The indicator system to evaluate the distribution network status is based on systematic, scientific, objective, and practical principles to guide the investment orientation for the power network. The indicator system is constructed from four aspects: network structure, power supply level, electric power equipment level, and economic benefit (Chai et al., 2020; Ming et al., 2020; Ning et al., 2021). The weights of the four first-level indicators are 0.2, 0.3, 0.3, and 0.2, respectively. Moreover, 20 typical evaluation indicators are selected, which can be seen in the following figure.

According to the distribution network status assessment, the difference between the score of each region and the total score is calculated, and the full score of the distribution network evaluation is 100 points. The results are normalized to obtain the ratio of investment allocation. The formula is as follows: k = ∑ s = 1 q ( ( ∑ t = 1 m E s t × q s t ) × E s ) . (1)

E s refers to the first-level index weight, E s t refers to the next level index weight, q s t is the second-level index score, m is the number of the second-level indicators under each first-level indicator, and q is the number of the first-level indicators: P i = 100 - k i ∑ 1 n ( 100 − k i ) × 100 % . (2)

P i is the investment ratio of the ith area, k i is the score of the status of the distribution network of the ith area, and n is the number of the planning areas.

In view of the systematic, comprehensive, and long-term characteristics of the investment benefit analysis of power grid projects, the evaluation indicator system, based on identifying the factors affecting the investment benefit, contains these parts: production service benefits, production and operation benefits, investment economic benefits, and social and environmental benefits. The indexes selected are enumerated in Figure 1.

The indicator system to evaluate investment benefit includes subjective and objective indicators so that the assessment of investment benefit can be more persuasive. The set-valued iterative method is a subjective weighting method, which can reflect experts’ opinions concentratedly. The objective weight can be obtained by the entropy method, and the weight is modified through entropy weight calculation to make the weight scientific, objective, and feasible (Li et al., 2016; Li et al., 2019; Ge et al., 2021). Based on moment estimation theory, this study combines the results of the above two methods to obtain a comprehensive weight.

Considering the thought of moment estimation theory, it follows that the expected values of subjective and objective weight are the actual value of each indicator (Liu et al., 2019; Sakthivel and Sathya, 2021).

The coefficients of colligation of the subjective and objective weight vector can be calculated using the actual value of each indicator, as shown in the following formula: { α j = t j t j + s j β j = s j t j + s j . (3)

α j refers to the subjective weight vector’s coefficient of colligation, β j refers to the objective weight vector’s coefficient of colligation, and t j and s j refer to the jth index’s subjective and objective weight, respectively.

Suppose the indicators are extracted from two sample systems. The coefficients of colligation of the total subjective and objective weight vectors, derived from the moment estimation theory, can be calculated in the following formula: α = ∑ j = 1 n α j ∑ j = 1 n α j + ∑ j = 1 n β j = ∑ j = 1 n α j n , (4) β = ∑ j = 1 n β j ∑ j = 1 n α j + ∑ j = 1 n β j = ∑ j = 1 n β j n . (5)

α is the coefficient of colligation of the overall subjective weight vector, β is the coefficient of colligation of the overall objective weight vector, and n is the number of indicators.

A single-objective optimization model is constructed to minimize the deviation between the comprehensive weight and the subjective and objective weight (He et al., 2018; Zhang et al., 2018; Lai et al., 2019) as follows:   m i n H  = ∑ j = 1 n [ α × ( w j − t j ) 2 ] + ∑ j = 1 n [ β × ( w j − s j ) 2 ] . (6)

w j refers to the jth index’s comprehensive weight.

The TOPSIS method can get the closeness of each scheme to the optimal scheme. Based on the combined weight derived from the above weight methods, a TOPSIS evaluation model for investment benefit is established, assessing the pros and cons of the schemes (Zou et al., 2017). The key steps to calculate the comprehensive evaluation value of distribution network investment benefit based on the TOPSIS method are as follows:

1) Multi-objective decision matrix:

Suppose the index set is C = ( C 1 , C 2 , ... , C m ) , the plan set is M = ( M 1 , M 2 , ... , M n ) , and the evaluation value of scheme M j to index C i is r i j = ( i = 1,2 , ... , n ; j = 1,2 , ... , m ) . Then, the matrix R of evaluation values is constructed as follows: R = [ r 11 r 12 ⋯ r 1 m r 21 r 21 ⋯ r 2 m ⋯ … … … r n 1 r n 2 ⋯ r n m ] . (7)

2) Positive and negative ideal solution calculation:

h i + is the positive ideal solution vector, h i − is the negative ideal solution vector, and h i refers to the ideal solution vector of the ith indicator.

3) Relative distance calculation:

K j + is the difference between the jth scheme and the positive ideal solution, and K j − is the difference between the jth scheme and the negative ideal solution.

4) Comprehensive evaluation value:

C j refers to the comprehensive evaluation value of the jth scheme.

According to the comprehensive evaluation value of investment benefit, the result is normalized, and the investment distribution ratio of each region can be obtained as follows: Q j = C j ∑ 1 n C j × 100 % . (12)

Q j is the investment ratio, C j is the comprehensive evaluation value, and n refers to the amount of the planning regions.