Analysis of Dynamic Characteristic for Solar Arrays in Series and Global Maximum Power Point Tracking Based on Optimal Initial Value Incremental Conductance Strategy under Partially Shaded Conditions
Partial shading (PS) is an unavoidable condition which significantly reduces the efficiency and stability of a photovoltaic (PV) system. With PS, the system usually exhibits multiple-peak output power characteristics, but single-peak is also possible under special PS conditions. In fact it is shown that the partial shading condition (PSC) is the necessary but not sufficient condition for multiple-peak. Based on circuit analysis, this paper shows that the number of peak points can be determined
... can be determined by short-circuit currents and maximum-power point currents of all the arrays in series. Then the principle is established based on which the number of the peak points is to be determined. Furthermore, based on the dynamic characteristic of solar array, this paper establishes the rule for determination of the relative position of the global maximum power point (GMPP). In order to track the GMPP within an appropriate period, a reliable technique and the corresponding computer algorithm are developed for GMPP tracking (GMPPT) control. It exploits a definable nonlinear relation has been found between variable environmental parameters and the output current of solar arrays at every maximum power point, obtained based on the dynamic performance corresponding to PSC. Finally, the proposed method is validated with MATLAB ® /Simulink ® simulations and actual experiments. It is shown that the GMPPT of a PV generation system is indeed realized efficiently in a realistic environment with partial shading conditions. Energies 2017, 10, 120 2 of 23 PV modules connected in series to achieve the required output voltage and power. When some of the modules receive lower solar irradiance due to occlusion of the sun by objects such as clouds, trees and buildings, a condition known as partially shaded condition (PSC), the output of the PV system is affected  . Usually when PSC occurs the system has multiple-peak output power characteristics. Only one of these peak powers has the highest power, which is called global maximum power point (GMPP), and other peak powers are the local maximum power point (LMPP). According to statistic studies the power loss can vary from 10% to 70% due to PS [3, 4] . Moreover, under some special weak PS conditions, a PV system may have just one peak point. Therefore, the PSC is a necessary but not sufficient condition for multiple-peak. Finding the sufficient and necessary condition of multiple-peak is of course beneficial for analyzing the dynamic characteristic of solar arrays in series. In this paper, the circuit analysis method is used to determine the working principle of the photovoltaic array in series under PSC, and to explore the reasons for the phenomenon of multiple peak output power characteristics. Meanwhile, the sufficient and necessary condition of multiple-peak and the calculation method of the number of multiple peaks are presented in this paper. To achieve the MPP, the maximum power point tracker (MPPT) is implemented as a controller to adjust the duty cycle of the power electronic part, which is an interface between the PV system and load [5, 6] . Many MPPT methods have been developed and implemented, including the perturbation and observation (P&O) algorithm [7-12], which is known as the hill climbing (HC) method, the incremental conductance (INC) algorithms [11,      , the neural network (NN) method  , and the fuzzy logic method [19, 20] . These methods execute MPPT based on the fact that the slope of the P-V characteristic is equal to zero at MPP. Most of this type of control methods, like INC and P&O, could produce problems including a large delay, the inaccuracy of the detection circuits and sensors, and the power oscillation under low irradiation conditions [21, 22] . But, these methods are still used extensively because of theirs high tracking accuracy at the steady state, flexibility to adapt to rapidly changing atmospheric conditions, and simplicity in application. Meanwhile, these drawbacks can be reduced by controlling the step size that is added or subtracted to the duty cycle. It is worth noting that the aforementioned traditional MPPTs are not able to identify the GMPPT form the LMPPs when the PV characteristic curve consists of more than one peak  . Many algorithms were proposed to find the GMPP under shading condition with the aim to avoid the local maxima of the power while tracking the global maxima [24-27], which including the particle swarm optimization (PSO) methods , differential evolutionary and particle swarm optimization DEPSO) methods , artificial intelligence techniques , neural network methods , scanning methods , equilibration algorithm  . These methods execute GMPPT by two ways: scanning method-swings the converter's duty cycle from zero to one to determine the maximum power delivering capacity of the panel at a given operating condition and controls the power conditioning unit to extract the same from the PV panel; search algorithm-searching the global extreme of a function which describes the PV power and voltage or power and current relationship in an interval. The scanning program can find the GMPP at any condition, but it has a significant power loss because the program will frequently restart when the environmental condition changes. The search algorithms have the same issue during the computation of the open-circuit voltage and the short-circuit current  . From the perspective of maximizing the energy production of the PV array itself during its lifetime, the objective of the maximization of the energy production of a PV array during its lifetime is not necessarily in complete agreement with the objective of the maximization of its power production in any operating condition. It may be preferable to give up a part of the available energy today if it is possible to gain greater energy tomorrow. Based on the thought, some new methods have been proposed    . The problem of local minimum is caused by the fact that the existing MPPT methods tend to converge to the first peak closest to the algorithms' operation initial value (OIV). In order to achieve the GMPP, the OIV of the algorithms should be placed within the GMPP zone or at least nearby. But this requires the knowledge of the GMPP zone or an algorithm that could determine I pmax in PS conditions.