Keywords

1 Introduction

The electrical energy consumption rate is surprisingly increasing now, and it becomes challenging to fulfil the total demand, as the natural sources of fossil fuels are limited and decreasing from nature. So, researchers are paying more concentration to find ways of efficiently utilizing the nonconventional resources. Solar energy is a very significant energy source and most sustainable choice of power generation among the nonconventional and renewable energy families.

Though the efficiency of solar cell is low, the panels can be installed on the rooftop of the house [1] or large area which can produce sufficient power at low cost as sunlight can be achieved free and abundantly from nature.

Solar cells are basically a p-n junction diode. When sunlight (photon) falls upon the cell, electron–hole pairs are generated, and current starts flowing through it. The transmitted light is absorbed within the semiconductor material, and it uses this energy to excite free electrons from a low energy label to high energy label. Standalone photovoltaic systems are the best solutions in the locality where grid-connected system is impossible to set up or in many small electrical energy demand applications such as communication systems, water pumping, and low power [2]. The efficiency of the cell is less, so it is more beneficial to operate the solar panel at its maximum power point (MPP). MPP of the system depends on the power (voltage and current) generation from the solar panel which in turn depend on temperature and solar irradiation. So, it is necessary to predict the power generation from the solar panel at the different atmospheric conditions to operate the system in its maximum power point. Different strategies are implemented to predict the power generation like fuzzy logic [3, 4] and neural network [5]. Solar radiation is used in [6, 7] to obtain a reference power. In this paper, ANFIS-based power prediction model is designed. In the next section, analytical calculation procedure is mentioned to find nominal operating cell temperature, solar irradiance, and annual solar energy output of the photovoltaic system. In Sect. 3, ANFIS is designed in Matlab/Simulink to obtain a generation of solar power. The power generated from prototype solar PV panel is validated with the results.

2 Mathematical Modeling

2.1 Operating Cell Temperature

The operating cell temperature (expressed in Eq. (1a, 1b)) depends on nominal operating cell temperature and certain environmental conditions like (a) irradiance on the cell surface, (b) air temperature, and (c) wind velocity.

$$ T_{\text{cell}} = T_{\text{air}} + \frac{{{\text{NOCT}} - 20}}{80} \times S $$
(1a)

where S = irradiance in W/m2.

Tair is air temperature, and the nominal operating cell temperature (NOCT) is the temperature obtained by the open-circuited cell in the solar panel at predefined environmental condition stated below:

  1. 1.

    Irradiance on cell surface = 800 W/m2,

  2. 2.

    Air temperature = 20 °C, and

  3. 3.

    Wind velocity = 1 m/s.

The solar panel temperature will be lower than this when wind velocity is high, but higher under still conditions. The relationship between wind speed and solar panel temperature as used by Kurtz et al. [8] is shown in Eq. 1b:

$$ T_{\text{cell}} = T_{\text{air}} + S \times { \exp }( - 3.473 - 0.0594 \times {\text{Wind}}\,{\text{Speed}}) $$
(1b)

2.2 Calculation of Solar Irradiance

Solar irradiance is the energy received from the Sun in the form of electromagnetic radiation per unit area. The current generation of the solar cell mainly depends on solar irradiance, and the relationship is mentioned in Eq. (2).

$$ I_{\text{Gen}} = I_{{{\text{Gen}}\,{ \hbox{max} }}} \times \frac{{S_{\text{op}} }}{{S_{\hbox{max} } }} $$
(2)

where IGen is generated current at Sop irradiance, and IGenmax is a current generation at a maximum irradiance of Smax, i.e., 1000 W/m2. The average daily irradiation for each month is broken down into hourly using the ratio rt and expressed in Eq. (3). The diffused component of the total irradiation for each hour is also shown in Eq. (4).

$$ r_{t} = \frac{\text{hourly total irradiance}}{\text{daily total irradiance}} $$
(3)
$$ r_{d} = \frac{\text{hourly diffused irradiance}}{\text{daily total diffused irradiance}} $$
(4)

2.3 Calculation of Annual Electrical Energy Generation from Solar System

The global formula to estimate the electrical energy generation from the solar photovoltaic system is expressed in Eq. (5):

$$ E = A \times r \times H \times PR $$
(5)

where

E:

Electrical Energy (kWh),

A:

Total solar panel Area (m2),

r:

\( {\text{Solar panel efficiency (}}\% )= \frac{\text{Electrical power of one solar panel}}{\text{The area of that panel}} \)

H:

Annual average solar radiation on tilted panels (shadings not included), and

PR:

Performance ratio, coefficient for losses (range between 0.5 and 0.9, default value = 0.75).

3 Results and Discussions

ANFIS model is developed using a Sugeno-type fuzzy controller and multilayer feedforward neural network.

3.1 Design of Fuzzy Logic Controller

The fuzzy logic controller has two inputs, irradiance and temperature, and power is considered as output. Input 1 is irradiance and its range varies from 100 to 1000 W/m2 in a step of 100 W/m2 and consists of eight membership functions. The structure is shown in Fig. 1. Temperature is Input 2, and it varies from 10 to 30 °C in a step of 5 °C. It consists of six membership functions, and the structure is shown in Fig. 2. The output power has ranged from 1 to 420 mW. The fuzzy rules have been given in Table 1.

Fig. 1
figure 1

Membership function of input 1

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Fig. 2
figure 2

Membership function of input 2

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Table 1 Fuzzy rules
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3.2 Development of ANFIS Model

It is a multilayer feedforward neural network. The ANFIS structure is shown in Fig. 3. The model is trained by training data, and after training process, the model was tested with the checking data (shown in Figs. 3 and 4). The ANFIS decision surface view is shown in Fig. 4 for the solar power estimation. The overall structure of ANFIS model is shown in Fig. 5 based on fuzzy logic rule base shown in Table 2 and Figs. 6, 7. This system is then compared with the real time, i.e., experimental value of power. The two inputs, power through ANFIS and experimental power through the entire dataset used in this system, are given in Table 1.

Fig. 3
figure 3

Structure of the ANFIS model

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Fig. 4
figure 4

Trained data

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Fig. 5
figure 5

Validation result

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Table 2 Comparison of power prediction from ANFIS and power generation from real-time model
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Fig. 6
figure 6

Surface view of ANFIS model

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Fig. 7
figure 7

Real-time experimental model of solar panel

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3.3 Model Validation

The system aims to demonstrate the precision of the proposed model on solar power prediction. This is ensured by a comparison made between the proposed ANFIS model and experimental model. The performance analysis of this model is determined by the number of epochs reached. The result presented in Table 2 indicates that the ANFIS model has the best capability for estimating global solar power. Figure 7 shows the real-time experimental model of solar panel rated as 6 V, 0.5 W.

% Error is calculated as

$$ \% {\text{Error}}\, = \,\frac{{{\text{Power}}\,{\text{from}}\,{\text{ANFIS}}\,{ - }\,{\text{ Power}}\,{\text{from}}\,{\text{Experiment}}}}{{{\text{Power}}\,{\text{from}}\,{\text{Experiment}}}}\, \times \,100 $$
(6)

4 Conclusion

The current generation from the solar panel is highly influenced by solar irradiance, and the open-circuit voltage mainly depends on temperature. It is highly difficult to form the exact mathematical model to get exact power from the solar panel. Hence, in this paper, the authors tried to predict the power using ANFIS, and the model is validated by the real-time experimental solar panel. The irradiance is varied by a solar simulator. The real-time experiment is done over a stipulated time period, and so the temperature is varied from 10 to 30 °C only. But this model can be utilized for higher temperature also. The % error comes negligible and less than 0.5%, so this model can be utilized in association with MPPT controller also.