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Transmission Technical Project Investment Forecasting Under the High-dimension Small Sample Conditions

The electricity market will realize the separation of transmission and distribution, in the new environment, the main profit model of the power grid company will be dominated by transmission and distribution services, it will require the grid company to control its investment and cost accuracy. As a routine maintenance work to ensure the safe and stable transportation of electric energy, the grid technical transformation project has a great impact of the grid operation cost. Due to the lack of the history data, it is difficult to forecast the project’s investment, and the current investment always relies on experience. It needs to construct a quantitative forecasting model to make scientific and objective predictions of investment in technological transformation projects. In this paper, the principal component analysis (PCA) is employed to analysed the history data, then the main factors are obtained, which are used as input variables into SVM models. Finally, from a case study of a certain grid company, the proposed PCASVM forecasting model has better performance on the grid technology transformation project investment prediction, it confirms the effectiveness of the proposed method.


Introduction
With the development of low-carbon economy and green ecological economy in China, in order to meet the energy demand in the future, the State Grid Corporation of China highlights the clean characteristics of electric power, and implements the development strategic direction of electric energy instead of fossil energy. The effective use and development of energy will help to improve people's quality of life. As an important carrier of power transmission channel, power grid plays an important role in ensuring its safe and stable operation. As one of the routine work to ensure the safe operation of power grid, the power grid production and technical transformation project plays a key role in ensuring the safe and stable operation of power grid, improving the quality of power supply and promoting the benign upgrading of power grid assets. With the deepening of power market reform in China, power grid enterprises will shift from the main business of power purchase and sale to the main business of power grid transmission and distribution, and their profit model will change greatly. In the new power market environment, power grid enterprises need to more lean management of their own costs, pay attention to their own transmission benefit and efficiency, and constantly strengthen the competitiveness of power grid enterprises in the power market. This requires power grid enterprises to make reasonable and accurate predictions for investment in power grid technology transformation projects, so as to manage power grid assets more accurately. The investment environment of power grid project is not only affected by various factors in the power market, but also by national economy and policy factors. In this case, it is a complex problem to find the investment law and predict the investment of power grid [1]. According to the whole process of technical transformation project, some scholars extract the investment control indexes in the investment control process, establish an investment control technology and economic indicator system for substation projects and line projects, calculate the influence degree through examples, and combine trend extrapolation models to predict grid investment trends [2,3]. With the increase of the sample data of power grid investment, some scholars have made investment analysis on the final accounts of the completion of the line project and the substation project. It is concluded that the probability distribution of the line project investment and the substation project investment is similar to the normal distribution. According to the probability distribution, the investment range of the relevant investment can be predicted [4]. The above research has made a macroscopic analysis on the power grid investment and achieved some results, which can predict the trend and range of power grid investment. However, due to the regional characteristics of power grid technical transformation projects, the cost factors of power grid projects in different regions are often quite different, such as the labor costs in the East and West, so it is still necessary to further study the quantitative model for accurately predicting the investment amount of power grid.
The prediction of power grid investment can be summed up as the problem of time series prediction, so some scholars build the prediction model of time series to predict the demand of power grid investment [5,6]. Many scholars have summarized the characteristics of power grid investment prediction, and pointed out that there are many factors affecting the investment of power transmission and transformation projects. In the actual cost of power transmission and transformation projects, different line voltage levels, terrain, outlet method, construction scale and other factors will cause a large deviation in the project cost. Therefore, when forecasting grid investment issues in an area, it is difficult to obtain a large number of data samples. In this case, the prediction of power grid investment belongs to the small sample prediction problem, and use the gray model [7] and support vector machine model [8], which perform well under small sample conditions, to make relevant predictions for grid investment. In order to achieve a more accurate prediction, many scholars predict the power grid investment by building a combination prediction model [9]. When using the combination prediction model to predict the power grid investment, aiming at the problem that it is difficult to assign the weights of various prediction models, the particle swarm optimization method is used to weight the combination prediction model to get a better prediction accuracy [10].
All of the above researches are focused on the prediction of power grid investment, and good results have been achieved. From the above studies, it can be found that the influencing factors of power grid investment are relatively complex. In the study of regional power grid investment, due to the relatively small amount of relevant data, the regional power grid investment belongs to the prediction problem under small samples. In this paper, the investment data of a provincial power grid technological transformation is taken as the research object, and the first choice is to analyze the main factors which influence the investment, and the factors are input SVM models that perform well under small sample conditions for prediction.

Principle of PCA algorithm
The method of analyzing influencing factors is referred to as factor analysis method, which is a quantitative analysis of the degree of influence between the research object and the relevant influencing factors by using statistical methods. The more commonly used factor analysis is principal component analysis(PCA). PCA method can transform the high-dimensional space into the lowdimensional space for processing by the projection method. Reducing attributes while retaining most of the original attribute information. PCA is based on the variance of the original data, and regarded as the information contribution rate. The steps of applying principal component analysis to attribute screening are as follows: indicates the number of sample records, indicates the index, and normalizes the matrix.
(2) Calculate the covariance matrix correlation coefficient matrix R (3) Calculate the eigenvalues λ , arrange them according to their value, and calculate the variance contribution rate and cumulative variance contribution rate of each component according to the eigenvalues. The calculation methods are as follows: 1 ( 1, 2, , )

Prediction method of support vector machine
Support vector machine inherits the advantages of neural network, and improves the global optimization ability of neural network, so that the prediction value trained with the same sample has a unique value, and performs well in small sample. At present, it is a relatively new prediction method, which is considered to be able to completely replace the intelligent prediction method of neural network in the case of small samples. The basic principles of support vector machine are as follows: Suppose there is training sample set By introducing two relaxation variables ζ and * ζ , the above functions can be changed into the following forms: By using Lagrange and Karush Kuhn Tucker condition, we can get that the dual type of the problem is： The regression function of SVM can be obtained by solving the above problems： In the formula, K(x i , x) is called kernel function, which needs to meet Mercer condition. Generally, the most commonly used Gaussian kernel function is selected as follows:

Empirical analysis
In the experiment, the investment data of a regional power grid technological transformation project in 2003-2017 for 15 years is used, and the normalized original time series is shown in Figure 1. to 2017 Firstly, the factors of the transmission project investment are selected including: main transformer capacity, static investment, dynamic investment, current capacitor scale, construction project cost, equipment purchase fee, installation project cost, investigation fee, power cable engineering volume, power cable investment, control cable engineering volume, control cable investment, earthwork volume, earthwork volume investment, cable support volume, cable support unit price, 110kV current output, 35kV current output, 10kV current output, etc.
Secondly, the PCA is used to reduce the dimension of the substation project. In order to eliminate the dimensional impact before the dimension reduction calculation, first normalize the index data to [0,1]. Using Matlab for PCA calculations, the results after principal component analysis can be obtained as shown in Table 1.
From the results, it can be seen that the attribute factors after the screening include current period scale, land occupation investment, power cable investment, control cable investment, construction From the results in Table 2, it can be seen that the prediction accuracy can be effectively improved by using VMD to decompose the original sequence and then further predict. Basically, the relative error values of all prediction points are improved to varying degrees compared with those predicted directly by SVM. From the whole prediction results, the average absolute error (MAPE) of VMD-SVM prediction model is 1.51%, and the MAPE of direct SVM prediction is 2.02%, which also has a greater accuracy improvement in the whole level. The example shows that the investment prediction using VMD-SVM can further control the investment of power grid technical transformation projects. An example shows the validity of the model.