from Fig. 5 thatthe output current of the PV array decreases as the irradiancechanges without any undershooting. Moreover, the PV outputvoltage is tracking its reference Vref closely. A further declineof the irradiance occurred at t = 3 s. The irradiance reducesfrom 800 W/m2 to 600 W/m2. It is demonstrated that bothPV voltage and current change their values correspondinglybecause of the new irradiance level. Again, it is clear thatthe PV output voltage follows its reference value. Therefore,the proposed control strategy provides a fast response as wellas good dynamic performance under the varying irradianceconditions.

TABLE IICASE STUDY SYSTEM PARAMETERS

Parameter Symbol Value

Standard Testing Irradiance G 1000 W/m2

Standard Testing Temperature T 25°CPV Array Maximum Power (STC) Pmax 133 kWPV Array Maximum Point Point Voltage (STC) Vref 190 VDC Capacitor Ci 5000 uFOutput Filter Inductor 1 L1 1 mHOutput Filter Inductor 2 L2 1 mHOutput Filter Capacitor Co 5000 uFGrid Side Voltage Vg 100 VSampling Period Ts 100 usPV Parasitic Capacitance CP 13300 nF

1

g

2 2.5 3 3.5

170

180

190

V(V

)Vref VPV

2 2.5 3 3.5

400

600

800

Time (s)

I(A

)

IPV

Fig. 1.Fig. 5. PV output voltage and current using the proposed control method.

Case Study 2

The following case aims at validating the capability of theproposed control strategy for further reducing the CM leakagecurrent in a transformerless PV system with a H5 inverter.Fig. 6 illustrates the instantaneous CM leakage currents ofthe transformerless PV system by the proposed MPC andconventional PI controllers, as well as the leakage currentof a PV system with a single-phase full-bridge inverter bya PI controller. Fig. 7 presents their RMS values. To presenta reasonable comparison, the MPPT algorithm for all thesecase are based on the Incremental Conductance method. Fromthese figures, it is obvious that H5 inverter itself reduces theCM leakage current (RMS) from 3 A to 2.5 A approximately(black and red curves in Fig. 7).

The results also presents that, for the same configuration(transformerless H5 inverter), the proposed method furtherreduces the leakage current by almost 50% compared withconventional PI controller (blue curve in Fig. 7). This isbecause that, during operation, the proposed method reducesthe switching modes of the H5 inverter as is analyzed in

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1

g

3.8 3.85 3.9 3.95 4

−5

0

5

Time (s)

I Leak

(A)

MPC-H5

Fig. 1.

3.8 3.85 3.9 3.95 4

−5

0

5

Time (s)

I Leak

(A)

PI-H5

Fig. 2.

3.8 3.85 3.9 3.95 4

−5

0

5

Time (s)

I Leak

(A)

PI-full bridge

Fig. 3.

1

g

3.8 3.85 3.9 3.95 4

−5

0

5

Time (s)

I Leak

(A)

MPC-H5

Fig. 1.

3.8 3.85 3.9 3.95 4

−5

0

5

Time (s)

I Leak

(A)

PI-H5

Fig. 2.

3.8 3.85 3.9 3.95 4

−5

0

5

Time (s)

I Leak

(A)

PI-full bridge

Fig. 3.

1

g

3.8 3.85 3.9 3.95 4

−5

0

5

Time (s)

I Leak

(A)

MPC-H5

Fig. 1.

3.8 3.85 3.9 3.95 4

−5

0

5

Time (s)

I Leak

(A)

PI-H5

Fig. 2.

3.8 3.85 3.9 3.95 4

−5

0

5

Time (s)

I Leak

(A)

PI-full bridge

Fig. 3.Fig. 6. Leakage current comparison among the MPC-controlled H5 inverter,PI-controlled H5 inverter, and PI-controlled full-bridge inverter.

1

g

3.8 3.85 3.9 3.95 4

0

2

4

Time (s)

I Leak

(A)

MPC-H5 PI-H5 PI-full bridge

Fig. 1.Fig. 7. RMS values of the leakage current

Section III. The large leakage current that occurs with theconventional controller will affect the reliability and efficiencyof the PV system. More importantly, it may cause safetyhazards to the system operator and maintenance personnel.Fig. 8 demonstrates the PV output voltage and current usingboth the proposed control strategy and conventional PI controlfor H5 inverter, which shows that the leakage current affectsthe performance of the PV system and makes it more oscil-latory while proposed method gives a smoother and steadierperformance.

1

g

5 5.5 6 6.5 7

170

180

190

Time

Vpv

(V)

MPC

PI

5 5.5 6 6.5 7

200

400

600

Time (s)

I pv

(A)

MPC

PI

Fig. 1.

1

g

5 5.5 6 6.5 7

170

180

190

Time

Vpv

(V)

MPC

PI

5 5.5 6 6.5 7

200

400

600

Time (s)

I pv

(A)

MPC

PI

Fig. 1.Fig. 8. Comparison of the PV output voltage and current using the proposedcontroller and a conventional PI controller.

1

g

1 1.2 1.4 1.6 1.8 2

0

100

200

Time

Vpv

(V)

MPC PI

1 1.2 1.4 1.6 1.8 2

500

1,000

1,500

Time (s)

I pv

(A)

MPC PI

Fig. 1.

1

g

1 1.2 1.4 1.6 1.8 2

0

100

200

Time

Vpv

(V)

MPC PI

1 1.2 1.4 1.6 1.8 2

500

1,000

1,500

Time (s)

I pv

(A)

MPC PI

Fig. 1.Fig. 9. Output PV voltage and current using both proposed controller andconventional PI.

Case Study 3

This case demonstrates the fault-ride-through capability ofthe proposed control method. To this end, a ground fault wasapplied to system at the output terminal of the PV array. Fig. 9plots the PV output voltage and current of H5 inverter (usingboth the proposed method and PI controller) before, during,and after the fault. The ground fault is applied at t = 1.4 sand it is cleared after 100 ms (Fig. 9). It can be seen thatthe system controlled by the PI controller is vulnerable. ThePV voltage and current become unstable during and even

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after the clearance of fault (red curves). The PV currentincreases immediately when the fault occurs, which may causedamage to the system if no further protection actions areapplied. Nevertheless, the proposed control strategy showsa robust performance (blue curves) and a better fault-ride-through capability under faulted conditions. The PV voltagetracks its reference value Vref both during and after the faultcleared, while the current is limited within a reasonable range.

V. CONCLUSIONS

This paper introduces an innovative control strategy fortransformerless grid-connected PV systems with H5 inverters.A model-predictive-controlled method is designed to extractthe PV maximum power under various operational conditions.The control strategy predicts the future behavior of the PVoutput voltage and generates the optimal control signals for theH5 inverter, which minimizes the error between the referenceand the controlled variable. The case studies verifies that theproposed method provides a better dynamics response compar-ing with conventional methods. Moreover, the control strategyfurther reduces the CM leakage current in the H5 inverter byalmost 50% compared with conventional PI controller. It alsodemonstrates the robustness and fault-ride-through capabilityof the proposed method.

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