Power quality enhancement of single phase grid tied inverters with model predictivecurrent controllerAditi Chatterjee, Kanungobarada Mohanty, Vinaya Sagar Kommukuri, and Kishor Thakre

Citation: J. Renewable Sustainable Energy 9, 015301 (2017); doi: 10.1063/1.4973714View online: http://dx.doi.org/10.1063/1.4973714View Table of Contents: http://aip.scitation.org/toc/rse/9/1Published by the American Institute of Physics

Power quality enhancement of single phase grid tiedinverters with model predictive current controller

Aditi Chatterjee, Kanungobarada Mohanty, Vinaya Sagar Kommukuri, andKishor ThakreDepartment of Electrical Engineering, National Institute of Technology, Rourkela, India

(Received 7 October 2016; accepted 23 December 2016; published online 5 January 2017)

Recognition of renewable energy sources as alternative sources for power

generation has augmented the number of distributed generation plants being

incorporated into the conventional power distribution system. The single phase

voltage source inverter allying the distributed generation plant with the grid has to

address various issues related to the quality of current injected into the grid, output

power factor, and power exchange between the plant and the grid. This paper

focuses on the analysis, design, and implementation of a digital predictive current

control technique known as model predictive current controller for the control of

single phase power inverter integrating renewable energy based plant with the grid.

The proposed controller is tested in diverse operating conditions and is compared

with the existing proportional resonant current control scheme. The simulation and

experimental results validate the efficacy of the proposed control technique.

Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4973714]

I. INTRODUCTION

In this era of globalization, modernization, and industrialization, the chief concerns are

environmental pollution and population explosion. The ever increasing population is putting a

great pressure on energy resources. The conventional power plants, reliant on fossil fuel

reserves, are not enough to meet the electricity demand because of the exhaustion of these

reserves. Moreover, the fossil fuel-based power plants contaminate the environment with the

emission of toxic gasses and residues. To overcome these tribulations, renewable energy resour-

ces (RES) have been accepted as alternative power generation sources. To meet the growing

electricity demand distributed generation (DG) plants based on RES are integrated into power

distribution system.

The form of generated power from these plants is not attuned to the conventional distribu-

tion system. To alter the generated power into the required form, power electronic converters

(PEC) are essential.1 Single phase distribution system mostly serves residential areas and the

DG plants are installed there. A single phase voltage source inverter (VSI) is used to interface

DG plant with DC power output such as solar power plants or fuel cells based plants with the

grid. Photovoltaic (PV) based DG plants are gaining importance. Although the installation cost

is high, the maintenance cost is low. Researchers have proposed different inverter topologies

for integrating PV based DG with the grid.2–4 The PEC interfacing the DG plant with grid

gives rise to various power quality issues such as harmonic contamination in the current

injected into the grid, grid synchronization, and low output power factor.5,6 The control of these

PEC is crucial to meet the standards set for grid interconnection of DG plants. Utility interac-

tive PEC must satisfy standards such as IEEE 1547 and IEC 61727.6

Generally, two controllers are employed for control of RES based power plants. One is the

input side MPPT controller which takes into account the dynamics of the renewable and the

other one is the grid side controller.6 The grid side controller performs multiple tasks such as

control of real and reactive power trade between DG source and grid, injecting current free

from harmonic pollution into the grid and grid synchronization. The prime concern of this

1941-7012/2017/9(1)/015301/17/$30.00 Published by AIP Publishing.9, 015301-1

JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 9, 015301 (2017)

research work is only the grid side controller, which focuses on the quality of current waveform

injected into the grid and power exchange between the grid and RES based power plants.

To accomplish this task, researchers have proposed various grid side current control strate-

gies.7,8 The current controller mitigates the inverter output current harmonics thereby reducing

the total harmonic distortion (THD). The controller also regulates the power exchange between

the DG plant and grid and also performs reactive power compensation. It also strives to achieve

high output power factor. Various current control strategies have been projected and imple-

mented for single phase grid-tied VSI out of which the significant ones are current hysteresis

control (CHC),11,12 proportional integral (PI) control,13,14 proportional-resonant (PR) control,15–19

and dead beat control (DBC).20

The current controllers can be broadly classified as linear and nonlinear controllers.6,7

Among the nonlinear controllers, CHC is the most common strategy and is implemented in

natural reference frame. CHC is easy to implement, but it suffers from inconsistent switching

frequency and higher switching losses. This limits its application to lower power range.

Among the linear controllers, PI controllers are conventional ones that are implemented in

synchronous reference frame. It can achieve fast dynamic response. The design of PI control-

ler turns out to be a tedious task for single phase systems as it involves reference frame trans-

formation of control variables. Moreover, two PI controllers are required, one for active and

the other for reactive power control. It has been reported in literature that the PI controller

fails to achieve perfect sinusoidal reference current tracking due to non-zero steady state

error.14 On the other hand, the PR controller is a relatively new breed of linear current controller

designed in stationary reference frame. Many researchers have successfully implemented PR con-

troller for single phase grid tied VSI. The PR controller introduces a very high gain at grid fre-

quency thereby eliminating steady-state error. Hence, the current injected by VSI into the grid is

perfectly sinusoidal.16 It also has the provision of selective harmonic mitigation by cascading har-

monic compensators (HCs) along with the original current controller.19 The controller can achieve

good steady state response but its transient response is poor and it is prone to instability with

change in system parameters. The dead-beat current control strategy is effective in achieving fast

dynamic response with simpler design.20 The lacuna of this strategy lies in its sensitivity to system

parameters like sampling frequency and filter inductance.

Hence, in this paper a model predictive current controller (MPCC) is introduced for single

phase grid tied VSI which can perform well in both steady state and transient state operations.

The present work also demonstrates the hardware implementation of the digital MPCC using

low cost digital signal processor (DSP). A 1 kW single phase grid connected VSI is modelled

and simulated. The simulation results obtained with the proposed control strategy is compared

with the linear PR current control (PRCC) scheme. The experimental implementation of the

proposed strategy validates the simulation results.

II. SINGLE PHASE GRID TIED DG BASED INVERTER SYSTEM

A. System modelling

The single phase VSI shown in Fig. 1 consists of four insulated gate bipolar transistor

(IGBT) arranged in H-bridge configuration. The VSI is connected to the grid through a line

inductor L with an internal resistance R. The purpose of the inverter is to transmit the power

generated by the DG plant to the grid,

vo ¼ Rio þ Ldio

dtþ vg; (1)

where v0 is the output voltage of the inverter, vg is the grid voltage, and i0 is the inverter output

current. For grid tied VSI, the grid voltage is sinusoidal with invariable frequency and ampli-

tude. The design procedure for filter is detailed in Ref. 9. Taking the Laplace transform of (1),

the transfer function of the plant can be expressed as in (2),

015301-2 Chatterjee et al. J. Renewable Sustainable Energy 9, 015301 (2017)

io sð Þvo sð Þ � vg sð Þ

¼ 1

Rþ Ls: (2)

Hence, the inverter model can be expressed as a first-order system.

B. Control system structure

The objective of the control system is to regulate the output current of the inverter that is

injected into the grid and also administer the power exchange between DG plant and grid.

1. Generation of orthogonal signal

In single phase system, only a solitary signal is available. For designing and implementing,

a controller for single phase circuits, two signals orthogonal to each other is necessary. One to

control the active and the other to control the reactive power trade between the DG plant and

the grid. Hence, a fictitious signal orthogonal to the original single phase signal has to be cre-

ated. Several methods have been proposed in literature to meet this requirement. In this work,

the fictitious signal is generated by delaying the original signal by a quarter of the fundamental

period.10 This method is selected for its simplicity and ease of implementation and absence of

any tuning parameters.

2. Generation of reference current

The block diagram in Fig. 1 shows that the signal vga is in phase with the original grid

voltage. The fictitious signal, vgb, created by introducing delay unit is orthogonal to vga. Both

of these signals are in stationary (a-b) reference frame and transformed to synchronous (d-q)

reference frame by utilizing the knowledge of phase angle of grid voltage obtained from the

phase locked loop (PLL) unit. The transformation from a-b frame to d-q frame is performed

using (3) and (4),

vgd ¼ vga sin xt� vgb cos xt; (3)

vgq ¼ vga cos xtþ vgb sin xt: (4)

Using the voltage signals in synchronous reference frame and the reference power signals,

the reference currents in d-q frame can be calculated by

FIG. 1. Schematic diagram of single phase grid-tied IGBT based H-bridge inverter.

015301-3 Chatterjee et al. J. Renewable Sustainable Energy 9, 015301 (2017)

irefd

irefq

!¼ 2

v2gd þ v2

gq

� � vgd vgq

vgq �vgd

� �Pref

Qref

� �: (5)

Here, Pref and Qref are the active and reactive power references. The calculated d-q refer-

ence current irefd and iref

q controls the active and reactive powers of the system, respectively. A

reference current synchronized with the grid voltage is generated using the calculated reference

current in the d-q frame without converting it back to stationary frame. The synchronized refer-

ence current is given by

iref ¼ irefd sin xt� iref

q cos xt: (6)

The error between the desired reference current and measured current is fed to the current

controller. In the following section (Section III), the proposed MPCC scheme is discussed in

detail and compared with the PR control approach.

III. CURRENT CONTROLLERS DESIGN AND ANALYSIS

A. Proportional resonant current control

The PR current controller (PRCC) has gained ample recognition in recent years for single

phase grid tied RES based DG plants.16–19 It is a linear control technique where the current

control operation gets exhibited in the stationary reference frame, and the coordinate transfor-

mation can be eliminated.15 The block diagram of current controller is shown in Fig. 2.

The synchronized reference current generated by (6) is compared with the measured

inverter output current. The output of the controller is the reference voltage signal for the pulse

width modulation (PWM) modulator. Unipolar sinusoidal PWM (SPWM) technique is used to

generate pulses for the IGBTs. The transfer function of an ideal PR compensator is given by16

Gipr sð Þ ¼ kp þ2kis

s2 þ x2: (7)

Here, kp is the proportional gain and ki is the integral gain for the resonant term, which

acts as an integrator for the sinusoidal signal and x is the grid frequency. From the frequency

response of ideal PR compensator, it is observed that the gain becomes interminably high at the

resonant frequency and much lower at other frequencies.19 Hence, a damping factor is intro-

duced to diminish the gain and enhances the bandwidth of the controller. The transfer function

of non-ideal PR compensator with the damping term is mentioned by18

Gnpr sð Þ ¼ kp þ2kixcs

s2 þ 2xcsþ x2: (8)

From the block diagram in Fig. 2, the output of the current control loop can be written as in

ioðsÞ ¼ HpiðsÞiref ðsÞ þ HpvðsÞvgðsÞ; (9)

FIG. 2. Block diagram of the current controller.

015301-4 Chatterjee et al. J. Renewable Sustainable Energy 9, 015301 (2017)

where Hpi and Hpv are given by (10) and (11), respectively,

Hpi sð Þ ¼Gnpr sð ÞGf sð Þ

Gnpr sð ÞGf sð Þ þ 1; (10)

Hpv sð Þ ¼Gf sð Þ

1þ Gnpr sð ÞGf sð Þ; (11)

where Gnpr(s) and Gf(s) are the transfer functions of current controller and plant, respectively,

where Gnpr(s) is given by (8) and Gf(s) is given by

Gf sð Þ ¼ 1

Rþ Ls: (12)

To obtain zero steady state error and track the reference current signal iref(s) effectively,

the PR controller introduces a very high gain; hence, Gnpr(jx) value is very high at fundamental

frequency. The magnitude of Hpi (jx) and Hpv (jx) approaches unity and zero at the same fre-

quency. So, the grid voltage feed forward in the current loop can be detached. The current loop

equation can be given in (13). The closed loop transfer function of current control loop is given

in (14)

ioðsÞ ¼ HpiðsÞiref ðsÞ; (13)

io sð Þiref sð Þ

¼ s2kp þ 2xckp þ 2kixcð Þsþ kpx2

s3Lþ kp þ Rþ 2xcLð Þs2 þ 2xckp þ 2kixc þ 2xcRþ x2L� �

sþ kp þ Rð Þx2: (14)

The performance of the controller depends on three parameters kp, ki, and xc which is the

damping speed. For tuning these parameters, a frequency response analysis is performed. To

study the effect of each parameter on the controller performance, one of the three parameters is

varied keeping the other two fixed.

From the corresponding bode plots shown in Fig. 3 it is observed that the value of integral

gain does not affect the phase plot but it has a notable effect on the magnitude plot. The magni-

tude of controller enhances with the increase in the value of ki. Both magnitude and phase of

the controller are affected by variation of xc. The increment in the value of xc reflects an

increase in magnitude and phase but at the same resonant frequency. The gain magnitude of PR

controller increases with an increase in the kp value. On the other hand, the phase magnitude

decreases with the increment in the value of kp.

By studying the frequency response plots, an appropriate value for the controller parameter

is selected to obtain the desired response. The corresponding value of kp, ki, and xc used for

simulation are 20, 1000, and 10 rad/s, respectively.

To ensure the stability of the PRCC with the calculated parameters, bode plot analysis is

performed. The chief benefit of bode plot lies in the fact that closed loop stability of the system

can be evaluated with the open loop data. The closed loop gain of the current control loop with

the PR controller is given by

GðsÞ ¼ GnprðsÞGf ðsÞ: (15)

From the bode plot of G(s) in Fig. 3, it can be observed that the gain margin (GM) is infinite

and phase margin (PM) is 88.9�. It reveals the fact that since the PM is positively large, the

system is stable; and due to infinite GM, if the gain of the system is further increased the PM

may decrease, but it will always remain positive. However, the phase plot never crosses �180�

margin. Hence, the controller designed for the system is stable.

Since the controller is designed in continuous time domain, the closed loop transfer func-

tion has to be discretized for experimental implementation on the digital platform.

015301-5 Chatterjee et al. J. Renewable Sustainable Energy 9, 015301 (2017)

B. Model predictive control theory

The development of the model predictive control (MPC) scheme dates back to late seven-

ties when it was first applied in chemical process industries. The term MPC does not describe a

specific control technique but it includes a wide range of control methods and implementation.

The application of MPC strategy in the area of electrical drives and PEC is more recent.21–26

The MPC application for the control of power converter takes into account its discrete nature.

The discretized system model is used to predict the future values of states of the system, which

has to be controlled until a time horizon. A cost function is used to optimize the error between

the reference and predicted values of states in order to obtain the desired output.

Since MPC is not a unique control strategy, it includes an extensive family of controllers.

The basic working principle of this control methodology can be described by the following fun-

damental steps.

• A model of the system to be controlled is first obtained by considering the system dynamics.• The model of the system is used to forecast the future values of system states until a time

horizon.• A cost function is used to optimize the error between the desired and forecasted output. The

cost function optimization can be on-line or off-line depending upon the system and the type of

control method opted.

A discrete time model of the system in state space form can be represented by (16)–(17)

xðk þ 1Þ ¼ AdxðkÞ þ BduðkÞ; (16)

yðkÞ ¼ CdxðkÞ þ DduðkÞ: (17)

In which, k 2 I � 0. Here, k denotes the sampling instant and I � 0 is a set of non-negative inte-

gers. A cost function is defined to represent the desired characteristic of the system. The cost

function consists of references, predicted value of states, and also future actuations as given by

g ¼ f ðxðkÞ; uðkÞ; uðk þ 1Þ:::; uðk þ PÞÞ: (18)

FIG. 3. Bode diagrams for the PR controller.

015301-6 Chatterjee et al. J. Renewable Sustainable Energy 9, 015301 (2017)

MPC strategy aims to minimize the cost function g, for a predefined horizon in time P,

considering the model of the system and its constraints. The approach for solving the optimisa-

tion problem is also termed as receding horizon strategy. The details of receding horizon opti-

misation is illustrated in Fig. 4.

• At sampling instant k, with available measurements of states, the values of the manipulated var-

iables u, at the next sampling instant C, {u(k), u(kþ 1), u(kþC-1)}, are calculated. The set of

“C” control moves is calculated so as to minimize the forecasted deviations from the reference

target over the next P sampling instants, while considering the system restrictions. Where P is

the prediction horizon, which defines the lower and upper limits of the time horizon in the

future over which the controller tries to induce a desired response to the plant outputs and C is

the control horizon.• The first control move, u(k), is applied.• At the next sampling instant (kþ 1), the C step control policy is re-calculated for the next C

sampling instants, i.e., from (kþ 1) to (kþC) and the first control move u(kþ 1) is

implemented.• The entire procedure is repeated again for each sampling instant considering the new control

move.

Most of the power converters are non-linear systems with high switching frequency.

Hence, by taking into account the discrete nature of power converters, the optimization problem

can be solved online. Although the computation burden is expected to be more, it is possible to

lessen it by considering finite number of switching states of the converter. With the develop-

ment of high computational speed microprocessors, the real time online optimization of MPC is

quite easy and flexible. In the next subsection (Sec. III C), the MPC scheme is proposed and

implemented for current control of single phase grid connected VSI.

C. Proposed model predictive current control

The real time implementation of MPC scheme for current control of single phase grid-tied

VSI integrating RES based DG plants has not yet been explored. In this section, the MPC strat-

egy has been applied to control the current injected by VSI into the single phase grid to

improve the power quality and termed as model predictive current controller (MPCC). The total

harmonic distortion (THD) has been taken as the performance index of the controller in steady

state. The performance of MPCC is also evaluated during transient conditions like change in

reactive power demand and grid voltage distortions.

FIG. 4. Receding horizon optimization strategy.

015301-7 Chatterjee et al. J. Renewable Sustainable Energy 9, 015301 (2017)

The proposed MPCC uses a discretized model of the system to predict the future value of

current that has to be injected into the grid by the inverter. Taking into account the fixed num-

ber of switching states that can be generated by a static PEC the model of the system can be

used to envisage the behaviour of the control variables for each switching state. The block dia-

gram of the MPCC scheme is shown in Fig. 5.

The reference current is generated using (6) and the output current at k-th instant of time

io(k) is measured. The system model is used to predict the value of the output current in the

next sampling interval (kþ 1). A cost function is defined to evaluate the error between the ref-

erence and predicted current commands in the next sampling interval. The voltage level that

minimizes the cost function is selected and applied.22

1. Cost function

The cost function plays the most significant role for improved performance of the control

scheme. The central goal of the cost function is to control a particular system variable by mini-

mizing the error between the reference and predicted values. One of the major benefits of this

scheme is that several variables and constraints can be incorporated into a single cost function.

In this paper, the cost function is the square of error between the reference and predicted cur-

rents and is expressed in orthogonal coordinates as in (19),

gi ¼ ðirefa � iP

a Þ2 þ ðiref

b � iPbÞ

2; (19)

where irefa and iref

b are the real and imaginary parts of the reference current that controls the real

and reactive powers of the system, respectively, iPa and iPb are the real and imaginary parts of

the predicted current vector io(kþ 1). Since the sampling frequency is quite high, the reference

current at (kþ 1) interval is considered equal to k-th interval current vector. The cost function

is not subjected to any constraints, and since both the terms of the functions are of same physi-

cal nature, no weighting matrices are involved. Since the number of switching states is fixed

for single phase VSI, the optimization is performed online.

2. H-bridge inverter model

Model of the inverter shows a relationship between the switching states and output voltage

levels. As a single phase H-bridge inverter consists of four switches, Sa and Sb are the gate sig-

nals which controls the switching of the switches S1–S4. The four possible switching states of the

inverter are tabulated in Table I. The inverter output voltage vo can be associated with the

switching state as in (20). The consequent four voltage levels obtained are tabulated in Table II,

vo ¼ vdcS: (20)

FIG. 5. Block diagram of the MPCC scheme.

015301-8 Chatterjee et al. J. Renewable Sustainable Energy 9, 015301 (2017)

3. Discretization of system model

The differential equation describing the dynamics of the system (1) has to be discretized

for a sampling time Ts. The discretized model is used to predict the future value of current vec-

tor with the knowledge of measured current and voltage at k-th instant of time. Euler forward

method is opted for discretization of the first order system equation,

dio

dt� io k þ 1ð Þ � io kð Þ

Ts: (21)

Substituting (21) in (1), the future output current at time kþ 1, for each one of the four val-

ues of output voltage vector v0(k) generated by the inverter can be given by (22),

iP k þ 1ð Þ ¼ 1� RTs

L

� �io kð Þ þ Ts

Lvo kð Þ � vg kð Þ� �

: (22)

The cost function evaluates the error between the reference and predicted current vectors.

The value of the cost function decides which voltage vector is selected for switching. The volt-

age vector for which the current prediction is nearby to the desired current reference is selected

for the next sampling instant to be applied, which implies that the cost function is minimized

for that selected vector. For example, Table III shows the voltage levels and the corresponding

value of cost function for a particular sampling instant. The voltage vector v2 is selected for

switching as the cost function is optimum for that level at that instant.

IV. SIMULATION RESULTS AND DISCUSSION

A 1 kW grid tied single phase inverter system is simulated using the MATLAB/

SIMULINK software. The parameters used in the simulation study are tabulated in Table IV.

A. Steady state performance evaluation

While operating in steady state, the task of the inverter is to supply 1 kW of active power

to the grid from the source. Hence, the reactive power reference Qref is set to zero and the

active power reference Pref is 1000 W. The current injected by the VSI into the grid has to be

in phase with the grid voltage so that an output power factor of unity can be maintained. The

rate of harmonic pollution in case of each current controller is measured in terms of THD.

From Fig. 6, it can be observed that the performance of MPCC is very good. The grid cur-

rent is in phase synchronisation with the grid voltage and the calculated output power factor is

TABLE I. Switching states of the inverter.

Sa ¼ {1, if S1 ON and S2 OFF

Sa ¼ {0, if S1 OFF and S2 ON

Sb ¼ {1, if S3 ON and S4 OFF

Sb ¼ {0, if S3 OFF and S4 ON

TABLE II. Voltage levels generated by inverter.

Sa Sb Voltage level

0 0 v0¼ 0

1 0 v1¼ vdc

0 1 v2¼�vdc

1 1 v3¼ 0

015301-9 Chatterjee et al. J. Renewable Sustainable Energy 9, 015301 (2017)

0.99. The THD value for grid current is 1.49%. Similar behaviour is observed from Fig. 7, for

PR current controller but the THD value of grid current is 3.31% and the current settles down

to steady state after two cycles.

B. Transient state performance evaluation

To evaluate the performance of current controllers in transient state, different loading sce-

narios are considered. When the grid has to supply an inductive load, the inverter needs to

inject reactive power into the grid. On the other hand, when a capacitive load is connected, the

reactive power demand falls and the inverter draws reactive power from the grid.

TABLE III. Cost function optimization.

Voltage vector Cost function value

v0 gi0¼ 0.0145

v1 gi1¼ 0.0841

v2 gi2¼ 0.0097 (optimum)

v3 gi3¼ 0.0145

TABLE IV. Simulation parameter.

Parameter Values

Grid voltage (vg) 220 V (rms)

DC link voltage (vdc) 360 V

Grid side filter inductance (L) 10 mH

Internal resistance of inductance (R) 0.05 X

Switching frequency (fsw) 10 kHz

Sampling time (Ts) 5 ls

Simulation time (t) 0.2 s

FIG. 6. Steady state waveforms for MPCC.

015301-10 Chatterjee et al. J. Renewable Sustainable Energy 9, 015301 (2017)

The objective of the controller is to maintain constant active power flow to grid while there

is a change in the reactive power demand. To study this, the reactive power demand is changed

from 500 Var to �500 Var at 0.1 s. From Fig. 8, it can be observed that the transient perfor-

mance of MPCC is very fast. At 0.1 s, the power factor changes from 45� lagging to leading,

without any dynamics in the current waveform. The active power flow to grid is maintained

constant at 1 kW, which demonstrates the decoupling control of active and reactive powers.

Similar performance evaluation tests are performed for the PR controller and the results are

shown in Fig. 9. The transient response of PRCC is observed to be sluggish, with dynamics in

grid current.

The controller performance is also evaluated under voltage sag and swell conditions. A

30% of voltage sag is created for grid voltage at 0.1 s and the system is simulated with the

active current reference of 6.4 A and the reactive current reference set to zero. It is clear from

Fig. 8 that as the grid voltage sags, the current remains constant and is in phase with voltage

for MPCC. On the other hand, from Fig. 9, it is observed that for PRCC the current waveform

is also aligned with the voltage waveform, but with some dynamics in the waveform.

Likewise, a grid voltage swell of 20% is created at 0.1 s. It is observed from Fig. 8 that

the proposed current controller shows an exceptional performance during voltage swell by

maintaining a stable output current aligned with the grid voltage. Fig. 9 depicts that though the

grid current and voltage are in phase synchronization, the current magnitude reduces with some

dynamics as the voltage swells with PRCC.

V. EXPERIMENTAL IMPLEMENTATION

The proposed MPCC strategy for single phase grid connected VSI is validated by experi-

mental implementation. The PRCC scheme is also implemented on digital platform. The snap-

shot of experimental setup is shown in Fig. 10. The intelligent power module (IPM)

(PEC16DSM01) is basically a three level inverter, but for the experimental purpose it is oper-

ated as a single phase inverter by giving pulses to only two legs. The control algorithm is exe-

cuted using TMS320F2812, 32-bit fixed point digital signal processor (DSP). A Joint Test

Action Group (JTAG) made emulator is used to dump the control algorithm from PC to DSP.

PWM control signals at 10 kHz switching frequency is generated from DSP. LEM manufac-

tured current transducer LA 55-P and voltage transducer LV 25-P are used to sense inverter

FIG. 7. Steady state waveforms for PRCC.

015301-11 Chatterjee et al. J. Renewable Sustainable Energy 9, 015301 (2017)

output current and grid voltage, respectively. The Hall effect transducers transform the sensed

voltage and current quantities to low power level signals. The voltage and current sensors are

calibrated to scale down a voltage of 6220 V (rms) to 65 V range and current of 64.5 A (rms)

to 65 V signal, respectively. The sensed signals are feedback to the DSP via the analog to digi-

tal conversion (ADC) channels. A single phase auto transformer emulates the grid. The output

of the IPM is connected to the single phase grid by a toroid ring ferrite core inductor.

Yokogawa WT500 power analyzer is used to perform the harmonic analysis of the experimental

waveforms. The results are viewed on digital storage oscilloscope (DSO).

A. Experimental results

From Fig. 11, it can be observed that the grid current is aligned with the grid voltage and

the power factor is 0.982 and 0.965 in the case of the proposed and existing control schemes,

respectively. But the experimental THD value of MPCC is 2.808% and PRCC is 5.629%. This

reveals that the proposed controller shows better steady state response than the PRCC.

The transient state experimental results are illustrated in Fig. 12. When the inverter sup-

plies an inductive load, the reactive power demand is þ500 Var, and the current starts lagging

the voltage by almost 45�. On the other hand, when it powers a capacitive load, the reactive

power demand is �500 Var and the current leads the voltage waveform by 45�. The

FIG. 8. Transient state waveforms for MPCC.

015301-12 Chatterjee et al. J. Renewable Sustainable Energy 9, 015301 (2017)

experimental results show that the proposed controller shows an excellent performance during

the change in reactive power demands. In case of PRCC, the current waveform shows distor-

tions during transient conditions with the change in reactive power demands.

There is a significant difference between the experimental and simulation results. This dif-

ference arises due to the fact that the simulation study is performed under ideal conditions but

experimental platform does have some restrictions. The converter switches may incur some

conduction losses, minute calibration errors may also be present in the sensors. Moreover, while

implementing a digital control algorithm on a DSP platform, there are delays in the system.

The system delay may deteriorate the performance of the system.

VI. COMPARATIVE ASSESSMENT

The proposed controller is compared with the PR controller which is well known for con-

trol of single phase grid-tied DG based inverter. The comparative assessment is performed in

steps given below.

FIG. 9. Transient state waveforms for PRCC.

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A. Controller design

The design of MPCC is intuitive. The PWM modulator is eliminated. Hence, there is no

need of linearizing the system model. Tuning of controller parameters is not obligatory. On the

other hand, the PR controller is a linear control technique which involves PWM modulator for

generating pulses for the converter. Moreover, it requires tuning of controller gains to obtain

the desired performance.

It is expected that as MPCC involves online optimisation of the cost function, the computa-

tion time will be more. But for control of PEC the computational burden is lesser because of

FIG. 10. Snapshot of the experimental setup.

FIG. 11. Steady state experimental results. (a) Steady state voltage and current with MPCC. (b) Steady state voltage and

current with PRCC. (c) Harmonic analysis for MPCC. (d) Harmonic analysis for PRCC.

015301-14 Chatterjee et al. J. Renewable Sustainable Energy 9, 015301 (2017)

the finite number of switching states. With the advent of low cost and high computing speed

digital signal processor, the MPCC scheme can be implemented practically with effortlessness.

B. Steady state performance

The PR controller can achieve good steady state response with lower value of THD of grid

current. The PR controller does have the provision for additional harmonic compensators (HC)

especially for lower order harmonics but inclusion of HC will increase the order of the system

and leads to instability. Hence, in our research work we have not included the HC in the PR

control.

The proposed controller tracks the sinusoidal reference current perfectly, with almost zero

steady state error. The cost function minimizes the current error, which is the major reason

behind its superior performance. The THD value of grid current is lower that the THD value

obtained with the PR control.

C. Dynamic response

The major drawback associated with the PR controller is its sluggish transient response.

The MPCC overcomes this drawback and shows an excellent performance in transient state by

controlling the reactive power exchange with the grid, and without any dynamics in the grid

current. During grid voltage distortion conditions like in case of voltage sag or swell, it success-

fully maintains a constant current output.

The proposed MPCC for single phase VSI can accomplish a better steady state and tran-

sient response than the PR controller because of its cost function optimisation.

The comparative analysis is summarized in Table V.

FIG. 12. Transient state experimental results. (a) Voltage and current waveforms with MPCC for lagging power factor. (b)

Voltage and current waveforms with PRCC for lagging power factor. (c) Voltage and current waveforms with MPCC for

leading power factor. (d) Voltage and current waveforms with PRCC for leading power factor.

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VII. CONCLUSION

In this paper, a model predictive current control strategy is proposed for single phase grid

connected VSI. The projected controller is evaluated in terms of its design, steady state perfor-

mance, and dynamic response. The MPCC is also compared with the well-known PR current

controller. The simulation and experimental results confirm that the MPCC is successful in

achieving high output power factor and low THD value for grid current during the steady state

operation. It also shows superior performance by regulating power exchange between the grid

and the source during transient conditions like the change in the reactive power demands and

grid voltage distortions. Hence, the proposed strategy stands out to be one of the advance con-

trollers for control of power inverters in the single phase grid integration of distributed power

generation systems.

1F. Blaabjerg, Z. Chen, and S. B. Kjaer, “Power electronics as efficient interface in dispersed power generation systems,”IEEE Trans. Power Electron. 19(5), 1184–1194 (2004).

2Y. Xue, L. Chang, S. B. Kjaer, J. Bordonau, and T. Shimizu, “Topologies of single-phase inverters for small distributedpower generators: An overview,” IEEE Trans. Power Electron. 19(5), 1305–1314 (2004).

3S. Nema, R. K. Nema, and G. Agnihotri, “Inverter topologies and control structure in photovoltaic applications: Areview,” J. Renewable Sustainable Energy 3, 012701 (2011).

4T. Ngo and S. Santoso, “Grid-connected photovoltaic converters: Topology and grid interconnection,” J. RenewableSustainable Energy 6, 032901 (2014).

5G. M. Shafiullah, A. M. T. Oo, A. B. M. S. Ali, P. Wolfs, and A. Stojcevski, “Experimental and simulation study of theimpact of increased photovoltaic integration with the grid,” J. Renewable Sustainable Energy 6, 033144 (2014).

6F. Blaabjerg, R. Teodorescu, M. Liserre, and A. V. Timbus, “Overview of control and grid synchronization for distributedpower generation systems,” IEEE Trans. Ind. Electron. 53(5), 1398–1409 (2006).

7A. Timbus, M. Liserre, R. Teodorescu, P. Rodriguez, and F. Blaabjerg, “Evaluation of current controllers for distributedpower generation systems,” IEEE Trans. Power Electron. 24(3), 654–664 (2009).

8M. Monfared and S. Golestan, “Control strategies for single-phase grid integration of small-scale renewable energy sour-ces: A review,” Renewable Sustainable Energy Rev. 16(7), 4982–4993 (2012).

9H. Kim and K. H. Kim, “Filter design for grid connected PV inverters,” in IEEE International Conference on SustainableEnergy Technologies, Singapore (2008), pp. 24–27.

10S. Sakamoto, T. Izumi, T. Yokoyama, and T. Haneyosh, “A new method for digital PLL control using estimated quadra-ture two phase frequency detection,” in Proceedings of the Power Conversion Conference, Osaka (2002), pp. 671–676.

11Krismadinata, N. A. Rahim and J. Selvaraj, “Implementation of hysteresis current control for single-phase grid connectedinverter,” in Proceedings of the International Conference on Power Electronics and Drive Systems, Bangkok, Thailand(2007), pp. 1097–1101.

12P. A. Dahono, “New hysteresis current controller for single-phase full-bridge inverters,” IET Power Electron. 2(5),585–594 (2009).

13B. Bahrani, A. Rufer, S. Kenzelmann, and L. A. C. Lopes, “Vector control of single-phase voltage-source convertersbased on fictive-axis emulation,” IEEE Trans. Ind. 47(2), 831–840 (2011).

14Y. Cheng, K. Chen, L. Bai, and J. Yang, “Improvement of the grid-connect current quality using novel proportional-integral controller for photovoltaic inverters,” Rev. Sci. Instrum. 85, 025110 (2014).

15D. N. Zmood and D. G. Holmes, “Stationary frame current regulation of PWM inverters with zero steady-state error,”IEEE Trans. Power Electron. 18(3), 814–822 (2003).

16R. Teodorescu, F. Blaabjerg, M. Liserre, and P. C. Loh, “Proportional-resonant controllers and filters for grid connectedvoltage-source converters,” IEE Proc., Electr. Power Appl. 153(5), 750–762 (2006).

17M. Castilla, J. Miret, J. Matas, L. G. Vicuna, and J. M. Guerrero, “Linear current control scheme with series resonant har-monic compensator for single-phase grid-connected photovoltaic systems,” IEEE Trans. Ind. Electron. 55(7), 2724–2733(2008).

18M. Castilla, J. Miret, J. Matas, L. G. Vicuna, and J. M. Guerrero, “Control design guidelines for single phase grid con-nected photovoltaic inverters with damped resonant harmonic compensators,” IEEE Trans. Ind. Electron. 56(11),4492–4501 (2009).

19A. Chatterjee and K. B. Mohanty, “Design and analysis of stationary frame PR current controller for performanceimprovement of grid tied PV inverter,” in Proceedings of IEEE 6th India International Conference on Power Electronics(IICPE), Gwalior (2014), pp. 1–6.

20R. Kadri, J. Gaubert, G. Champenois, and M. Mostefai, “Design of a single-phase grid-connected photovoltaic systembased on deadbeat current control with LCL filter,” in 14th International Conference on Power Electronics and MotionControl Conference (EPE/PEMC), Ohrid (2010), pp. 147–153.

TABLE V. Comparative study of current controllers.

Controller

Steady state

performance

Transient state

performance

THD (simulation)

(%)

THD (expt.)

(%)

Power factor

(expt.)

PRCC Good Poor 3.31 5.629 0.965

MPCC Excellent Fast 1.49 2.808 0.982

015301-16 Chatterjee et al. J. Renewable Sustainable Energy 9, 015301 (2017)

21P. Cortes, M. P. Kazmierkowski, R. M. Kennel, D. E. Quevedo, and J. Rodriguez, “Predictive control in power electron-ics and drives,” IEEE Trans. Ind. Electron. 55(12), 4312–4324 (2008).

22S. Kouro, P. Cortes, R. Vargas, U. Ammann, and J. Rodriguez, “Model predictive control—A simple and powerfulmethod to control power converters,” IEEE Trans. Ind. Electron. 56(6), 1826–1838 (2009).

23J. Rodriguez, J. Pontt, C. A. Silvam, P. Correa, P. Lezana, P. Cortes, and U. Ammann, “Predictive current control of avoltage source inverter,” IEEE Trans. Ind. Electron. 54(1), 495–503 (2007).

24P. Cortes, G. Ortiz, J. I. Yuz, J. Rodriguez, S. Vazquez, and L. G. Franquelo, “Model predictive control of an inverterwith output LC filter for UPS applications,” IEEE Trans. Ind. Electron. 56(6), 1875–1883 (2009).

25J. Hu, J. Zhu, and D. G. Dorrell, “Model predictive control of inverters for both islanded and grid-connected operations inrenewable power generations,” IET Renewable Power Gener. 8(3), 240–248 (2014).

26S. Vazquez, J. I. Leon, L. G. Franquelo, J. Rodriguez, H. A. Young, A. Marquez, and P. Zanchetta, “Model predictivecontrol - A review of its applications in power electronics,” IEEE Ind. Electron. Mag. 8(1), 16–3 (2014).

015301-17 Chatterjee et al. J. Renewable Sustainable Energy 9, 015301 (2017)