# Designing a Solar Photovoltaic System for Generating Renewable Energy of a Hospital: Performance Analysis and Adjustment Based on RSM and ANFIS Approaches

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## Abstract

**:**

^{2}, the module surface temperature is 41.4 °C, the outdoor temperature is 36.2 °C, the wind direction and speed are 305.6 and 6.7 m/s, respectively. The ANFIS model (with nine rules) gave the highest performance with lowest residual for the same design parameters. Hence, it was determined that the hourly electrical energy requirement of the hospital can be met by the PV system during the year.

## 1. Introduction

^{2}per year which is acceptably higher when compared to some countries heavily investing in solar energy generation technologies. During the summer seasons, the electricity need reaches its peak load, which is twice higher than in the winter. Therefore, it is worthwhile to generate clean solar PV energy via sunlight [4]. In Saudi Arabia, the electricity consumption is estimated to exceed 40 GW nowadays and reach 120 GW per hour until the year 2028. The electricity consumption of industrial and service sectors is increasing about 6.9% per year mainly due to the investments and capacity expansions. This growth will require more fossil fuel consumption and eventually release a higher amount of CO

_{2}into the atmosphere. Although the Kingdom’s annual solar irradiance is about 2000–2450 kWh/m

^{2}, the availability of immense empty lands and ideal locations for solar installations and PV generation [4]; the renewable energy share of Kingdom is still less than 0.1%, compared to 14% share of the rest of the world [5]. In this context, Alnaser and Alnaser [6] claimed that only 0.1% of Kingdom’s land is sufficient for the solar PV projects to meet the electricity demand estimated for 2050. Many countries are interested in reliable, sustainable, suitable, and diversified energy sources, and technologies due to the pros and cons of non-renewable energy sources and technologies. The challenging problem for a country is the determination of the proper energy sources and technologies for the public and private investments. Although Saudi Arabia has wind, and geothermal resources that can solve all energy demand in the future, the new PV technologies are more productive and can generate more energy efficiently. This study also aims to encourage government bodies and private organizations to invest in solar PV energy generation systems for achieving sustainable energy infrastructure.

^{2}. Mohammadi et al. (2016) [36] developed and employed an ANFIS model to identify the solar radiation relevant parameters and predict the daily level of solar radiation. The results revealed that the climate conditions influence the solar radiation characteristic which is not identical for all locations. Aldair et al. (2018) [37] validated the effectiveness of ANFIS for tracking the maximum power point tracking (MPPT) approach in a stand-alone PV system. The results indicated that the ANFIS model controllers are more efficient and give better dynamic responses than the incremental conductance method and constant voltage method. Khosravi et al. (2020) [38] investigated the ANFIS and genetic algorithm combination and based on teaching-learning optimization algorithms and determined the optimum design parameters of different 100 MW solar power stations with a molten salt storage system.

^{2}, surface temperature 25 °C and air mass (A.M.) 1.5 as ideal conditions, the reality is different; these parameters do not always represent the optimal field circumstances in which the PV panel operates [13]. In this study, to determine the optimal solar PV energy generating conditions and the panel performance, as a statistical and mathematical approach RSM was employed for modeling and analysis of this complex problem. As it was clearly stated, the response (the amount of solar PV energy generated) is affected by several factors. However, the response (PV generated) and the independent parameters’ relations are not usually clearly known. On the other hand, the response cannot be formed well by linear approximations due to the complexity of problems, therefore higher degree polynomials might be employed.

^{2}), outdoor temperature (°C), and wind direction. The RSM aimed to find out the optimal operating conditions of the solar PV panels and the factor space operating intervals required for the PV panel system. Our investigations depicted that generating maximum solar PV of 42.27 MW is possible for the KAU hospital, if the radiation level is about 896.3 W/m

^{2}, the module surface temperature is 50.0 °C, the outdoor temperature is 40.3 °C, the wind direction is 305.6 and the wind speed is 6.7 m/s. On the other hand, the operation conditions of solar PV panels were simulated under different conditions, for instance, it was determined that obtaining a 33.96 MW solar PV system, the radiation should be 896.3, the module surface temperature should be 43.4 °C, the outdoor temperature should be 40.3 °C, the wind direction should be 305.9 and the wind speed should be 6.7 m/s.

## 2. Materials and Methods

#### 2.1. Solar Energy Generation Design for KAU Hospital

#### 2.2. The Solar Power Plant Types

#### 2.3. PV System Design

#### 2.3.1. Determining the Hourly Distribution of the Energy Consumption of the Harran University Hospital

- The maximum energy consumption of HUH is in July.
- Electricity consumption is the highest in 4 months (summer period) from June to September,
- Electricity consumption is the lowest in the period of 6 months (winter period) from November to April,
- The electricity consumption profiles of an average day obtained for May and October are similar to the consumption profile obtained for an average day determined according to annual data.

#### 2.3.2. Determining the Load Profile of the Energy Consumption of the Harran University Hospital

_{hour}and annual/monthly average hourly energy need with Q

_{average}. According to the 2019 data of HUH, the daily average electrical energy consumption profile for 2019 is presented in Figure 6.

#### 2.3.3. The Hourly Energy Consumption Distribution of the KAU Hospital

_{hour}) of KAU hospital was calculated according to following equation:

^{2}solar radiation and 25 °C outdoor temperature conditions.

## 3. Solar PV System Analysis and Performance Prediction

#### 3.1. Data Collection and Analysis

^{2}), module surface temperature (°C), wind speed (m/s), outdoor temperature (°C), and wind direction which were gathered from Harran University solar power plant located in the university campus. Wind direction measurement is expressed with an angle showing 0° of the north, 90° of the east, 180° of the south and 270° of the west. Historical data for the (37.158/39.007) [Lat/Lon] of variabilities of solar resources were obtained from monitoring stations located in Sanliurfa, Turkey. A comprehensive statistical analysis was conducted to determine the multicollinearity to show the intercorrelation between the independent factors. The findings showed that the module surface temperature and outdoor temperature are highly related to the remaining independent variables. The ‘P, F, t and VIF’ tests indicated the availability of redundant information among the independent variables, and weak linear relations, the interactions of predictors may be nonlinear, and the nonlinear relations can be dealt with RSM, ANFIS and simulation approaches.

#### 3.2. RSM for Optimization of Solar PV System

_{1}), module surface temperature (x

_{2}), outdoor temperature (x

_{3}), wind direction (x

_{4}) and wind speed (x

_{5}) were established according to the following equation.

_{jj}, $\mathrm{and}{\beta}_{ij}$ represent the overall mean effect, the effect of the j-th level of the row factor, the effect of the j-th level of column factor, and the effect of the interaction effect in the quadratic model, respectively. ${\in}_{ijk}$ is a random error component of a second order RSM, where ${y}_{ijk}$ is the response and refers to the solar PV generation level in this study. x

_{i}and x

_{j}present the variables that are called factors. Dirnberger and Kraling (2013) [42] described the measurement procedure and uncertainty analysis which covers the complete daily calibration process of measurement devices in detail, the correction to standard testing conditions, and determination of electrical module parameters. They presented recent progress in reducing the measurement uncertainty for crystalline silicon and thin-film PV modules.

_{1}, x

_{2}, x

_{3}, x

_{4}and x

_{5}. The interactions between the parameters x

_{1}x

_{2}, x

_{1}x

_{3},… are presented in the regression model with the coefficients presented above in the model.

#### 3.3. ANFIS Approach for PV Efficiency Estimation and Analysis

_{k}) to show the solar PV model outcome for the output layer. Hence, the ANFIS model has a total of sixty eight nodes arranged with thirty linear and fifty nonlinear parameters corresponding to the five input parameters.

^{2}; x

_{1}), module surface temperature (°C; x

_{2}), outdoor temperature (°C; x

_{3}), wind direction (x

_{4}), and wind speed (m/s; x

_{5}) and the outcome parameter of network is the PV generated (P

_{k}). The input-hidden and hidden-output layers’ coefficients called weights are presented by ${w}_{ij}$ and ${w}_{jk}$, correspondingly. The following equation was used to calculate the k-th neuron’s outcomes in the hidden layer.

_{k}) outcomes presented in Equation (8). The learning constant value η was set up as 0.25, 0.50, and 0.70 as given in the following equation.

_{k}) and the predicted outcomes (P

_{k}) are presented in the equation given above. The (E) shows the error estimator, is a squared error minimization function and called the Least-Squares Estimator (LSE). For specifying Gaussian membership functions (MFs), two parameters (c, σ) are used; the center ‘c’ of MFs and the width ‘σ’ of MFs are used for identifying the MFs.

_{4})’.

_{n}= f

_{n}(x

_{1}, x

_{2},…, x

_{m}) is the consequent part of the fuzzy rule. The input parameters (x

_{1}, x

_{2},…, x

_{m}) are depicted as polynomial functions f

_{n}(x

_{1}, x

_{2},…, x

_{m}), and r

_{n}is the constant, presented as follows:

_{1}is B and x

_{2}is C …… THEN y

_{n}= f

_{n}(x

_{1}, x

_{2},…, x

_{m}) = b

_{n}x

_{1}+ c

_{n}x

_{2}+ d

_{n}x

_{3}+ …k

_{n}x

_{m}+ r

_{n}

**Rule**

**1.**

^{2}) and the module surface temperature is 28 °C AND the outdoor temperature is 31.2 °C AND the wind direction is 180. AND the wind speed is 2.92 m/s THEN The amount of PV energy generated is (kWh) = 4.575x

_{1}− 14.39x

_{2}+ 14.13x

_{3}− 0.0469x

_{4}− 6.22x

_{5}+ 339.4934 (1490 kWh).

**Rule**

**2.**

^{2}) and the module surface temperature is 26.7 °C AND the outdoor temperature is 15.6 °C and the wind direction is 134. AND the wind speed is 3.22 m/s THEN The amount of PV energy generated is (kWh) = 6.785x

_{1}− 65.26x

_{2}+ 25.35x

_{3}− 0.574x

_{4}− 67.35x

_{5}− 275.995 (363 kWh).

## 4. Results and Discussions for Solar PV System Findings

#### 4.1. The Assessment of PV System Simulation

#### The Assessment of Solar PV Module Using RSM Approach

^{2}. Figure 16c,d shows the three-dimensional graph called response surface plot of solar PV energy generation versus wind speed, outdoor temperature, and radiation.

^{2}, the module surface temperature is 50 °C, the outdoor temperature is 40.3 °C, the wind direction is 305.6 and the wind speed is 6.7 m/s.

_{1}, x

_{2}, x

_{3}, x

_{4}and x

_{5}and the interactions x

_{1}x

_{2}, x

_{1}x

_{3}, x

_{1}x

_{4}and etc are presented in the regression model. The effects of interactions and main factors showed that four factors positively affect the solar PV generation, only wind direction negatively affected it. Our investigation showed that the coefficients of x

_{1}x

_{2}, x

_{1}, x

_{1}x

_{2}, x

_{1}

^{2}and x

_{1}

^{2}are very small, hence these interactions can be bounded. The effects of interactions and the main parameters are plotted in Figure 17 and Figure 18, respectively. Four effects are positive in this equation, only wind direction has a negative effect. Hence all main effects are only considered to determine the optimal level and maximize the solar PV level.

#### 4.2. The Assessment of Performance of Developed Models Using ANFIS Approach

^{2}, the module surface temperature is 28 °C, the outdoor temperature is 31.2 °C, the wind direction is 180 and the wind speed is 2.92 m/s, then according to ANFIS approach, the PV module can generate 14.90 MW power.

^{2}, the module surface temperature is 48.56 °C, the outdoor temperature is 38.70 °C, the wind direction is 278.39 and the wind speed is 4.42 m/s, the ANFIS model predicts the PV panels’ performance to be 24.96 MW. Similarly, it is also predicted by the ANFIS approach that the PV module can generate 41.19 MW power when the radiation is 750 W/m

^{2}, the module surface temperature is 25 °C, the outdoor temperature is 20 °C, the wind direction is 250 and the wind speed is 12.43 m/s.

#### 4.3. Comparison of the Results with the Cases Introduced by Other Works

^{2}for 32 fuzzy rules and 129.13 for 243 fuzzy rules models, and the correlation coefficients were found to be 0.923 and 0.905 for these models, respectively. Mohammadi et al. (2016) [36] developed an ANFIS model for solar radiation based on RMSE during training and testing phases with 1, 2 and 3 fuzzy input parameters. They found that when the number of inputs is increased, the RMSE decreases, and the prediction accuracy enhances. Similarly, in our study, three ANFIS models were developed including five, nine and eleven fuzzy rules based on the sub clustering algorithm. The RMSE of ANFIS model with nine rules gave the best results with minimum error of solar PV generation. The results are presented in Table 3 for comparison. The RMSE was found to be 66.98 for the training process of ANFIS model with nine fuzzy rules, and RMSE was found at 113.52 for ANFIS model with nine rules, and 68.47 for the ANFIS model with eleven fuzzy rules. Aldair et al. (2018) [37] developed ANFIS controllers to determine the stand-alone PV system for which two input variables: the radiation and temperature were considered for the ANFIS model development. The difference between our model and Aldair’s [37] model is that our model was established based on more variables.

## 5. Conclusions

- A solar PV system with a capacity of 35 MW and/or more will be sufficient for the KAU hospital and meet the electrical energy demand of the hospital;
- For a PV system of 40 MW capacity, the maximum electricity generation is approximately between 26 and 31 MWh. Hence, the hourly maximum electrical energy requirement of the hospital between 11:00 and 15:00 h can be met by the PV system during all months;
- In all PV designs and simulation tests, the highest electrical energy production during the year was observed in March;
- The self-sufficiency ratio for March was 31% for PV25, 37% for PV30, 43% for PV35, 50% for PV40, 56% for PV45, 62% for PV50, 93% for PV75 and 124% for PV100;
- The self-sufficiency ratio for the yearly period was found as 24% for PV25, 29% for PV30, 34% for PV35, 39% for PV40, 44% for PV45, 48% for PV50, 73% for PV75 and 97% for PV100.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**Monthly and yearly average distribution of the electricity consumption of Harran University hospital.

**Figure 6.**Average daily electrical energy consumption profile of Harran university hospital for 2019.

**Figure 8.**The comparison of monthly electricity generated from both PV-GIS and Solar-GIS programs for a 25 MW PV system.

**Figure 11.**Average hourly profiles of total photovoltaic power output for; (

**a**) 25 MW of PV capacity, (

**b**) 35 MW of PV capacity, (

**c**) 45 MW of PV capacity.

**Figure 12.**Average hourly profiles of total photovoltaic power output in March for 25 MW of PV capacity, 35 MW of PV capacity and 45 MW of PV capacity.

**Figure 13.**The ratio of PV systems meeting the hourly electricity need of the hospital (

**a**) 25 MW of PV capacity, (

**b**) 35 MW of PV capacity, (

**c**) 45 MW of PV capacity.

**Figure 16.**The contour plot of solar PV generation versus wind speed and outdoor temperature (

**a**) and wind speed and radiation (

**b**). The three-dimensional graph of solar PV energy generation versus wind speed, outdoor temperature (

**c**), and wind speed radiation (

**d**).

PV25 | PV30 | PV35 | PV40 | PV45 | PV50 | PV75 | PV100 | |
---|---|---|---|---|---|---|---|---|

January | 0.22 | 0.27 | 0.31 | 0.36 | 0.40 | 0.45 | 0.67 | 0.90 |

February | 0.19 | 0.23 | 0.27 | 0.31 | 0.35 | 0.39 | 0.58 | 0.78 |

March | 0.26 | 0.31 | 0.36 | 0.41 | 0.47 | 0.52 | 0.78 | 1.03 |

April | 0.27 | 0.32 | 0.37 | 0.42 | 0.48 | 0.53 | 0.80 | 1.06 |

May | 0.31 | 0.37 | 0.43 | 0.50 | 0.56 | 0.62 | 0.93 | 1.24 |

June | 0.24 | 0.29 | 0.33 | 0.38 | 0.43 | 0.48 | 0.72 | 0.96 |

July | 0.25 | 0.29 | 0.34 | 0.39 | 0.44 | 0.49 | 0.74 | 0.98 |

August | 0.26 | 0.31 | 0.36 | 0.41 | 0.46 | 0.51 | 0.77 | 1.02 |

September | 0.25 | 0.30 | 0.36 | 0.41 | 0.46 | 0.51 | 0.76 | 1.01 |

October | 0.23 | 0.28 | 0.33 | 0.37 | 0.42 | 0.46 | 0.70 | 0.93 |

November | 0.22 | 0.27 | 0.31 | 0.36 | 0.40 | 0.45 | 0.67 | 0.90 |

December | 0.23 | 0.27 | 0.32 | 0.36 | 0.41 | 0.45 | 0.68 | 0.90 |

Yearly | 0.24 | 0.29 | 0.34 | 0.39 | 0.44 | 0.48 | 0.73 | 0.97 |

Radiation-(W/m^{2}) | Module Surface Temperature-(°C) | Outdoor Temperature-(°C) | Wind Direction | Wind Speed-(m/s) | Actual PV (MW) | Predicted PV by ANFIS (MW) | Predicted PV by RSM (MW) |
---|---|---|---|---|---|---|---|

896.33 | 43.73 | 26.16 | 232.64 | 3.63 | 19.98 | 19.98 | 19.99 |

826.38 | 41.64 | 25.05 | 235.65 | 3.33 | 21.01 | 22.00 | 21.22 |

658.68 | 37.27 | 28.08 | 59.63 | 3.02 | 19.93 | 19.95 | 19.94 |

589.66 | 49.96 | 39.08 | 262.91 | 3.35 | 24.95 | 24.96 | 24.93 |

573.58 | 48.56 | 38.70 | 278.39 | 4.42 | 25.64 | 25.64 | 25.65 |

570.30 | 46.60 | 36.26 | 218.72 | 3.95 | 25.81 | 25.72 | 25.59 |

561.30 | 41.62 | 30.26 | 125.83 | 1.28 | 24.64 | 24.65 | 24.91 |

552.27 | 46.25 | 36.21 | 216.56 | 3.97 | 25.03 | 25.05 | 25.29 |

548.65 | 38.49 | 32.64 | 63.35 | 3.15 | 26.20 | 26.21 | 26.33 |

538.25 | 46.39 | 37.40 | 89.96 | 2.52 | 24.23 | 24.22 | 24.13 |

533.89 | 47.18 | 36.54 | 214.12 | 3.25 | 23.76 | 23.79 | 23.51 |

530.75 | 37.48 | 33.72 | 182.00 | 5.90 | 25.26 | 25.28 | 25.37 |

526.28 | 35.71 | 30.55 | 39.37 | 3.73 | 25.41 | 25.45 | 25.31 |

520.78 | 47.59 | 38.69 | 285.97 | 4.44 | 23.36 | 23.37 | 23.42 |

PV Model Power Output (Aldair et al.) [37] | Our PV Model Power Output | |||
---|---|---|---|---|

Radiation | Temperature (°C) | ANFIS (MW) | ANFIS (MW) | RSM (MW) |

500 | 0 | 33.36 | 46.14 | 48.50 |

500 | 25 | 27.72 | 34.78 | 35.23 |

500 | 50 | 22.58 | 32.02 | 30.61 |

750 | 0 | 51.4 | 56..12 | 52.98 |

750 | 25 | 43.6 | 47.78 | 41.19 |

750 | 50 | 35.98 | 36.86 | 34.53 |

1000 | 0 | 69.4 | 70.25 | 71.36 |

1000 | 25 | 59.1 | 58.17 | 60.88 |

1000 | 50 | 48.74 | 43.79 | 39.24 |

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**MDPI and ACS Style**

Alamoudi, R.; Taylan, O.; Aktacir, M.A.; Herrera-Viedma, E. Designing a Solar Photovoltaic System for Generating Renewable Energy of a Hospital: Performance Analysis and Adjustment Based on RSM and ANFIS Approaches. *Mathematics* **2021**, *9*, 2929.
https://doi.org/10.3390/math9222929

**AMA Style**

Alamoudi R, Taylan O, Aktacir MA, Herrera-Viedma E. Designing a Solar Photovoltaic System for Generating Renewable Energy of a Hospital: Performance Analysis and Adjustment Based on RSM and ANFIS Approaches. *Mathematics*. 2021; 9(22):2929.
https://doi.org/10.3390/math9222929

**Chicago/Turabian Style**

Alamoudi, Rami, Osman Taylan, Mehmet Azmi Aktacir, and Enrique Herrera-Viedma. 2021. "Designing a Solar Photovoltaic System for Generating Renewable Energy of a Hospital: Performance Analysis and Adjustment Based on RSM and ANFIS Approaches" *Mathematics* 9, no. 22: 2929.
https://doi.org/10.3390/math9222929