W/m2) is the lower value than the current generated by the modules 11 (1000 W/m2), 21 (1000 W/m2) as shown in Figure 2.10(a). So the lowest current generated by the module (which receive low solar irradiation) is flowing in the string because of a series connection of the PV modules in a string. So the current flowing in the first and second string is the current generated by the modules receive low solar irradiation, i.e., 500 W/m2 and similarly, the current flowing in the string third, fourth and fifth is the current generated by the modules receive low solar irradiation, i.e. 300 W/m2. Thus the current generated by a PV array is the sum of the current of each strings. Neglecting the small variations in voltage of each module under PSC, the voltage of each string is consider to be V. Therefore, the voltage of an array is same as the string voltage.
The P-V curve of a PV array for the two different shading conditions (case-I and case-II) is plotted by using MATLAB simulation as shown in Figure 2.10(c). The Pmax,(est) of the array is denoted by small square in the P-V curve. From Figure 2.10(c), it is observed that the Pmax,(est) is more or less same asPmax,(act) and a minor deviation between the two powers is presented in Table 2.10.
Table 2.10: MPP of a PV array under two different shading conditions Shading Vmp Imp Pmax,(est) Pmax,(act) (%) Error
conditions (V) (A) (W) (W)
case-I 149.62 15.75 2357.0 2410.0 2.19 case-II 150.94 33.25 5019.0 4977.0 -0.84
2.7 Summary of the chapter
The Pmax,(est) and Pmax,(act) of a PV array of monthly average daily and hourly basis are presented in power versus sunshine time in hours characteristics. It is observed that the deviation of thePmax,(est) of a PV array and thePmax,(act)on an hourly basis is minimal.
3. The MPP results estimated by using the LM algorithm of a 15 W PV module under different environmental conditions are validated with the actual and experimental results. It is observed that the deviation of estimated MPP w.r.t. actual and measured MPP are minimal.
4. The MPPT of a PV array under PSC is estimated numerically by using the proposed algorithm and the estimated MPP results closely match with the actual MPP of a PV array.
Also a comparison of LM method with three different existing methods such as PO based on PI, GA and GS is presented. From the simulation results, it is observed that the accuracy of the proposed method is high and the time taken to achieve the MPP of a PV array is less as compared with the other methods. Therefore, the proposed method is robust, accurate and computationally efficient. Thus, this proposed numerical method will help the PV plant promoters to estimate the MPP of a PV array under uniform and nonuniform (partial shading) conditions.
In this chapter, the MPP of a PV array is estimated numerically by solving (2.10) and (2.31) using LM method. In the next chapter, instead of solving above two equations, a simple explicit expression of current (i.e., current is a function of voltage only) derived from an implicit current expression, is solved using bisection method (BM) for MPP tracking of an SDM PV module accurately and efficiently.
Note: This work, Numerical approach to estimate the maximum power point of a photovoltaic array has been published in IET Generation, Transmission & Distribution.
TH-1895_11610232
3
MPPT of a PV Module from Current-Voltage Explicit Expression
Contents
3.1 Introduction . . . . 48 3.2 Parameters estimation of an SDM PV module . . . . 49 3.3 Conversion of implicit to explicit form of I-V characteristic of an SDM PV module 49 3.4 Other different MPPT methods . . . . 54 3.5 Results and discussion . . . . 55 3.6 Summary of the chapter . . . . 61
TH-1895_11610232
3.1 Introduction
The PV system converts light energy into electrical energy without any environmental pollu- tion [78]. The output power of a PV source varies with different environmental conditions. The output current and voltage relationship of the PV array is highly nonlinear and depends on the solar irradiation and temperature conditions. Thus, an estimation of MPP of a PV array under DEC is not simple. Many researchers have proposed different methods to track the MPP of the PV array [38].
MPPT methods are used to track the MPP of a PV module at which the module operates and the MPP lies in the power region of the I-V or P-V curve [88]. In this power region, the MPP will deliver an actual maximum power from the PV module. The more popular MPPT techniques are fractional OCV (Vf rac) and fractional SCC [53]. However, the accuracy of these methods are not good enough, and hence, power losses occur in these methods. The AI techniques such as neural fuzzy logic, neural network and GA [50–52] have been used for the MPPT of a PV module. However, the AI techniques are computationally demanding, and their practical implementation is difficult. Therefore, the imple- mentation of AI techniques may not be the first choice for many applications. Some of the methods such as, PO [13], IC [89], and HCB [19] do not depend on the characteristics parameters of the PV module. However, the searching nature of these methods are slow to some extent, and hence, these methods are not suitable for the application purpose (i.e., solar car, moving broken clouds) due to the rapid change of environmental conditions.
In order to overcome the aforementioned limitations, a novel mathematical explicit function is derived from the implicit I-V function of the PV module to estimate the MPP of a module accurately with less computational cost. Since the explicit I-V function is used for the estimation of MPP of a PV module under DEC, it ensures simple, accuracy and computationally efficient. A comparative study of MPPT of a PV module in different existing methods for the steady and rapid change of solar irradiation conditions has been carried out, and it is observed that the proposed method is more accurate and computationally efficient. For validation of the proposed method, the maximum power obtained in the simulation and experimentally for a 250 W PV module under DEC are compared, and the results show that the performance of the proposed method is superior to the existing methods.