Comparison of intelligent modelling techniques for forecasting solar energy and its application in solar PV based energy system

: The measurement of solar energy data is a difficult task and rarely available even for those stations where measurement has already been done. Further, the PV power forecasting is an important element for smart energy management system. In the present scenario, utilities are developing the smart-grid application and PV power forecasting is an important key tool for a new paradigm. The forecasting of solar energy during clear sky-condition can be easily estimated using mathematical models; however, forecasting under the influence of hazy, cloudy, and foggy sky-conditions do not provide accuracy with these models. Therefore, an intelligent modelling techniques i.e. fuzzy logic, artificial neural network (ANN), and adaptive-neural-fuzzy-inference system (ANFIS) models are proposed based on sky-conditions namely clear/sunny sky, hazy sky, partially cloudy/foggy sky, and fully cloudy/foggy sky-conditions for forecasting global solar energy. To design the model, 15 years averaged datasets of meteorological parameters were used for distinct climate zones across India. Further, comparison of intelligent models has been carried out with regression models using statistical indicators. The proposed model has been implemented for short-term PV power forecasting under composite climatic conditions. Simulation results confirm that the ANFIS model provides supremacy for PV power forecast as compared to other models.

Greek symbols δ solar declination angle (°) γ temperature parameter at MPP (dimensionless) ϕ latitude of the region (°) ω s mean sunrise hour angle (°) n day days in a year beginning from 1st January onwards (dimensionless) η o optical efficiency (%)

Introduction
Renewable energy resources and its effective use are intermittently allied with the sizing, optimisation, and operation of solar energy systems. It is an environment-friendly, clean, and inexhaustible source of energy that can be effectively utilised for the generation of power. A reasonable accurate knowledge of solar resource availability is of prime importance for solar engineers in the development and designing of solar photovoltaic (PV)-based energy systems. Unfortunately, the availability of solar radiation data is scarce because of high instrument cost, limited spatial coverage, and limited length of the record. Due to unavailability of the measured data, global solar energy forecasting is of prime importance at the Earth's surface. For this purpose, it is essential to develop models based on more readily available meteorological data for forecasting global solar energy [1][2][3][4][5][6][7][8][9][10]. Solar radiation model ranges from mathematical models to hybrid intelligent models. In the past, various mathematical models such as REST, Modified Hottel's, CPRC2, and REST2 and so on, have been developed for estimating global solar energy under IET Energy Syst. Integr., 2019, Vol. 1 Iss. 1, pp. [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51] This is an open access article published by the IET and Tianjin University under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/) cloudless skies [11][12][13][14]. Recent research carried out shows that the mathematical models available in the literature are not accurate, primarily due to the extreme simplicity of parameterisation; however, empirical models based on multiple regression analysis are presented for estimating global solar energy. Angstrom presented the first attempt for estimating global solar energy using sunshine hours under clear sky conditions [15]. In recent research, Bayrakci et al. [16] proposed empirical models for estimating global solar energy for the Turkey region. In this work, 105 literature models are assessed with the aid of statistical validation tests. Also Benson's models are investigated and compared. It is found in this research that the cubic and quadratic models are appropriate for January-June and July-December periods, respectively. Further, several correlations are available for the estimation of global solar energy correlated with one or more meteorological parameters [17][18][19][20]. Most of the previous researches have been carried out for Middle East countries; however, very few models discussed forecasting global solar energy for Indian climatic conditions [21,22]. In recent work by Khalil and Aly [23] empirical models have been evaluated based on statistical error-tests for estimating global solar energy using sunshine hours, relative humidity, and ambient temperature for Saudi Arabia region. It is observed in this research that maximum solar energy can be achieved during summer while this value diminishes during autumn and winter. The regression models developed so far for assessing global solar energy were available for clear sky conditions; however, such models are unsuitable for estimating global solar energy during cloudy sky conditions. Presence of moisture, dust, clouds, and aerosols in the lower atmospheric region causes uncertainty in the atmosphere. The reduction in extra-terrestrial solar radiation occurs due to the external atmosphere which varies from 30% in a clear sky condition to 100% in a cloudy/foggy sky condition. For Indian climatic conditions where about 50-100 days are cloudy, accurately estimating global solar energy based on multiple regression analysis is a tedious task [24][25][26][27]. Therefore, intelligent modelling techniques have been introduced for forecasting global solar energy. A detailed literature survey on the issue reveals artificial intelligence techniques focusing on the theoretical aspects, principles, and design methodology. Further, the hybrid intelligent system has been introduced like the adaptive-neuralfuzzy inference system (ANFIS) which integrate the features of artificial neural network (ANN) and fuzzy logic approach [28].
The fuzzy logic models are introduced wherein probabilistic approaches do not give a realistic description of the phenomenon. Sen [29] proposes a fuzzy logic model using sunshine duration for estimating solar energy. Most of the previous researches investigated the fuzzy model for forecasting solar energy and its application in the field of renewable energy system [30][31][32][33][34][35]. In recent research, Suganthi et al. presented an application of fuzzy logic based models in renewable energy systems namely solar, wind, bio-energy, micro-grid, and hybrid systems. In this research, it is found that the fuzzy-based models are extensively used in recent years for site assessment, for installing of PV systems, power point tracking in solar PV systems, and its optimisation [36]. Recently, Perveen et al. proposed a sky-based model employing fuzzy logic modelling for forecasting global solar energy using meteorological parameters namely dew point, sunshine duration, ambient temperature, wind speed, and relative humidity. It is observed in this research that with the inclusion of dew point as a meteorological parameter the accuracy of the model significantly increases [37].
For complex systems with large datasets, maintaining accuracy for such data sets using fuzzy logic modelling would be a tedious task. Therefore, ANN-based models are introduced, employing artificial intelligent techniques which are data-driven and can subsequently perform the structure simulation. The ANN model is ideal for modelling non-linear, dynamic and complex system [38][39][40][41][42][43][44][45][46][47][48][49]. Chang et al. proposed a radial basis function neural network (RBFNN) based model for short-term power forecasting wherein 24 h of input data at 10-min resolution have been considered for training the proposed neural network. In this research, obtained results have been compared with other ANN-based methods, and the result shows that the RBFNN model is more accurate [50]. In recent research, Khosravi et al. proposed a comparison of the multilayer feed-forward neural network (MLFFNN), and support vector regression with a radial basis function (SVR-RBF) for forecasting wind speed. In this research, temperature, pressure, relative humidity, and local time are considered as input parameters, and statistical indicators show that the SVR-RBF model outperforms MLFFNN model [51].
Detailed literature review reveals that for estimation of complex functions, an accurate analysis of some neurons and hidden layers with the aid of ANN is a difficult task as they are large in number. Also, large training time is involved in such a neural network, which subsequently slows down the response of the system. The existing neural network model does the summation operation; however, it does not operate based on the product of weighted inputs. Therefore, hybrid intelligent systems are introduced for forecasting solar energy which is a fusion of ANN and fuzzy logic approach for forecasting global solar energy. Many researchers have investigated the integrated features of ANFIS in forecasting global solar energy and its application in wind power forecasting [52][53][54][55][56][57][58][59]. Jang [60] has presented an architecture underlying the principle of ANFIS which is implemented within the framework of adaptive networks. In this work, the proposed ANFIS can construct an input-output mapping based on stipulated data pairs. In recent research, Liu et al. [61] proposed a hybrid methodology for shortterm power forecasting using ANFIS. In this research, individual forecasting models are presented such as back-propagation neural network, least squares support vector machines, and RBFNN. The results of the comparison reveal that the proposed hybrid methodology using ANFIS presents a significant improvement in accuracy.
Most of the intelligent models discussed in the literature for forecasting global solar energy were available for clear sky conditions; however, very few researchers have explained about modelling based on variation in sky-conditions defined as clear sky, hazy, foggy, and cloudy sky conditions and for widely changing climatic conditions based on distinct climate zones. Further, most of the previous researches employing hybrid intelligent systems were based on forecasting global solar energy using meteorological parameters like duration of sunshine hours, wind speed and others; however, very few literature is available that elucidated about using dew-point in addition to other available meteorological parameters; the inclusion of which as significantly increased the accuracy of the models.
Therefore, in this work, an attempt has been made to establish intelligent models such as fuzzy logic approach, ANN, and ANFIS models for forecasting global solar energy based on sky-conditions defined as clear (type-a) sky, hazy (type-b) sky, partially cloudy/ foggy (type-c) sky, and fully cloudy/foggy (type-d) sky conditions and for five weather stations across India covering widely changing climatic condition thereof, i.e. composite, warm and humid, hot and dry, cold and cloudy, and moderate climatic conditions, respectively. Simulations have been carried out for global solar energy forecasting based on meteorological parameters namely dew-point, ambient temperature, sunshine hours, relative humidity, and wind speed, respectively. Further, comparisons of the proposed intelligent model have been carried out with empirical regression models with the aid of statistical validation tests. The obtained results have been further implemented for short-term PV power forecasting of solar PV-based energy system employing 250 W multi-crystalline solar PV modules operated at maximum power point (MPP) operating conditions under composite climatic conditions. This work is arranged in the following manner. Section 2 presents the methodology. Section 3 discusses the implementation of intelligent modelling techniques for solar PV-based energy systems. Section 4 presents statistical validation tests. Section 5 presents results and discussions. The conclusion has been carried out in Section 6 and Section 7 presents the references. In this work, meteorological parameters include the duration of sunshine hours, dew-point, relative humidity, ambient temperature, wind speed, and global solar energy. The 15 years averaged measured data have been obtained from IMD (Indian Meteorological Department), NIWE (National Institute of Wind Energy), and NISE (National Institute of Solar Energy) [62,63]. The normalisation of the data has been done and defined in 0.1-0.9 range so to avoid convergence issues for five weather stations which represent distinct climatic conditions. The Indian climatic condition possesses wide-ranging weather conditions and the criteria for assigning location to depend on sky conditions prevailing for six months or more. The factors affecting climate include location, latitudinal extent, monsoon winds and so on. In 1988, Bansal and Minke [64] evaluated the mean averaged data from 233 weather stations, and explained five distinct climate zones and are presented in Table 1.

Sky-based classification
In this work, the classification based on sky-conditions can be described as follows [65]: 2.2.1 Clear/sunny (type-a) sky: If sunshine duration equals or more than 9 h, and diffuse radiation equals or less than 25% of global solar energy.

Hazy sky (type-b):
If sunshine duration lies in the middle of 7-9 h and diffuse radiation is >25% and <50% of global solar energy.

Partially cloudy/foggy sky (type-c):
If sunshine duration lies in the middle of 5-7 h and diffuse radiation is >50% and <75% of global solar energy.

Fully cloudy/foggy sky (type-d):
If the sunshine duration is lower than 5 h and diffuse radiation is >75% of global solar energy.

Regression models for global solar energy estimation
Angstrom proposed the first ever model based on global solar energy correlation with a sunshine duration which is later improved by Page and Prescott [66,67]. In this, the value of (H g ) global solar energy can be attained by multiplying the forecasted clearness index (H g /H o ) by H o which represents extra-terrestrial solar radiation and can be calculated using standard geometric relations [68,69]. In equation with different meteorological parameters, the correlation is of multiple linear regressions and expressed by (1) given below: p = a + bq 1 + cq 2 + dq 3 + eq 4 + f q 5 + ⋯ + nq n , where G sc is 1367 W/m 2 , δ is the declination angle, ϕ represents the location latitude, ω s is the mean sunrise angle, and n day is days beginning from 1st January. S o is the maximum possible sunshine hours; and S is the daily sunshine hours.

Forecasting global solar energy using the fuzzy logic approach
Fuzzy logic models are employed in forecasting global solar energy. In this work, the variables L, M, and H are defined with fuzzy terms as VL, LM, MH, HH, and VH, respectively, and five such membership functions in 0.1-0.9 range are defined in a fuzzy inference system of MATLAB for forecasting global solar energy. The fuzzy membership function for ambient temperature is presented in Fig. 1 and the models have been developed using MATLAB fuzzy logic toolbox.

Assessment of global solar energy based on ANN
The ANN architecture employing a feed-forward neural network is designed in a way that output variables are calculated from variables at the input side. The ANN architecture presented in this research comprises three layers out of which the first layer has five input parameters, a hidden layer with tan-sigmoid function 'tansig', which is described by the following equation: where x is the input, and linear activation 'purelin' transfer function has been used in the output that would solve the hard problem as shown in Fig. 2. The neural network toolbox in MATLAB has been used for implementing a neural network algorithm, and 'TRAINLM' is used for training the network. The output of the network can be modelled by where x ij is the j th neuron incoming signal (at the input layer), θ i is the i neuron bias, and w ij is the connection weights directed from j neuron to i neuron (at the hidden layer).

Hybrid intelligent system for forecasting global solar energy
The ANFIS is a graphical analysis of the fuzzy-Sugeno system which lies within the framework of adaptive networks. The ANFIS architecture makes use of a hybrid learning rule which combines gradient-descent, back-propagation, and least-squares algorithm. In this, there is no effect of input-output mapping to the response of the network, i.e. complexity reduces. One of the advantages of the hybrid system is the faster convergence rate. In this, MATLAB software has been used for data training and testing using function 'anfisedit' in the command window.

ANFIS architecture:
It is a multilayer feed-forward network which comprises nodes with directed links, with a function similar to the Takagi-Sugeno FIS model as shown in Fig. 3 [70].

Layers of ANFIS: It comprises five layers as follows:
2.6.3 Layer 1: In layer 1, node acts as an adaptive function node which gives a degree of membership function as shown below: where O 1,i and O 1,j represent the output functions and µ x,i is the membership function degree for fuzzy sets A i and B i , respectively.

Layer 2:
In this, the node is either fixed or non-adaptive and labelled as '∏' where the output is the incoming signals product and shown as: 2.6.5 Layer 3: In layer 3, the node is either non-adaptive or fixed labelled as 'N', which indicates normalisation to the firing strength as 2.6.7 Layer 5: It is the output layer which comprises a single fixed node which is labelled as 'Σ' and sums the incoming signals as

Implementation of intelligent modelling techniques for solar PV-based energy system
The large-scale penetration of solar PV technology in the smart energy management system has become a challenging task. The output power variation in a solar PV-based energy system can lead to the unstable operation of the power system. The fluctuations in the output lead to the issues in its use and subsequently reduce the PV generation capacity. Damage may arise in the stability of the utility grid and the power quality because of the imbalance between the demand and supply. In this research, 250 W multicrystalline solar PV modules have been employed for short-term PV power forecasting operated at MPP operating conditions under composite climatic conditions.

Performance specification of 250 W multi-crystalline solar PV modules
The efficiency of module, The generation of power from solar PV-based energy system can be explained by the following equations [71]: and where P PV , STC is the PV system rated power output of single array at MPP conditions, N PVS is the number of photovoltaic arrays in series, G T is solar irradiance in W/m 2 at STC, P PV is the power output of PV array at MPP, γ is a temperature parameter at MPP, N PVP is the number of PV arrays in parallel, T j is the junction temperature of the solar panel in °C, T amb is the ambient temperature in °C, and N OCT is a constant.

Statistical validation tests
Various statistical validation tests have been performed for evaluating the performance of the models.

Mean percentage error (MPE)
It is defined as the variation in the measured and forecasted value given below:

Mean bias error (MBE)
It gives the correlation performance between the measured and forecasted data given below:

Root mean square error (RMSE)
It is expressed by the equation given below:

Coefficient of determination (R 2 )
It can be defined as where x is the number of observations, m i and f i are the ith measured and forecasted data, and m a and f a are the averaged measured and forecasted data, respectively.

Estimating global solar energy using regression modelling
In this, empirical models have been established using multiple regression analysis correlating meteorological parameters such as global solar energy with sunshine duration, atmospheric pressure, wind speed, ambient temperature, relative humidity, rainfall, and cloudiness index to estimate global solar energy. Statistical validation tests are used for evaluating the model performance and are illustrated in Table 2. Principal component analysis has been applied to the developed model for obtaining a correlation with the highest correlation coefficients, and it is observed that the sevenparameter correlations, provides the best fit and makes it useful for global solar energy estimation for distinct climatic zone across India and are presented in Table 3. From Table 3, it is revealed that for hot and dry climate the best fit model is achieved by (55) with MPE = 0.36%, and R 2 = 0.64; for a warm and humid climate (see Fig. 4), the best fit model is achieved by (56) with MPE = 1.93%, and R 2 = 0.87; for composite climate, (57) gives the best fit with MPE = 0.42%, and R 2 = 0.71; for moderate climate, (58) gives the best fit with MPE = 0.25%, and R 2 = 0.81; and for cold and cloudy climate, (59) gives the best fit with MPE = 1.5%, and R 2 = 0.71, respectively.

Intelligent models for forecasting global solar energy
In this section, a comparison between fuzzy logic, ANN, and ANFIS based model has been carried out for global solar energy forecasting based on different sky-conditions using meteorological parameters namely dew-point, relative humidity, sunshine hours, wind speed, and ambient temperature, respectively, for distinct climatic conditions. The performance has been evaluated using statistical validation tests and is presented in Table 4 from which the following inferences can be drawn as follows.

Clear/sunny (type-a) sky:
Jodhpur climatic conditions are favourable for this skycondition as the MPE obtained by simulating the measured and forecasted data using intelligent models are observed to be less for this station as compared to other stations. The averaged MPE is observed to be 0.31% by employing a fuzzy logic approach, 0.05% by using ANN, and with ANFIS based model the error reduced to 0.00002681%, respectively. The reason behind is that the Jodhpur   climate is hot and dry wherein sunny climatic conditions exists throughout the year. Further, the graphical representation between the measured and forecasted data has been shown in Fig. 5a.

Hazy (type-b) sky:
Delhi climatic conditions are favourable for this sky-condition as the MPE obtained by simulating the measured and forecasted data using an intelligent model is observed to be less for this station as compared to other stations. The averaged MPE is observed to be 0.42% by employing fuzzy logic, 0.14% by using ANN, and the error reduced to 0.00001653% with the ANFIS model. The reason behind is the higher humidity levels, which vary from 25-35% during dry periods to 60-90% during wet periods. Further, the graphical representation between the measured and forecasted data has been shown in Fig. 6b.

Partially cloudy/foggy (type-c) sky:
Chennai climatic conditions are favourable for this sky-condition as the MPE obtained by simulating the measured and forecasted data using intelligent models are observed to be less for this station as compared to other stations. The averaged MPE is observed to be 0.30% by employing fuzzy logic, 0.20% by using ANN, and with ANFIS based model the error reduced to 0.00002036%, respectively. This condition is apparently due to high diffused radiation owing to cloudy sky conditions. During summer, the temperature can reach as high as 30-35°C, whereas during winter, the temperature lies between 25 and 30°C. Further, the graphical analysis between the measured and forecasted data has been shown in Fig. 4c.

Fully cloudy/foggy (type-d) sky:
Shillong climatic conditions are favourable for this sky-condition as MPE obtained by simulating the forecasted, and measured data using intelligent models are observed to be less for this station as compared to other stations. The averaged MPE is observed to be 1.30% by employing  fuzzy logic, 0.46% by using ANN, and the error reduced to 0.00001428% with the ANFIS model (see Fig. 7). This is due to the reason that during winter the global solar radiation is low with a high amount of diffused radiation, which makes winter extremely cold. Further, the graphical representation between the measured and forecasted data has been shown in Fig. 8d.

Comparison of intelligent models with regression models
Further, the comparative analysis of intelligent models namely fuzzy logic, ANN, and ANFIS based model have been carried out with regression models, and the performance has been evaluated using statistical validation test for the composite climate of India are presented in Table 5. It is evident from Table 5 that the hybrid intelligent systems perform best in comparison to other models for forecasting global solar energy. The averaged MPE obtained by using regression models is 1.67% for composite climatic conditions. However, the obtained result is far better by using intelligent models for global solar energy forecasting. With fuzzy logic methodology, the averaged MPE reduced to 0.41%, which is comparatively lesser than the regression models. The MPE further reduced to 0.12% by  It is, therefore, revealed from the results that by employing hybrid intelligent systems, the obtained error obtained is less. This is due to the reason that the ANFIS based model presents a specified mathematical structure and makes it a good adaptive approximator. Further, for a network of similar complexity, the

Implementation of intelligent models in solar PV-based energy systems
The solar PV power forecasting is an important element for the smart grid approach which helps in optimisation of the smart energy management system which can integrate the renewable power generation efficiently. Since the power generating from solar energy resource is fluctuating and non-linear in nature, it becomes very difficult to estimate power output with mathematical models; therefore, intelligent approaches based on fuzzy logic, ANN, and ANFIS models have been presented for power forecasting of solar PV-based energy system employing multi-crystalline 250 W solar PV modules operating at MPP tracking conditions are presented in Table 6.
From Table 6, it is evident that by employing a hybrid intelligent approach, i.e. the ANFIS model, the averaged MPE obtained is 0.0001% which is far less as compared to other models. By employing fuzzy logic, the MPE obtained is 0.01%, while with the ANN model, 0.0021% of MPE is achieved, respectively. Hence, the hybrid modelling approach is far accurate and precise as compared to other models.
Further, it is seen from the results that for all months of the year, MPE is less in the case of the ANFIS model. For the winter season (January), the averaged MPE by employing a fuzzy logic approach is 0.09%, using ANN the error reduced to 0.004%, and with ANFIS model the error further reduced to 0.0003%. Similarly, for the summer season (June) the averaged MPE by employing fuzzy logic is 0.07%, by using ANN the error reduced to 0.0033%, and with ANFIS model the error further reduced to 0.0001%, respectively. It can also be observed that error is large for the rainy season (August) because of large uncertainties associated with the data. The averaged MPE by employing fuzzy logic is 0.28%, using ANN error reduced to 0.0304%, and with the ANFIS model, the error further reduced to 0.0003%, respectively.
Given those above, it is found that the ANFIS model performs better than other models in terms of a faster convergence rate with learning and training ability. The ANFIS methodology makes use of training pattern as compared to other methods and hence reduces the computational time complexity. It has certain advantages such as the ease of design, robustness, and adaptability with the nonlinearity associated with the data. The ANFIS methodology integrates the features of both fuzzy logic and ANN which increases the system accuracy and makes the system response much faster. Further, parallel computation is allowed in ANFIS structure which presents a well-structured representation with a hybrid platform for solving complex problems and is a feasible alternative to the conventional model-based control schemes. This hybrid approach deals with the issues associated with variations and uncertainty in the power plant parameters and structure, thereby improving the system robustness. Further, it allows a better integration with other control design methods.

Intelligent model for short-term PV power forecasting
The generation of power from a renewable energy resource is gaining attention because of advancement in the field of solar PVbased energy systems. In the present scenario, power bidding is done on 10 min timescale by many distribution companies. Further, the uncertainty and the variability associated with the solar PV power plant leads to inappropriate operation. Hence, this mandates the short-term power forecasting for successful and efficient integration of solar power generating plants into the utility grid.
In this research, an intelligent modelling technique such as fuzzy logic, ANN, and a hybrid approach is presented for very short-term power forecasting of a solar PV-based energy system under composite climatic conditions. The input included the measurements of solar irradiance, cell temperature, and PV generation for the day at a timescale of 10 min and used as input for short-term PV power output forecasting which varies according to different weather conditions. Various factors affect the power generation, such as climatic variations, solar insolation, the temperature of solar panel, ambient temperature, and the topographical position. So, it becomes a tedious task to define the output with a single model; therefore, the output is modelled based on different sky-conditions, namely sunny sky, hazy sky, partially cloudy/foggy sky, and fully cloudy/foggy sky conditions, respectively, using different meteorological parameters as these factors make a significant impact on the power output of the solar PV systems and are presented in Tables 7-10, respectively. Table 7, it can be seen that the performance of the sunny sky model is better in power forecasting of a solar PV-based energy system. The averaged measured power during a sunny sky day is 98 W. However, the MPE obtained is 0.077% by employing a fuzzy logic methodology, the error reduces to 0.0079% by using ANN, and it further reduces to 0.000054% with ANFIS methodology. The day variation between the measured and forecasted power for the duration of 24 h by employing intelligent models have been presented in Fig. 9a.

Hazy sky:
It is observed that the MPE obtained by employing a fuzzy logic methodology for this sky condition is 0.049%, the error reduced to 0.022% by using ANN, however, with ANFIS model the MPE is least and further reduced to 0.004%, respectively, as shown in Table 8. The averaged measured power during a hazy sky day is 82 W. The day variation between the measured and forecasted power for the duration of 24 h by employing intelligent models have been presented in Fig. 9b.

Partially cloudy/foggy sky:
For this sky condition, the averaged measured power is 76 W. By using fuzzy logic, the MPE is 1.20%, this error reduced to 0.20% by using ANN, however, with ANFIS model the MPE is least and further reduced to 0.003%, respectively, as shown in Table 9. The day variation between the measured and forecasted power for the duration of 24 h by employing intelligent models have been presented in Fig. 9c. Table 10, it is evident that the PV power output is less during fully foggy/cloudy sky condition with the averaged measured power of only 27 W. The MPE is 0.21% by employing a fuzzy logic methodology, the error reduces to 0.091% by using ANN, and with ANFIS the error obtained is 0.0014%, respectively. The day variation between the measured and forecasted power for the duration of 24 h by employing intelligent models have been presented in Fig. 9d.

Fully cloudy/foggy sky: From
Such forecasts would help manage supply and demand for energy building in a smart grid environment. This research will help the stakeholders such as power engineer, technocrats, utility, designer, service provider, and operation engineer for developing the smart energy management system wherein the PV-based power forecasting is one of the key components for this new paradigm.
This research would be practically useful in providing appropriate control, optimisation, power smoothening, real-time dispatch, the requirement of additional generating stations and the selection of appropriate energy storage system which may mitigate the issues of power fluctuations obtained from solar PV-based energy systems.
From Fig. 9, it is evident that the generation of power in a solar PV-based energy system varies significantly with variation in skyconditions. This observation reveals that the forecasting model should be based on weather classifications. However, for composite climatic conditions, the sunny and hazy model outperforms other models. In this case, the PV system is installed in National Institute of Solar energy, Delhi, where the sunny days are present during most of the year.

Conclusion
In this research, different models based on intelligent approaches such as fuzzy logic, ANN, and ANFIS have been developed and presented for solar energy forecasting using meteorological parameters. The results obtained from different models are compared with a regression model by statistical indicators. Based on the comparative analysis, it is revealed that the performance of the ANFIS based model provides more accurate results in comparison to other intelligent models. The short-term PV power forecasting may be implemented for many applications such as providing appropriate control for PV system integration, optimisation, power smoothening, real-time power dispatch, the requirement of additional generating stations and the selection of appropriate energy storage.