Keywords

1 Introduction

Renewable energy refers to the primary energy that can be continuously regenerated and used continuously from nature. It includes passive energy sources such as solar energy and shallow geothermal energy. They can replace conventional energy sources to a certain extent and become an important way to adjust energy structure [1] (Fig. 1).

Fig. 1
figure 1

Solar resource distribution map

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To study the suitability of solar energy utilization in public institutions across the country, it is necessary to take into account the national conditions of large land areas, different solar resource richness, significant climate differences, and different levels of economic development in various regions, combined with the energy consumption per unit area of different types of public institutions in different regions. To determine the suitability of solar energy utilization in public institutions, to draw a suitability map of solar energy utilization in public institutions, and to develop appropriate suitability software to provide a theoretical basis for the rational use of solar energy in public institutions across the country.

2 Principal Component Analysis

Above all, the selection of evaluation indicators is carried out. The evaluation index system consists of a series of indicators, which can comprehensively reflect the comprehensive situation of all aspects of the research object. According to the status quo and characteristics of solar energy application in China, we select the evaluation factors that can significantly affect the suitability of solar energy utilization in public institutions in various regions: (1) Solar energy resources: year total solar radiation; (2) Climatic conditions: the coldest month, the hottest month average temperature; (3) Economic situation: fixed assets investment in various regions; (4) Energy consumption: energy consumption per unit area of different types of public institutions across the country [2].

Principal component analysis can try to recombine the original indicators into a new set of relatively independent indicators that reflect the original indicators on the basis of maximally retaining the original data information [3]. Its mathematical model is as follows:

  1. (1)

    The standardized calculation formula for indicator data is

    $$x_{ij}^{*} = \frac{{x_{ij} - \overline{{x_{j} }} }}{{s_{j} }},\quad (i = 1,2, \ldots ,n;\;j = 1,2, \ldots ,p)$$
    (1)
  2. (2)

    Calculate the correlation coefficient matrix R of the indicator.

    $$R = \left( {r_{ij} } \right),r_{ij} = \frac{1}{n}\mathop \sum \limits_{k = 1}^{n} x_{ki}^{*} x_{kj}^{*} ,\quad (i = 1,2, \ldots ,p)$$
    (2)

    In the middle, rii = 1, rij =  rji, (i, j = 1, 2, 3…, p)

  3. (3)

    Calculate feature values and feature vectors.

  4. (4)

    Calculate the contribution rate and the cumulative contribution rate.

    $$d_{i} = \frac{{\lambda_{i} }}{{\mathop \sum \nolimits_{i = 1}^{p} \lambda_{i} }},\quad D_{m} = \frac{{\mathop \sum \nolimits_{i = 1}^{m} \lambda_{i} }}{{\mathop \sum \nolimits_{i = 1}^{p} \lambda_{i} }}$$
    (3)
  5. (5)

    Determine the number of principal components.

  6. (6)

    Calculate the principal component score and the composite score.

    $$F = \mathop \sum \limits_{i = 1}^{m} a_{i} y_{i} ,\quad (i = 1,2, \ldots ,m)$$
    (4)

In the middle, ai is the variance contribution rate of the i-th principal component, and yi is the i-th principal component score.

Therefore, the principal component analysis method is used to comprehensively analyze the suitability of solar energy utilization in public institutions across the country, the main components of the evaluation index system are screened out, the comprehensive score is obtained, and the degree of suitability is distinguished by the comprehensive level.

3 Fuzzy Clustering Analysis

Fuzzy clustering analysis is a kind of analysis of the fuzzy relationship between things or phenomena affected by many or more factors, and based on this, the similarity between samples is determined according to a certain degree of membership, and the similarity is high [3]. The fuzzy mathematics of the respective clusters of objects. After selecting the principal components by principal component analysis, the comprehensive scores of the principal components are classified according to the fuzzy clustering analysis method. Its mathematical model is as follows [4,5,6]:

  1. (1)

    In order to eliminate the influence of dimension on cluster analysis, it is necessary to standardize the data before using cluster analysis, so that each index value is unified in a certain range of common data characteristics.

$$x_{ij}^{*} = \frac{{x_{ij} - \bar{x}_{j} }}{{s_{j} }},\quad (i = 1,2, \ldots ,n;\;j = 1,2, \ldots ,m)$$
(5)
$$\overline{{x_{j} }} = \frac{1}{n}\mathop \sum \limits_{i = 1}^{n} X_{ij} ,\quad s_{j} = \sqrt {\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \left( {x_{ij} - \overline{{x_{ij} }} } \right)^{2} }$$
(6)

In the middle, Xij and sj are the mean and standard deviation of the j-th variable, respectively.

  1. (2)

    For the above-mentioned normalization matrix, calculate the similarity degree between each classification object and establish the fuzzy similarity matrix R = (rij). This process is also called calibration. Here, we choose the absolute value subtraction method calibration.

$$r_{ij} = \left\{ {\begin{array}{*{20}l} 1 \hfill & {{\text{when}}\,i = j} \hfill \\ {1 - c\mathop \sum \limits_{k = 1}^{m} \left| {x_{ik} - x_{jk} } \right|} \hfill & {{\text{when}}\,i \ne j} \hfill \\ \end{array} } \right.$$
(7)

where c is appropriately selected, the parameters may be 0.1, 0.2, …, and the fuzzy similar matrix R  = (rij) may be obtained.

  1. (3)

    The matrix R obtained from the established fuzzy similarity relationship is only a fuzzy similar matrix, and it is not necessarily transitive. In order to classify, it needs to be transformed into an equivalent matrix. Therefore, the transitive closure t(B) of R is obtained by the flat method, and t(B) is the equivalent matrix obtained.

$$t(B):R \to R^{2} \to R^{4} \ldots ,{\text{when}}\,R^{p} *R^{P} = R^{P} ,t(B) = R^{P}$$
(8)
  1. (4)

    After processing the original matrix into a fuzzy equivalence matrix through the above steps, select the appropriate k ∈ [0,1] and select the best partition result from the different partitioning results obtained by clustering different k values.

4 Research Process

4.1 Principal Component Analysis

Enter the initial evaluation index data matrix x to simulate in the software of Matlab, taking the solar energy suitability of colleges and universities as an example, the process is as follows:

figure a

The MATLAB programming simulation of principal component analysis was performed, and the simulation results were as follows:

figure b

The first three columns of the matrix represent the scores of the first three principal components of the original evaluation index, the fourth column represents the composite score of the principal component, and the last column represents the city code. The comprehensive score is positive, indicating that the city’s solar energy suitability is higher than the average level; the comprehensive score is negative, indicating that the city’s solar energy suitability is lower than the average. The higher the score, the more appropriate, the lower the corresponding score, the less appropriate.

4.2 Fuzzy Clustering Analysis

The scores of the first three principal components in the matrix of the above graph, which are the initial matrix x of MATLAB in the fuzzy clustering analysis method, are simulated as follows [7, 8]:

figure c

After the fuzzy clustering analysis MATLAB programming simulation, a 32 * 32 [0,1] distribution matrix can be obtained, the cities corresponding to the same distribution are divided into one region, and ten regions with different degrees of appropriateness can be obtained. Combined with the comprehensive scores of the principal components of each city obtained by principal component analysis, the average score of the principal components of each region is calculated, the solar energy suitability zoning is obtained, and the solar utilization suitability distribution map of the public institutions in the country is formed.

5 Research Results

  • University solar energy suitability (Fig. 2; Table 1).

    Fig. 2
    figure 2

    Solar energy suitability distribution map of universities

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    Table 1 Average scores of university solar energy districts
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6 Result Analysis

It can be seen from the above research results that because the energy consumption per unit area of different types of public institutions is different, the corresponding suitability distribution map is also different. The research on the suitability of solar energy utilization in public institutions across the country provides a theoretical basis for the rational use of solar energy in public institutions across the country.