Analysis of harmonics currents in the case of grid connected photovoltaic generator

ABSTRACT


INTRODUCTION
The interest that science has brought to clean electricity of solar origin, has allowed a remarkable development in recent years of photovoltaic technology and each year, a considerable number of articles appear on the subject with all its ramifications.Journal articles help focus new research on actionable leads.However, this technology is still under development, and several new architectures appear each year.Barater et al. [1], which appeared in 2015, the authors worked on 53 articles (40 articles from the same database), the oldest of which appeared in 1981 and the most recent in 2014.In their comparative study, they presented a state of the art of converters dedicated to single-phase PV systems without transformer with measurement of the voltage between the terminals of the PV field and the ground.The waveform of this voltage allows adaptation between power converters and PV panels.
Another comparative study is presented in the article [2] published in 2020, also concerns the singlephase PV system without transformer.Authors carried out the study on 130 papers  and focused on the issue of safety.Common risks are earth fault currents, leakage currents and on compliance with the standards.They presented a detailed comparative study where they discussed in addition to the leakage  ISSN: 2088-8694 Int J Pow Elec & Dri Syst, Vol.14, No. 4, December 2023: 2379-2387 2380 current; the cost, size, and efficiency.Authors represent an important classification in addition to a summarizing of a comparative study of the elements constituting the adaptation stage (inverter + filter) for 44 different topologies.The table provides another comparative study of the most used categories of transformer less single-phase inverters and offers an aid in identifying the respective advantages and limitations of different transformer less inverter topologies as it represents the main characteristics like common mode behavior, reactive power transfer capability, leakage current, efficiency and the number of components.
Alluhaybi et al. [3] worked on 90 articles (1999-2018) and classified the design of grid-connected photovoltaic micro inverters into four categories; according to the galvanic isolation (isolated or nonisolated) and according to the number of stages (one or two).In each of the four categories, the authors have chosen from the literature only the topologies that have been confirmed experimentally in terms of efficiency, power density, reliability, and cost.The criteria for comparison between topologies are implementation, battery integration, modular structure, number of components, and input voltage range.The study gave the superiority to single-stage micro inverters (with and without transformer) due to their simplicity and efficiency.However, single-stage transformer less topology offers low losses and lower cost compared to isolated topology.Besides, with a control scheme ensuring smooth switching operation for power switches, buck-boost remains the optimal solution for PV micro inverter design.
The article [4] is a state of the art of the photovoltaic conversion system.The author compared and analyzed the work of 56 papers (2002-2020).The two comparison criteria are also the galvanic isolation and the number of stages.In the case of a PV chain with transformer, the photovoltaic voltage can increase by placing a high frequency (HF) transformer on the DC side.However, to amplify the output voltage to the voltage values of the distribution network, a low frequency (LF) type transformer must be placed on the output side of the inverter.The major inconvenient of the inverter with transformer are losses, size and weight.While the major advantage is the galvanic isolation which ensures the safety of equipment and persons.
The PV inverter is a necessary element in the electro-energetic system connecting the photovoltaic source to the conventional electrical network.The conversion principle remains the same, but the topology of the chain changes depending on whether the integration takes place in the transmission network or in the distribution network.A photovoltaic power system is a chain made up of several elements and each plays a specific role.The chain must fulfill several sequential tasks, namely: conversion, adaptation and integration into the electrical network.
Increasingly, PV sources considered as dispersed production sources are being connected to the network and more particularly in its distribution part.Then, it requires interfacing them to the electrical network with inverters and in this paper, a single-stage single-phase inverter will connect the PV source to the network and a load.The point of common coupling (PCC) is the node that connects the load to the grid and to the output of the inverter.Then, the inverter must apply across of the load, a tension synchronized with the tension of the network.In this article, a single-phase single-stage inverter is chosen to interface the PV array to the grid.For this, it is necessary to control the power delivered by the inverter using a regulation loop that uses the network voltage as a reference.
Several simulations were made under MATLAB/Simulink to show the effect of the shift angle on the quality of current delivered by the inverter before and after filtering.The price of the filter increases with its size and if it is possible to reduce the harmonics before the filter, it will be possible to reduce the size of the inductances.The goal in this work is to separate the effect of the phase angle from that of the modulation index and the switching frequency in order to determine the harmonic levels targeted by a particular parameter.

DESCRIPTION OF THE PROPOSED SYSTEM 2.1. Power system description
The topology of the photovoltaic chain varies depending on whether the PV generator is connected to the medium or low voltage part of the electrical network.The use of the boost converter becomes essential if the DC source voltage is lower than the network voltage.On the other hand, the presence of the inverter is crucial since it allows converting direct current into alternative current.Since the aim of this study is analysis of currents at the PPC, it is preferable to adjust DC source voltage to an enough value to be equal to the voltage delivered by the grid and in this case, the converter DC/DC should not be used.The output of the DC source must be connected to the input of the inverter by using a DC link.The role of the inverter is to generate alternative voltage from sources providing direct voltages such as fuel cell, batteries or photovoltaic generators.This power can be injected into the electrical grid or supply a load because it can be connected to the load at the same time as the grid.For this, it is essential to synchronize the voltage delivered by the inverter with the grid voltage.Figure 1 shows the standard one stage topology of the power system.PCC relays the load to the grid and the inverter output.

Control description
The control system is presented in Figure 2 as a synoptic diagram.To synchronize PV array with electrical grid, the voltage grid is used as an input to the PLL bloc.The PLL bloc output is used with index modulation ma and shift angle to build the reference sine wave.Uref is compared with carrier wave in PWM bloc to generate pulses.

Inverter
In this paper, Inverter is a Universal bridge (IGBT) controlled by PWM.Therefore, it is interesting to remember that IGBT technology is chosen for [5], [6]: i) Very high switching power which enables the output signal to be as close as possible to the sinusoidal shape; ii) High current which enables it to supply loads such as motors modeled in series RL circuit; and iii) Control in voltage and not in current to avoid switching losses.

Pulse width modulation PWM
The grid fundamental frequency (either 50 Hz or 60 Hz) is used as an input variable to obtain the reference sinusoidal wave.the reference wave is then compared with a carrier triangular wave at the switching frequency to produce pulses at the intersection points.The switching frequency has a considerable effect on the switching cells of the inverter since it affects the harmonic content [7]- [9].Therefore, the switching frequency must be well chosen to reduce the harmonics.IEC and IEEE standards suggest that PV system output should have low current-distortion levels to ensure security of other equipment connected to the utility system as described in [10], [11].Total harmonic current distortion shall be less than 5% at rated inverter output.Both references present table of limits for individual harmonic.Also, even harmonics shall be less than 25% of the lower odd harmonic limits listed.

Phase locked loop PLL
In general, PLL is used as a part of control system and whose output signal is synchronized in phase, in frequency with the fundamental voltage component of the grid.PLL provides synchronization information with protection against harmonics and other disturbances.The word [12] summarizes in a table different single-phase PLL based techniques already published in literatures.

Index modulation
Many indexes are cited in literature but the most important in this case is the modulation index (ma) which defined as the ratio of amplitudes of the reference wave to the triangular wave [13]- [16].
reference wave amplitude,   triangular wave amplitude.

Power decoupling
These power-decoupling techniques are categorized into three groups in terms of the decoupling capacitor locations: 1) PV-side decoupling; 2) DC-link decoupling; and 3) AC-side decoupling.Power decoupling is achieved by means of an electrolytic capacitor but can be substituted with film capacitors because of the lifetime problem.In this work, the capacitor is placed in parallel with the PV modules in the dc link, between the PV array and inverter stage as can be seen in Figure 1.According to [17], [18], the size of the decoupling capacitor is expressed as (2).
is the nominal power of the PV modules,   is the mean voltage across the capacitor,   ̂ is the amplitude of the ripple.

MODELLING AND SIMULATION
To synchronize PV array with electrical grid, the grid voltage is used as an input to the PLL bloc.The output pLL bloc is used with index modulation ma and shift angle to build the reference sine wave.Uref is compared with carrier wave in PWM bloc to generate pulses.The modeling of the LCL filter must take into consideration variables which concern on the one hand the inverter such as the nominal power and the switching frequency and on the other hand the network such as its nominal voltage and its frequency.The base impedance, ZB, and base capacitance, CB, are then defined as [19]- [21]: Since the filter capacitor value is based on the reactive power absorbed at the rated condition and is referred to in a percentage of the base capacitor value   = 5% of   .(5) The filter can contain one or two inductors depending on the chosen topology: L, LC or LCL.In this paper, the LCL filter has been chosen.The inductor connected to the inverter is defined as the inverter side inductor.It concerns on maximum permissible current ripple that is limited to 20% of the rated current.The inductor size can be expressed as: where   represent the dc link voltage [22]- [24].

𝑟 = 𝐿 𝑔𝑟𝑖𝑑
(7) The total inductance is selected according to the maximum voltage drop across the inductor.As the upper limit on the fundamental voltage drop as 10%, [25] the total inductor is expressed: 1 + 2 = .2. ..(  +   ) = 0.1 The inductor connected to the grid can be calculated by subtraction from the equation.The resonance frequency of the LCL-filter can be expressed as ( 11) [26], [27].
Moreover, the resonance frequency must satisfy the inequality: the Table 2 summarizes system specification used in simulation

RESULTS AND ANALYSIS
Simulation has been done under MATLAB/Simulink environment.After running simulation, the output voltage of the inverter represented in Figure 3, is three level (-Vin 0 +Vinv) periodic but not sinusoidal.The peak value is equal to the direct voltage of 380 V.The Figure 4 shows the synchronization between grid voltage Vgrid and inverter voltage Vinv after setting the following parameters as follows: fs=10000 Hz ma=0.85 shift=2, it should be noted that in this simulation, the time required for synchronization is 0.04 s.The Figure 5 represents the synchronization between the different voltages (grid, inverter, and load) and their respective currents.The Figure 6 represents plots of all currents circulating in the power system.For each current, we represent the waveform and the FFT waveforms of currents in Figure 6(a) is grid, Figure 6(b) is inverter before filter, Figure 6(c) is load, and Figure 6(d) is after filter.Simulation has been done for the values already mentioned.THD values meet the requirement of currents and recommendations.THD of output inverter voltage is relatively high and above the limit but is attenuated by the filter.
In Figure 7, we can see the synchronization between the grid voltage waveform and the reference waveform.The PLL uses the grid voltage as the input voltage to slave the frequency of the voltage.This frequency will be used to obtain a reference voltage whose amplitude varies between -1 and +1.This frequency voltage should be injected into the PWM to obtain the inverter control signal.
The phase shift controls the active power and then the current needed to supply the load completed by the current provided by the grid.The current of the load was fixed previously at 10 amperes by fixing active power.In test simulations not presented in paper, the current was provided by grid when disconnecting the DC source and by the DC by disconnecting the grid.It is the sum of both currents when the grid and the DC current are connected together with the load according to Kirchhoff's current law.
In order to show the influence of the phase shift on the composition of the current wave, a tracing of the THD was carried out by modifying the parameter α around the optimal value.The Figure 8 shows the shape of the curves as a function of the change in phase shift.By changing α, the phase shift is changing too.α is the parameter that intervenes in the calculation of the phase shift angle.
= .sin ( + ) = .sin ( + . 180 ⁄ ) The curves in the Figure 9 show the variation of THD as a function of the phase shift for the grid current, the inverter current before and after the filtering.The optimal values of the modulation index and of the switching frequency are necessary to highlight the intervention of the phase shift.Switching frequency has been fixed to10000 Hz and modulation index to 0.85.For α<2.2, even after filter, the THD of the inverter current remains above the recommended limits (>5%).While the current THD in the grid is low.It is the value α=2.2 which makes it possible to attenuate the harmonics before and after the filtering at the lowest of their values.This value allows two major conclusions to be drawn: i) The filter is not solely responsible for the drop-in harmonics; and ii) It is possible to reduce the size of the filter and its price by reducing the harmonics to their minimum possible by regulating the cut-off frequency and the modulation index before filtering.Thus, the filter intervenes to reduce the persistent harmonics until the standards and recommendations are met.

CONCLUSION
The paper has analyzed the behavior of the currents at PCC in a single-phase single stage grid connected PV system when varying the three important parameters: index modulation, phase shift and swift frequency.A control loop containing PLL, Uref sub-system and PWM, synchronized successfully the inverter with the grid.The simulation in MATLAB/Simulink environment has allowed a detailed analysis of THD variation when varying one of the three parameters.The proposed control loop shows that by keeping constant the modulation index and the switching frequency, the variation of α gives one point (α=2.2) where THD is less than 5% for inverter current after filtering (4.79%) and for grid current simultaneously.This point represents the optimal value of phase shift.

Figure 1 .
Figure 1.Standard topology of single-stage single-phase grid connected PV system

Figure 2 .
Figure 2. Synoptic diagram of the control system

Figure 3 .
Figure 3. voltage waveform at the output of inverter compared with grid voltage waveform

Figure 4 .Figure 5 .
Figure 4. Wave form of the grid voltage and inverter voltage after filtering

Table 1 .
[12]e 1 classifies the synchronization techniques into two types: PLL based methods non-PLL based methods.Classification of single-phase grid synchronization techniques[12]

Table 2 .
System specification used in simulation