Design and digital implementation of power control strategy for grid connected photovoltaic inverter

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 10, No. 3, Sep 2019, pp. 1564~1574
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v10.i3.pp1564-1574  1564
Journal homepage: http://iaescore.com/journals/index.php/IJPEDS
Design and digital implementation of power control strategy for
grid connected photovoltaic inverter
Linda Hassaine, Mohamed Rida Bengourina
Centre de Développement des Energies Renouvelables, CDER, BP62 Route de l’observatoire 16340 Bouzaréah, Algeria
Article Info ABSTRACT
Article history:
Received Oct 29, 2018
Revised Mar 6, 2019
Accepted Apr 13, 2019
This paper presents the optimization design and a detailed implementation in
FPGA (Field-Programmable Gate Array) of a power control strategy. This
strategy is based on the phase shift angle of the inverter output voltage with
respect to the grid voltage and DSPWM (Digital Sinusoidal Pulse Width
Modulation) patterns “Phase shift angle-DSPWM” for an inverter for
photovoltaic system connected to the grid. The proposed control can
synchronize a sinusoidal inverter output current with a grid voltage and
control the power injected into the grid. Detailed development of a digital
controller with lower hardware and computation requirement is proposed.
Description on the digital implementation of the A/D converter, the PI
compensator, the phase shift and the DPWM, is provided. This digital control
exhibit simplicity, reduction of the memory requirements and power
calculation for the control. The functional structure of this system with
digital control has been validated with simulations and experimental results.
Keywords:
Digital control
DSPWM Patterns
FPGA
Grid connected
Inverter
Copyright © 2019 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Linda Hassaine,
Centre de Développement des Energies Renouvelables, CDER
BP62 Route de l’observatoire 16340 Bouzaréah, Algiers, Algeria.
Email: l.hassaine@cder.dz
1. INTRODUCTION
The overall efficiency of grid-connected photovoltaic power generation systems depends on the
efficiency of the DC-into-AC conversion of the inverter. Important improvements in the design and
implementation of this power converter device can be carried out [1–6]. Control of active and reactive power
injected into the grid; control of dc-link voltage; guarantee high quality of the injected power; reduction of
the harmonic distortion, elimination of the DC component injected into the grid; grid synchronization and
digital implementation of the control [7, 8]. Pulse width modulation (PWM) technique is used for controlling
the voltage source inverters, which injects currents into the grid. Two methods of PWM techniques can be
adopted: The PWM technique consist on the comparison of a triangular carrier signal “high frequency” with
a sinusoidal reference waveform “low frequency”. The intersection point determines the switching
waveform. The second method, the PWM technique based on generated switching patterns. The PWM
pattern reduce the low order of harmonic components [9], [10]. In this case, the switching patterns are
calculated a priori for certain operating conditions and are then stored in memory (look-up table) for use in
real time [11–13]. Digital implementation offers advantages over their analogue counterparts [14–17]:
immunity to the noise and insensitiveness in the changes of voltage and temperature [13]. FPGA's
implementation give suppleness in changing the designed circuit, easy and fast circuit modification without
modifying the hardware and rapid prototyping [12].
In this work, the objective is to implement an inverter with a simple power control strategy. That
implies to reduce both hardware and software required resources (reducing memory and computing needs of
the control system) using FPGA design platform. The proposed control strategy implementation allows to
design an inverter with low cost and high reliability, while many other implementations are based on

Int J Pow Elec & Dri Syst ISSN: 2088-8694 
Design and digital implementation of power control strategy for grid connected … (Linda Hassaine)
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complex mathematical algorithms that require many resources of both software and hardware. FPGA
technology offers a flexible programmable environment and a higher level of versatility. The code is written
as blocks to be processed in parallel, which makes the FPGA implementation more attractive.
In PV systems connected to the grid, system control can be divided into two important parts. The
MPP control, which extract the maximum power from the PV generator and the inverter control, which
ensure the control of active and reactive power generated to the grid, the control of DC-link voltage, high
quality of the injected power and grid synchronization [2, 3, 7, 9, 17–19]. The proposed power control
method [20–22] is based on the phase shift angle of the inverter output voltage with respect to the grid
voltage and DSPWM patterns “Phase shift angle-DSPWM”. High power factor can be achieved for a large
range of output current. The main advantages are simplicity, few resources, less memory, less circuitry and
high accuracy.
This control strategy allows the control of power injected into the grid. Using DPWM patterns for
different modulation index ma and the phase shift angle of the inverter output voltage as control parameter.
The output current amplitude and the power factor can be controlled, changing the power factor; the injected
inductive or capacitive reactive power can be dynamically changed and controlled, for achieving an inverter
with advanced accuracy and reliability. In [20–22], the strategy has been developed with methodical
description and mathematical analysis. The theoretical predictions has been validate with simulation and first
experiment results.
In this paper a detailed implementation in FPGA of this power control strategy, “Phase shift angle-
DPWM” for PV inverters based on the look up table, is presented. Description on the digital implementation
of the main control blocks, which are the A/D converter, the PI controller, the phase shift and the DPWM, is
provided. The proposed control is simple and adapted to FPGA platform; it is attractive for low power grid
connected applications and allows controlling the active and reactive power injected into the grid. Moreover,
robustness of the proposed control allows designing a low cost and simple inverter with a reduced amount of
components, based on a full bridge topology that can be implemented with minimum computational
resources.
2. POWER CONTROL STRATEGY
In photovoltaic power system, the control of power factor is achieved by adjusting amplitude and
phase angle between inverter voltage and grid voltage as is shown in the phase diagram of the equivalent
electrical circuit of the inverter connected to the grid Figure 1.
Figure 1. Phase diagram of the equivalent electrical circuit of inverter connected to the grid inverter
The power control is obtained by means of the phase shift angle (δ) of the inverter output voltage,
with respect to the grid voltage and the use of SPWM patterns. The power factor is determined by angle (φ)
between the grid voltage and the fundamental current component of inverter output current.
Controlling the phase shift of the inverter output voltage, the output current amplitude and the power
factor can be controlled, and therefore the magnitude of the active and reactive power injected into the grid
[20], [22].
The analysis is established using the inductive filter between the inverter and the grid [24].
Considering the fundamental harmonic (pure sinusoidal wave), as a first approach, the total harmonics (THD)

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Int J Pow Elec & Dri Syst, Vol. 10, No. 3, Sep 2019 : 1564 – 1574
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of the current injected into the grid is assumed equal zero (THD≈0). Therefore, the power factor, PF, is
determined, only, by the displacement factor (cosφ), as will be shown in (1) [20–22]
cos sin
a dc
out
m V
PF
L I
 


  

(1)
To valid the performance of the proposed power control strategy it is necessary, to guarantee a total
harmonic distortion not higher than specified 5% as suggests the International Standard IEEE Std 929-2000
[2, 5, 18]. This condition can be achieved calculating and optimizing of using different digital SPWM pattern
and selecting an appropriate coupling filter [23] and frequency modulation index (mf); and the displacement
factor (cosφ) has to be within the pre-calculated limits, to guarantee the specified output current. This
magnitude can be controlled selecting an adequate amplitude modulation index, ma, and a phase shift,, of
the inverter output voltage. In Figure 2, which shows PF vs , for two different values of ma and of the
inverter output voltage, Vinv, (Vinv = ma.Vdc), it can be seen, that with two values of ma we can reach the PF
 1 In a wider range of .
Figure 2. Power factor (PF) according to the phase shift 
The choice of inductance grid connection influences the harmonic content of the current injected
into the grid and the maximum active and reactive power that the inverter can deliver to the grid. High
inductances lead to reduced harmonic distortion. However increasing the inductance in the filtrate shows a
number of drawbacks: cost reduction and transfer of power inverter.
To analyze the behavior of this control strategy for single-phase inverter connected to the grid via an
L or LCL filter. It has been using the expression of power factor mentioned in (1) and to measure the
distortion of the output current, the total harmonic distortion, THD is often used. Total Harmonic Distortion
is a measure of the proportionality between the fundamental and the sum of all other frequencies in the
current waveform. As show in (2) defines the THD used here:
2 2
1
1
out out
i
out
I I
THD
I

 (2)
Where Iout is the total current; (RMS) is the Root means square and Iout1 is the fundamental current
(RMS). The relationship between the switching frequency fc and the inductance value of output filter is
presented, assuming a power factor PF= 0.996.
In Figure.3, the simulation results of the inverter connected to the grid via an L filter and an LCL
filter. Assuming a PF = 0.996, it can be conclude that for lower switching frequencies (modulation indexes
for low frequencies) less than 5kHz, the inductance value of the L filter is higher than the value of the
inductance (L1 + L2) of the LCL filter.

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Figure 3. Inductance of L filter and LCL filter as function of switching frequency fc, for PF = 0,996.
3. PROPOSED CONTROL STRUCTURE
The proposed control system, for a photovoltaic system connected to the grid is shown in Figure 4.
The photovoltaic generator (PVG), DC/DC for a maximum power point tracking (MPPT) and a PWM
inverter (DC/AC).
Figure 4. Control structure for a single phase inverter [20]
The DC/DC converter is employed to boost the PV-array voltage to an appropriate level based on
the magnitude of grid voltage, while the controller of the DC–DC converter is designed to operate as a
maximum power point tracker (MPPT). The perturb-and-observe method is adopted owing to its simple
structure and it requires fewer measured parameters [24, 25]. This strategy is implemented to operate under
rapidly changing solar radiation, using only one variable. The constant voltage method is accomplished by
keeping the voltage in the PV terminals constant and close to the MPP.
The control loop for the PWM inverter is assured by the output current control, the DC bus control
and synchronizing to the grid, to inject power into the grid at all time. The output voltage of the PWM
inverter is already set by the utility PV modules. Therefore, the inverter is controlled to ensure only power
injection into the grid. In Figure 5, are represented an internal and an external control loops of a controller.
The internal one in order to control the inverter output current and the external one to control the DC bus Vdc.
The reference of the output current (Iref) depends on the DC bus voltage (Vdc) and its reference (Vref). A low
pass Filter is incorporate in order to ensure that high frequency switching noise present in the measured
inverter output current signal does not pass through to the PI controller.
The control structure is associated with proportional–integral (PI) controllers since they have a
satisfactory behavior when regulating dc variables. The gain and time constants has been calculated for the
two PI controllers. The Gain of the current PI controller is equal to 0.9819, where the time constant is about
0.001717. In addition, the gain of the voltage PI controller is 2.438, and the time constant is about 0.02758. A
look up table to store the different patterns and the zero crossing detector (ZCD) for synchronizing the
DPWM with the grid voltage.
Vref
IMPPT
Digital control
DPWM
ZCD (Vgrid)
PI
Look_up
Table (δ)
PI
Vgrid
L
Iout
Iref
Iout
MPPT
PVG DC/AC
Vdc
Vinv
C
Vref
IMPPT
Digital control
DPWM
DPWM
ZCD (Vgrid)
PI
Look_up
Table (δ)
Look_up
Table (δ)
PI
Vgrid
L
Iout
Iref
Iout
MPPT
PVG DC/AC
Vdc
Vinv
C

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4. PROPOSED CONTROL IMPLEMENTATION
The block diagram of the control is detailed in Figure 5. To each amplitude modulation index ma
corresponds a switching pattern SPWM characterized by switching angles (α1, α2, α3, α n, αn+1) defined by
the number of intersections, Only the change angles are stored, High accuracy resolution can be achieved and
when using symmetric patterns the look up table can be reduced. Each pattern is accompanied by attributes
such as a maximum and a minimum phase angle, a minimum and a maximum current stored in the lookup
table (ROM). Once the data are stored, the DPWM converts the data code patterns and its attributes in a
pulsed signal that will be generate the switching signals for the inverter transistors.
Figure 5. Scheme of the proposed control implementation
The control algorithm implemented in FPGA is shown in Figure 6. The reference current is update
in each period of the control system and compared with the output current of the inverter. Depending on the
sign error, the controller increases or decreases the phase angle δ between Vinv and Vgrid to compensate the
error. Once the output current is equal to the reference current, the control keeps the current phase angle. The
design method of inverter proposed in this work is attractive to medium and low power PV system, which
can control active and reactive power for relative low cost.
Figure 6. Control algorithm

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In this control scheme, the controller is implemented by specific hardware in FPGA. These devices
are particularly suitable for the direct generation of trigger signals for the switches, so the DPWM block is
actually embedded within the controller; it is one of the advantages of the specific hardware features.
However, the specific hardware features two distinctive advantages: greater accuracy and flexibility in block
DPWM, it is reached and it is possible to generate any number of trigger signals, which is impossible in a
DSP because they have one or as many two DPWM block. Normally, all signals involved in the control loop
are continuous. However, when using a digital controller some of the continuous functions are replaced by
discrete sequences, thus two distinct domains appear the continued dominance (Analog) connector on the
process side and the (digital) discrete domain on the side of the regulator. To connect both domains some
kind of interface is needed. Usually these interfaces are analog / digital converters (DAC) and digital / analog
converters (DAC).
The following describes and requirements for each of the digital blocks that are part of the control
loop to ensure certain design specifications are discussed: filter, PI controller, modulator DPWM, look up
table, zero crossing detector ZCD. It is clear that each of the blocks forming the control loop, directly affect
the system response.
5. DIGITAL CONTROLLER
The proportional integral controllers PIs are a good compromise between the simplicity in digital
implementation and the obtained performances. The PI compensator designed in this study guarantee the
stability of the output-regulated variable, the phase shift. The hardware realization of the compensator
transfer function in the FPGA platform is achieved by using the corresponding difference equation:
[ 1] [ ] [ ]
p i i
D n k e n k D n
   (3)
Where: kp and ki are the coefficients that determine the proportional, derivative and integral gain,
respectively. D[n] is the value of the duty cycle at discrete time n; e[n] is the digitized value of the error;
Di[n], is the state of the integrator; Once the digital code of the error, e[n] is obtained, the value of the phase
shift angle [n] is generated following the scheme shown in Figure 8.
The coefficients of each gains (Kp and Ki), may be rounded to powers of 2 in practice. This makes it
implementation easy using binary shifts. This control law can be implemented using difference equations,
look-up tables or calculated directly using microprocessors with high performance. In this paper, the
proposed phase shift control is based on that for a determined voltage of the DC bus and current modulation
index, ma, it can inject current into the grid by varying the phase angle between the inverter output voltage
and the grid voltage.
The control parameter in this case, is the angle phase δ generated between output voltage of the
inverter and the grid voltage. The updating of the current value of the phase shift according to the law of the
implemented control is realized. It is clear that the method used is to average the error between the reference
current and the actual measured value in several cycles of grid voltage, so that regulatory requirements will
ensure stability of the system [19], [36]. Direct representation of differentials equation and operating modes
of Linear Regulator for this case are shown respectively in Figure 7(a) and Figure 7(b).
(a) (b)
Figure.7. (a). Direct representation of differentials equation and (b). Operating modes Linear Regulator
The A/ D converter needed to implement the controller must have better performance (resolution)
with greater number of bits (n + 1). This is due a greater number of levels of quantification are needed. The

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voltages that define the tolerance band limit these levels. Once the error signal e [n] is obtained, the value of
phase shift δ [n] is generated according to Figure 7.
    0 1 2
1 [ ] [ 1] [ 2]
n n b e n b e n b e n
 
        (4)
To avoid excessive FPGA resource consumption, fixed-point format is used in the rounding of the
difference equation coefficients (b0, b1 and b2) when implementing the compensator transfer function in
hardware. Moreover, in order to improve the transient response of the converter, the time delay of the
analog/digital (A/D) converter should be minimized. Therefore, a high-speed A/D converter is needed.
6. DIGITAL SPWM
In this work, the PWM generator is based on only one counter witch guarantee the synchronism of
all signals, the address signal, syncro-signal and the control signal. In Figure 8, is shown the simulation
results of DPWM signals implemented in ModelSim. (Vg1, Vg2, Vg3, and Vg4) which represent the PWM
signal for each IGT of the single-phase inverter.
Figure 8. DPWM signals
7. DIGITAL PHASE SHIFT IMPLEMENTATION
Figure 7 (4 section), shows the control algorithm of the inverter output current based on the phase
shift of the inverter output voltage. The phase shift is designed to provide flexibility in order to produce
either lagging, leading or in phase, in order to adjust the power factor.
Initially the phase counter is loaded to the shift phase angle value equal zero (δ = 0). The control
have to maintain the adequate shift phase angle which accomplish that the inverter output current Iout equal to
the reference Iref. The sign of the phase angle depends on the power factor character (inductive or capacitive).
From the resolution with which the magnitude of the output current Iout is represented, the resolution (number
of bits) of the phase shift, IADC resolution of the analog digital A / D converter, expressed in current, will
depend on maximum output current Imax and increment current Iq:
The resolution of the converter A/D depend on the magnitude of the current to steady
q
I
Imax
2
ADC log
N 
 (9)
From design topology, the selected approach has been the regulation of the output current of the
inverter (Iout) as a function of the δ offset [2]-[4].
2 2 2 2 2
1
cos
2
inv red s
inv red
V V L I
V V

   
   
  
 
 
(10)

1571
From (9), each value of the angles  can be calculated for each output current value of the inverter
Iout corresponding to the current of the maximum power point on the side of the photovoltaic system. Once
the phase shift angle  has been calculated, the phase shift angle φ between the inverter output current and
the grid voltage (1), is determined, which allows to determine and to control the active power and reactive
power injected into the grid by the inverter.
Since the output current Iout is a function of the output voltage of the inverter Vinv and the phase shift
, then Vinv can be expressed as a function of the duty cycle (d) (10).
dc
V
d
inv
V 
 (11)
The principle operation of this control strategy, based on the PWM control and phase shift, consists
of sensing the current and calculating the phase shift. The output current can be represented by a single PWM
switching pattern (d = constant) as a function of a single state variable: phase shift angle δ between the output
voltage of the inverter Vinv and the voltage of the grid Vgrid.
)
(
f
out
I  (12)
This is a very important function since it greatly simplifies the hardware complexity by transferring
the previous calculations to a PC of the SPWM switching pattern. In a "look up table" we store each phase
shift angle values bye their corresponding current magnitude Iout. Using as a design platform an FPGA, the
phase shift angle can be generated according to the clock and the grid frequency (ts corresponding to fs).


 N
q
2
max
 (13)
Taking the maximum number of pulses corresponding to the maximum phase shift angle for an Iout
max, the counter of the phase shift angle can be sized.
q
N



max
2
log
 
q
N


 max
2  (14)
The design of the look up table will be determined by the maximum angle of phase shift max and by
the resolution of the output current Iout. Figure.9, shows the inverter output current Iout as a function of the
phase angle δ. This figure represents the output current Iout1 for an inverter output voltage Vinv1 = 342 V
(ma1 = 0.910) and the output current Iout2 for Vinv2 = 370 V (ma2 = 0.986), ensuring a power factor PF> 0. 99.
Only two patterns are necessary to cover range from 3.5 A to 33.4 A, while PF remains always higher than
0.99. Therefore, the number of DSPWM patterns is determinate by the ma, and the minimum affordable PF
(with respect to the quality of injected current).
Figure 9. Inverter output current, Iout vs angle phase δ

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In Figure 9, it is possible to observe how the current Iout changes as a function of the phase shift .
As a result, the output current Iout. Discretized in 
N
2 intervals as a function of the phase shift  represented
by a finite number NCD bits for each values of the current of the system.
The condition of the limited duty cycle to be happened:
q
N



max
2
log
 (15)
Then:
N = NADC +1 (16)
qADC
q I
I 
 (17)
It means that the resolution expressed in current must be greater than that of the A / D converter.
The FPGA used in this work is Xilinx SPARTAN-3 XC3S200 FPGA family board processor. To
implement the proposed control strategy, XC3S200 processor is used as a PWM generator to build the
appropriate gating signals to the inverter switches. Figure 10, shows the simulation results of the control
Strategy “Phase shift angle-DPWM”; the DPWM signals, the angle phase and the DZC.
.
Figure 10. Proposed high-resolution control strategy based on FPGA resources
The proposed Digital Pulse Width Modulator (DPWM) takes advantage of the capability of FPGA
to shift the phase of the clock in small increments. A Spartan-3E device from Xilinx has been used in the
experimental results. The solution has been implemented by means of a counter based DPWM architecture
and a specific block available in the FPGA [37]. The time period of the system clock is sliced by means of
the proper phase shifting of the clock signal. This solution provides a lower equivalent FPGA clock period.
8. EXPERIMENTAL RESULTS
Figure 11 shows a prototype of single-phase inverter with the digital control “Phase shift angle-
DSPWM” implemented in a FPGA platform (Spartan-3 of Xilinx) realized and tested
Vgrid =230 V, and coupling inductance L=20 mH.
Figure 11. Single-phase inverter prototype

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Figure 12(a) shows the PWM Pattern, the inverter output current Iout and inverter output voltage
Vinv. Figure 12(b) shows the Inverter output current and grid voltage and PWM Patterns.
(a) (b)
Figure 12. (a). PWM Pattern, inverter output current and inverter output voltage, (b). Inverter output current
and grid voltage.
The experimental results show the viability of the SPWM method proposed and validate the
theorical predictions. The current total harmonic distortion (THD) is 3.5%, which is below the suggested
value by Standard IEEE Std 929-2000.
9. CONCLUSION
The paper has focused on the detailed implementation of the power control strategy of PV inverter
connected to the grid. The proposed strategy based on a “Phase shift angle–DSPWM” pattern is able to
control both the active and reactive power and reduce both hardware and software required resources using
FPGA design platform. Digital implementation of the main control blocks, which are the A/D converter, the
compensator PI, the phase shift and the DPWM, has been provided. However, the proposed control algorithm
provide flexibility to adjust the power factor and regulate the reactive power. This digital power control
strategy has been implemented in FPGA platform and validated with experimental results. The experimental
results show the viability of the SPWM method proposed, the simplicity of the digital implementation,
reduction of the memory requirements and power calculation for the proposed control.
This technique is simple and adapted to FPGA platform, it is attractive for low power grid
connected applications and allows to control the active and reactive power injected into the grid. Moreover,
robustness of the proposed control allows designing a low cost and simple inverter with a reduced amount of
components, based on a full bridge topology that can be implemented with minimum computational
resources.
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