Keywords

74.1 Introduction

Solar energy production is one of the fastest growing renewable energy productions as the energy utilized is the light energy which comes from the sun which is inexhaustible. There are specific types of materials which generate current upon absorbing light. Those materials are called as photovoltaic materials. This voltage can be effectively utilized by series and parallel combination of cells [1]. The energy produced by the solar panels cannot be delivered efficiently to the load. Maximum power point controllers are modeled to extract the maximum power from the solar panels. Throughout the literature studies many authors have concentrated in the modeling of solar panels. Also many types of algorithms have been implemented in many papers. In [2], a fuzzy logic based controller is used to track the maximum power and the results are compared for various types of solar modules. In [3–6], a grid connected solar panel is modeled and [5] the controllers are developed to sense the grid active and reactive power. In [3], a buck boost converter is designed and a microcontroller is used to control the converter for maximum power transfer. In [7], simulation models for solar cells are developed in simelectronics environment. In [8], analytical techniques are used for modeling non-linear DC-AC switching converter for PV systems under islanding conditions. In [9, 10], a new algorithm is proposed to extract maximum power from the radiation. A detailed study is made for the solar energy in [1, 11]. In [12], solar based thermo electric generators are developed. The performance of PID controller and Fuzzy Logic controller are compared for various operating conditions in [13]. In this work, mathematical modeling of solar panels is done. Along with the conventional inputs such as insolation and temperature, series and shunt resistances are taken as additional inputs. The solar panel characteristic curves are checked for various input variables such as temperature, irradiation, series resistance and shunt resistance. To track the maximum power, MPPT controllers employing P&O type and also a fuzzy logic controller is implemented along with the boost converter. The performances of the MPPTs are compared with each other.

74.2 Mathematical Modeling of Solar Panel

The Fig.74.1 shows the equivalent circuit of the PV panel and it’s represented by a current source in parallel with a conventional diode. Since an average solar cell produces less than 2 W, the cells must be added in series and parallel in order to get a higher voltage [2].

Fig. 74.1
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Equivalent circuit of a PV cell

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74.3 Maximum Power Point Tracking Algorithm

The voltage obtained for loads such as battery, DC motors, resistors could be enhanced with a better efficiency if the operating points are kept near the knee of the P-V and I-V curves. The devices used to maintain such a constant voltage are maximum power point trackers. A fuzzy logic MPPT controller tracks the maximum power when compared to other methods. The flowchart shows the algorithm for the implementation of fuzzy logic based algorithm for MPPT. In this algorithm, PV input voltage and current are taken as inputs. The duty cycle of the converter is taken as output [13] (Fig. 74.2).

Fig. 74.2
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Flowchart for the fuzzy logic controller implemented

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The equations associated for the calculation of error and changes in error are as below.

$$ {\text{E(K)}} = \frac{\text{I}}{\text{V}} + \frac{{\Delta {\text{I}}}}{{\Delta {\text{V}}}} = \frac{{\Delta {\text{P}}}}{{\Delta {\text{I}}}} = \frac{{\Delta {\text{P}}}}{{\Delta {\text{V}}}}. $$
(74.1)
$$ {\text{CE(K)}} = {\text{E(K)}} - {\text{E}}({\text{K}} - 1). $$
(74.2)
$$ \Delta {\text{I(K)}} = {\text{I(K}}) - {\text{I}}({\text{K}} - 1). $$
(74.3)
$$ \Delta {\text{V(K}}) = {\text{V(K}}) - {\text{V(K}} - 1). $$
(74.4)
$$ \Delta {\text{P(K)}} = {\text{P(K)}} - {\text{P}}({\text{K}} - 1). $$
(74.5)

where, E(K)—error value, CE(K)—change in error value, \( \Delta {\text{I}}({\text{K}}) \)—change in current value, \( \Delta {\text{V(K)}} \)—change in voltage value, \( \Delta {\text{P(K)}} \)—change in power value [13]. The function of the fuzzy logic controller is to maintain a constant duty cycle for varying output voltage at the load so that power transfer is maximum.

74.3.1 Membership Functions

In this work five triangular and two trapezoidal shaped membership functions are selected. Their ranges are calculated based on the oscillation of each signal. The inputs are error and change in error. The output is the duty cycle given to the boost converter. The degree of membership function ranges from 0 to 1.

Figures 74.3, 74.4 and 74.5 are the membership function plot for error, change in error and duty cycle respectively. Each of the variables has seven membership functions. Thus a total of fourteen membership functions are used for input variables and seven membership functions are used for output variables.

Fig. 74.3
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Membership function plot for error

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Fig. 74.4
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Membership function plot for change in error

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Fig. 74.5
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Membership function plot for duty cycle

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74.3.2 Rule Settings for Fuzzy Controller

Different subsets can be used for tuning the rules for fuzzy logic controller. The subset used for this work consists of 49 rules which have been tuned. These rules give better accuracy and dynamic response although their tuning is difficult. The fuzzy rules are given in Table 74.1.

Table 74.1 Fuzzy rules formulation
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74.3.3 Perturb and Observe Type of MPPT

Perturb and observe type is the simplest and the most common method. The input variables taken are change in current, voltage and power. The output variable is the change in power. The flowchart implemented in the algorithm is shown [11]. The flowchart make uses the voltage perturbation as shown in Fig. 74.6. An alternative method uses the same input variables to perturb the duty cycle. This method is not used in the project as the duty cycle perturbations are random in this method and not accurate.

Fig. 74.6
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Flowchart of the P&O algorithm implemented

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74.4 Operation and Design of the Boost Converter

Figure 74.7 shows the basic circuit configuration of a boost converter, where Vin is the dc input voltage, L is the boost inductor, S is the controlled switch, D is a diode, C is a filter capacitor, and RL is the load resistance. Boost converter works in two states. When the switch S is open, current in the boost inductor increases linearly, and the diode D is off at that time. When the switch S is closed, the energy stored in the inductor is released through the diode to the output RL circuit.

Fig. 74.7
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Circuit diagram of the implemented boost converter

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74.5 Results and Discussions

74.5.1 Variation of I-V and P-V Curves with Series Resistance

Addition of series resistance reduces the voltage which reduces the slope of the curves and the maximum power point is also reduced as seen in Figs. 74.8 and 74.9. Thus it is evident that with the increase in series resistance, the efficiency of the solar panel reduces.

Fig. 74.8
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Effect of variation of I-V and P-V curves with series resistance

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Fig. 74.9
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Effect of variation of I-V and P-V curves with series resistance

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74.5.2 Variation of I-V and P-V Curves with Shunt Resistance

The shunt resistance for a PV cell should be high. Lower value of shunt resistance leads to a steeper collapse of the curves which lowers the fill factor which is shown in Figs. 74.10 and 74.11.

Fig. 74.10
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Effect of variation of I-V and P-V curves with shunt resistance

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Fig. 74.11
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Effect of variation of I-V and P-V curves with shunt resistance

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74.5.3 Duty Cycle Obtained by FLC and P&O Controller

Figures 74.12 and 74.13 show the duty cycle waveform obtained by both the controllers. It can be seen that the fuzzy logic controller used tracks a constant duty cycle whereas the perturb and observe controller used does not track the duty cycle as efficiently as fuzzy logic controller.

Fig. 74.12
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Duty cycle tracked by the fuzzy logic controller and P&O controller

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Fig. 74.13
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Duty cycle tracked by the fuzzy logic controller and P&O controller

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A constant duty cycle is achieved at the beginning of the simulation whereas the P&O MPPT controller does not track a constant duty cycle for a very long time. The fuzzy logic controller shows an efficient operation when compared with the P&O controller.

74.6 Conclusion

The solar PV array is successfully modeled and the characteristics curves are observed for the change in irradiation, temperature, series and shunt resistances. Maximum power point controllers based on P&O and fuzzy logic controllers are modeled. The duty cycle curves for both the controllers are noted and it is evident that the fuzzy logic controller proves to be the best in comparison with the P&O MPPT controller. Thus the robustness of the fuzzy logic controller is justified. The simulation is done in MATLAB simulink environment (R2011).