The performance of the solar photovoltaic (PV) module is more sensitive to its operating temperature. A PV module with a cooling system produces higher electrical power output than a PV module without a cooling system. In addition, the PV module with the integrated cooling system is capable of generating electrical and thermal energy simultaneously. Such an integrated (hybrid) system is termed as a solar photovoltaic thermal (PV/T) system. When two or more collectors connected in series as a mean to have higher output, then such a system is termed as series-connected PV/T water collectors. This study presents two fuzzy inference systems (FISs), namely, Mamdani and Sugeno, for predicting the performance of series-connected PV/T water collectors. The set of rules was framed individually for both models in a way to predict the power output of PV/T water collectors in an inaccurate manner. The predicted results by inference systems are compared with experimental values to check their prediction accuracies. The accuracy of such a proposed Mamdani and Sugeno FIS is 95.67% and 99.92%.
Among different sources of renewable energies, the energy obtained from the sun is considered as the principal source of all. A device which converts such energy obtained from the sun into necessary mean is known as solar energy conversion devices (SECDs). SECDs, which convert solar energy into electricity, are termed as a photovoltaic (PV) module. The performance of the PV module is more sensitive to its operating temperature, while SECDs, which convert cold fluid into the hot fluid, are termed as a flat plate collector (FPC) module. Similarly, SECDs are capable of generating thermal and electrical energy, simultaneously known as a solar photovoltaic thermal (PV/T) water collector. In this study, the performance of series-connected PV/T is investigated and predicted using a fuzzy inference system (FIS).
Various advantages are available with such a PV/T water collector system. They occupy 50% of the space occupied by stand-alone SECDs. Payback period and return on investment of such SECDs are fast in comparison with stand-alone SECDs. Origination of solar PV/T water collectors is in the middle of the year 1970 and 1980. PV based researchers identified that the reason for the drop in PV module performance is due to its higher operating temperature. Researchers , among the middle of the year 2000 and 2015, introduced various configurations of solar PV/T water collectors. To have high power output, Kumar et al. [2,3]conducted experiments with series and parallel connected solar PV/T water collectors. They observed parallel-connected PV/T water collectors have high instantaneous exergy than the series-connected rig.
Mojumder et al.  in their forecasting work fabricated two types of air collectors and estimated electrical, thermal, and overall efficiency using extreme learning machine. Predicted values of such extreme learning machine are in good agreement with experimental values with less than 1% of error. Table 1 presents various applications of fuzzy logic in the solar thermal energy field.
Sridharan et al.  in their fuzzy logic-based predictive work compared experimental values of the power output of PV/T water collectors with fuzzy predicted power output values. Accuracy and error of such a model are 94.38% and 5.62%.
Rizwan et al.  in their fuzzy logic-based modeling work estimated global solar radiation using meteorological parameters. Results obtained from fuzzy logic expert system (FLES) are in good agreement with experimental real-time values. Besides, results are compared with the artificial neural network (ANN) based predictive model. Based on advantages such as tolerance of imprecise data and model flexibility, they suggested fuzzy model as a useful tool for predicting the global solar radiation.
Sivanesan et al.  forecasted the solar radiation using ANN with a fuzzy based preprocessing backpropagation model. Such a model overcomes disadvantages of a pure ANN-based model with its high accuracy in predicting the exact results.
Among various applications of fuzzy listed in Table 1, it is clear that major researchers worked with Mamdani FIS to predict, optimize, and control solar energy conversion devices.
The fuzzy logic expert system is mainly used in the modern control system for decision making based on feedback. In such a case, prediction accuracy of the fuzzy logic expert system becomes a primary factor to be concentrated. Future study of this paper includes the development of a performance control system for solar PV/T water collectors. So as a preliminary measure to select an effective decision-making system, this study compares the prediction accuracy of two fuzzy inference systems.
2 Experimental Setup
Figure 1 shows a fully covered PV/T water collectors' experimental setup. Its working component includes an ammeter (0–10 A) for measuring current, a voltmeter (0–120 V) for measuring voltage, a rheostat (250 Ω–1.8 A) for varying loads, and a storage tank (100 L) with an inlet and outlet. The PV module used in this work is made of polycrystalline silicon cells connected in series. Each PV/T system consists of an inlet and outlet.
Heat transfer fluid enters through the inlet and then using the thermosyphon effect leaves through the outlet. To have a high temperature at the outlet, the PV/T-1 system outlet is connected in series with a PV/T-2 system inlet. The rated power and voltage are 40 W and 22.2 V. The overall dimension of a series-connected PV/T module is 0.8174 m2. Two Mextech digital thermometers are used to measure inlet and outlet temperatures of incoming and outgoing heat transfer fluid temperature. An High Tech Corporation instrument noncontact type temperature sensor is used to measure the surface temperature of PV modules. A pyrometer (Gantner instrument) is used to measure the intensity of radiation. Table 2 presents the detailed technical specifications of series-connected PV/T water collectors under this study.
This PV/T experimental setup is installed on the rooftop of the solar thermal laboratory at Saranathan College of Engineering, Tiruchirappalli (10.7905°N, 78.7047°E). Experiments were conducted in May 2018. To reduce the rate of accumulation of dust, both PV/T modules are mounted in north-south direction sloping downward to the south at a tilt of 20 deg about the horizontal. The performance of the PV/T module is observed from 10.00 am to 4.00 pm at 60 min interval.
The initial process includes experimentation with a series-connected solar PV/T water collector test rig. Then, by the fuzzification process, such experimental outputs (datasets) are fuzzified to fuzzy quantities. Then, a set of rules framed based on human knowledge is applied over such fuzzified datasets. It is followed by the defuzzification process, in which fuzzy quantities are converted to precise datasets.
3 Formula Used
3.1 Quantitative Analysis
3.1.1 Overall PV/T Output.
where PO is the combined power output of PV/T (W).
3.1.2 Overall PV/T Efficiency.
3.2 Data Reduction.
Experiments are conducted to estimate the performance of series connected solar PV/T water collectors, but its measured quantities are subjected to uncertainties. Such uncertainties in the measurement are due to various errors  in observation. Such quantities are measured, and the probable errors in each of them are calculated in order to estimate the uncertainties associated with the experimental data.
Table 3 consists of calculated uncertainties for the quantities associated with this study.
4 Fuzzy Model
It is one of the various practical tools used for approximating nonlinearly varying dynamic systems based on real-time measured input and output variables. There are two types of FISs: (i) Mamdani FIS and (ii) Takagi Sugeno or Sugeno FIS. Figures 2 and 3 present the general architecture of both inference systems. Among the two fuzzy inference systems, Mamdani differs from Sugeno in terms of its output. Output membership functions of Sugeno are either constant or linear, while the output of Mamdani FIS is a fuzzy set.
It is the initial process of fuzzy modeling. It includes the art of converting any set of crisp inputs to a required fuzzy set or a specific fuzzy set toward a fuzzier set.
4.2 Membership Functions.
A technique to solve realistic problems by experience rather than ability is known as membership functions. The selection of the membership functions for fuzzification mainly depends on the event and type of membership function. In this model, the Gauss shaped membership function was employed to describe fuzzy sets for series-connected solar PV/T water collectors input variables and output variables. Among various polygonal membership functions (MF) available in fuzzy logic, this study uses Gauss shaped MF only. Both the trapezoidal and the Gaussian MF fall under the category polygonal MF. Advantages of such polygonal MFs are listed below
A small amount of data is needed to define the membership function.
Easy to modify values based on the measured input–output of a system.
The possibility of obtaining an input–output mapping of a model which is a hypersurface consisting of linear segments.
Polygonal membership functions mean the condition of a partition of unity (it means that the sum of membership grades for each value x amounts to 1) are easily satisfied.
Fuzzy logic is capable of predicting the results more accurately even with a less number of datasets, while the remaining prediction techniques require a large number of training datasets .
The input variable has been partitioned according to series-connected solar PV/T water collectors' experimental ranges. Membership functions for the fuzzy input are PV power output and FPC power output, while MF for fuzzy output is PV/T power output. Table 4 consists of fuzzy linguistic variables and fuzzy expression for input and output parameters. Eight membership functions were used as input and output, namely, low (L), low medium-1 (LM-1), low medium-2 (LM-2), medium-1(M-1), medium-2(M-2), medium high-1(MH-1), medium high-2(MH-2), and high (H) as listed in Table 5. Figures 4–7 present input and output membership functions of fuzzy architecture.
In specific, Fig. 4 represents how each point in the PV input space is mapped to membership value between 0 and 1. In the scalar form, the power output delivered by the PV part varies between 21 W and 53.20 W. Figure 4 also represents the mapping of real-time scalar values to fuzzy values using eight linguistic variables.
Similarly Fig. 5 represents how each point in the FPC input space is mapped to membership value between 0 and 1. In the scalar form, the power output delivered by the FPC part varies between 38.19 W and 194.93 W.
Figure 6 represents how each point in the PV/T output (Mamdani) space is mapped to membership value between 0 and 1. In the scalar form, the power output delivered by the FPC part varies between 59.29 W and 245.33 W, while Fig. 7 represents how each point (as constant) in the PV/T output (Sugeno) space is mapped to membership value between 0 and 1. The output membership functions of Sugeno are either constant or linear.
4.3 Rules of Fuzzy.
It is an event or activity that includes a series of steps taken for selecting the most suitable alternative as a means to attain individual goals . A set of eight rules were constructed based on experimental values for Mamdani FIS and another eight rules for Sugeno FIS with standard input rules and different output rules. Table 6 lists different rules for FIS. Preliminary results were simulated using matlab 2016a software based on Sugeno and Mamdani fuzzy logic.
This process includes the procedure for converting quantities of fuzzy into a precise value. The different methods of defuzzification are centroid method, max-membership method, mean-max membership, and weighted average method. Because of its additional advantages , the rapid response centroid defuzzification method is used in this model. This method is also known as the center of gravity method or the center of the area. In this rapid response centroid defuzzification method, the resultant member function is created by referring to the output of each rule. It means that the overlapping area of the fuzzy output set is connected as one, thus providing more results. Figure 4 shows the power output of series-connected PV/T water collectors' concerning changes with PV and FPC. As the output of PV and FPC increases, the power output of series-connected PV/T increases, and when the output of PV and FPC decreases, the series-connected power output of PV/T decreases.
4.5 Investigating the Fuzzy Model Error and Accuracy.
5 Results and Discussion
Real-time experiments are conducted with series-connected solar PV/T water collector test rig at Saranathan College of Engineering, Tiruchirappalli (10.7905°N, 78.7047°E). This series-connected test rig is capable of generating higher performance than stand-alone solar PV/T water collector test rig proposed by Sridharan et al. . Such an increased performance (power output and efficiency) is obtained by integrating two stand-alone solar PV/T water collector test rigs.
As a mean of such integration, electrical power output increased by 48.12% and thermal power output increased by 30.13% than . Specifically, an increase in both electrical and thermal performance is due to the increased contact surface area (50% higher than ) of the PV/T water collector. Figure 1 represents such a series integrated PV/T system. Variations in electrical and thermal performance by this series-connected solar PV/T water collector are discussed in Secs. 5.1.1–5.1.3.
5.1.1 Electrical Part
126.96.36.199 Power output.
From Table 7, it is clear that the variation in electrical power output ranges between 21 W (±0.2608%) and 53.2 W (±0.2608%). The average electrical power output (per day) of the setup under the study is 44.07 W (±0.2608%). A uniform variation in electrical power output of a PV module is observed due to the maintenance of its optimal operating temperature by heat transfer fluid, which conducts heat.
From Table 7, it is clear that the variation in electrical efficiency is between 6.19% (±0.00546%) and 9.72% (±0.00546%). The average electrical efficiency (per day) of the setup under the study is 7.71% (±0.00546%). A uniform variation in the electrical efficiency of the PV module is observed due to its bonding on FPC.
5.1.2 Thermal Part
188.8.131.52 Power output.
From Table 8, it is clear that the variation in thermal power output is between 38.29 W (±0.056%) and 194.93 W (±0.056%). The average thermal power output (per day) of the setup under the study is 116.86 W (±0.056%).
From Table 8, it is also clear that the variation in thermal efficiency is between 3.70% (±0.267%) and 27.19% (±0.267%). The average thermal efficiency (per day) of the setup under the study is 13.88% (±0.267%). A nonuniform variation in thermal efficiency is due to the transient state of irradiance (due to rapid movement of occasional clouds).
5.1.3 Hybrid PV/T System
184.108.40.206 Power output.
From Table 5, it is clear that the variation in overall combined efficiency is between 9.89% (±0.2726%) and 36.91% (±0.2726%). The average overall combined efficiency (per day) of the setup under the study is 21.59% (±0.2726%). Figure 9 presents variations in electrical, thermal, and PV/T efficiencies.
5.2 Fuzzy Model.
Besides the real-time experiments, two different FISs for predicting the performance of a series-connected rig are proposed. The primary objective of these proposed two FISs is to predict the power output of the series-connected PV/T system more accurately than .
For this, the number of linguistic variables is increased than by Sridharan et al. . This study proposed a Sugeno based FIS, which is the first of its kind in the solar energy field for performance prediction. Section 5.2.1 includes discussion on the effects of such linguistic variables.
These two Mamdani and Sugeno FISs require real-time experimental datasets for their modeling. Real-time experimental values from Table 5 are observed from 10.00 h to 04.00 h, respectively.
5.2.1 Mamdani Fuzzy Inference System.
Mamdani predicted series-connected PV/T results varied between minimum values of 62.5 W to a maximum of 240 W. Such a predicted overall (combined) power output was observed which is close to the measured power output with an accuracy of 95.67%. Table 4 presents the results of individual and overall accuracy percentage. Figure 8 represents the variations in Mamdani FIS predicted results with experimental results.
5.2.2 Sugeno Fuzzy Inference System.
Sugeno predicted series-connected PV/T results varied between minimum values of 59.30 W to a maximum of 245 W. Such a predicted overall (combined) power output was observed in closer to the measured power output with an accuracy of only 99.92%. Results of individual and overall accuracy percentages are listed and calculated from Tables 9 and 10. Figure 8 represents the variations in Sugeno FIS predicted results with experimental. Such a value assures that the proposed model can satisfactorily predict the power output of series-connected PV/T water collectors.
In this study, the performance of a series-connected solar PV/T water collector system is predicted using two fuzzy inference systems. From the predicted results of two individually developed fuzzy inference systems, the following conclusions are obtained:
The increase and decrease in series-connected PV/T power output depending on its PV power output and FPC power output.
An increase in the contact surface area by 50% (than stand-alone rig), increases electrical performance by 48.12% and thermal performance by 30.13%. As a whole, the increment of 78.25% is observed.
The prediction accuracy of both Mamdani and Sugeno systems depends on the number of linguistic variables. A model with an increased number predicts accurate experimental output than lower.
The previous study  with only four linguistic variables is capable of predicting the performance of the system with an accuracy of 94.26%. Performance prediction accuracy of Mamdani FIS with eight linguistic variables is capable of predicting the performance with an accuracy of 95.67%. Thus, an increase in linguistic variables increases the overall accuracy of the fuzzy model.
For the same eight linguistic variables, the performance prediction accuracy of Sugeno FIS is 99.92%.
- AFPC =
flat plate collector area (m2)
- Ain =
individual accuracy (%)
- AO =
overall model accuracy (%)
- APV =
PV module area (m2)
- APV/T =
PV/T module area (m2)
- Cp =
specific heat of water (J/kg K)
- er =
- FF =
- G =
- IL =
load current (A)
- Isc =
short-circuit current (A)
- m =
mass flow rate (kg/s)
- PE =
electrical power (W)
- PO =
overall power output (W)
- PT =
thermal power output (W)
- Ta =
ambient temperature (°C)
- Tfi and Tfo =
fluid inlet and outlet temperature (°C)
- VL =
load voltage (V)
- Voc =
open-circuit voltage (V)
- ΔT or dt =
difference between Tfi and Tfo (°C)
- ηE =
electrical efficiency (%)
- ηPV/T or ηo =
PV/T efficiency or overall efficiency (%)
- ηT =
thermal efficiency (%)
- μ =
degree of membership (dimensionless)
- σx =