Optimisation Study of Investment Decision-Making in Distribution Networks of New Power Systems—Based on a Three-Level Decision-Making Model

Abstract

This paper addresses the scientific needs for investment decision-making in distribution networks against the backdrop of new power systems, constructing a three-tier decision-making system that includes investment scale decision-making, investment structure allocation, and investment project prioritization. Initially, it systematically analyzes the new requirements imposed by the new power systems on distribution networks and establishes an investment index system encompassing four dimensions: “capacity, self-healing, interaction, and efficiency”. Next, the Pearson correlation coefficient is employed to screen key influencing factors, and in conjunction with the grey MG(1,1) model and the support vector machine algorithm, precise forecasting of the investment scale is achieved. Furthermore, distribution network projects are categorized into ten classes, and an investment direction decision-making model is constructed to determine the investment scale for each attribute. Then, for the shortcomings of the traditional project comparison method, the investment project decision-making model is established with the attribute investment amount as the constraint and the maximisation of project benefits under the attribute as the goal. Finally, the effectiveness of the decision-making system is verified by taking the Lishui distribution network as a case study. The results show that the system keeps the investment scale prediction error within 5.9%, the city’s total investment deviation within 0.3%, and the projects are synergistically optimized to provide quantitative support for distribution network investment decision-making in the context of a new type of electric power system, and to achieve precise regulation.

1. Introduction

On 15 March 2021, the ninth meeting of the Central Financial and Economic Commission proposed to build a new type of power system mainly based on new energy and to promote the achievement of the goals of carbon peaking and carbon neutrality. State Grid emphasized the role of the grid hub platform, innovating the grid development method, enhancing the system regulation capability, and promoting the construction of a new type of power system. According to the ‘14th Five-Year’ Renewable Energy Development Plan, new energy will usher in explosive growth, ‘14th Five-Year’ period of renewable energy power generation will account for more than 50 percent of the incremental share of wind and solar power generation to achieve double. For every 1 percentage point increase in the share of electricity consumption in final energy consumption, energy intensity decreases by 3.7 percent. Accelerating the process of terminal electrification is an important way to achieve the dual-carbon target, and the share of electric energy consumption needs to reach more than 70 percent by 2060. As of July 2021, China’s electricity consumption increased by 16.6% year-on-year, and the share of electricity in end-use energy consumption increased to 27.0% in 2020, but there is still much room for improvement in the electrification level of the industry, building heating, transport, and other areas.

In August 2021, the State Grid and the Southern Power Grid launched green power trading pilots, focusing on wind and PV power generation with green certificates attached 2022, the two grid companies further improved the green power trading mechanism. The construction of the power market provides market information for grid investment, with trading prices and sizes becoming the wind vane for investment and medium- and long-term trading driving investment in key sections and lines. Market-based trading has changed the traditional mode of power planning by linking supply and demand balance through ‘power flow’, providing a new category of information for new grid investment.

As a power transmission hub, the power grid faces the dual challenges of clean energy on the supply side and electrification on the demand side, and the existing physical structure and management mode of the power grid need to be adjusted. In addition, with the deepening of the electricity reform, power grid enterprises are facing stricter regulatory constraints, increased pressure on investment growth and cost control, and higher requirements for the precision of investment control. Under the new situation, power grid enterprises need to meet the business development at the same time, enhance the concept of effective assets in power transmission and transformation, and optimize the scale, structure, and timing of investment to ensure that the new investment in the formation of effective assets and obtain a higher permitted return, and to promote the high-quality development of the company and the power grid.

To achieve sustainable development and promote the revolution of energy production and consumption, the development of the Lishui power grid faces new tasks and new requirements. The development goal of the grid needs to be shifted from a crude expansion of the total amount of power to building a strong power system, improving the quality of service, and perfecting the access and consumption capacity of low-carbon energy. This paper aims to accelerate the upgrading of the Lishui power grid to an energy Internet by establishing the investment principles and investment decision-making system for distribution grid projects of new power systems. It ensures the overall healthy and stable operation of the Lishui power grid, promotes the rational distribution of new energy sources in the region, improves the efficiency and effectiveness of Lishui’s power grid investment, meets the healthy development of local new energy development and utilization, and contributes to the realization of Lishui’s carbon-peak and carbon-neutral goals.

The rest of this paper is as follows: the second part is the literature review; the third part is the principle of investment in the distribution network project for the new power system; the fourth part is the investment decision system for the distribution network for new power system; the fifth part is the calculation example of investment in Lishui distribution network for new power system; and the sixth part is the conclusion.

2. Literature Review

Firstly, they focus on the transformation and innovation of the power system under the goal of carbon neutrality and discuss in depth the connotation, characteristics, and key technologies of the new power system. From the perspective of national macro-strategy, these studies analyze the requirements of the energy revolution for the construction of new power systems and sort out the evolution process from the traditional fossil energy-led power system to the new power system dominated by new energy. Kang et al. [1] proposed six key elements of the new power system, i.e., ‘source, network, load, storage, carbon, and number’, and explained the coupling relationship between these elements. Shu et al. [2] further divided the development of the new power system into several stages, combined with the technical characteristics and the scale of new energy access, and put forward the development proposals for each stage, emphasizing the high security, openness, and adaptability of the new power system. Zhang et al. [3], on the other hand, revealed the connotation and characteristics of the new type of power system from the aspects of structure, shape, technology, and mechanism, and analyzed its evolution path. These studies not only provide theoretical support for the construction of the new power system but also explore and look forward to the key technologies from the low-carbon and digital perspectives, pointing out the direction for the safe, efficient, and low-carbon transformation of the power system.

On the other hand, focusing on power system investment decision-making and benefit assessment, scholars have proposed a variety of optimization models and evaluation methods. Ji et al. [4] used game theory combined with subjective and objective weights to construct a program ranking method based on the TODIM model, which provides a scientific basis for investment decision-making. Gao et al. [5] introduced the input-output benefit analysis strategy, established a distribution network investment benefit evaluation platform, guided the investment decision-making by the evaluation results, and improved the precise investment management level of the distribution network. Xu et al. [6] constructed a set of three-level hierarchical structure rating index systems, which fully considered various factors in grid construction investment. Zhu et al. [7] proposed a decision-making model for grid project investment optimization in the context of transmission and distribution tariff reform, which optimized the investment scheme to maximize the return on investment over the whole life cycle. Niu et al. [8] improved the traditional TOPSIS method by introducing integrated proximity and constructed an investment efficiency index system that is more suitable for the characteristics of China’s distribution network. Li et al. [9] established a techno-economic assessment framework, balanced technical and economic factors, and verified its effectiveness in improving reliability. Hesamzadeh et al. [10] explored the complexity of transmission network investment from economic and engineering perspectives and analyzed the relationship between transmission investment and smart grid development. Chen et al. [11] proposed a multi-criteria investment prioritization evaluation method based on hyperplane projection transformation, which provides a scientific basis for incremental distribution network planning. Carvalho et al. [12] investigated the relationship between investment decisions in standby circuits and the cost of unsupplied energy and proposed an investment decision criterion for reliability adequacy. Grimm et al. [13], on the other hand, proposed a two-stage equilibrium model, analyzed the impacts of different regulatory frameworks on the investment in the distribution network and the investment in energy storage, and provided theoretical support for the reduction in the system costs. These studies provide diverse methods and tools for investment decision-making and benefit assessment of power systems and promote the sustainable development of power systems.

3. Principles for Investment in Distribution Network Projects for New Power Systems

To achieve the goals of carbon peaking and carbon neutrality, China is accelerating the development of a modernized power structure centred on renewable energy. This initiative aligns with the nation's commitment to peak carbon emissions and achieve carbon neutrality, while advancing sustainable development principles, fostering innovative economic frameworks, and driving high-quality growth.

The revamped power framework prioritizes energy security as its foundation, ensures a reliable electricity supply to support socioeconomic progress, and focuses on optimizing the integration of renewable energy sources. It relies on advanced smart grid technology as its core infrastructure, enhanced by coordinated source-grid-load-storage systems and synergistic multi-energy integration. Key characteristics of this system include environmental sustainability, operational reliability, adaptive efficiency, intelligent management, and seamless interconnectivity.

The new power system shares conceptual similarities with smart grids and the energy Internet, yet places greater emphasis on establishing renewable energy as the dominant power source. This system is specifically designed to accommodate the rapid expansion of wind and solar power generation capacity while maintaining an optimal balance between security, economic viability, and environmental sustainability. Its development process essentially represents an adaptation to the large-scale integration of renewable energy into the grid.

3.1. Requirements of New Power Systems for Distribution Networks

China's transition to a new power system serves as a crucial pathway for realizing its dual carbon objectives (peak carbon and carbon neutrality), playing a pivotal role in transforming the nation's energy mix. As the critical interface between energy generation and consumption, distribution networks form the backbone of grid infrastructure and represent the frontline in implementing this innovative power framework. The integration of renewable energy into distribution networks is triggering fundamental transformations, characterized by: The proliferation of novel energy consumption entities; dynamic source-grid-load-storage interactions; evolving operational paradigms. These developments necessitate corresponding upgrades and adaptations in distribution grid capabilities to meet emerging challenges and opportunities.

Firstly, the distribution network is undergoing a fundamental transformation from a unidirectional passive system to an interactive active grid. This transition introduces several operational challenges: Increased complexity in supply–demand balancing, blurring boundaries between generation and consumption, potential reverse power flow to the main grid, and emergence of complex multi-directional power flows. These developments demand enhanced reliability and safety measures to ensure stable grid operation.

Secondly, the integration of distributed generation at scale introduces significant stochastic variability into distribution systems, necessitating a paradigm shift in planning methodologies. Key impacts include increased operational complexity due to heightened uncertainty, obsolescence of conventional deterministic planning approaches, critical need for probabilistic multi-scenario planning frameworks. This transition better accommodates the stochastic nature of renewable-dominated power systems while maintaining grid reliability.

Thirdly, with the emergence of multiple interests, the planning objectives in the carbon trading environment tend to be more diverse and dynamic. Distribution network planning needs to shift from the traditional technical and economic indicators as the planning objectives to the consideration of market factors such as balancing the interests of multiple investment subjects, accounting for grid revenues under the influence of the market, as well as macro objectives such as security of energy supply and low-carbon environmental protection.

Fourth, the current state of some areas of the distribution network sensing capability is insufficient, the distribution side and the power side of the information interaction are not smooth, fault handling capacity needs to be improved; the existing regulation and control system of the global situational awareness, unified optimization decision-making and the source of the network and the interaction between the load and storage is insufficient to meet the demand for distributed new energy flexible consumption and intelligent control.

Fifthly, distributed power sources are characterized by smaller single units, larger quantities, and shorter construction cycles, which put forward new requirements for distribution grids. To adapt to the rapid development of distributed power supply, the distribution grid needs to carry out upgrading and technological upgrading in advance, including close tracking of the development situation of distributed PV, optimizing grid-connected services, perfecting the transaction and settlement mechanism, improving the operation and maintenance regulation mode and perfecting the management system and technical standard system measures. Through the above measures, the distribution network can provide efficient and high-quality grid-connected operation services for distributed power sources, promote their large-scale development, and at the same time promote the optimization of the energy structure and the transformation and upgrading of the power system.

3.2. Principles of Distribution Network Investment Under the New Power System

To fulfil its carbon peak and neutrality commitments, China is vigorously developing a clean, low-carbon power system dominated by renewable energy, which presents both opportunities and challenges for distribution grid modernization. The investment focus has expanded beyond traditional substation upgrades to include renewable generation facilities, energy storage systems, and EV charging infrastructure, while introducing new operational complexities like bidirectional power flows and intermittent generation patterns. This transformation demands innovative planning approaches to effectively integrate diverse components and maintain grid reliability amidst evolving technical requirements. Modern distribution network development must simultaneously address multiple objectives: ensuring a reliable power supply, optimizing operational efficiency, enhancing renewable integration, and reducing carbon emissions. The evolving landscape presents dual challenges—while growing energy demands necessitate extensive grid upgrades and expansion, utility companies face constrained investment capacities. Concurrently, the entry of private enterprises into the distribution infrastructure has created competitive dynamics in investment returns and operational benefits. These conditions demand innovative solutions to achieve three critical outcomes: (1) meeting essential grid modernization requirements, (2) maximizing renewable energy penetration, and (3) ensuring cost-effective, low-carbon infrastructure development through targeted investments.

Traditional distribution network project selection and investment decision-making focuses only on economic objectives, mainly considering the economic benefits brought about by the project investment, and lacks consideration of the technical and security aspects of the grid. With the development of the theory of investment optimization for distribution network projects, the investment decision-making for distribution networks under the new power system has been greatly improved, and when evaluating the decision-making, not only are the characteristics of the distribution network projects reflected as comprehensively as possible from several perspectives such as economy, technology, and security but also the theory of investment optimization has been introduced.

3.3. Indicator System for Distribution Network Investment Under the New Power System

The comprehensive evaluation of the investment efficiency of distribution networks involves many factors in the fields of society, economy, technology, resources, environment, etc. A complete and feasible index system is not only the prerequisite for the establishment of the evaluation system of the investment efficiency of the distribution network but also the key to ensuring the reasonableness of the evaluation results.

The traditional sense of security, reliability, high quality, and economic indicators only reflect the electrical attributes of the distribution network-related characteristics and do not intuitively reflect the distribution network's development of ability to support the development of society. In different stages of grid development or different levels of development of the region, the focus of the distribution network is also different, to take into account the economic and social benefits, as well as the stability of the distribution network, the planning objectives of the high flexibility distribution network needs to include the four dimensions of ‘load-bearing, self-healing, interaction, efficiency’, a total of 18 refinement index. Specific indicators are shown in Figure 1.

4. Distribution Network Investment Decision-Making System for New Power System

At present, the research on the investment decision of distribution networks mainly focuses on the comparison and selection of planning schemes and the allocation of investment amounts under certain constraints, but the research on the investment scale and investment direction of distribution networks is not in-depth and systematic enough. To solve this problem, we construct a distribution network investment decision-making system composed of investment scale decision-making, investment direction decision-making, and investment project decision-making. This decision-making system can realize hard investment scale prediction, attribute investment scale allocation, and investment project portfolio optimization layer by layer, to ensure the integrity, coordination, and network of the distribution network investment, and finally achieve accurate investment.

4.1. Distribution Network Investment Decision-Making Process

Distribution network investment decision is a multi-level and all-around decision-making process to determine the investment scale, investment direction, and investment project. The solution to this decision-making process in this paper is shown in Figure 2, which mainly includes three parts:

First, the decision on investment scale. For the scientific calculation of the distribution network investment scale, distribution network companies first need to determine the total investment. Based on meeting the local electricity demand, factors such as operating benefits should also be considered comprehensively to achieve the balanced development of the regional distribution network and encourage the growth of operating benefits.

Second, the investment direction decision. According to the amount of investment allocated in a certain region, how to choose the most urgent and efficient investment direction is very important. Through the analysis of the status quo and planning objectives of the regional power grid, the importance of each project attribute to the construction of the regional distribution network is determined, to determine the investment amount of each attribute to ensure the maximization of investment efficiency.

Third, investment project decision-making. For the investment projects reported by various cities, it is necessary to classify them according to the project attributes and conduct a comprehensive evaluation and ranking for similar projects, to obtain the optimal portfolio of investment projects under the constraint of the investment amount of this attribute, to ensure high investment accuracy.

4.2. Investment Scale Decision

4.2.1. General Idea

Our distribution network investment scale assessment follows a four-stage analytical framework: (1) identifying critical influencing factors through comprehensive grid analysis; (2) forecasting future trends of these factors using grey prediction models; (3) calculating total investment requirements via support vector machine algorithms; and (4) allocating regional investments based on systematic evaluations of existing grid infrastructure. This methodology ensures scientifically grounded investment decisions that balance technical requirements with regional development priorities.

Regarding data selection, our study utilizes Lishui City’s distribution network investment records and related influencing factor data from 2015 to 2021, a period reflecting significant policy impacts following China's 2015 power sector reform. This seven-year dataset provides a robust foundation for developing our predictive learning model, capturing both reform-induced market transformations and recent development trends.

4.2.2. Determine the Influencing Factors

(1)

Influencing factors of the primary election

Distribution network investment must consider two aspects—local economic and social development needs, the company’s overall investment capacity, and investment performance. Therefore, eight influencing factors are selected from three aspects: economic development, corporate operation, and investment performance, as follows:

First, economic development factors include regional GDP, electricity consumption of the whole society, the maximum load of electricity consumption of the whole society, and the net increase in capacity of industrial expansion. To be specific, regional GDP is an important indicator reflecting the trend of local economic development, while the electricity consumption of the whole society, the maximum load of electricity consumption of the whole society, and the net increase capacity of industry expansion reflect the changing trend of regional power demand, which are all important factors affecting the investment decision of distribution network.

Second, the company’s operational factors include electricity sales and electricity sales income (two factors). Among them, electricity sales are closely related to the above “electricity consumption of the whole society”, reflecting the changing trend of electricity demand; Electricity sales income is an important indicator reflecting the company’s investment ability, and the above two factors affect the company’s investment decision.

Thirdly, investment performance factors include two factors: the increment of electricity sales per unit of power grid investment and the increment of load per unit of power grid investment. This is an important indicator to measure the company’s input-output benefits, which should be taken into account in the preliminary analysis.

(2)

Analysis to determine the influencing factors—correlation analysis

To assess the impact of various factors on distribution network investments, we employ correlation analysis to identify key determinants. This approach calculates correlation coefficients between potential influencing factors and actual investment data, enabling the selection of the most statistically significant variables for subsequent investment modeling.

Correlation analysis examines the statistical relationship between variables to quantify their degree of association. This method requires variables to demonstrate meaningful connections or probabilistic dependencies. Among various correlation analysis techniques, preliminary assessment of our dataset confirmed the suitability of Pearson’s correlation coefficient [14] for measuring the relationship between each influencing factor and distribution network investments. Consequently, our study employs this parametric measure for its appropriateness to our data characteristics and research objectives.

① Covariance [15]. To understand Pearson’s correlation coefficient, we first need to understand Covariance. Variance represents the fluctuation of a variable from the mean value; covariance represents the relationship between two variables X and Y, and its calculation formula is as follows:

$$COV(X,Y)={\displaystyle \frac{1}{n-1}}{\displaystyle \sum _1^n(X_i-\overline{X})(Y_i}-\overline{Y})$$

(1)

When X = Y, the covariance is the variance. If the change trend of X and Y is consistent, COV(X,Y) > 0, and if the change trend is opposite, COV(X,Y) < 0. From this, the covariance can be used to measure the correlation of X and Y.

Although the covariance can reflect the correlation degree of two random variables (when the covariance is greater than 0, the two random variables are positively correlated; A value less than 0 indicates a negative correlation), its absolute value is greatly affected by the dimension. If X expands 10 times, COV(X,Y) increases 10 times, but the X/Y correlation does not change substantially. To eliminate the effect of this dimension, the standard deviation of the two variables is divided and standardized to obtain a stable and comparable correlation coefficient.

② Pearson correlation coefficient. Pearson correlation coefficient (R-value) is extended from the above covariance formula, which is used to measure the correlation degree (linear correlation) between two variables X and Y. The value is between −1 and 1, with a negative value indicating a negative correlation and a positive value indicating a positive correlation. The closer the value is to ±1, the higher the correlation is. When the value of the Pearson correlation coefficient is equal to 1, it indicates that there is a completely positive correlation between the two variables. When the value of the Pearson correlation coefficient is equal to −1, it indicates a completely negative correlation between the two variables. When the Pearson correlation coefficient is 0, it means that the two variables are linearly independent. It is defined as the product of the covariance of two variables divided by their standard deviation, and the specific formula is as follows [14]:

$$COR(X,Y)={\displaystyle \frac{{\displaystyle \sum _1^n(X_i-\overline{X})(Y_i-\overline{Y})}}{\sqrt{{\displaystyle \sum _1^n{(X_i-\overline{X})}^2{\displaystyle \sum _1^n{(Y_i-\overline{Y})}^2}}}}}$$

(2)

The application scope of the Pearson correlation coefficient has the following three aspects: first, the relationship between two variables is linear, and both are continuous data. Second, the population of both variables is normally distributed, or nearly normally unimodal. Third, the observations of the two variables are paired, and each pair of observations is independent of the other.

③ Test of normal distribution-S-W [16]. The Shapiro–Wilk (S-W) test compares the sample distribution with the normal distribution in statistical significance to determine whether the data show deviations from normality or conformity and is suitable for small data samples. The S-W test is based on two hypotheses: H0: the population distribution from which the sample comes follows a normal distribution; H1: The population distribution from which the sample comes does not follow a normal distribution. The two hypotheses are mutually exclusive, and only one of them is true. Otherwise, it does not conform. Because the number of samples selected in this study is small, the Shapiro–Wilk test is conducted on the data to check its significance. If it is not significant (p > 0.05), it indicates that it conforms to the normal distribution; otherwise, it does not conform to the normal distribution (Note: in general, it is difficult to meet the test in real research situations).

4.2.3. Forecast the Trend Value of Influencing Factors—Grey Forecast

The grey prediction model [17] is a forecasting technique that extracts developmental patterns from limited historical data to construct mathematical models for future projections. This method analyzes equidistant time-series observations to identify system dynamics, enabling predictions of either future states or the timing of specific milestones. Particularly effective with incomplete datasets, it provides scientifically grounded forecasts by systematically extrapolating past and present trends through quantitative modeling.

Recent research has successfully applied grey prediction models to various domains, including socioeconomic forecasting, energy systems analysis, traffic management, power grid planning, and engineering projections. Given our study's characteristics–limited sample size, short forecasting horizon, and system uncertainties–this method proves particularly suitable for predicting factors influencing distribution network investments. The model's effectiveness with small datasets and its ability to handle indeterminate variables make it an ideal choice for our research context.

(1) Related concepts of grey prediction

① The grey prediction method is a forecasting approach specifically designed for analyzing uncertain systems with limited data. This technique: (1) evaluates trend correlations among system factors through dissimilarity analysis, (2) processes raw data to identify underlying patterns, (3) generates regularized data sequences, and (4) constructs differential equation models to project future developments. By systematically transforming irregular data into predictable patterns, it effectively handles the inherent uncertainties in complex systems.

② GM(1,1) [18,19,20,21]. Gray system theory establishes mathematical models through three key steps: (1) defining gray derivatives and differential equations within correlation space using smooth discrete functions, (2) transforming discrete data sequences into dynamic differential equation models, and (3) processing random variables into regularized sequences with reduced randomness. This approach enables effective analysis of system dynamics by converting irregular data into tractable mathematical forms suitable for studying evolutionary processes.

The gray derivative of $x^{\left(1\right)}$ is defined as follows.

$$d\left(k\right)=x^{\left(0\right)}\left(k\right)=x^{\left(1\right)}\left(k\right)-x^{\left(1\right)}\left(k-1\right)$$

(3)

Let $z^{\left(1\right)}\left(k\right)$ be the neighbor value of the sequence $x^{\left(1\right)}$ to generate a sequence, that is,

$$z^{\left(1\right)}\left(k\right)=\alpha x^{\left(1\right)}\left(k\right)+(1-\alpha )x^{\left(1\right)}$$

(4)

Therefore, the gray differential equation model of GM(1,1) is defined as:

$$d\left(k\right)+\alpha x^{\left(1\right)}\left(k\right)=b \mathrm{or} x^{\left(0\right)}\left(k\right)+\alpha z^{\left(1\right)}\left(k\right)=b$$

(5)

where $x^{\left(0\right)}\left(k\right)$ is the grey derivative, α is the development coefficient, $z^{\left(1\right)}\left(k\right)$ is the whitening background value, and b is the grey action.

Let k = 2, 3,…, n is substituted into the above equation:

$$\left\{\begin{array}{c}{x}^{\left(0\right)}\left(2\right)+\alpha z^{\left(1\right)}\left(2\right)=b\\ x^{\left(0\right)}\left(3\right)+\alpha z^{\left(1\right)}\left(3\right)=b\\ \dots \\ x^{\left(0\right)}\left(n\right)+\alpha z^{\left(1\right)}\left(n\right)=b\end{array}\right.$$

(6)

Introduce matrix–vector notation:

$$u=\left[\begin{array}{c}a\\ b\end{array}\right], Y=\left[\begin{array}{c}{x}^{\left(0\right)}\left(2\right)\\ x^{\left(0\right)}\left(3\right)\\ \dots \\ x^{\left(0\right)}\left(n\right)\end{array}\right], B=\left[\begin{array}{c}\begin{array}{cc}{-z}^{\left(1\right)}\left(2\right)& 1\end{array}\\ \begin{array}{cc}{-z}^{\left(1\right)}\left(3\right)& 1\end{array}\\ \begin{array}{cc}\dots & \dots \end{array}\\ \begin{array}{cc}{-z}^{\left(1\right)}\left(n\right)& 1\end{array}\end{array}\right]$$

(7)

Therefore, the GM(1,1) model can be expressed as Y = B*u. So now the problem is to find the value of a and b, we can use the univariate linear regression, that is, the least square method to find their estimated values as follows:

$$u=\left[\begin{array}{c}a\\ b\end{array}\right]={\left(B^{T}B\right)}^{-1}{B}^{T}Y$$

(8)

(3) GM(1,1) albino type [18]. For the gray differential equation of GM(1,1), if k = 2, 3,…, n is regarded as a continuous variable t, then the previous $x^{\left(1\right)}$ is regarded as a function of time t, so the gray derivative $x^{\left(0\right)}\left(k\right)$ becomes the derivative of the continuous function ${\displaystyle \frac{{dx}^{\left(1\right)}\left(t\right)}{dt}}$, and the whitened background value $z^{\left(1\right)}\left(k\right)$ corresponds to the derivative $x^{\left(1\right)}\left(t\right)$. Thus, the gray differential equation of GM(1,1) corresponds to the white differential equation of:

$${\displaystyle \frac{{dx}^{\left(1\right)}\left(t\right)}{dt}}+\alpha x^{\left(1\right)}\left(t\right)=b$$

(9)

(2) The steps of grey prediction [18,20]

① Data testing and processing. To ensure the feasibility of the GM(1,1) modeling method, it is necessary to perform the necessary test processing on the known data.

Let the original data column $x^{\left(0\right)}=(x^{\left(0\right)}\left(1\right), x^{\left(0\right)}\left(2\right),\dots , x^{\left(0\right)}\left(n\right))$, calculate the rank ratio of the sequence:

$$\lambda \left(k\right)={\displaystyle \frac{x^{\left(0\right)}\left(k-1\right)}{x^{\left(0\right)}\left(k\right)}}, k=2, 3,\dots ,n$$

(10)

If all the level ratios fall within the allowable coverage region $X=(e^{{\displaystyle \frac{-2}{n+1}}},e^{{\displaystyle \frac{2}{n+1}}})$, then the sequence $x^{\left(0\right)}$ can establish the GM(1,1) model and grey prediction can be carried out. Otherwise, perform appropriate transformation processing on the data, such as translation transformation:

$$y^{\left(0\right)}\left(k\right)=x^{\left(0\right)}\left(k\right)+c, k=1, 2,\dots ,n$$

(11)

Take c so that the level ratios of the data columns fall within the allowable coverage.

② The GM(1,1) model is established. Let $x^{\left(0\right)}=(x^{\left(0\right)}\left(1\right),{ x}^{\left(0\right)}\left(2\right),\dots ,{ x}^{\left(0\right)}\left(n\right))$ meet the above requirements, and use it as the data column to establish the GM(1,1) model.

$$x^{\left(0\right)}\left(k\right)+\alpha z^{\left(1\right)}\left(k\right)=b$$

(12)

The estimated values of a and b are obtained by regression analysis, so the corresponding whitening model is

$${\displaystyle \frac{d{x}^{\left(1\right)}\left(t\right)}{dt}}+\alpha x^{\left(1\right)}\left(t\right)=b$$

(13)

The solution is

$$x^{\left(1\right)}\left(t\right)=\left(x^{\left(0\right)}\left(1\right)-{\displaystyle \frac{b}{a}}\right)e^{-a(t-1)}+{\displaystyle \frac{b}{a}}$$

(14)

Then the predicted value is obtained:

$${\widehat{x}}^{\left(1\right)}\left(k+1\right)=\left(x^{\left(0\right)}\left(1\right)-{\displaystyle \frac{b}{a}}\right)e^{-ak}+{\displaystyle \frac{b}{a}}, k=1, 2,\dots ,n-1$$

(15)

Accordingly, the predicted value is obtained:

$${\widehat{x}}^{\left(0\right)}\left(k+1\right)={\widehat{x}}^{\left(1\right)}\left(k+1\right)-{\widehat{x}}^{\left(1\right)}\left(k\right), k=1, 2,\dots ,n-1$$

(16)

③ The test of the grey GM(1,1) model [18]. The posterior difference ratio c value is used to judge the model accuracy, which is shown in

Table 1. Accuracy table of grey prediction model.

Accuracy Grade	c Value
good	c ≤ 0.35
qualified	0.35 < c ≤ 0.50
Barely qualified	0.50 < c ≤ 0.65
unqualified	c > 0.65

.

4.2.4. Construction of Investment Scale Prediction Model

Power grid investment forecasting typically employs two conventional approaches: (1) econometric regression (including multiple regression and cointegration analysis) and (2) comprehensive evaluation methods. However, these methods present notable limitations: traditional regression techniques often fail to account for nonlinear relationships between influencing factors and investment scale, while most existing studies overlook critical endogeneity issues in their econometric models. These methodological constraints reduce the accuracy and reliability of investment predictions. Current comprehensive evaluation methods for grid investment forecasting exhibit significant limitations, particularly in their handling of complex factor relationships. These approaches demonstrate: (1) inherent subjectivity in indicator weighting, (2) oversimplification of nonlinear factor interactions, and (3) predominant reliance on linear assumptions. Such constraints are particularly problematic given the multi-dimensional, nonlinear nature of investment determinants in power grid systems, where most influencing factors demonstrate complex, non-proportional relationships with investment outcomes.

The support vector machine (SVM) method [22] offers distinct advantages for grid investment forecasting by effectively addressing nonlinear relationships through kernel-based transformation. This approach: (1) employs kernel functions to project nonlinear input data into higher-dimensional feature spaces, (2) enables linear separability of complex patterns, and (3) demonstrates particular strength in small-sample scenarios. These capabilities make SVM particularly suitable for grid investment prediction, where limited historical data and strong nonlinearities among influencing factors render conventional linear regression methods suboptimal. The SVM approach is particularly well-suited for predicting grid investment scales due to its inherent advantages in handling the problem's key characteristics. SVM demonstrates superior performance where traditional methods fail, specifically in addressing: (1) the limited sample size of investment data, (2) complex nonlinear relationships between factors, and (3) the need for robust generalization from sparse datasets. These capabilities make SVM the preferred methodological choice for this forecasting challenge.

The SVM algorithm excels at solving classification and regression problems through structural risk minimization. Its core methodology involves: (1) constructing optimal regression functions by transforming problems into convex quadratic programming formulations, and (2) employing nonlinear mapping to convert low-dimensional data into linearly separable high-dimensional features. Particularly effective for moderate-sized datasets, SVM demonstrates superior prediction accuracy and generalization capability compared to alternative algorithms, especially when training samples are limited [23,24,25,26]:

Suppose the sample is $(x_1,y_1),(x_2,y_2),\dots ,(x_k,y_k)\in R^N\times R$, where $x_i\in R^N$ is the input parameter, $y_i\in R$ is the corresponding output parameter, and k is the number of samples. Input parameters and output parameters can be expressed as the following equation:

$$f\left(x\right)=\omega \theta \left(x\right)+b$$

(17)

where ω is the weight vector and b is the threshold.

The regression function of SVM is calculated through the empathy theory, and the objective function and constraints are as follows:

$$R\left(\omega \right)=\mathit{min}\left[{\displaystyle \frac{1}{2}}{‖\omega ‖}^2+C{\sum }_{i=1}^n({\xi }_i+{{\xi }_i}^{\ast })\right]$$

(18)

$$s.t.\left\{\begin{array}{c}{y}_i-f\left(x_i\right)\le \epsilon +{\zeta }_i\\ f\left(x_i\right)-y_i\le \epsilon +{{\zeta }_i}^{\ast }\\ {\zeta }_i{{\zeta }_i}^{\ast }\ge 0\\ 0\le i\le 1\end{array}\right.$$

(19)

where ${\zeta }_i$ and ${{\zeta }_i}^{\ast }$ are non-negative slack variables; C is the penalty factor. The penalty degree of samples exceeding the error range is controlled to balance the empirical risk and model complexity. ε is the parameter of the insensitive loss function.

The Lagrange method [27] is used to solve the above optimization problem as follows:

$$W(a_i,{a_i}^{\ast })=\mathit{max}\left[{\displaystyle \frac{1}{2}}{\sum }_{i=1}^n{\sum }_{j=1}^n(a_i-{a_i}^{\ast }\left)\right(a_j-{a_j}^{\ast }\left)K\right(x_i,x_j)\right]$$

(20)

where $K(x_i,x_j)=\left[\theta \left(x_i\right)\ast \theta \left(x_j\right)\right]$ is the kernel function of SVM; $a_i,{a_i}^{\ast }$ is the Lagrange coefficient.

Then the regression function of SVM is

$$f\left(x\right)={\sum }_{i=1}^n(a_i-{a_i}^{\ast })K(x_i,x_j)+b$$

(21)

where $K(x_i,x_j)=\mathit{exp}(-g{\left|x_i-x_j\right|}^2)$, the radial basis function is adopted for the kernel function, and g is the parameter of the kernel function.

4.2.5. Regional Allocation of Investment Scale

Grid investment planning requires a thorough assessment of regional grid development status to optimize resource allocation and enhance investment precision. While existing research has extensively explored single-region grid evaluations ("horizontal" comparisons), significant gaps remain in comparative analyses of distribution network investment efficiency across multiple regions. This limitation hinders the development of data-driven investment strategies that could maximize returns across diverse grid infrastructures.

We establish a complete index system for the evaluation scheme of power grid construction status, as shown in

Table 2. Evaluation index of the current situation of power grid construction.

Evaluation Index of the Current Situation of Power Grid Construction	Power Supply Quality	Power supply reliability
		Comprehensive voltage qualification rate
	Power Grid Structure	10 kVN-1 pass rate
		10 kV average power supply radius
		Interconnection rate of 10 kV main line
	Equipment Level	Cable conversion rate of 10 kV line
		Insulation rate of overhead power lines
		Proportion of high-loss distribution transformers
		Household average distribution transformer capacity (proportion of household average distribution transformers)
	Power Supply Capability	Average load rate of distribution lines
	Intelligent Level	Distribution automation coverage rate
	Power Grid Benefits	Electricity sales
		Net increase in capacity due to business expansion
	Planning Scheme	Conversion rate
		Proportion of completed investments in the previous year

, and use the Delphi method [20] to modify the traditional analytic hierarchy process for comprehensive evaluation, to make full use of expert experience.

After the total investment is obtained, the initial allocation proportion of investment in each region is calculated based on the evaluation score of the current situation of the distribution network construction in each region. To ensure the balanced development of the distribution network in each region, the allocation proportion can be adjusted appropriately according to the construction situation of the region to obtain the final allocation result of regional investment. Comprehensive consideration of the project progress, investment effectiveness, and proportion of new energy in each region to make feedback adjustments, investment plan completion rate, capital entry rate, the proportion of new energy as feedback indicators to divide regional levels, all indicators of the excellent performance of the region appropriate increase in the proportion of allocation, all indicators of good performance of the region appropriate allocation proportion unchanged. The regions with poor indicator performance are appropriately reduced in proportion to the allocation shown in

Table 3. Table of feedback adjustment ratio of regional investment scale.

Gradation	Specific Basis	Feedback
First level	Indicators are excellent (≥90%)	Increase appropriately
Second level	Indicators are performing well (80%~90%)	Constant proportion
Third level	The presence indicators perform poorly (≤80%)	Reduce appropriately

.

4.3. Allocation of Investment Structure

4.3.1. Project Attribute Analysis

Firstly, each project is classified according to its attributes, and the importance of each attribute to the construction of the distribution network is determined according to the gap between the status quo of each attribute and the planning target, to match the resource input to ensure high investment efficiency.

Taking distribution network projects as an example, distribution network projects include 13 categories: substation supporting outlet, interval expansion, line connection project, main line construction and transformation, new energy supporting outlet, distribution and transformation and low-voltage transformation, distribution and transformation of new distribution points, distribution and transformation of capacity expansion, branch line construction and transformation, emergency repair package, precise loss reduction, distribution automation, and industry expansion project. Distribution network project attributes can be roughly divided into ten categories, such as meeting the requirements of new load power supply, supporting substation delivery, solving low voltage station area, solving “jam neck”, solving equipment overload or overload, eliminating equipment security risks, strengthening network structure, transforming high-loss distribution transformer, intelligent construction, and new energy access. The attributes of distribution network projects are correlated with the evaluation indexes of distribution network construction effectiveness, as shown in

Table 4. Association table of project attributes and construction indicators.

Properties of the Project	Evaluation Indicators
Projects of the “New Load Power Supply Requirements” category	Common index; Line N-1 pass rate; each household has variable capacity; power supply reliability rate.
Projects of the “Substation Supporting Transmission” category	Common index; reasonable rate of line segmentation; Line N-1 pass rate; average line load rate.
Projects related to “solving low voltage substation areas”	Common index; comprehensive voltage qualified rate; load peak-valley difference; variable load rate.
Projects related to “solving neck problems”	Common index; 10 kV/400 V divider line loss rate; Line N-1 pass rate; average line load rate.
Projects related to “solving equipment overload” and “overloading”	Common index; Line N-1 pass rate; each household has variable capacity; average line load rate.
Projects related to eliminating equipment safety hazards	Common index; 10 kV/400 V divider line loss rate; insulation rate of overhead line.
Projects related to strengthening grid structures	Common index; reasonable rate of line segmentation; Line N-1 pass rate; Line overload rate.
The project of “transforming high loss distribution transformers”	Common index; variable load ratio; average value of maximum load rate of distribution variable.
Projects related to “intelligent construction”	Common index; coverage of automation standards; transparency rate of distribution network.
Projects related to “new energy access”	Common index; energy storage penetration; load peak-valley difference; distributed power penetration.

Note: The common indicators are capital balance rate, investment deviation, and matching degree with substation.

.

4.3.2. Optimal Allocation of Project Attributes for Distribution Network Investment

Both the analytic hierarchy process [28] and the entropy weight method [29] are often used to weight indicators, but the entropy weight method ignores the importance of indicators themselves and cannot take into account the horizontal influence between indicators.

For a certain area, the AHP method is used to solve the improvement urgency of each construction index, to match the importance of each associated attribute to the distribution network construction.

Specifically, the judgment matrix is constructed based on the gap between the current value of each index and the target value of the planned power grid: the greater the difference is, the greater the urgency of improvement of the index is, and the greater the importance is assigned to the pairwise comparison [30,31]. The value formula for constructing the judgment matrix is as follows:

$$a_{ij}=\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{d}\left({\displaystyle \frac{\Delta M_i}{\Delta M_j}}\right)$$

(22)

$$\Delta M_i={\displaystyle \frac{\left|\stackrel{—}{M_i}-M_i\right|}{M_i}}$$

(23)

where $a_{ij}$ is the value of the importance degree of indicator i relative to indicator j, round() is the rounding function, and $\Delta M_i$ is the percentage difference between the current value of the indicator $M_i$ and the target value $\stackrel{—}{M_i}$.

For the judgment matrix $A{\left(a_{ij}\right)}_{n\times n}$, the maximum eigenvalue ${\lambda }_{max}$ is calculated, and the relative consistency index CR is introduced to verify whether the judgment matrix has satisfactory consistency. The eigenvector method is used to solve the weight vector $W^{\mathrm{\text{'}}}\left(w_1^{\mathrm{\text{'}}},w_2^{\mathrm{\text{'}}},\dots ,w_n^{\mathrm{\text{'}}}\right)$, where

$$A{W}^{\mathrm{\text{'}}}={\lambda }_{max}{W}^{\mathrm{\text{'}}}$$

(24)

By normalizing $W^{\mathrm{\text{'}}}$, the relative weight of each evaluation index in a certain layer for its upper-level index can be obtained $w_j$, which is the improvement urgency of the index of j.

$$w_j={\displaystyle \frac{w_j^{\mathrm{\text{'}}}}{\sum _{j=1}^n w_j^{\mathrm{\text{'}}}}},{\sum }_{j=1}^n w_j=1, 0\le w_j\le 1$$

(25)

For a certain project attribute, the more indicators it is associated with, the greater the improvement urgency of the indicator, and the higher the importance of the attribute to the distribution network construction. Therefore, the attribute importance is as follows:

$$P_k={\sum }_{j\in n_k} w_j,k=1, 2,\dots , 9$$

(26)

where $P_k$ is the importance degree of the k attribute, $n_k$ is the construction index set associated with the attribute, $w_j$ is the improvement urgency degree of the j indicator.

The optimal allocation model of project attributes of the distribution network investment is as follows:

$${\delta }_1:{\delta }_2:\dots :{\delta }_9=P_1:P_2:\dots :P_9$$

(27)

$$\begin{array}{c} \\ H_k={\displaystyle \frac{{\delta }_k}{\sum _{k=1}^9 {\delta }_k}}{C}_i,k=1, 2,\dots , 9\end{array}$$

(28)

where ${\delta }_k$ is the allocation proportion of the k attribute, $C_i$ is the investment scale of the i region, and $H_k$ is the investment scale of the k attribute.

4.4. Distribution Network Investment Project Decision-Making

4.4.1. Classification and Comprehensive Evaluation of Investment Projects

The construction project of the distribution network is directly related to the receiving end, and its planning and construction are more likely to interact with the consumption behavior of users.

Taking the project of “power distribution and low-voltage transformation” as an example, refer to the construction index corresponding to this attribute in Table 4 for the index of power grid operation effect. To eliminate the influence of the investment scale of each project and the construction status of the region, the indices are modified as “improvement degree of energy storage penetration per unit investment”. “Net present value” is the most important index in the project economic evaluation, considering the time value of capital and investment risk, while “return on investment” reflects the comprehensive profitability of the investment project. Therefore, by selecting it to measure the economic benefits of the project, the final comprehensive evaluation index system for project benefits is shown in

Table 5. The comprehensive evaluation index system of the “distribution and low voltage transformation” project benefits.

Layer of Criterion	Evaluation Index Layer
Effect of operation	Degree of improvement of the commonality index of unit investment
	Improvement degree of the qualified rate of comprehensive voltage per unit investment
	Improvement degree of peak-valley difference per unit investment load
	Degree of improvement of heavy load rate per unit investment
Economic benefits	Net present value
	Return on investment

.

4.4.2. Indicator Weight Determination Method

The weighting of evaluation indicators represents a critical yet challenging component of comprehensive assessments, currently addressed through either subjective or objective methods. Subjective approaches like AHP and Delphi incorporate valuable expert judgment but risk introducing bias through over-reliance on qualitative scoring, potentially distorting indicator importance. Conversely, objective methods rely solely on quantitative data analysis, which, while statistically rigorous, may neglect crucial domain expertise. This fundamental methodological dichotomy underscores the need for more balanced approaches that integrate both expert insight and data-driven rigor in evaluation frameworks. Objective weighting methods determine indicator weights by quantitatively analyzing intrinsic dataset characteristics, thereby eliminating subjective bias. Typical techniques include: (1) the entropy weight method, measuring information uncertainty, (2) principal component analysis, identifying variance patterns, and (3) the mean square error approach [32], evaluating prediction deviations. These data-driven methods derive weights solely from statistical relationships and variability patterns within the dataset itself, ensuring mathematically validated and reproducible results that accurately reflect underlying metric interrelationships.

The entropy weight method is employed for objective index weighting, utilizing information entropy to quantify each indicator's informational value. This approach offers two key advantages: (1) eliminating human bias in weight determination through purely mathematical computation, and (2) preserving maximal original information by measuring each indicator's entropy-based contribution. By converting entropy values into weights, the method ensures evaluation results accurately reflect the dataset's inherent characteristics while overcoming the subjectivity limitations of alternative weighting approaches.

We comprehensively consider the characteristics of indicators and relevant regulations of the power industry and divide the 18 indicators in Figure 1 into positive indicators (such as power supply reliability rate) and negative indicators (such as load peak-to-valley difference rate).

(1) Dimensionless processing of indicators [33]

Normalization of positive indicators:

$$r_{ij}={\displaystyle \frac{x_{ij}-\underset{1\le i\le m}{\min }\left\{x_{ij}\right\}}{\underset{1\le i\le m}{\max }\left\{x_{ij}\right\}-\underset{1\le i\le m}{\min }\left\{x_{ij}\right\}}}$$

(29)

Normalization of negative indicators:

$$r_{ij}={\displaystyle \frac{\underset{1\le i\le m}{\max }(x_{ij})-x_{ij}}{\underset{1\le i\le m}{\max }(x_{ij})-\underset{1\le i\le m}{\min }(x_{ij})}}$$

(30)

where $x_{ij}$ is the index value of the j index of the ith object in the evaluation year (2022); m is the number of evaluation objects. The value of $r_{ij}$ index after normalization.

(2) Determination of the weight of the evaluation index [34]

$x_{ij}(i=1, 2,\dots ,m;j=1, 2,\dots ,n)$ is the observed data of the j index in the ith evaluation object. For a given j, the greater the difference of $x_{ij}$ is, the greater the comparative effect of this index on the system is, that is, the more information this index contains and transmits. The steps of using the entropy method to determine the weight of indicators are as follows:

① Calculate the entropy value of each index, set $e_j$ as the entropy value of the j evaluation index, then the entropy value $e_j$ has been calculated as follows:

$$f_{ij}={\displaystyle \frac{x_{ij}}{{\displaystyle \sum _{i=1}^m{x}_{ij}}}}$$

(31)

$$e_j={\displaystyle \frac{-1}{\ln m}}{\displaystyle \sum _{i=1}^m{f}_{ij}}\ln f_{ij}$$

(32)

where $f_{ij}$ is the characteristic proportion of the ith evaluation object under the j index; $x_{ij}$ is the observed data of the j index in the i evaluation object (i = 1, 2,…, m; j = 1, 2,…, n); $\sum _{i=1}^m{x}_{ij}$ is the sum of the observed data of all evaluation objects of the j index.

(2) Calculate the entropy weight of each index. Let $w_j$ be the entropy weight of the j evaluation index, then the entropy weight of the index is as follows:

$$w_j={\displaystyle \frac{1-e_j}{n-{\sum }_i^n{e}_j}},j=1, 2,\dots ,n$$

(33)

where $e_j$ is the entropy value of the j index.

③ Comprehensive evaluation score. For the index values of the index layer, the multiplication and addition operators M(*,+) are used for weighted integration, and the comprehensive score of the current situation of Lishui distribution network construction can be obtained. The calculation method is as follows:

$$S_i=100{\sum }_{j=1}^n(w_j\ast r_{ij})$$

(34)

where $S_i$ is the comprehensive evaluation score of the evaluation object of i; $r_{ij}$ is the normalized value of the j index of the object of i; $w_j$ is the weight of the evaluation index of j.

4.4.3. Project Optimization Model

Based on the investment scale constraints and project evaluation results of each attribute, the optimal model is established to maximize the total benefit of project construction under each attribute [35]:

$$\begin{array}{l}\max F={\displaystyle \sum _{i=1}^{l}R(p_i})\\ s.t\left\{\begin{array}{l}{p}_i\in P_k\\ {\displaystyle \sum _{i=1}^{l}C({\mathrm{p}}_{\mathrm{i}})\le H_k}\end{array}\right.\end{array}$$

(35)

where ${R(P}_i)$ is the comprehensive score value of the project $P_i$, $P_k$ is the set of projects under the k investment structure, k = 1, 2,…, 13; ${C(P}_i)$ is the investment amount of the project; $H_k$ is the investment scale constraint under the k investment structure.

The project optimization of each investment structure is carried out, respectively, and the final result is the optimal project portfolio, which can be used as the outbound scheme of investment projects.

5. Example of Lishui Distribution Network Investment for New Power System

5.1. Application of Investment Scale Decision

5.1.1. Determination of Influencing Factors of Lishui Distribution Network Investment

To identify key determinants of distribution network investments in Lishui, this study implemented a rigorous two-phase analytical process. First, Shapiro–Wilk tests were conducted to verify the normality and statistical significance of potential influencing factors. Subsequently, correlation analysis was performed to quantify relationships between these factors and actual investment data, with only those demonstrating strong, statistically significant correlations being selected for the predictive model. This dual verification approach–combining distribution testing with correlation screening–ensures objective, data-driven selection of investment drivers while maintaining methodological robustness and eliminating selection bias. The resulting factors serve as the quantitative foundation for reliable investment forecasting in Lishui's power grid development.

(1)

Normal distribution test of influencing factors

The results of descriptive statistics and normality tests are presented in

Table 6. Overall description of results.

Variables	Sample Size	Median Number	Average Value	Standard Deviation	Degree of Skewness	Degree of Kurtosis	The S-W Test	The K-S Test
Electricity consumption of the whole society (100 million KWH)	7	103.45	103.34	20.203	0.386	−0.788	0.962 (0.835)	0.191 (0.922)
Electricity sold (100 million KWH)	7	95.96	96.071	19.193	0.428	−0.855	0.956 (0.780)	0.196 (0.908)
GDP of Lishui (100 million yuan)	7	1354.22	1351.591	238.058	0.177	−1.052	0.973 (0.917)	0.145 (0.993)
Net expansion capacity (kVA)	7	1,020,633.6	997,985.613	190,949.695	−0.062	−0.334	0.958 (0.801)	0.202 (0.889)
Maximum electricity load of the whole society (10,000 kW)	7	186.44	191.826	37.685	0.842	−0.266	0.892 (0.285)	0.221 (0.818)
Investment load increment per unit of power grid (10,000 kW/Yuan)	7	23.773	26.915	7.747	0.505	−1.589	0.880 (0.156)	0.213 (0.734)
Incremental electricity sales per unit of grid investment (100 million KWH/Yuan)	7	11.845	13.353	3.622	0.646	−1.369	0.873 (0.131)	0.217 (0.714)

, including medians, means, etc., which are used to test the normality of the data.

Table 6 reveals that all examined variables–including societal electricity consumption (100 million kWh), electricity sales (100 million kWh), regional GDP (100 million yuan), industrial capacity expansion (kVA), peak load (10 million kW), and investment efficiency metrics (per-yuan increments of electricity sales and load)–demonstrate limited sample sizes. Given this data characteristic, the Shapiro–Wilk (S-W) test was appropriately employed to assess distribution normality, as this method is particularly suitable for small-sample analyses while maintaining rigorous statistical validity. The normality test results indicate all variables follow normal distributions, as exemplified by the societal electricity consumption sample (p = 0.835). This non-significant p-value (α = 0.05) fails to reject the null hypothesis, confirming normal distribution–a pattern consistent across all examined factors. Consequently, Pearson correlation analysis becomes appropriate for evaluating relationships between these normally distributed predictors and distribution network investments.

(2)

Correlation analysis to determine the influencing factors

To accurately analyze the impact of various influencing factors on distribution network investment, the correlation analysis method was adopted. By calculating the Pearson correlation coefficient between each influencing factor and distribution network investment, the strongly correlated influencing factors were selected as the basis for constructing the subsequent distribution network investment model. The calculation results are shown in

Table 7. The correlation coefficients between distribution network investment and various influencing factors.

Variables	Correlation Coefficient
Distribution network investment (100 million yuan)	1
Regional GDP (100 million yuan)	0.879
Total electricity consumption of the whole society (100 million KWH)	0.871
Maximum electricity load of the whole society (10,000 kW)	0.797
Electricity sold (100 million KWH)	0.855
Net expansion capacity (kVA)	0.776
Incremental electricity sales per unit of grid investment (100 million KWH/YUAN)	−0.613
Investment load increment per unit of power grid (10,000 kW/YUAN)	−0.679

.

The correlation analysis reveals the following descending order of factor influence: regional GDP (strongest correlation), followed by total electricity consumption, electricity sales, peak load demand, and industrial capacity expansion. However, multicollinearity analysis identified redundant variables—particularly among electricity metrics (total consumption, sales, and revenue), which demonstrate strong intercorrelations. These interdependent factors require consolidation to avoid model overfitting while preserving the most representative indicators. The study ultimately selected four core determinants of distribution network investment through systematic evaluation: regional GDP, electricity sales, peak load demand, and industrial capacity expansion. This optimized factor combination provides comprehensive coverage of critical investment drivers across four dimensions: (1) socioeconomic development needs (GDP), (2) grid demand quantification (peak load), (3) operational performance metrics (electricity sales), and (4) infrastructure requirements (capacity expansion). The selection prioritizes objectively measurable variables, with electricity sales specifically chosen for its data accuracy and reliability, ensuring robust predictive validity.

5.1.2. Forecast the Trend Value of the Influencing Factors of the Lishui Distribution Network

(1)

Regional GDP forecast

The grey MG(1,1) model prediction algorithm is used to calculate the GDP value of Lishui City in 2022 according to the GDP data of Lishui City from 2015 to 2021 (see

Table 8. The GDP value of Lishui City from 2015 to 2021.

Year	2015	2016	2017	2018	2019	2020	2021
Regional GDP (100 million yuan)	1038.63	1134.13	1215.42	1354.22	1480.96	1527.75	1710.03

). The main calculation steps are as follows: first, data preprocessing, the accumulation of historical data, and the generation of data series with strong regularity, from which to find the change law of historical data. Second, the GDP of Lishui City in 2022 is predicted by the grey MG(1,1) model. Thirdly, the accuracy test: that is, to test the accuracy of judging the gray MG(1,1) model, we use the posterior difference test.

Calculated according to the steps of the algorithm of grey forecasting, it can be obtained that the forecast value of GDP of Lishui city in 2022 is 184.076 billion yuan. According to Equation (10) and Equation (11), the grade ratio test is calculated, and the results are shown in

Table 9. Table of rank ratio test results.

Item of Index	Original Value	Ratio of Rank
2015	1038.63	-
2016	1134.13	0.916
2017	1215.42	0.933
2018	1354.22	0.898
2019	1480.96	0.914
2020	1527.75	0.969
2021	1710.03	0.893

. According to Equations (3)–(8), the related accuracy test is calculated, and the results are shown in

Table 10. Grey model construction.

Coefficient of Development a	Grey Action b	The Posterior Difference Ratio C Value
−0.08	1008.619	0.01

. The a posteriori difference ratio c is 0.01, which belongs to the first class-good against the model accuracy scale. According to Equation (9), Equations (12)–(16), the GDP of Lishui was fitted, and the results are tabulated in

Table 11. Table of fitting results for Lishui GDP.

Year	Original Value	Value of Prediction	Residual Error	Relative Error (%)
2015	1038.63	1038.63	0	0
2016	1134.13	1137.048	−2.918	0.257
2017	1215.42	1232.107	−16.687	1.373
2018	1354.22	1335.113	19.107	1.411
2019	1480.96	1446.731	34.229	2.311
2020	1527.75	1567.681	−39.931	2.614
2021	1710.03	1698.742	11.288	0.66

. Therefore, it is judged that the predicted value of GDP of Lishui city, calculated by the grey MG(1,1) model, has a high degree of confidence.

The modeling results demonstrate strong validity across multiple validation metrics: (1) level ratio analysis confirms the data's suitability for grey modeling (0.779–1.284 interval), (2) exceptional predictive accuracy (posterior difference ratio = 0.01), and (3) excellent fit (average relative error = 1.232%). These collective indicators verify the model's robustness, with all diagnostic parameters meeting or exceeding established quality thresholds for reliable forecasting.

(2)

Forecast of maximum electricity load, electricity sales, and net increase in capacity of industry expansion in the whole society

Using the same forecast idea of Lishui GDP, this paper predicts the 2022 trend value of the other three influencing factors, namely, the maximum social electricity load, electricity sales, and the net increase in capacity of industry expansion. After the operation of the program, the specific prediction results are 13,687.8 billion KWH of electricity sold, the maximum electricity load of the whole society is 2.77057 million kW, and the net increase capacity of industry expansion is 1,363,334.782 kVA. The accuracy of the prediction results is also tested, and the posterior difference test C values of the maximum social electricity load, electricity sales, and net increase capacity of industry expansion are 0.029, 0.029, and 0.03, respectively, indicating that the prediction results are also “good.” See Appendix A for the specific results of the rank ratio test, the correlation accuracy test, the table of the model fitting results, and the figure of the model fitting results.

5.1.3. Prediction of Lishui Distribution Network Investment Scale

On the basis of the trend prediction of the core influencing factors mentioned above, the prediction model containing the core influencing factors is simulated and analysed based on the support vector machine algorithm. On this basis, the investment demand for the distribution network in Lishui City in 2022 is forecasted. According to the support vector machine method, i.e., Equations (17)–(21), the data of each influencing factor and the investment data of the distribution network in Lishui from 2015 to 2021 are shown in

Table 12. The influencing factors and Lishui distribution network investment data from 2015 to 2021.

Year	Net Expansion Capacity (kVA)	Electricity Sold (100 Million KWH)	GDP of Lishui (100 Million Yuan)	Maximum Electricity Load of the Whole Society (Ten Thousand kW)	Distribution Network Investment in Lishui (Ten Thousand Yuan)
2015	724,926.12	72.9	1038.63	156.74	53,546.14
2016	797,070.67	82.08	1134.13	161.14	82,778.38
2017	992,008.76	79.95	1215.42	158.62	72,756.22
2018	1,020,633.6	95.96	1354.22	186.44	99,414.56
2019	1,027,445.98	104.19	1480.96	200.87	98,000
2020	1,138,079.38	110.75	1527.75	222.28	93,500
2021	1,285,734.78	126.67	1710.03	256.69	66,543.8

.

The SVM model, developed using Equations (17)–(21), achieved strong predictive performance with a 70% training set allocation. As evidenced in

Table 13. Results of model evaluation.

The Training Set	MSE	RMSE	MAE	MAPE	R2
Results	67,732,090.863	8229.951	5320.778	0.059	0.755

, the model demonstrates excellent explanatory power (R² = 0.755), indicating robust capability in capturing the underlying investment patterns. This performance metric confirms the model's effectiveness in fitting the training data while maintaining generalization potential for investment forecasting applications.

According to the support vector machine algorithm, the predicted value of Lishui city in 2022 is 101,941,626,000 yuan, and the relative error (MAPE) of the investment scale prediction model is 0.059, and the model has good accuracy. The data for 2022 is predicted according to the support vector machine model, i.e., Equations (17)–(21), and the predicted value of investment and its independent variable data are shown in

Table 14. Forecast value of investment in Lishui City.

Year	Results of Prediction	Net Expansion Capacity (kVA)	Maximum Electricity Load of the Whole Society (Ten Thousand kW)	Electricity Sold (100 Million KWH)	GDP of Lishui (100 Million Yuan)
2015	6560.269459	724,926.12	156.74	72.9	1038.63
2016	7084.417403	797,070.67	161.14	82.08	1134.13
2017	8470.69611	992,008.76	158.62	79.95	1215.42
2018	8696.39054	1,020,633.6	186.44	95.96	1354.22
2019	8765.805585	1,027,445.98	200.87	104.19	1480.96
2020	9253.684381	1,138,079.38	222.28	110.75	1527.75
2021	9625.172936	1,285,734.78	256.69	126.67	1710.03
2022	10,194.12587	1,363,334.782	277.057	136.878	1840.76

, and Figure 3 shows the bar chart of the trend of the results of the investment prediction for Lishui City.

From the forecast results, the forecast value of investment in 2022 is 1,019,412,600 yuan. It can be seen from the chart that the predicted value shows a steady growth trend, while the actual investment shows periodic changes with the forecast results, which is reflected in the difference between the actual investment allocated in the previous year and the predicted value will be compensated to a certain extent in the next year. In other words, the actual value in the graph is lower than the predicted value in the previous year and higher than the predicted value in the next year. Among them, the investment in Lishui power grid construction declined in 2021, mainly because power grid enterprises completed the new round of national rural grid transformation and upgrading task one year in advance, and the investment in a power grid of 35 kV and below, which accounts for a large proportion of power grid investment, decreased significantly. In 2022, the State Grid Corporation of China increased its investment in the power grid, and the steady recovery of economic operation is the main reason for the recovery of investment.

5.1.4. Regional Allocation of Investment Scale in Lishui

For the 10 county-level utilities in Lishui, the model estimates a total 2022 grid investment of ¥1,019.4126 million. This allocation decision integrates: (1) predicted investment requirements from the SVM model, and (2) 2021 operational performance metrics across all subsidiaries, ensuring balanced resource distribution aligned with both projected needs and historical grid performance.

First, the evaluation framework integrates multiple data sources through a systematic process: (1) collecting baseline metrics from regional grid companies (both direct reports and calculated values), (2) establishing scoring criteria using the Urban Distribution Network Assessment Guidelines combined with expert operational insights, and (3) determining hierarchical indicator weights via analytic hierarchy process (AHP). This methodology yields comprehensive percentage-based evaluations, with detailed results presented in

Table 15. Evaluation results of the status quo of power grid construction in each region of Lishui City in 2021.

Region	Liandu	Qingtian	Jinyun	Yuanhe	Songyang	Suichang	Jingning	Longquan	Qingyuan	Nancheng
Score	97.25	81.20	97.47	57.96	84.12	76.14	80.49	59.04	66.36	71.37
Proportion	12.69%	10.60%	12.72%	7.57%	10.98%	9.94%	10.51%	7.71%	8.66%	9.31%

.

Second, based on the above evaluation scores of the status quo of distribution network construction in each region, the initial allocation proportion of investment in each region is calculated. To ensure the balanced development of the distribution network in each region, the final allocation result of regional investment can be obtained by appropriately adjusting the allocation proportion according to the regional construction situation. The distribution is shown in

Table 16. Distribution network regional investment scale distribution table (ten thousand yuan).

Region	Score	Initial Proportion	Initial Scale (Ten Thousand Yuan)	Proportion of Adjustment	Final Proportion	Final Scale (Ten Thousand Yuan)
Liandu	97.26	12.69%	12,940	0	12.69%	12,940
Qingtian	81.21	10.60%	10,804	0	10.60%	10,804
Jinyun	97.47	12.72%	12,968	1%	13.72%	13,988
Yuanhe	57.97	7.57%	7713	−1%	6.57%	6693
Songyang	84.13	10.98%	11,193	1%	11.98%	12,213
Suichang	76.14	9.94%	10,131	−1%	8.94%	9111
Jingning	80.50	10.51%	10,710	0	10.51%	10,710
Longquan	59.05	7.71%	7856	−1%	6.71%	6836
Qingyuan	66.37	8.66%	8830	1%	9.66%	9849
Nancheng	71.37	9.31%	9496	−1%	8.31%	8476
Total	771.46	1	102,640	−0.01	0.99	101,621

, and after adjustment, the total investment in each region of Lishui City is RMB 1016.21 million.

Taking the 10 county companies under the jurisdiction of Lishui City as an example, based on the status quo score of power grid construction of each subsidiary in 2021, the annual power grid investment allocation decision is made according to the total investment amount of Lishui power grid in 2022, calculated above. Taking into account the project progress, investment effectiveness, and the proportion of new energy in all regions of Lishui City, feedback adjustment is made. The distribution proportion of regions with excellent performance in all indicators is appropriately increased, such as Jinyun, while the distribution proportion of regions with good performance in all indicators remains unchanged, such as Qingtian, and the distribution proportion of regions with poor performance in indicators is appropriately reduced, such as Longquan.

5.2. Application of Investment Direction Decision

Taking the Lishui distribution network as an example, the current status and target values of indicators related to project attributes in the Lishui distribution network in 2021 and 2022 were statistically analyzed. Based on the urgency of indicator improvement, a judgment matrix was established, and the weight of each indicator was determined using the eigenvector method. The results are shown in

Table 17. Distribution network associated index value and index weight of Lishui City.

Indicators	Present Value	Target Value	Percentage of Gap	Weight
Each household is equipped with variable capacity	3.97	4.1	39.39%	0.06
Insulation rate of overhead line	43.01	42.87	27.45%	0.04
Comprehensive voltage-qualified rate	99.88	99.83	41.67%	0.06
Power supply reliability rate	99.9726	99.98	72.55%	0.11
Energy storage penetration	6.8	8	37.50%	0.06
Peak-to-valley difference in load	36.8	35	26.47%	0.04
Distributed power penetration	13.6	15	31.82%	0.05
Transparency rate of distribution network	42.8	46	44.44%	0.07
Average value of maximum load rate of distribution variable	32.6	35.78	42.97%	0.07
Line overload rate	7.86	7.43	5.47%	0.01
Variable load rate	2.22	0.69	68.92%	0.10
10 kV partial voltage line loss rate	2.35	2.23	34.29%	0.05
Automation standard coverage	95.2	98	58.33%	0.09
Reasonable rate of line segmentation	94.6	97	44.44%	0.07
Line N-1 pass rate	78.6	84.29	26.59%	0.04
Average line load rate	36.82	32	28.66%	0.04
Index of commonality	-	-	-	0.05

.

The investment scale of the distribution network in Lishui City is 1119.4126 million yuan. Based on the weights of various indicators in the table, the investment allocation results were further calculated and shown in

Table 18. Investment distribution results.

Project	Investment Distribution (Ten Thousand Yuan)
New construction and renovation of main lines	46,456
Line liaison works	4702
The substation is equipped with outgoing lines	9739
New energy-supporting line	896
Distribution and low-voltage transformation	17,127
Emergency repair kit	1735
Solve neck jams	5933
Solve equipment overload and overload	4970
Industry expansion supporting projects	14,440
Other	5944

.

5.3. Application of Investment Project Decision-Making

Assuming that Lishui City reports a total of 6 “distribution and low-voltage transformation” projects in 2022, with an investment scale of 1 million yuan for this attribute. Refer to the indicator system in Table 4 for a comprehensive evaluation, and use the entropy weight method to calculate the weights of each indicator. The specific data is shown in

Table 19. Time table of “distribution and low voltage transformation” project in Lishui City.

Indicators	Project 1	Project 2	Project 3	Project 4	Project 5	Project 6
Estimated investment/ten thousand yuan	34	26	20	17	29	25
Percentage improvement of common indicators/%	1.3	1.4	1	0.9	1	1.6
Comprehensive voltage qualified rate improvement percentage/%	4.6	6.3	2.5	2.8	5.2	4.8
Percentage of load peak-valley difference improvement/%	3.7	2.8	3.9	3.6	2.4	2.5
Distribution variable load rate improvement percentage/%	5.3	3.2	4.7	3.6	4.2	5.1
Net present value/ten thousand yuan	16.7	37.6	20.3	14.4	30.7	22.7
Return on investment/%	15.7	16.3	15.4	11.9	14.6	17.5
Total score	75.58	61.32	45.17	21.08	38.22	62.51
Ranking	No. 1	No. 3	No. 4	No. 6	No. 5	No. 2

.

Based on the project optimization model, the project optimization results under this attribute are obtained as follows: Projects 1, 6, and 2. In this way, the optimal investment portfolio of Lishui construction projects in 2022 can be obtained by obtaining the optimal project selection results under the other nine types of attributes.

6. Conclusions

This paper constructs a three-level distribution network investment decision-making system containing investment scale decision-making, investment attribute decision-making, and investment project decision-making, and achieves Lishui city distribution network investment scale allocation, attribute investment scale allocation, and investment project portfolio optimization in turn by advancing layer by layer. This decision-making system not only ensures the holistic, coordinated, and networked characteristics of distribution network investment but also ultimately achieves the goal of precision investment. The main conclusions are as follows:

Firstly, based on the analysis of the existing data, the Pearson correlation coefficient is used to screen out the factors that have a greater impact on the distribution network investment. Then, the grey MG(1,1) model is used to predict the GDP in the investment planning year. Finally, the support vector machine algorithm is used to predict the distribution network investment in the investment planning year.

Secondly, the distribution network project is divided into ten categories, and based on the urgency of improvement of each indicator, an investment direction decision-making model is constructed to determine the investment scale of each attribute in a targeted manner, laying the foundation for accurate investment. For example, Jinyun County won the highest investment with 97.47 points (the highest in the city), increasing its share from 12.72% to 13.72% and increasing its investment amount by 7.9% to 139.88 million yuan; Yunhe County won the lowest with 57.96 points (the lowest), decreasing its share from 7.57% to 6.57% and decreasing its investment amount by 13.2% to 66.93 million yuan. The program achieved optimal allocation of resources through precise regulation.

Thirdly, due to the variety of distribution network construction projects, the irrationality problem of comparing all projects with the same criteria in the traditional method is addressed. This paper constructs an investment project decision-making model with the attribute investment amount as the constraint and the maximum project benefit under the attribute as the goal, and carries out the preferential selection of projects from the attribute to realize accurate investment. For example, assessed by the entropy right method, the preferred projects 1, 6 and 2 have a total investment of RMB 850,000 (85%), with a NPV of RMB 770,000 and a rate of return of 16.5% better than the average, and have realized an increase in the voltage qualification rate by 5.23% and an improvement in the reloading rate by 4.53%, which are significantly better than those of other projects. The remaining $150,000 can be deployed to high-efficiency areas, fully reflecting the dual advantages of the preferred project in terms of economic benefits and technology enhancement.

The shortcomings of the study are as follows: the indicator system selected in this paper has a strong relevance, and it is mainly applicable to the comprehensive evaluation of the distribution network in recent years, because most of the references are experts’ opinions and have a certain subjectivity. Therefore, the evaluation index system for the future period or other regions needs to be optimized.