# Provincial Grid Investment Scale Forecasting Based on MLR and RBF Neural Network

Authors: Ersheng Pan; Dong Peng; Wangcheng Long; Yawei Xue; Lang Zhao; Jinchao Li
Journal: Mathematical Problems in Engineering
 (2019)

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## Abstract

Accurate calculation of power grid investment scale is an important work of power grid management. It is very important to power grid efficient development. Due to the characteristics of short data time series, lots of influencing factors, and large change of power grid investment, it is very difficult to calculate grid investment accurately. Firstly, this paper uses hierarchical clustering analysis method to divide the 23 provinces into four classes with considering fifteen power grid influencing factors, then uses spearman’s rank-order correlation to find out five key influencing factors, and then establishes the regression relationship between the growth rate of investment scale and GDP, permanent population, total social electricity consumption, installed power capacity of operation area, maximum power load, and other growth rates by using the multiple linear regression method (MLR), and the estimation error is corrected by using RBF neural network. Finally, the validity of the model is verified by using data related to power grid investment. The calculation error indicates that the model is feasible and effective.


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## Body

## 1. Introduction

Power Grid Corporation is responsible for guaranteeing the sustainable development of power grid and improving the reliability of power supply. Power grid investment is one kind of the fixed assets investment, which has the general fixed assets characteristic. Fixed asset investment has been affected by many factors, including GDP, interest rate, and other macroeconomic factors. However, due to the inability to store electricity, the power gird has some specific characteristics, such as instantaneity and network-based. So the power grid investment needs satisfy transmission demand and network construction demand. Following the development of human society, power grid also needs to satisfy the energy source optimization distribution, renewable resources combined to the grid, and environment protection. As a result, the power grid investment has a lot of influencing factors and it is difficult to be forecasted. But it is very important for optimizing planning and development work of Power Grid Corporation to know the investment scale. Especially, China State Grid Corporation has invested more than CNY (China Yuan) 2770 billion on power grid capital construction from 2005 to 2015. The average increase rate is 14.29%. While provincial corporations’ investments have vast difference, change from CNY 1.12 billion to 14.9 billion, investment average increasing rate changes form -1.2% to 19.38%. So it is very important to study the forecasting model to realize the accurate calculation of provincial corporation investment.The second part of this paper is literature review, summarizing the existing research methods; the third part introduces the proposed method; the fourth part forecasts the provincial power grid corporations’ annual investments with the proposed method; the fifth part is the main conclusion and policy suggestion.


## 2. Literature Review

In order to study the power grid investment forecasting models, previously popular forecasting models employed in other fields are worthy references for us; some classical forecasting models such as error correction model, autoregressive integrated moving average model, and Grey model are widely employed for forecasting among different fields. Until now, the research on investment prediction model has been studied by a lot of academics and obtained a great deal of achievements at home and abroad; the specific literatures are shown in Table1.Table 1
Researches on investment forecasting.
Authors Forecast object Method Yu Hao, Ling'ou Wang, Lingyun Zhu, Minjie Ye [1] Rural investment Error correction model Kaiji Motegi, Akira Sadahiro [2] Private investment Mixed frequency vector auto-regression approach Coskun Hamzacebi, Coskun Hamzacebi [3] Annual electricity consumption Optimized grey model Taegu Kim, Deok-Joo Lee, Sanghoi Koo [4] R&D investment Comparative analogy approach WANG Dongjin, LI Xiusheng, ZHANG Haiying, WANG Zhen [5] drilling and completion investment BP neural network Sheng-Tun Li, Shu-Ching Kuo [6] Financial investment Wavelet-based SOM networks Xiuquan Li, Zhidong Deng, Jing Luo [7] Financial investment Ensemble artificial neural network Kurt G. Lunsford [8] Residential investment Multi Co-integration Yuan-Yeuan Tai, Jenn-Yang Lin, Ming-Shi Chen, Ming-Chyuan Lin [9] Investment in the core competitiveness of product development Analytic hierarchy process and grey model GM(1,1) Stephan Leitner, Alexandra Rausch, DorisA. Behrens [10] Distributed investment decisions Multi-agent simulation Zhao, H.; Yang, L.; Li, C.; Ma, X [11] Investment demand of power grid Co-integration theory and error correction model Hu, B.C.; Hu, G.; Hu, C.H.; Qin, S.; Li, M.W.; Peng, C. [12] Grid Infrastructure Investment Gray Prediction and analytic hierarchy process Fang, J.L.; Xie, Y.J.; Jin, Y.; Feng, S. [13] Power Grid Investment Grey prediction method and hierarchical analysis method Shuyu Dai, Dongxiao Niu and Yaru Han [14] Power Grid Investment Support Vector Machine Hong, W.-C. [15] Traffic flow forecasting Seasonal SVR with chaotic immune algorithm Geng, J., Huang, M.-L., Li, M.-W., Hong, W.-C [16] Load forecasting Seasonal chaotic cloud simulated annealing algorithm and SVR


## 3. Model and Estimation Methods

### 3.1. Research Route

The technical route is shown in Figure1.Figure 1
The technical route.


### 3.2. Spearman’s Rank-Order Correlation

Spearman’s rank-order correlation is equivalent to Pearson’s product-moment correlation coefficient performed on the ranks of the data rather than the raw data, and it is the nonparametric version of the Pearson product-moment correlation. Spearman’s correlation coefficient can measure the strength of association between two ranked variables. Spearman’s correlation coefficient of two variablesxi and yi (i is the number of samples) can be calculated by formula (1) [17].(1)rs=∑i=1nxi-x-yi-y-∑i=1nxi-x-2∑i=1nyi-y-2Here,rs is Spearman’s correlation and x-,y- are the average values of the two variables xi and yi. Spearman’s correlation rank will yield a value -1≤rs≤1. Higher absolute values of rs correspond to stronger correlations between the two variables. A positive value suggests a positive correlation, while a negative value represents a negative correlation.


### 3.3. Multiple Linear Regression Method

Multiple linear regression attempts to model the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. Every value of the independent variablex is associated with a value of the dependent variabley. In general, the multiregressive model can be expressed as (2)y=b0+b1x1+b2x2+⋯+bpxp+εwhereb 0 = intercept,x i = ith independent variable with effect on y,b i = slope or regression coefficient of xi, which can get by least-squares estimates method [18],ε = prediction error.


### 3.4. RBF Neural Network

Radial basis function (RBF) neural network is a three-layer forward neural network model with good performance and global approximation and is free from the local minima problems [19]. It is a multi-input, single-output system consisting of an input layer, a hidden layer, and an output layer. During the data processing, the hidden layer performs nonlinear transforms for feature extraction and the output layer gives a linear combination of output weights.The transformation of the RBF neural network from the input space to the hidden layer space is nonlinear, and the transformation from the hidden layer space to the output layer space is linear. RBF neural network has a simple structure, simple training and fast learning convergence, which can fit any nonlinear function, so it is widely used in time series analysis forecasting [19–22].The RBF neural network commonly uses the Gauss radial basis function as the activation function of the hidden layer neurons. The Gauss radial basis function can be expressed as follows:(3)Rxp-ci=exp⁡-12σ2xp-ci2in whichxp is the input to the hidden layer, ci is the center of the Gaussian function, xp-ci is the distance between the input vector and the center of the Gaussian function, andσ is the variance of the Gaussian function. The output of the network can be express as follows:(4)yi=∑i=1hωijepx-12σ2xp-ci2j=1,2,…,nIn the formula,xp=(x1p,x2p,…,xmp)T is the pth input sample of the network; p=1,2,…,P. P is the total number of samples; i=1,2,…,h is the number of hidden layer nodes; yi is the actual output of the jth output node of the network corresponding to the input sample.There are three parameters that need to be solved in the RBF neural network model: the centerci of the radial basis function, the variance σ of the radial basis function, and the weightωijfrom the hidden layer to the output layer.According to the different selection methods of radial basis function centers, there are many learning methods for parametersci and σ, such as random selection center method, self-organization selection method, supervised selection center method, and orthogonal least-squares method [23]. The least square algorithm is also applied to train the output weight ωij.


### 3.5. Hierarchical Clustering Analysis Method

Hierarchical clustering analysis method (also called hierarchical cluster analysis or HCA) is a method of cluster analysis which seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two types [24]:(1) Agglomerative (Bottom-Up) Clustering (1)
Start with each example in its own singleton cluster. (2)
At each time-step, greedily merge 2 most similar clusters. (3)
Stop when there is a single cluster of all examples, else go to(2).(2) Divisive (Top-Down) Clustering (1)
Start with all examples in the same cluster. (2)
At each time-step, remove the “outsiders” from the least cohesive cluster. (3)
Stop when each example is in its own singleton cluster, else go to(2).In this paper, we use the SPSS software to realize the clustering function.


## 3.1. Research Route

The technical route is shown in Figure1.Figure 1
The technical route.


## 3.2. Spearman’s Rank-Order Correlation

Spearman’s rank-order correlation is equivalent to Pearson’s product-moment correlation coefficient performed on the ranks of the data rather than the raw data, and it is the nonparametric version of the Pearson product-moment correlation. Spearman’s correlation coefficient can measure the strength of association between two ranked variables. Spearman’s correlation coefficient of two variablesxi and yi (i is the number of samples) can be calculated by formula (1) [17].(1)rs=∑i=1nxi-x-yi-y-∑i=1nxi-x-2∑i=1nyi-y-2Here,rs is Spearman’s correlation and x-,y- are the average values of the two variables xi and yi. Spearman’s correlation rank will yield a value -1≤rs≤1. Higher absolute values of rs correspond to stronger correlations between the two variables. A positive value suggests a positive correlation, while a negative value represents a negative correlation.


## 3.3. Multiple Linear Regression Method

Multiple linear regression attempts to model the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. Every value of the independent variablex is associated with a value of the dependent variabley. In general, the multiregressive model can be expressed as (2)y=b0+b1x1+b2x2+⋯+bpxp+εwhereb 0 = intercept,x i = ith independent variable with effect on y,b i = slope or regression coefficient of xi, which can get by least-squares estimates method [18],ε = prediction error.


## 3.4. RBF Neural Network

Radial basis function (RBF) neural network is a three-layer forward neural network model with good performance and global approximation and is free from the local minima problems [19]. It is a multi-input, single-output system consisting of an input layer, a hidden layer, and an output layer. During the data processing, the hidden layer performs nonlinear transforms for feature extraction and the output layer gives a linear combination of output weights.The transformation of the RBF neural network from the input space to the hidden layer space is nonlinear, and the transformation from the hidden layer space to the output layer space is linear. RBF neural network has a simple structure, simple training and fast learning convergence, which can fit any nonlinear function, so it is widely used in time series analysis forecasting [19–22].The RBF neural network commonly uses the Gauss radial basis function as the activation function of the hidden layer neurons. The Gauss radial basis function can be expressed as follows:(3)Rxp-ci=exp⁡-12σ2xp-ci2in whichxp is the input to the hidden layer, ci is the center of the Gaussian function, xp-ci is the distance between the input vector and the center of the Gaussian function, andσ is the variance of the Gaussian function. The output of the network can be express as follows:(4)yi=∑i=1hωijepx-12σ2xp-ci2j=1,2,…,nIn the formula,xp=(x1p,x2p,…,xmp)T is the pth input sample of the network; p=1,2,…,P. P is the total number of samples; i=1,2,…,h is the number of hidden layer nodes; yi is the actual output of the jth output node of the network corresponding to the input sample.There are three parameters that need to be solved in the RBF neural network model: the centerci of the radial basis function, the variance σ of the radial basis function, and the weightωijfrom the hidden layer to the output layer.According to the different selection methods of radial basis function centers, there are many learning methods for parametersci and σ, such as random selection center method, self-organization selection method, supervised selection center method, and orthogonal least-squares method [23]. The least square algorithm is also applied to train the output weight ωij.


## 3.5. Hierarchical Clustering Analysis Method

Hierarchical clustering analysis method (also called hierarchical cluster analysis or HCA) is a method of cluster analysis which seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two types [24]:(1) Agglomerative (Bottom-Up) Clustering (1)
Start with each example in its own singleton cluster. (2)
At each time-step, greedily merge 2 most similar clusters. (3)
Stop when there is a single cluster of all examples, else go to(2).(2) Divisive (Top-Down) Clustering (1)
Start with all examples in the same cluster. (2)
At each time-step, remove the “outsiders” from the least cohesive cluster. (3)
Stop when each example is in its own singleton cluster, else go to(2).In this paper, we use the SPSS software to realize the clustering function.


## 4. Case Study

### 4.1. Provincial Power Grid Investment Influencing Factors

Power grid investment demand is determined by various influencing factors such as economic activities; social development; power stable and reliable; etc. In this paper, we divide the influencing factors into 5 categories; they are economy society development; electricity transmission; power grid security; quality of electric energy; and generation grid-connected, all of which consist of three specific factors which can be measured numerically, as depicted in Figure2.Figure 2
Power grid influencing factors.As we can see form Figure2, we choose 15 power grid investment influencing factors to analyze. In this section, we firstly collect provincial historical data of the above-mentioned influencing factors; all these data are obtained from China statistical yearbook, state grid statistical information, and so on. The descriptive statistics of these influencing factors values of 23 provinces from 2012 to 2014 are showed in Table 2.Table 2
The descriptive statistics of clustering indexes’ values.
Variable Unit N Mean StDev Min Max GDP Billion Yuan 69 2299.882 1566.55 230.332 6518.832 POP Ten thousand 69 4413.391 2636.949 583 9789 FI Billion Yuan 69 1424.546 1090.764 286.13 4249.55 SEC GWh 69 172514.94 115942.01 66781 501254 PL GW 69 26.41 18.42 8.99 82.06 UL % 69 58.17 12.91 41.68 89.58 RPS % 69 99.969 0.013 99.929 99.988 EAF % 69 91.167 15.468 60 100 ICS % 69 99.903 0.123 99.58 100 RQV % 69 99.991 0.006 99.976 99.997 CLLR % 69 6.472 1.545 3.08 9.45 RFNT Minute 69 2.2 0.35 0 5 REG GWh 69 6516.391 8479.611 663 40114 EIC MW 69 3744.143 3859.259 216.2 15278.2 EVO Thousand 69 38.561 49.551 0.5 175Then Spearman’s rank-order correlation method is employed to select key influencing factors of the power grid investment demand from the above-mentioned influencing factors. These key influencing factors have significant impact on power grid investment demand, so these key influencing factors are employed to forecast the provincial power grid investment demand.Here we calculated the spearman rank degree between upper influencing factors and power grid investment. The calculation results are showed in Table3. The results showed that gross domestic product (GDP), population (POP), social electricity consumption (SEC), electric installed capacity (EIC), and peak load (PL) are the main influencing factors of the electric grid investment (EGI). All these key influencing factors are selected for the power grid investment forecasting.Table 3
Spearman rank degree of influencing factors.
Correlation Sig. (Two side) N GDP 0.800∗∗ 0.000 69 POP 0.672∗∗ 0.001 69 FI 0.531∗ 0.009 69 SEC 0.859∗∗ 0.000 69 PL 0.904∗∗ 0.000 69 UL 0.222 0.308 69 RPS 0.537∗ 0.008 69 EAF 0.091 0.678 69 ICS 0.322 0.134 69 RQV 0.447∗ 0.032 69 CLLR -0.157 0.474 69 RFNT 0.133 0.544 69 REG -0.013 0.954 69 EIC 0.645∗∗ 0.001 69 EVO 0.016 0.943 69


### 4.2. Multiple Linear Regression (MLR) Method of 23 Provinces Power Grid Investment

Here we use the increasing rates of power grid investment demand, GDP, POP, SEC, EIC, and PL to set up the multiple linear regression (MLR) models of 23 provinces from 2004 to 2016. The independent variables of the MLR model are GDP, POP, SEC, EIC, and PL while the dependent variable is power grid investment. The coefficients of the multiple linear regression models are showed in Table4.Table 4
Coefficients of the 23 provinces.
β 0 β 1 β 2 β 3 β 4 β 5 Beijing -1.252 25.966 -26.062 -3.578 2.32 -1.203 Shanghai 0.1 1 -3.998 -0.507 -1.198 0.783 Tianjin -0.967 11.579 -11.922 -8.989 2.258 3.6 Shanxi -0.054 5.034 -30.391 1.255 0.275 -1.642 Shandong -0.701 9.923 -20.112 -1.062 -0.097 -0.291 Jiangsu 0.403 -4.563 101.958 -4.745 -0.075 1.316 Zhejiang 0.053 2.067 -30.981 5.087 0.746 -2.936 Liaoning -0.272 5.972 14.675 -2.423 -4.043 4.89 Anhui -1.636 18.555 15.906 -9.941 2.406 2.166 Fujian 0.103 -5.274 0.483 2.408 -0.549 4.847 Hubei 3.03 -19.21 -276.206 1.274 1.566 -0.183 Hunan -0.724 13.39 14.354 -3.084 -8.444 -1.891 Henan -0.588 4.556 14.016 -7.029 5.462 3.526 Jiangxi -0.083 -4.391 58.609 7.987 -0.992 -3.408 Jilin -0.36 9.024 -98.534 1.346 -3.6 0.274 Heilongjiang 0.29 4.216 -51.134 2.4 -3.068 -5.405 Shaanxi 0.655 -1.403 -73.253 -3.666 0.153 1.775 Sichuan -1.121 9.558 -40.638 -0.487 -0.645 4.974 Chongqing 0.308 -0.944 -31.873 0.698 0.825 0.24 Qinghai -7.269 60.606 103.254 -9.225 9.492 -4.382 Ningxia -0.275 -4.009 91.636 1.535 -0.824 -1.476 Gansu 1.461 -9.799 -85.198 1.939 -1.35 -0.378 Xinjiang -0.464 -1.121 13.056 0.992 1.748 -1.12


### 4.3. The Forecasting Error Correction by RBF Neural Network

In this part, we firstly collect the provincial power grid investment demand forecasting errors of multiple linear regression (MLR) model. All the provincial power grid investment demand forecasting errors of MLR models are showed in Figure3 (A total of 299 sample data). All these samples are used to train the RBF neural network model.Figure 3
Provincial power grid investment demand forecasting errors of the MLR model.Then RBF neural network models are employed to fit the provincial power grid investment demand forecasting errors of multiple linear regression model, the inputs of the RBF models are GDP, POP, SEC, EIC, and PL while the output of the RBF models are corresponding forecasting errors of MLR models.Finally, the fitting results of RBF models are used to modify the forecasting results of the MLR forecasting model. MLR and MLR-RBF forecasting results as well as the actual power grid investment of four typical provinces are showed in Figures4–7. From these figures we can conclude that the forecasting results of MLR-RBF model do have a little improvement to single MLR model.Figure 4
Jiangsu power grid investment forecasting result.Figure 5
Beijing power grid investment forecasting result.Figure 6
Shanxi power grid investment forecasting result.Figure 7
Gansu power grid investment forecasting result.To further validate the accuracy of the proposed MLR-RBF model, Grey model is also put forward as a benchmark model of the proposed model. The specific provincial power grid investment demand forecasting errors by different forecasting model are showed in Table5. The results showed that the MLR-RBF model has the best forecasting performance and the RBF error correction method has positive effect to improve the MLR model forecasting accuracy. In addition, both MLR and MLR-RBF model outperform the Grey model in terms of average forecasting errors. These results demonstrate the proposed MLR-RBF model is a promising tool for provincial power grid investment demand forecasting.Table 5
The average forecasting errors of 23 provinces power grid investment.
Number Provinces Grey model MLR model average error MLR-RBF average error 1 Beijing 32.28% 8.74% 8.65 % 2 Tianjin 35.96% 0.11% 0.10 % 3 Shanxi 28.92% 12.04% 12.01 % 4 Shandong 25.40% 10.77% 10.74 % 5 Shanghai 17.61% 12.34% 12.00 % 6 Jiangsu 13.01% 12.94% 12.93 % 7 Zhejiang 19.87% 18.36% 18.31 % 8 Liaoning 33.60% 17.98% 17.63 % 9 Anhui 30.90% 8.00% 7.84 % 10 Fujian 15.48 16.54% 15.31 % 11 Hubei 1 2.16 % 17.79% 17.77% 12 Hunan 37.17% 23.52% 23.32 % 13 Henan 17.08% 16.35% 16.26 % 14 Jiangxi 10.77% 7.83% 7.80 % 15 Jilin 1 9.85 % 25.21% 24.89% 16 Heilongjiang 43.68% 24.36% 24.23 % 17 Shaanxi 21.56% 18.96% 18.72 % 18 Sichuan 41.81% 22.03% 21.94 % 19 Chongqing 1 6.99 % 23.64% 23.39% 20 Qinghai 45.26% 21.21% 20.25 % 21 Ningxia 1 9.15 % 23.73% 23.36% 22 Gansu 57.53% 24.27% 24.17 % 23 Xinjiang 16.58% 13.39% 13.26 %


### 4.4. The Power Grid Investment Forecasting Results and Analysis

In this section, we employ the proposed MLR-RBF model to forecast the provincial power grid investment in 2018. Provincial historical data from 2004 to 2016 are used to estimate model parameters. To forecast future provincial power grid investment, influencing factors (GDP, POP, SEC, EIC, and PL) should be defined firstly for 2018 provincial power grid investment demand forecasting. So it is a key issue to ascertain the input data of the MLR-RBF model to forecast 2018 provincial power grid investment demand. In this paper, these provincial input variables for 2018 are got from relevant provinces’ statistical bureaus and development planning. In addition, based on these relevant provinces’ statistical bureaus and development planning, three different scenarios are set to forecast 2018 provincial power grid investment demand.To simplify the complexity of forecasting process, we firstly employ the hierarchical clustering analysis (HCA) method to divide 23 provinces into 4 categories; the clustering results are showed in Figure8 and Table 6. Then three different scenarios are set for all different categories; the specific scenario setting results are shown in Table 7. Finally, 2018 provincial power grid investment demand forecasting results are obtained based on the proposed MLR-RBF model and scenario setting results.Table 6
Provinces clustering results.
Class Provinces First class Shandong, Jiangsu  Second class Beijing, Tianjin, Shanghai, Zhejiang, Anhui, Fujian, Hubei, Hunan, Henan, Jiangxi, Shaanxi, Sichuan, Chongqing  Third class Shanxi, Liaoning, Jilin, Heilongjiang, Qinghai, Ningxia  Forth class Gansu, XinjiangTable 7
Influencing factors’ value of four classes.
Regions Influencing Factor Min Mean Max Shandong, Jiangsu GDP, POP, SEC, EIC, PL 7.5%, 0.242%, 3.866%, 4.555%, 4.9% 8.00%, 0.426%, 4.067%, 10.543%, 6.25% 8.5%, 0.61%, 4.267%, 16.531%, 7.6%  Beijing, Tianjin, Shanghai, Zhejiang, Anhui, Fujian, Hubei, Hunan, Henan, Jiangxi, Shaanxi, Sichuan, Chongqing GDP, POP, SEC, EIC, PL 6.50%, 0.3048%, 0.2678%, 1.0478%, 2.33% 8.013%, 0.8022%, 5.0321%, 9.4295, 6.8991% 9.5%, 1.4775%, 8.2452%, 28.0538%, 13.07%  Shanxi, Liaoning, Jilin, Heilongjiang, Qinghai, Ningxia GDP, POP, SEC, EIC, PL 5.6%, -0.1%, 2%, 7.80%, 3.6% 6.64%, 0.38%, 5.238%, 11.87%, 5.92% 7.5%, 0.9%, 9.3685%, 19.52%, 9.809%  Gansu, Xinjiang GDP, POP, SEC, EIC, PL 7%, 0.365%, 5.41%, 6.922%, 5.6% 7.425%, 1.26%, 8.12%, 8.299%, 8.06% 7.85%, 2.156%, 10.82%, 9.676%, 10.52%Figure 8
Hierarchical clustering results.The forecasting results of 2018 provincial power grid investment demand under different scenarios are showed in Figure9.Figure 9
The power grid investment forecasting results of 23 provinces.


## 4.1. Provincial Power Grid Investment Influencing Factors

Power grid investment demand is determined by various influencing factors such as economic activities; social development; power stable and reliable; etc. In this paper, we divide the influencing factors into 5 categories; they are economy society development; electricity transmission; power grid security; quality of electric energy; and generation grid-connected, all of which consist of three specific factors which can be measured numerically, as depicted in Figure2.Figure 2
Power grid influencing factors.As we can see form Figure2, we choose 15 power grid investment influencing factors to analyze. In this section, we firstly collect provincial historical data of the above-mentioned influencing factors; all these data are obtained from China statistical yearbook, state grid statistical information, and so on. The descriptive statistics of these influencing factors values of 23 provinces from 2012 to 2014 are showed in Table 2.Table 2
The descriptive statistics of clustering indexes’ values.
Variable Unit N Mean StDev Min Max GDP Billion Yuan 69 2299.882 1566.55 230.332 6518.832 POP Ten thousand 69 4413.391 2636.949 583 9789 FI Billion Yuan 69 1424.546 1090.764 286.13 4249.55 SEC GWh 69 172514.94 115942.01 66781 501254 PL GW 69 26.41 18.42 8.99 82.06 UL % 69 58.17 12.91 41.68 89.58 RPS % 69 99.969 0.013 99.929 99.988 EAF % 69 91.167 15.468 60 100 ICS % 69 99.903 0.123 99.58 100 RQV % 69 99.991 0.006 99.976 99.997 CLLR % 69 6.472 1.545 3.08 9.45 RFNT Minute 69 2.2 0.35 0 5 REG GWh 69 6516.391 8479.611 663 40114 EIC MW 69 3744.143 3859.259 216.2 15278.2 EVO Thousand 69 38.561 49.551 0.5 175Then Spearman’s rank-order correlation method is employed to select key influencing factors of the power grid investment demand from the above-mentioned influencing factors. These key influencing factors have significant impact on power grid investment demand, so these key influencing factors are employed to forecast the provincial power grid investment demand.Here we calculated the spearman rank degree between upper influencing factors and power grid investment. The calculation results are showed in Table3. The results showed that gross domestic product (GDP), population (POP), social electricity consumption (SEC), electric installed capacity (EIC), and peak load (PL) are the main influencing factors of the electric grid investment (EGI). All these key influencing factors are selected for the power grid investment forecasting.Table 3
Spearman rank degree of influencing factors.
Correlation Sig. (Two side) N GDP 0.800∗∗ 0.000 69 POP 0.672∗∗ 0.001 69 FI 0.531∗ 0.009 69 SEC 0.859∗∗ 0.000 69 PL 0.904∗∗ 0.000 69 UL 0.222 0.308 69 RPS 0.537∗ 0.008 69 EAF 0.091 0.678 69 ICS 0.322 0.134 69 RQV 0.447∗ 0.032 69 CLLR -0.157 0.474 69 RFNT 0.133 0.544 69 REG -0.013 0.954 69 EIC 0.645∗∗ 0.001 69 EVO 0.016 0.943 69


## 4.2. Multiple Linear Regression (MLR) Method of 23 Provinces Power Grid Investment

Here we use the increasing rates of power grid investment demand, GDP, POP, SEC, EIC, and PL to set up the multiple linear regression (MLR) models of 23 provinces from 2004 to 2016. The independent variables of the MLR model are GDP, POP, SEC, EIC, and PL while the dependent variable is power grid investment. The coefficients of the multiple linear regression models are showed in Table4.Table 4
Coefficients of the 23 provinces.
β 0 β 1 β 2 β 3 β 4 β 5 Beijing -1.252 25.966 -26.062 -3.578 2.32 -1.203 Shanghai 0.1 1 -3.998 -0.507 -1.198 0.783 Tianjin -0.967 11.579 -11.922 -8.989 2.258 3.6 Shanxi -0.054 5.034 -30.391 1.255 0.275 -1.642 Shandong -0.701 9.923 -20.112 -1.062 -0.097 -0.291 Jiangsu 0.403 -4.563 101.958 -4.745 -0.075 1.316 Zhejiang 0.053 2.067 -30.981 5.087 0.746 -2.936 Liaoning -0.272 5.972 14.675 -2.423 -4.043 4.89 Anhui -1.636 18.555 15.906 -9.941 2.406 2.166 Fujian 0.103 -5.274 0.483 2.408 -0.549 4.847 Hubei 3.03 -19.21 -276.206 1.274 1.566 -0.183 Hunan -0.724 13.39 14.354 -3.084 -8.444 -1.891 Henan -0.588 4.556 14.016 -7.029 5.462 3.526 Jiangxi -0.083 -4.391 58.609 7.987 -0.992 -3.408 Jilin -0.36 9.024 -98.534 1.346 -3.6 0.274 Heilongjiang 0.29 4.216 -51.134 2.4 -3.068 -5.405 Shaanxi 0.655 -1.403 -73.253 -3.666 0.153 1.775 Sichuan -1.121 9.558 -40.638 -0.487 -0.645 4.974 Chongqing 0.308 -0.944 -31.873 0.698 0.825 0.24 Qinghai -7.269 60.606 103.254 -9.225 9.492 -4.382 Ningxia -0.275 -4.009 91.636 1.535 -0.824 -1.476 Gansu 1.461 -9.799 -85.198 1.939 -1.35 -0.378 Xinjiang -0.464 -1.121 13.056 0.992 1.748 -1.12


## 4.3. The Forecasting Error Correction by RBF Neural Network

In this part, we firstly collect the provincial power grid investment demand forecasting errors of multiple linear regression (MLR) model. All the provincial power grid investment demand forecasting errors of MLR models are showed in Figure3 (A total of 299 sample data). All these samples are used to train the RBF neural network model.Figure 3
Provincial power grid investment demand forecasting errors of the MLR model.Then RBF neural network models are employed to fit the provincial power grid investment demand forecasting errors of multiple linear regression model, the inputs of the RBF models are GDP, POP, SEC, EIC, and PL while the output of the RBF models are corresponding forecasting errors of MLR models.Finally, the fitting results of RBF models are used to modify the forecasting results of the MLR forecasting model. MLR and MLR-RBF forecasting results as well as the actual power grid investment of four typical provinces are showed in Figures4–7. From these figures we can conclude that the forecasting results of MLR-RBF model do have a little improvement to single MLR model.Figure 4
Jiangsu power grid investment forecasting result.Figure 5
Beijing power grid investment forecasting result.Figure 6
Shanxi power grid investment forecasting result.Figure 7
Gansu power grid investment forecasting result.To further validate the accuracy of the proposed MLR-RBF model, Grey model is also put forward as a benchmark model of the proposed model. The specific provincial power grid investment demand forecasting errors by different forecasting model are showed in Table5. The results showed that the MLR-RBF model has the best forecasting performance and the RBF error correction method has positive effect to improve the MLR model forecasting accuracy. In addition, both MLR and MLR-RBF model outperform the Grey model in terms of average forecasting errors. These results demonstrate the proposed MLR-RBF model is a promising tool for provincial power grid investment demand forecasting.Table 5
The average forecasting errors of 23 provinces power grid investment.
Number Provinces Grey model MLR model average error MLR-RBF average error 1 Beijing 32.28% 8.74% 8.65 % 2 Tianjin 35.96% 0.11% 0.10 % 3 Shanxi 28.92% 12.04% 12.01 % 4 Shandong 25.40% 10.77% 10.74 % 5 Shanghai 17.61% 12.34% 12.00 % 6 Jiangsu 13.01% 12.94% 12.93 % 7 Zhejiang 19.87% 18.36% 18.31 % 8 Liaoning 33.60% 17.98% 17.63 % 9 Anhui 30.90% 8.00% 7.84 % 10 Fujian 15.48 16.54% 15.31 % 11 Hubei 1 2.16 % 17.79% 17.77% 12 Hunan 37.17% 23.52% 23.32 % 13 Henan 17.08% 16.35% 16.26 % 14 Jiangxi 10.77% 7.83% 7.80 % 15 Jilin 1 9.85 % 25.21% 24.89% 16 Heilongjiang 43.68% 24.36% 24.23 % 17 Shaanxi 21.56% 18.96% 18.72 % 18 Sichuan 41.81% 22.03% 21.94 % 19 Chongqing 1 6.99 % 23.64% 23.39% 20 Qinghai 45.26% 21.21% 20.25 % 21 Ningxia 1 9.15 % 23.73% 23.36% 22 Gansu 57.53% 24.27% 24.17 % 23 Xinjiang 16.58% 13.39% 13.26 %


## 4.4. The Power Grid Investment Forecasting Results and Analysis

In this section, we employ the proposed MLR-RBF model to forecast the provincial power grid investment in 2018. Provincial historical data from 2004 to 2016 are used to estimate model parameters. To forecast future provincial power grid investment, influencing factors (GDP, POP, SEC, EIC, and PL) should be defined firstly for 2018 provincial power grid investment demand forecasting. So it is a key issue to ascertain the input data of the MLR-RBF model to forecast 2018 provincial power grid investment demand. In this paper, these provincial input variables for 2018 are got from relevant provinces’ statistical bureaus and development planning. In addition, based on these relevant provinces’ statistical bureaus and development planning, three different scenarios are set to forecast 2018 provincial power grid investment demand.To simplify the complexity of forecasting process, we firstly employ the hierarchical clustering analysis (HCA) method to divide 23 provinces into 4 categories; the clustering results are showed in Figure8 and Table 6. Then three different scenarios are set for all different categories; the specific scenario setting results are shown in Table 7. Finally, 2018 provincial power grid investment demand forecasting results are obtained based on the proposed MLR-RBF model and scenario setting results.Table 6
Provinces clustering results.
Class Provinces First class Shandong, Jiangsu  Second class Beijing, Tianjin, Shanghai, Zhejiang, Anhui, Fujian, Hubei, Hunan, Henan, Jiangxi, Shaanxi, Sichuan, Chongqing  Third class Shanxi, Liaoning, Jilin, Heilongjiang, Qinghai, Ningxia  Forth class Gansu, XinjiangTable 7
Influencing factors’ value of four classes.
Regions Influencing Factor Min Mean Max Shandong, Jiangsu GDP, POP, SEC, EIC, PL 7.5%, 0.242%, 3.866%, 4.555%, 4.9% 8.00%, 0.426%, 4.067%, 10.543%, 6.25% 8.5%, 0.61%, 4.267%, 16.531%, 7.6%  Beijing, Tianjin, Shanghai, Zhejiang, Anhui, Fujian, Hubei, Hunan, Henan, Jiangxi, Shaanxi, Sichuan, Chongqing GDP, POP, SEC, EIC, PL 6.50%, 0.3048%, 0.2678%, 1.0478%, 2.33% 8.013%, 0.8022%, 5.0321%, 9.4295, 6.8991% 9.5%, 1.4775%, 8.2452%, 28.0538%, 13.07%  Shanxi, Liaoning, Jilin, Heilongjiang, Qinghai, Ningxia GDP, POP, SEC, EIC, PL 5.6%, -0.1%, 2%, 7.80%, 3.6% 6.64%, 0.38%, 5.238%, 11.87%, 5.92% 7.5%, 0.9%, 9.3685%, 19.52%, 9.809%  Gansu, Xinjiang GDP, POP, SEC, EIC, PL 7%, 0.365%, 5.41%, 6.922%, 5.6% 7.425%, 1.26%, 8.12%, 8.299%, 8.06% 7.85%, 2.156%, 10.82%, 9.676%, 10.52%Figure 8
Hierarchical clustering results.The forecasting results of 2018 provincial power grid investment demand under different scenarios are showed in Figure9.Figure 9
The power grid investment forecasting results of 23 provinces.


## 5. Conclusion

This article uses spearman rank degree to find out the key influencing factors of power grid investment; they are GDP, POP, SEC, EIC, and PL and next, the 23 provinces power grid investment multiple linear regressive models with power grid investment and the five key influencing factors’ increasing rates. Then the RBF neural networks are used to modify the forecasting errors. At last, we divided the 23 provinces into four classes by hierarchical clustering analysis method with considering five key influencing factors. Based on the regional differences of electric grid investment development, this essay can represent, quantifiably, the correlations between electric grid investment and various influencing factors. And the min, mean, and max values of the influencing factors can realize the scenario analysis, which make the forecasting results become more reasonable. Predicting electric grid investment can help to perfect further project decision-making processes and improve management and decision levels of investment projects.



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*Source: 3197595-2019-01-20.xml*