# Predicting High or Low Transfer Efficiency of Photovoltaic Systems Using a Novel Hybrid Methodology Combining Rough Set Theory, Data Envelopment Analysis and Genetic Programming

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## Abstract

**:**

## 1. Introduction

## 2. An Overview of PV System

**Figure 1.**A diagram of a PV system [21].

#### 2.1. PV System

#### 2.2. Factors Influencing PV Systems

#### 2.3. Evaluating PV System Transfer Efficiency

## 3. Using DEA to Determine Efficiencies

_{o}($o=1,2,\mathrm{...},n$) be the DMU whose relative efficiency is to be maximized. The DEA model is displayed as LP as follows:

_{o}. Obviously, the maximum value (efficiency score), ${h}_{o}$, cannot exceed 1. If ${h}_{o}=1$, the DMU

_{o}is called the constant returns to scale (CRS) frontier [30]. There are two CCR models in practice. One minimizes input variables, and the other maximizes output variables. In this work, in order to obtain maximum energy efficiency, the maximized output variables of the CCR model are utilized to obtain the optimal value for the objective function, ${h}_{o}$.

## 4. Rough Set Theory and Genetic Programming

#### 4.1. Basic Concepts of Rough Set Theory

_{1},x

_{2},…,x

_{n}}), R is a finite set of attributes (features and variables), $V=\underset{r\in R}{\cup}{V}_{r}$, where V

_{r}is the domain of attribute r, and $f:U\times R\to V$ is an information function such that $f\left(x,r\right)\in {V}_{r}$ for all $x\in U$ and $r\in R$. In RST, highly accurate good-quality approximations are very important when extracting decision rules. Let $P\subseteq R$ and $X\subseteq U$, the lower approximation of X in S by P is denoted as $\underset{\_}{P}X$, and the upper approximation of X in S by P is denoted as $\overline{P}X$ and are derived as follows:

#### 4.2. Genetic Programming

## 5. The Proposed Hybrid Prediction Model

Items | Content |
---|---|

Population size | 400 |

Maximum number of generation | 1000 |

Function set | +, −, ×, ÷, sin, cos, exp, log constant |

Crossover rate | 0.8 |

Mutation rate | 0.02 |

## 6. Empirical Analysis

Variables | Description | Importance (obtained from RST) |
---|---|---|

X_{1} | Texture type | 0.6424 |

X_{2} | The output power of inverter | 0.5715 |

X_{3} | The selection of PV module | 0.4817 |

X_{4} | The number of inverter | 0.3914 |

X_{5} | The weights of PV module | 0.3367 |

X_{6} | The selection of inverter | 0.2893 |

X_{7} | PV module capacity | 0.2567 |

X_{8} | The selection of DC voltage | 0.2638 |

X_{9} | The location of PV setting | 0.2476 |

X_{10} | DMU (obtained from DEA) | － |

_{1}–X

_{9}) are significant (Table 2) because that the importance value of nine independent variables are greater than 0.2. It has not a clear criterion to determine the threshold value (importance value). Moreover, the nine independent variables (X

_{1}–X

_{9}) have high correlation to output variable (the low or high transfer efficiencies of PV systems). The correlation coefficient are greater than 0.6. Also, based on the opinion of experts in PV energy in Taiwan, these nine variables importantly influence for the transfer efficiency of PV systems.

_{10}). In applying DEA, input variables of DEA are the nine significant variables obtained in Step 2 and the output variable of DEA is PV system transfer efficiency. The DEA algorithm can be executed by LINGO software. Table 3 lists the DMU values of the PV systems. In Step 4, the significant independent variables obtained in Step 2 and DMU obtained in Step 3 are utilized as input variables for GP to predict the high or low level of PV system transfer efficiency. To demonstrate the effectiveness of the proposed hybrid model, some basic classification models such as K Nearest Neighbor (KNN), Naive Bayes (NB), SVM, ANN, and GP are utilized as benchmark models. The basic classification models belong to data-mining techniques and can obtain better prediction performance than traditional linear statistical method (e.g., linear regression) [8,10].

No | DMU | No | DMU |
---|---|---|---|

PV001 | 1.0000 | PV023 | 0.7735 |

PV002 | 0.9482 | PV024 | 0.8059 |

PV003 | 0.9879 | PV025 | 1.0000 |

PV004 | 0.8392 | PV026 | 1.0000 |

PV005 | 1.0000 | PV027 | 1.0000 |

PV006 | 1.0000 | PV028 | 1.0000 |

PV007 | 1.0000 | PV029 | 1.0000 |

PV008 | 1.0000 | PV030 | 0.6981 |

PV009 | 1.0000 | PV031 | 0.6417 |

PV010 | 0.6902 | PV032 | 0.6608 |

PV011 | 0.9215 | PV033 | 0.4919 |

PV012 | 0.5153 | PV034 | 1.0000 |

PV013 | 0.4955 | PV035 | 0.8274 |

PV014 | 0.9667 | PV036 | 0.4947 |

PV015 | 0.7484 | PV037 | 0.8405 |

PV016 | 1.0000 | PV038 | 0.9944 |

PV017 | 0.6144 | ||

PV018 | 0.8630 | ||

PV019 | 1.0000 | ||

PV020 | 0.8630 | ||

PV021 | 1.0000 | ||

PV022 | 0.8832 |

_{1}–X

_{9}, as the input variables for GP (model II). In both models I and II, this work adopts leave-one-out cross validation to test the accuracy of the prediction model.

Actual class | Classified class | |
---|---|---|

1 (High-level) | 2 (Low-level) | |

1 (High-Level) | 22 (95.65%) | 1 (4.35%) |

2 (Low-Level) | 2 (13.33%) | 13 (86.67%) |

Actual class | Classified class | |
---|---|---|

1 (High-level) | 2 (Low-level) | |

1 (High-Level) | 21 (91.30%) | 2 (8.70%) |

2 (Low-Level) | 4 (26.67%) | 11 (73.33%) |

Actual class | Classified class | |
---|---|---|

1 (High-level) | 2 (Low-level) | |

1 (High-Level) | 20 (86.96%) | 3 (13.04%) |

2 (Low-Level) | 4 (26.67%) | 11 (73.33%) |

Actual class | Classified class | |
---|---|---|

1 (High-level) | 2 (Low-level) | |

1 (High-Level) | 20 (86.96%) | 3 (13.04%) |

2 (Low-Level) | 5 (33.33%) | 10 (66.67%) |

Actual class | Classified class | |
---|---|---|

1 (High-level) | 2 (Low-level) | |

1 (High-Level) | 21 (91.30%) | 2 (8.70%) |

2 (Low-Level) | 5 (33.37%) | 10 (66.67%) |

Actual class | Classified class | |
---|---|---|

1 (High-level) | 2 (Low-level) | |

1 (High-Level) | 19 (82.61%) | 4 (17.39%) |

2 (Low-Level) | 5 (33.33%) | 10 (66.67%) |

Actual class | Classified class | |
---|---|---|

1 (High-level) | 2 (Low-level) | |

1 (High-Level) | 19 (82.61%) | 4 (17.39%) |

2 (Low-Level) | 5 (33.33%) | 10 (66.67%) |

Actual class | Classified class | |
---|---|---|

1 (High-level) | 2 (Low-level) | |

1 (High-Level) | 18 (78.26%) | 5 (21.74%) |

2 (Low-Level) | 5 (33.33%) | 10 (66.67%) |

Actual class | Classified class | |
---|---|---|

1 (High-level) | 2 (Low-level) | |

1 (High-Level) | 19 (82.61%) | 4 (17.39%) |

2 (Low-Level) | 5 (33.33%) | 10 (66.67%) |

Actual class | Classified class | |
---|---|---|

1 (High-level) | 2 (Low-level) | |

1 (High-Level) | 19 (82.61%) | 4 (17.39%) |

2 (Low-Level) | 6 (40%) | 9 (60%) |

Model | Computational time |
---|---|

Model I (RST-DEA-GP) | 65.13 |

Model II (RST-GP) | 62.34 |

Model III (RST-DEA-SVM) | 60.17 |

Model IV (RST-SVM) | 56.49 |

Model V (RST-DEA-ANN) | 63.28 |

Model VI (RST-ANN) | 60.67 |

Model VII (RST-DEA-KNN) | 55.23 |

Model VIII (RST-KNN) | 53.28 |

Model IX (RST-DEA-NB) | 54.87 |

Model X (RST-NB) | 52.81 |

Model XI (GP) | 51.78 |

Model XII (SVM) | 50.46 |

Model XIII (ANN) | 51.39 |

Model XIV (KNN) | 48.23 |

Model XV (NB) | 46.26 |

## 7. Conclusions

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**MDPI and ACS Style**

Lee, Y.-S.; Tong, L.-I. Predicting High or Low Transfer Efficiency of Photovoltaic Systems Using a Novel Hybrid Methodology Combining Rough Set Theory, Data Envelopment Analysis and Genetic Programming. *Energies* **2012**, *5*, 545-560.
https://doi.org/10.3390/en5030545

**AMA Style**

Lee Y-S, Tong L-I. Predicting High or Low Transfer Efficiency of Photovoltaic Systems Using a Novel Hybrid Methodology Combining Rough Set Theory, Data Envelopment Analysis and Genetic Programming. *Energies*. 2012; 5(3):545-560.
https://doi.org/10.3390/en5030545

**Chicago/Turabian Style**

Lee, Yi-Shian, and Lee-Ing Tong. 2012. "Predicting High or Low Transfer Efficiency of Photovoltaic Systems Using a Novel Hybrid Methodology Combining Rough Set Theory, Data Envelopment Analysis and Genetic Programming" *Energies* 5, no. 3: 545-560.
https://doi.org/10.3390/en5030545