The power generation of distributed power generation systems in regional power grids is mainly affected by external environmental factors, and there are volatility and intermittent power generation issues. This paper establishes a relatively simple multiple linear regression prediction model to predict gridconnected photovoltaic power generation systems. The article uses a hybrid modelling method to filter more important weather forecast input variables through a stepbystep linear regression method to realize the visual calculation of power data. The research results show that the multiple linear regression equation methods proposed in the article have pervasive application value in the actual application of solar photovoltaic power consumption data.
Keywords
 regional power grid
 multiple linear regression
 power data visualization
 photovoltaic power generation data
MSC 2010
 62J05
The rapid development of society and the economy has led to a sharp increase in energy consumption, increasingly depleted fossil energy sources, and increased environmental pollution. This poses a severe threat to the ecological balance of the earth and the survival of humankind. Largescale photovoltaic power plants are an effective way to meet human demand for energy. Because photovoltaic power generation is affected by solar radiation intensity, battery component temperature, weather, cloud cover, and some random factors, the system operation process is an unbalanced random process. Its power generation and power output are highly random, fluctuating, and uncontrollable. This is particularly prominent when the weather changes suddenly. This kind of power generation inevitably brings a series of problems to the safety and management of the power grid after it is connected to the power grid [1]. Therefore, it is imperative to predict the output of the photovoltaic system accurately. At present, there are several types of prediction models for the power generation of photovoltaic power generation systems, such as neural network models, radial basis function models, and multilayer perception models. In addition, the photovoltaic system is a typical grey system with partly clear and partly unknown information [2]. Grey theory forecasting models have a wide range of applications in power planning and load forecasting. Because these models are relatively complex, this paper establishes a relatively simple multiple linear regression prediction model to predict the power generation of gridconnected photovoltaic power generation systems.
Photovoltaic power generation uses the photovoltaic effect of the P–N junction to convert light energy into electrical energy. The equivalent circuit of its components and system under ideal conditions is shown in Figure 1. The maximum output power is represented as follows:
Here,
Here,
The performance of monolithic silicon solar cell modules is mainly affected by radiation intensity and temperature. Battery’s output power and power generation also strongly depend on both these factors. The shortcircuit current is proportional to the radiation intensity within several orders of magnitude and is proportional to the lightreceiving area of the battery [4]. The opencircuit voltage tends to saturate quickly with radiation, regardless of the battery area. The fill factor does not have a simple, functional relationship with the radiation amount. The opencircuit voltage, fill factor, and output power all decrease with an increase of component temperature. The temperature coefficients are −2.3 mV/°C, −0.0015/°C and −(0.004–0.005) W/°C, respectively. As the temperature of the components increases, the shortcircuit current also increases slightly. The temperature coefficient is +0.107 mA/°C. Therefore, the output power of the photovoltaic system can be expressed as a function of the radiation intensity and temperature:
Here,
In the equation,
Among them,
Therefore, the output power can be expressed as
Here,
The general form of the multiple linear regression model is
We perform Taylor series expansion on the term
In this expression,
Then, Eq. (11) can be changed to
Here,
We substitute Eq. (12) into Eq. (13) to get
Here, –
The photovoltaic system consists of 18 Kyocera KC130GH2P polysilicon solar cell modules connected in series. The parameters of the singlepiece components are shown in Table 1.
Kyocera KC130GH2P polysilicon module parameters
Polysilicon  130  17.6  7.39  21.9  8.02  0.81 
We calculate the relationship between the opencircuit voltage
When the component’s temperature does not change, there is a logarithmic relationship between the opencircuit voltage and the amount of radiation. When the radiation becomes >500 W/m^{2}, the opencircuit voltage tends to a particular value. There is a linear relationship between the shortcircuit current and the amount of radiation, and there is also a linear relationship between output power and radiation [9]. When the temperature of the component gradually increases, the output power decreases significantly. Therefore, photovoltaic modules should be kept in as lowtemperature working environments as possible.
We tested the 2 kW gridconnected photovoltaic system for several months. The test system is shown in Figure 3. We collected data after installing the test equipment according to the requirements of the instrument. The test parameters are as follows: radiation intensity (
We process classified and unclassified (IV) test data. The weather is classified into three categories: sunny (I), cloudy (II) and sunny to cloudy (or overcast to cloudy) (III). Then, we perform linear regression on the classified and unclassified test data. The regression results are shown in Tables 2–4.
Regression statistics
0.997415  0.99715  0.99652  0.99667  
0.994838  0.99431  0.99314  0.99336  
0.98404  0.98545  0.98373  0.99026  
Standard error, %  10.61  9.11  9.99  10.34 
3051.26  3379.02  2,652.47  8,301.23  
Significance value  0  0  0  0 
Observation point  101  122  117  340 
Note:
Analysis of variance
Sunny (I)  6  95  101  
205.93  1.068  206.998  
34.32  0.0112  –  
Cloudy (II)  6  116  122  
166.97  0.955  167.9272  
27.828  0.0082  –  
Partly cloudy/overcast to cloudy (III)  6  110  116  
160.17  1.107  161.2801  
26.69  0.0101  –  
Unclassified (IV)  6  333  339  
SS  532.81  3.562  536.38  
88.8  0.0106  – 
The output results of the coefficients of each equation in the regression calculation






−1.15  0.55  −0.08  0.01  0.00  1.49 × 10^{−4}  
Standard deviation, %  24.14  113.67  16.85  2.57  0.52  0.03  
−0.48  0.48  −0.49  0.52  −0.53  0.53  
Cloudy (II)  −0.80  0.40  −0.07  0.01  0.00  1.5 × 10^{−4}  
Standard deviation, %  63.56  31.45  5.05  0.94  0.20  0.01  
−1.26  1.29  −1.33  1.42  −1.43  1.44  
Partly cloudy/overcast to cloudy (III)  −0.68  0.34  −0.06  0.01  0.00  1.3×10^{−5}  
Standard deviation, %  53.43  26.59  4.31  0.82  0.17  0.01  
−1.28  1.29  −1.32  1.38  −1.38  1.39  
Unclassified (IV)  −0.47  0.24  −0.04  0.01  0.00  8.6 × 10^{−5}  
Standard deviation, %  34.72  17.13  2.73  0.50  0.10  5.6 × 10^{−3}  
−1.35  1.38  −1.43  1.51  −1.52  1.53 
From Tables 2–4, the following conclusions can be drawn:
The linear regression equation for the three weather types and unclassified conditions is shown in Eq. (15). That is the photovoltaic system generating the power prediction equation.
The complex correlation coefficient between the six independent variables and the dependent variable in the linear regression model is
The constant term in the regression Eq. (15) is zero. The regression coefficients are within the range of 95% confidence. The corresponding significance values are all zero. This shows that the results are significant.
In sunny and cloudy weather, the classified regression equation
It can also be seen from the data (Table x) that the regression coefficient and
We apply the prediction model to the 2 kW gridconnected photovoltaic system. Among them, the weather of sunny (I), cloudy (II), sunny to cloudy (or overcast to cloudy) (III) adopts the
We have carried out theoretical calculations on the monolithic components of silicon crystal cells. On this basis, we establish a multiple linear regression model of photovoltaic system power generation and power generation with radiation and module working temperature as variables. Multiple linear regression analyses were conducted on the data under weather classification (I, II, and III) and unclassified conditions. The model has a good fit, and its accuracy is high.
Regression statistics
0.997415  0.99715  0.99652  0.99667  
0.994838  0.99431  0.99314  0.99336  
0.98404  0.98545  0.98373  0.99026  
Standard error, %  10.61  9.11  9.99  10.34 
3051.26  3379.02  2,652.47  8,301.23  
Significance value  0  0  0  0 
Observation point  101  122  117  340 
The output results of the coefficients of each equation in the regression calculation






−1.15  0.55  −0.08  0.01  0.00  1.49 × 10^{−4}  
Standard deviation, %  24.14  113.67  16.85  2.57  0.52  0.03  
−0.48  0.48  −0.49  0.52  −0.53  0.53  
Cloudy (II)  −0.80  0.40  −0.07  0.01  0.00  1.5 × 10^{−4}  
Standard deviation, %  63.56  31.45  5.05  0.94  0.20  0.01  
−1.26  1.29  −1.33  1.42  −1.43  1.44  
Partly cloudy/overcast to cloudy (III)  −0.68  0.34  −0.06  0.01  0.00  1.3×10^{−5}  
Standard deviation, %  53.43  26.59  4.31  0.82  0.17  0.01  
−1.28  1.29  −1.32  1.38  −1.38  1.39  
Unclassified (IV)  −0.47  0.24  −0.04  0.01  0.00  8.6 × 10^{−5}  
Standard deviation, %  34.72  17.13  2.73  0.50  0.10  5.6 × 10^{−3}  
−1.35  1.38  −1.43  1.51  −1.52  1.53 
Kyocera KC130GH2P polysilicon module parameters
Polysilicon  130  17.6  7.39  21.9  8.02  0.81 
Analysis of variance
Sunny (I)  6  95  101  
205.93  1.068  206.998  
34.32  0.0112  –  
Cloudy (II)  6  116  122  
166.97  0.955  167.9272  
27.828  0.0082  –  
Partly cloudy/overcast to cloudy (III)  6  110  116  
160.17  1.107  161.2801  
26.69  0.0101  –  
Unclassified (IV)  6  333  339  
SS  532.81  3.562  536.38  
88.8  0.0106  – 
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