Benchmarking of the Conductance Increment Method and its improved versions

To increase the performance of a photovoltaic (PV) system, a circuit using MPPT (Maximum Power Point Tracking) technology must be used. There are several algorithms proposed in the literature and they need to be compared to select the best performing MPPT technology for a specific application or to make recommendations for future MPPT research. This article presents a benchmarking the most widely used MPPT algorithms, namely the "INC_C" (Classical Incremental Conductance), the "INC_AM" (Modified Adaptive Incremental Conductance). The comparative study presented in this work will confirm that "INC_AM» is the best MPPT technique to improve the efficiency of a PV system.


INTRODUCTION
The PV energy conversion system must operate near to the maximum power point (MPP) in order to increase solar system efficiency. It is therefore necessary to use MPPT which plays an important role in tracking maximum power points as they maximize the efficiency of the PV system under given conditions and minimize the overall cost of a PV installation [1,2]. Various MPPT techniques have been developed and used to monitor the MPP of PV systems, such as: the P&O technique [3], which is based on iterative algorithms and is easy to implement but with an inevitable oscillation problem. The Incremental Conductance technique [4]. The Fuzzy Logic Control (FLC) search technique [5], which is used very successfully in the implementation of MPP research, among these existing MPPT control methods, the P&O algorithm, is widely used in many PV systems [6]. The P&O method works well when solar irradiation and temperature do not vary rapidly over time [7], but it cannot quickly keep up with the MPP and therefore the output power oscillates around the MPP. The examination of the Incremental Conductance (INC) approach and its modifications is the subject of this work. This document is structured as follows: After the introduction, section 2 presents the mathematical model of the PV cell. Section 3 deals with the MPPT technique used to design a Boost Converter. In section 4 we present the simulation results with their discussion to evaluate the algorithm developed, finally, we conclude our work.

SOLAR CELL MATHEMATICAL MODEL
Photovoltaic models with one or two diodes have been widely used to model the I-V output characteristic of a photovoltaic cell or panel [8].
The single diode model is the simplest one. It is improved by the incorporation of an Rs series resistor [9]. However, despite its simplicity, it has relatively significant errors compared to experimental data when exposed to high temperature variations. Model optimization is achieved by including an additional shunt resistor Rsh [10]. In addition, its accuracy decreases at low irradiance, especially in the open circuit voltage range Voc. The electrical current of the PV panel for the one diodes model is given by: [11,12] "# = "% − '( − )% So, The following relation describes the current supplied by a solar cell in a single diode model : [13,14] / "# + ) "# ( 5% 6 − 18 With: Iph Photo-generated current (A).

Ipv
Solar cell terminal current (A).

I0i
Reverse saturation current of diode in conventional model (A).
The ideality factors

TECHNIQUE MPPT
The characteristics of the generator I (V) depend on the illumination and temperature "add reference". The maximum power point fluctuates as a result of these climatic variations. Due to these fluctuations, we often insert one or more controlled static converters that can follow the maximum power point. These commands are called MPPT and are associated with the chopper controls to ensure the coupling between the PV generator and the receiver by forcing the former to provide its maximum power.
. Figure 2: Synoptic diagram of the PV system studied As illustrated in Figure 2, the proposed framework comprises of a PV panel, a DC-DC converter lift, equipped with its MPPT control block and a battery. The MPPT control block ensures, under certain conditions, the control of the conduction and blocking of the MOSFET by changing the duty cycle α of the PWM signal driving this MOSFET.

Number of PV cells per module
Ncell 22 The specifications of the booster chopper converter used are summarized in Table 2:  Table 3 lists the specs of the battery that was utilized as a charge at the converter's output:

Method "Classic Conductance Increment" (INC_C)
The steady conductance was planned based on a perception of the trademark bend P(V). This calculation was created in 1993 and meant to conquer a portion of the hindrances of the P&O calculation [16]. This method depends on the information on the conductance of the PV module and the results on the working point according to the greatest force point (MPP). Accordingly, the conductance Gc of the PV not really settled in the connection between the current and the yield voltage of the PV module demonstrated underneath.
Let Vpv be the voltage at the PV module's output and Vmpp be the voltage at the PV module's maximum power point [17] [18]. The derivative dP/dV in this example can meet the following conditions: • If dP/dV > 0, the operating point is to the left of the MPP, Vmpp > Vpv.
• If dP/dV < 0, the operating point is to the right of the MPP, Vmpp < Vpv.
• If dP/dV = 0, the operating point is on the MPP, Vmpp = Vpv.  The results of Figure 7 show that the PV model with the algorithm "INC_C" converges to the desired optimal values with oscillations around the MPP (Zoom 2), The performance of the algorithm is rigid and good. The response to a rapid variation (Zoom 1) is done in a fluid way at around 0.075 s, corresponding to the passage of the irradiation from 100 W/m2 to 1000 W/m2, as well as the satisfactory monitoring of the MPP under different lighting conditions.

Method "Increment of Adaptive Conductance Modifiede" (INC_AM)
The processing is separated into two sections in this technique, each of which is critical for detecting the target MPP value. The first section addresses the discrepancy between tracking precision and convergence speed. The second half, on the other hand, provides for the removal of the influence of drift during a quick change in light.
• Part One: Given the contradictions between the accuracy of the tracking and the speed of convergence of the "INC_C", we present here in the first part of our improved adaptive algorithm, namely the "INC_AM" variable-step method. When the operating point is further away from the MPP, the primary principle is to pick a step high enough to speed up the optimization. When it's getting close to the MPP, you'll want to pick a tiny enough step to emphasize precision.
As illustrated in Figure 8, the P(V) curve is separated into three portions (1, 2 and 3). Let k = dP / dV, the slope at a point n of this curve; in zone (1), k is basically positive, and in zone (3) it is negative. In addition, the absolute value of k in zones (1) and (2) is greater than its absolute value in zone (3). The operating point can be determined according to the sign of k. When k > 0, essentially in zone (1), the disturbance can be set larger (d1). When k < 0 (zone 3), we can choose a small perturbation step (d2). When | k | < ε while tending towards 0, the system works in the region (2), corresponding to an operation around the MPP i.e. ε | dV | -| dP | > 0. In this case, all we need to do now is address a little stumbling block (d3). The flowchart of the first portion of the "INC AM" algorithm in Figure 9 illustrates this principle of action.  The PV module's maximum usable power is determined by the ambient temperature and the amount of solar irradiation.  The algorithm of INC_C exploit the slope of the P (V) curve to detect the MPP. If the algorithm finds that the operating point is at the top of the curve P (V), corresponding to a slope is zero, and equation (6) is satisfied, then the duty cycle α of the DC-DC converter is fixed and no oscillation occurs during this step until changes in the slope occur. In real life, the zero slope condition is rarely reached.
Generally, the algorithm INC_C fails to make a good decision when the irradiation is suddenly increased [20], as shown in Figure 11. Indeed, when the irradiation is at 0.3 kW/m², the MPPT algorithm adjusts the duty cycle to ensure that the PV system operates on the load line 2 and that the MPP (point B) is tracked. After some time, solar irradiation may increase to 1 kW/m², but the duty cycle is maintained at charge line 2. Therefore, the point M will be recorded by the load line 2 on curve I(V), corresponding to the power at point C on the curve P(V). Therefore, the algorithm of INC_C calculates the slope between point C and point B, which is then positive. However, the charge line 2 detects power at point C, which is coupled with a negative slope between point C and point A, which is the genuine MPP. As a result, the algorithm INC C increases the output voltage of the PV module without detecting the anomaly, causing the PV module's power to drift away from the real MPP. A < 0.06 (6) When the condition of equation (6) is met, the system operates in MPP. Therefore, the algorithm sets b to 1 and then switches to the improved algorithm.
In the improved adaptive algorithm, the program continues to check the state of the equation (6). If solar radiation and charge remain constant, the duty cycle α will not change.
When solar radiation changes, the algorithm sets the variable b to zero. The program then analyses the fluctuations in the PV module's voltage and output current. If the algorithm detects an increase in current or voltage, the duty cycle will rise as well.
Under the conditions mentioned at the beginning of this work, the result of the simulations of the algorithm "INC_AM" under Matlab / Simulink, are illustrated in Figure 13. The latter is composed of three graphs in a time interval of 0.3 s: The first represents the voltage Vmpp_INC_AM of PV output, the second corresponds to the output current Impp_INC_AM of the PV panel, and the third represents the power Pmpp_INC_AM produced by the PV module.
The results of Figure 13, show that for a rapid variation in the level of solar irradiation, the algorithm "INC_AM" responds better than the algorithm "INC_C", moreover, when the MPP is reached the oscillations in steady state no longer occur.

COMPARISON OF THE PERFORMANCE OF PROCESSED MPPT ALGORITHMS
In order to ensure a sufficient comparative study between the MPPT algorithms treated, we evaluated certain performance parameters, namely; for each of the two algorithms, the convergence time τc and the oscillation deviation εo for an irradiation ranging from 100 to 1000 W/m2 for each of the two algorithms. The calculation results are reported in the following table:

CONCLUSION
In this work dedicated to the study of MPPT methods, we began by exposing the most commonly used method which is "classical incremental conductance" (INC_C) and its improved version: "modified adaptive incremental conductance" (INC_AM). These technologies have easy-toimplement algorithms to control booster-type DC-DC converters.
Generally speaking, the traditional algorithm (INC_C) gives good results, but has big disadvantages. In order to overcome these problems, the improved version of this algorithm has been studied. For the purpose of evaluating the performance of these two algorithms "INC_C" and "INC_AM", we compared their convergence times τc,as well as their oscillation differences εo induced by their use. This allows us to understand and analyze the pros and cons of each of the two methods. It can then be concluded that, compared to the "INC_C" method, the "INC_AM" method is the best with aconvergence time τc lower; 16 msagainst 31 s, with a deviation of oscillation εo very minimized to the value of 0.01 W against 1.18 W.