Variable Step Size P & O MPPT Controller to Improve Static and Dynamic PV System Performances

In this paper, a variable step size P&O algorithm is used in order to improve the performance of a photovoltaic system in both dynamic and static plans. The e ciency of the proposed algorithm has been investigated successfully using the BP SX150S solar module connected to the DC-DC derived by a P&O MPPT algorithm. The comparative study results of both conventional xed step size and the proposed variable step size P&O algorithms prove the e ectiveness of the proposed algorithm compared to the standard xed step size PO MPPT. The proposed algorithm reduces response time between 13.86% and 45.28% and the steady state oscillation between 83.33% and 100% leading to less power loss especially in case of fast changing atmospheric conditions.


Introduction
Photovoltaic systems provide green renewable power by exploiting solar energy.They can be used as an alternative energy source in place of electricity generated from conventional fossil fuels.Photovoltaic, also called solar cells, are electronic devices that convert sunlight directly into electricity.This electrical energy can feeds many systems like: water pumping systems used for irrigation, hydrogen production, electrical power systems, . . .etc [1]- [4].
The I-V characteristics of a PV module will vary with solar insolation and atmospheric temperature.In general, there is a unique point on the I-V or P-V characteristics, called the Maximum Power Point (MPP), at which the entire PV system (array, converter, etc. . . ) operates with maximum eciency and produces its maximum output power [5].
In this work, a variable step size Perturbation and Observation algorithm is proposed to improve the performances in both dynamic and static regimes.The eciency of the proposed algorithm has been studied successfully using Matlab/Simulink environment where the whole system including PV module as well as the DC-DC boost converter derived by the proposed variable step size P&O MPPT algorithm is modeled and investigated.The results of a comparative study between the xed and variable step size P&O algorithms conrms that the proposed algorithm can eectively and simultaneously improve: the accuracy, the rapidity, the ripple and the overshoot in case of fast and changing atmospheric condition compared to the conventional xed step size algorithm.
The rest of this paper is organized as follows: Section 2 describes the PV system modeling.The proposed variable step size P&O MPPT is detailed in Section 3. While, Section 4 show the simulation results and their discussion.Finally, Section 5 concludes the paper by dressing the main contributions and giving the perspectives of some future works.

PV SYSTEM MODELING
A PV cell equivalent circuit is shown in Fig. 1.The mathematical model can be simply expressed as [19]: where I ph is the photo-current; I Rp is the shunt current; I d is the diode current.
The diode saturation current is given by: with and From equations ( 1) to ( 7), I pv is dened by: where The BP SX150S module parameters used to draw the PV characteristics are listed in Table 1.

PROPOSED VARIABLE STEP SIZE P&O MPPT
From mathematical model and Figures 2 to 5, it is clear that solar PV presents nonlinear characteristics varying with solar irradiation and temperature.Consequently, it is mandatory to integrate maximum power stage to adapt and guarantee the maximum power transfer to the load    and few control parameters required [15,16].
The P&O owchart is shown in Fig. 6.
The aim is to get the maximum power point by adjusting perturbation in the duty cycle by continually measuring voltage/current from PV panel, the power output is measured then: if the value of power output P k > P k−1 then perturbation is uninterrupted in the same sense.If the new value of power output P k < P k−1 then perturbation is applied in the opposite sense.This operation operates while maximum power point is not reached.In general, the conventional P&O algorithm with xed step size has two major drawbacks [17,18] represented by the relationship between the oscillation and response speed.With a small xed step size, we get low oscillation at the expense of response speed and in case of large step size we have a good speed with over strong oscillations.In order to overcome the drawbacks of the xed step size algorithm, a variable step size P&O algorithm operates with a variable step size, where the duty cycle is adjusted directly with large step size when far from the MPPT point and with small step size around the MPPT point.The novel step size is given by: where SF is the scaling factor equal to |dP/dV |; dP and dV are the changes in power and voltage.

RESULTS AND DISCUSSIONS
To verify the performance of the proposed variable step size P&O MPPT algorithm, the whole system including PV module as well as the DC-DC boost converter drived by the proposed variable step size P&O MPPT algorithm is modeled and investigated using Matlab/Simulink environment.
Figure 7 shows the output power for both conventional xed step size and proposed variable step size P&O method when the irradiance changes.From Fig. 7, we can see that both algorithms track the maximum power point in case of variable irradiation with best performances for the proposed algorithm compared to the xed step size algorithm in term of rapidity and overshoot.
A) Dynamic Performances.The MPP point tracking using both PO MPPTs in case of changing irradiation level from 600 W/m 2 to 750 W/m 2 and from 750 W/m 2 to 1000 W/m 2 is given in Fig. 14.While the zoomin around the MPP point is given in Figs. 15 and  16, respectively.In this case we evaluate the course of the MPP point (Osc-MPP) for both algorithms the classical xed step size and the proposed variable step size one.
From Figs.  15 and 16, we can see clearly that we have less oscillation around the MPP point with the proposed variable step size algorithm compared to

Figures 2 and 3
show the typical output characteristics (I-V) and (P-V) of PV cell, which are simulated under variable solar irradiation (ζ = 600, 700, 800, 900 and 1000 W/m 2 ) and constant temperature (T = 25 o C); while Figures4 and 5show the typical output characteristics (I-V) and (P-V) of PV cell under variable temperature (T = 25, 50 and 75 o C) with constant irradiance (ζ = 1000 W/m 2 ).

Figures 11 to 13
Figures 11 to 13 show the zoom-in of the points 600-2, 750-2 and 1000-2 giving the steady state response of both xed and variable step size PO MPPTs corresponding to irradiation level 600 W/m 2 , 750 W/m 2 and 1000 W/m 2 , respectively.In this case we compare the oscillation around the MPP point for the proposed variable step size MPPT (Osc-VSS) to the oscillation around the MPP of the classical xed step size MPPT (Osc-FSS).From Figures 11 to 13, it is clear that the proposed variable step size PO MPPT performs better than the standard xed step size PO MPPT in case of changing

Fig. 15 :
Fig. 15: P-V characteristics: Zoom in Point MPP (oscillation in the case of the variable step size MPPT).

Fig. 16 :
Fig. 16: P-V characteristics: Zoom in Point MPP (oscillation in the case of the xed step size MPPT).

Table 1 .
On diode PV cell model.Parameter Value Maximum Power (P max ) 150 W Voltage at P max (V mpp ) 34.5 V Current at P max (I mpp ) 4.35 A Warranted minimum P max 140 W Short circuit current (I SC

Table 3 .
Steady state oscillation reduction.Algeria.He received BSc, Master and PhD Degrees in Electronics from Ferhat Abbas University (UFAS), Setif, Algeria, in 1995, 1998 and 2011, respectively.In 2012, he received the HDR degree in electrical engineering from Mohamed Khider University, Biskra, Algeria.He worked as Project Manager during more than 10 years in France with French and American Societies.He is the creator of the standard Arabic language on all mobile and intelligent systems sold by Alcatel Lucent all over the world including Arab countries from Atlantic ocean to Arabic gulf.He taught at University Pierre Mendes France and Joseph Fourier 1999-2000, Grenoble, France, at Ferhat Abbas University 1996-1999, Setif, Algeria.In 2009, he joined Mohamed Boudiaf University, Msila, Algeria.Currently, he works as Professor at Ferhat Abbas University.His research interests mainly concerned intelligent control, renewable energy, heuristic and evolutionary optimization, embedded systems and signal processing.He is member of several research projects at University of Msila and CCNS Laboratory at UFAS University.