Quantitative Evaluation of Crucial Substations and Simulation-Driven Impact Assessment of Commissioning Delays in Multi-Voltage Grid Planning

Abstract

Rapidly expanding power demand in economically developing regions significantly amplifies the operational risks associated with the delayed commissioning of planned substations. This study proposes a data–physics fusion framework integrating analytic hierarchy process-based quantitative assessment with multi-voltage level grid evolution simulation. First, a novel set of evaluation indicators for assessing planned substation criticality, with weights determined through the analytic hierarchy process (AHP), was established, enabling rapid assessment of delay impacts on investments and identification of crucial substations. This approach addresses the fundamental limitation of traditional planning methodologies, which inadequately quantify the compound effects of substation commissioning delays on multi-voltage grid evolution and associated investment inefficiencies. Subsequently, a multi-voltage level grid evolution model was developed, which quantitatively measures the cascading effects of substation commissioning delays on both low-voltage grid development and multi-level grid construction investments. Case study validation demonstrated a strong linear correlation between the proposed substation importance scores and the incremental construction costs induced by delays. The simulation-driven impact assessment model exhibits superior accuracy in evaluating commissioning delay consequences on multi-voltage grid construction compared to conventional approaches. This research provides power grid planners with a robust decision support framework for optimizing substation construction scheduling and minimizing delay-related cost escalations in complex grid development scenarios.

1. Introduction

Power grid planning in rapidly developing regions confronts substantial challenges stemming from accelerated load growth, low predictability, and geographical misalignment of load development [1]. A critical issue manifests in urban areas with constrained land resources, where high-voltage substation sites encounter significant implementation delays. Consequently, emerging loads must be accommodated through extended lower-voltage distribution lines from distant substations, creating suboptimal operational conditions. When these delayed substations are eventually commissioned, the resulting redundant infrastructure generates substantial investment inefficiencies. Conversely, premature substation construction in regions experiencing slower-than-anticipated load growth results in prolonged periods of underutilization, similarly causing investment waste. This coordination challenge between upper and lower voltage level grid planning represents a particularly acute issue in rapidly developing economies such as China [2,3,4]. Therefore, quantitative assessment of investment impacts arising from substation commissioning uncertainty has become essential for optimizing construction timing and mitigating associated investment risks [5,6].

Substations function as critical interconnection nodes linking grids across different voltage levels, and uncertainties surrounding their commissioning timelines directly impact the execution of lower-voltage grid planning programs. Such uncertainties can precipitate substantial alterations in actual investment requirements across multiple grid hierarchies. However, a significant gap exists in quantitative analysis and assessment modeling studies addressing this specific challenge. Instead, existing research has predominantly focused on addressing load development uncertainty within the substation planning scheme generation process. Ref. [7] employed deep learning technology to develop a method for joint siting and capacity determination for distributed generation and substations, utilizing long short-term memory networks to forecast generation output and load demand. Their approach formulates a two-stage stochastic mixed integer bilinear programming model to determine optimal siting and capacity under uncertain load conditions. Ref. [8] incorporated fuzzy functions to characterize load uncertainty, employing clustering methods to determine substation and medium-voltage (MV) feeder locations and capacities while accounting for load distribution uncertainty. Similarly, Ref. [9] leveraged fuzzy logic theory to model both load and energy price uncertainties, providing a robust planning framework for siting, capacity determination, and feeder expansion of distributed generation and substations within distribution networks. Ref. [10] integrated game theory with robust optimization to construct a comprehensive planning and decision-making model encompassing multiple stakeholders, including DG investment operators, distribution grid companies, electricity consumers, and distributed energy storage operators. Meanwhile, Ref. [11] highlighted the impact of load forecasting errors on distribution substation planning cycles, employing robust optimization to address uncertainties associated with distributed generation.

The existing body of research on joint planning for multi-voltage level grids is extensive. Ref. [12] developed a transmission network expansion planning model that considers multiple voltage levels, solving the optimization problem through a hybrid algorithm that integrates meta-heuristic approaches, differential evolution, and continuous population-based incremental learning. Ref. [13] introduced a comprehensive grid expansion planning model encompassing the construction of transmission lines, transformers, and substations, with the optimization objective of minimizing the total cost associated with multi-voltage level grid development. Their work employed heuristic algorithms for solution derivation. In contrast to sequential approaches, Ref. [14] proposed a joint planning model that simultaneously considers transmission network substations, distribution network substations, and their corresponding feeders, establishing a comprehensive evaluation system to holistically assess the resulting planning scheme. Ref. [15] presented an open-source software tool called eGo 100, which employs a top-down approach to optimize and scale the grid across all voltage levels, implementing a heuristic optimization method based on nonlinear power flow to minimize both operating and investment costs in multi-voltage level grids. While these studies have advanced optimization methodologies, they generally overlook the financial implications when actual construction deviates from optimal plans—a critical gap this paper aims to address. Specifically, these approaches primarily focus on optimizing planning schemes while providing insufficient emphasis on the cascading effects of deviations from these schemes on actual construction investments and long-term economic efficiency.

In the assessment of planning programs, numerous studies have established comprehensive evaluation indicator frameworks. However, indicator selection frequently remains rooted in theoretical analysis or expert judgment, with limited empirical validation to confirm their practical accuracy and effectiveness. Ref. [16] developed an approach that adopts electricity demand as a guiding factor while incorporating broader economic and social considerations. Their work formulates a multi-dimensional investment effect evaluation index system linked for grid planning across multiple voltage levels, providing a methodologically rigorous framework for investment strategy development in grid infrastructure projects. Ref. [17] constructed an index system for evaluating substation project investments that considers four key dimensions: project maturity, rationality, effectiveness, and the investment and construction environment. They proposed an innovative combination weighting method based on the coefficient of variation, integrated with fuzzy comprehensive score calculations to enhance objectivity. Ref. [18] developed and quantified a distribution network evaluation index system spanning economy, reliability, environmental protection, and interactivity domains. To address the subjectivity and instability inherent in traditional analytic hierarchy process (AHP) methods, they implemented an AHP-entropy weighting method that balances expert judgment with data-driven insights. Despite these methodological advances, most existing evaluation frameworks exhibit significant limitations in empirical validation across diverse planning scenarios. Particularly, there remains a critical research gap regarding the quantitative assessment of financial implications associated with substation commissioning delays and their cascading effects on multi-voltage level grid investments.

In summary, significant research gaps exist regarding the systematic evaluation of delayed substation commissioning impacts on comprehensive grid construction investment. Additionally, robust methodologies for identifying critical planned substations from a grid evolution perspective remain insufficiently developed, particularly regarding their cascading effects on multi-voltage level infrastructure development.

To address these limitations, this paper evaluates the impact of the delayed commissioning of substations on multi-voltage-level power grids construction. It proposes evaluation and identification indicators for critical planned substations, as well as a quantitative scoring method for assessing planned substation importance. Building upon this foundation, a multi-voltage level grid evolution simulation model was developed to quantitatively evaluate the comprehensive impacts of substation commissioning delays on multi-level grid construction investments. The proposed methodology integrates both technical and economic dimensions to provide a holistic assessment framework for grid planning optimization. The effectiveness of the proposed indicators and simulation model was validated through a case study utilizing actual load development data and planning schemes from a regional power grid. The case study demonstrates the practical application of the methodology in identifying critical substations and quantifying the investment impacts of commissioning delays, thereby confirming the validity and utility of the proposed approach. Furthermore, through detailed numerical analysis, the research provides quantitative insights into how substation commissioning delays propagate through the grid hierarchy, affecting overall construction investment efficiency and long-term economic performance.

This paper makes four primary contributions:

(1)

Development of a comprehensive evaluation framework comprising quantitative assessment indicators and systematic scoring methodologies for analyzing the criticality of planned substations. This novel framework enables precise identification of key substations whose commissioning delays substantially impact investment efficiency across multi-voltage level grid infrastructure.

(2)

Formulation of an innovative multi-voltage level grid evolution model that integrates the coordinated planning of 220 kV, 110 kV, and 10 kV networks. The model facilitates dynamic rolling optimization across multiple planning horizons, generating intelligent evolutionary trajectories and optimal investment strategies for integrated multi-voltage level grid development.

(3)

Implementation of an intelligent automatic topology reconfiguration mechanism within the multi-voltage level grid evolution simulation framework. This feature autonomously establishes optimal connections for newly constructed substations, ensuring that the generated grid planning schemes accurately reflect practical power system expansion patterns and operational requirements.

(4)

Empirical validation through a detailed case study of an actual power grid in a rapidly developing region, providing quantitative insights into the cascading effects of substation commissioning uncertainties on overall grid construction efficiency and investment outcomes. This analysis offers valuable practical guidance for grid planning under load growth uncertainty.

This research provides practical insights for power grid planners to optimize construction sequencing while minimizing investment risks associated with substation commissioning uncertainties.

2. Quantitative Evaluation of Planned Substations Considering the Impact of Delayed Commissioning

2.1. Assessment Indicators for the Importance of Planned Substations

Power grid planning currently operates on a five-year cycle, implementing a hierarchical approach that cascades from high-voltage to low-voltage levels. This creates intricate temporal interdependencies between upper and lower grid tiers. The planning complexity becomes particularly acute in regions experiencing accelerated load growth, where the demand for new substations intensifies while the construction faces increasing constraints from scarce land resources and regulatory approvals.

During the planning and implementation process, construction and commissioning delays of substations are frequently encountered. When load growth in the distribution network outpaces the actual construction schedule of planned substations, distribution network development necessitates transitional solutions that often involve suboptimal infrastructure investments. These delays generate significant cascading effects on capital investment efficiency across multi-voltage level power grids and complicate subsequent planning iterations. The magnitude of impact from delayed substation commissioning varies substantially across the grid, contingent upon multiple factors: the spatial distribution of existing substations, the current operational status across all voltage levels, and the regional load growth dynamics. Consequently, developing a precise quantification methodology for substation importance within the grid framework has become imperative for effective grid planning.

To address this critical need for substation importance assessment, this paper proposes novel quantitative assessment indices. These indices are systematically formulated to incorporate regional load development, substation capacity utilization, and local network topology characteristics. The indices are as follows:

(1)

Substation load level—This index quantifies the actual power demand served by the substation, providing a direct measure of its operational significance within the regional power distribution framework. Substations handling higher load volumes typically occupy more critical positions within the network hierarchy:

$$x_{i1}={\displaystyle \sum q_i}$$

(1)

where $x_{i1}$ is the load level of the ith substation; ${\displaystyle \sum q_i}$ is the aggregate load demand served by substation i.

(2)

Influence of substation on low-voltage level grid—This index evaluates the substation’s integration with and impact upon downstream distribution networks by quantifying the number of 10 kV feeder lines emanating from the substation. A greater quantity of connected 10 kV lines indicates the substation serves as a critical node for power distribution to extensive service territories:

$$x_{i2}={\displaystyle \sum n_i}$$

(2)

where $x_{i2}$ is the value of the ith substation’s influence on the lower grid. ${\displaystyle \sum n_i}$ is the sum of the number of 10 kV lines connected to substation i.

(3)

Substation power supply coverage—This index characterizes the geographical service territory of a substation by measuring the distance to the farthest load point it supplies. A more extensive power supply radius signifies the substation’s broader spatial influence and critical role in maintaining electricity delivery across dispersed demand centers:

$$x_{i3}=\max l_i$$

(3)

where $x_{i3}$ is the power supply coverage of the ith substation. $\max l_i$ is the distance of the furthest load point supplied by substation i.

(4)

Spatial influence of the substation—This index quantifies the substation’s spatial influence by measuring the total length of all 10 kV lines connected to it. A greater cumulative distance indicates the substation’s broader geographical coverage and its significant role in supporting power distribution across the electrical network infrastructure:

$$x_{i4}={\displaystyle \sum l_i}$$

(4)

where $x_{i4}$ is the spatial influence of the ith substation. ${\displaystyle \sum l_i}$ is the sum of the distances of the 10 kV lines connected to substation i.

(5)

Load density—This index characterizes the spatial distribution of power demand by calculating the average distance between the substation and all its connected loads, providing insights into the density of loads in the vicinity of the substation:

$$x_{i5}={\displaystyle \frac{{\displaystyle \sum l_i}}{n_i}}$$

(5)

where $x_{i5}$ is the load density of substation i. ${\displaystyle \frac{{\displaystyle \sum l_i}}{n_i}}$ is the average distance between substation i and all connected loads.

2.2. Calculation of Crucial Substation’s Score Based on Analytic Hierarchy Process

A comprehensive weighted evaluation methodology is proposed to synthesize the aforementioned assessment metrics into a composite importance score for each planned substation. The analytic hierarchy process (AHP) represents a sophisticated mathematical framework for multi-criteria decision analysis, providing a systematic approach for addressing complex decision-making challenges [19]. This approach systematically decomposes multifaceted problems into a hierarchical structure of more tractable sub-problems, thereby facilitating comprehensive analysis and rational decision-making. Within the AHP framework, the relative importance of decision criteria is quantified through the construction of a pairwise comparisons matrix, followed by mathematical processing. These calculated weights represent the relative significance of each criterion within the decision hierarchy.

The implementation of AHP follows a systematic five-step process encompassing hierarchical decomposition, construction of pairwise comparison matrices, weight calculation, consistency verification, and comprehensive evaluation.

(1)

Hierarchical decomposition—The complex multi-criteria decision problem is systematically decomposed into a hierarchical structure of interconnected sub-problems, forming a comprehensive decision-making framework. This hierarchical model typically comprises three distinct levels: the objective layer, which represents the ultimate decision goal; the criteria layer, encompassing the various factors and attributes that influence decision outcomes; and the alternatives layer, containing the specific options under consideration.

(2)

Construction of pairwise comparison matrices—In AHP, decision-makers conduct systematic pairwise comparisons of elements within each hierarchical level to establish their relative importance and preference relationships. These comparative assessments are captured in pairwise comparison matrices, where each matrix element quantifies the relative weight or preference intensity between two criteria or alternatives. This study adopts the widely-accepted Santy scale to express the relative importance between pairwise elements, as detailed in

Table 1. Santy scale and its corresponding meanings.

Importance Scale	Substation Carrying Capacity
1	It indicates that the two elements before and after are equally important.
3	It indicates that the former element is slightly more important than the latter one.
5	It indicates that the former element is significantly more important than the latter one.
7	It indicates that the former element is far more important than the latter one.
9	It indicates that the former element is extremely more important than the latter one.
2, 4, 6, 8	It represents an intermediate value on a scale of 1 to 9.
1/k, k = 1, 2, 3, …, 9	If the ratio of the relative importance of factor i to factor j is cij, then the ratio of the relative importance of factor j to factor i is cji = 1/cij.

.

(3)

Weight Calculation—Following matrix construction, mathematical operations are performed to derive the relative weights of each criterion and alternative. This process typically involves eigenvalue decomposition or other mathematical techniques to extract the priority vectors from the comparison matrices.

(4)

Consistency Verification—To ensure the reliability of expert judgments, consistency checks are performed on all pairwise comparison matrices. This step identifies and addresses any significant inconsistencies in the comparison process, thereby enhancing the credibility of the final results.

(5)

Comprehensive Evaluation—The final step synthesizes the individual criterion weights and alternative scores to produce composite importance scores, enabling rational decision-making based on the integrated multi-criteria assessment.

Through the aforementioned AHP methodology, the relative weights of critical evaluation indicators for planned substations can be rigorously determined, enabling the calculation of quantitative importance scores for individual substations. This structured approach significantly enhances the scientific rigor and reliability of decision-making processes in substation planning.

The pairwise comparison matrix constructed for the evaluation indicators is presented in

Table 2. Comparison matrix for assessment indicator constructs.

Comparison Matrix	Substation Load Level	Influence of Substation on Low-Voltage Level Grid	Substation Power Supply Coverage	Spatial Influence of the Substation	Load Density
Substation load level	1	7	3	2	2
Influence of substation on low-voltage level grid	0.143	1	0.333	0.167	0.167
Substation power supply coverage	0.333	3	1	0.5	0.5
Spatial influence of the substation	0.5	6	2	1	1
Load density	0.5	6	2	1	1

.

Through normalizing the sum of columns in the comparison matrix and calculating the mean of rows, the weight of each criterion can be determined, as illustrated in

Table 3. Table of weighting factors for each criterion.

Criterion	Substation Load Level	Influence of Substation on Low-Voltage Level Grid	Substation Power Supply Coverage	Spatial Influence of the Substation	Load Density
Weighting factor	0.385	0.043	0.120	0.226	0.226

.

Following the consistency analysis, the calculated consistency ratio (CR) for this weighting factor is 0.00726, which is significantly below the threshold value of 0.1, thus validating the consistency of the judgments. The assessment score for each substation is determined by Equation (6):

$$scor{e}_i={\displaystyle \sum _{j=1}^5{w}_{ij}{X}_{ij}}$$

(6)

where score_i is the importance assessment score of substation i. X_ij (j = 1, 2, 3, 4, 5) represents the standardized scores of the five indicators: Substation load level, Influence of substation on low-voltage level grid, Substation power supply coverage, Spatial influence of the substation, and Load density of substation i, respectively. w_ij (j = 1, 2, 3, 4, 5) represents their corresponding weighting coefficients.

Given the absence of universally standardized benchmarks for the proposed substation evaluation indices, this study employs a normalization approach to ensure comparability across different assessment criteria. The evaluation indices are objectively quantified through a relative scoring methodology. The sum normalization technique is implemented according to Equation (7):

$$X_{ij}=x_{ij}/{\displaystyle {\sum }_{i=1}^{n_p}{x}_{ij}}$$

(7)

where x_ij (j = 1, 2, 3, 4, 5) represents the raw scores of five indicators. n_p is the number of substations actually participating in the scoring. The above equation calculates the relative scores of each assessment index, mitigating the influence caused by the subjective upper and lower limits of scores in traditional normalization.

3. Impact Assessment of Substation Commissioning Delay Through Multi-Voltage Level Grid Evolution Simulation

To comprehensively analyze the impact of delayed substation commissioning across different importance levels, this section develops an evolutionary simulation model for multi-voltage level grid development. This model employs the overall construction cost for each planning horizon as the objective function and autonomously generates grid evolution strategies based on the existing network topology from previous periods. Through implementation of this evolutionary simulation framework with configurable delay scenarios for critical substations, the model can simulate grid development trajectories both with and without commissioning delays. Comparative analysis between these scenarios and the baseline planning scheme enables quantification of the incremental investment changes attributable to delayed substation commissioning. This methodology facilitates precise assessment of the economic impact magnitude resulting from commissioning delays across substations of varying importance levels.

3.1. The Objective Function

The proposed multi-voltage level grid evolution model incorporates collaborative planning across 220 kV, 110 kV, and 10 kV voltage levels. The model aims to minimize the overall construction cost of the multi-voltage level grid, with decision variables encompassing the optimal siting and sizing of 220 kV and 110 kV substations, as well as the corresponding 110 kV network reconfiguration strategy. During the 110 kV network planning process, the model considers both new line construction and automatically generates adaptive retrofit schemes for existing 110 kV infrastructure, including tee-off connections to newly commissioned 110 kV substations. This holistic planning approach ensures that the generated schemes and associated investment calculations accurately represent practical implementation scenarios. For 10 kV distribution network planning, the model enforces N-1 security criteria for 10 kV feeder configurations. When load growth exceeds predetermined capacity thresholds, the algorithm automatically provisions additional 10 kV feeders and establishes connections to the nearest available substation operating below its maximum loading capacity.

The objective function incorporates construction costs, operating costs, and other factors, as Equation (8):

$$\min C=C_{SUB220kV}+C_{SUB110kV}+C_{LINE110kV}+C_{LINE10kV}$$

(8)

where $C_{SUB220kV}$ represents the annual investment in 220 kV substations and the annual operating cost. $C_{SUB110kV}$ represents the annual investment in 110 kV substations and the annual operating cost. $C_{LINE110kV}$ represents the annual 110 kV line investment converted to the annual network damage cost. $C_{LINE10kV}$ represents the annual 10 kV line investment converted to the annual network damage cost.

$$C_{SUB220\mathrm{kV}}={\displaystyle \sum _{i=1}^N\left\{C_{SUB-i}\left[\frac{r_0{(1+r_0)}^{t_{ms}}}{{(1+r_0)}^{t_{ms}}-1}\right]+C_{OP-i}\right\}}$$

(9)

$$C_{SUB110kV}={\displaystyle \sum _{i=1}^M\left\{C_{SUB-i}\left[\frac{r_0{(1+r_0)}^{t_{ms}}}{{(1+r_0)}^{t_{ms}}-1}\right]+C_{OP-i}\right\}}$$

(10)

where N represents the number of new 220 kV substations. M represents the number of new 110 kV substations. $C_{SUB-i}$ represents the investment cost of the ith substation. $C_{OP-i}$ represents the annual operating cost of the ith substation; r₀ is the discount rate, and t_ms is the depreciation life of the substation.

$$C_{LINE110kV}={\beta }_{LINE110kV}\epsilon \left[{\displaystyle \frac{r_0{(1+r_0)}^{t_{110kVml}}}{r_0{(1+r_0)}^{t_{110kVml}}-1}}\right]l_{110kV}$$

(11)

$$C_{LINE10kV}={\beta }_{LINE10kV}\epsilon \left[{\displaystyle \frac{r_0{(1+r_0)}^{t_{10kVml}}}{r_0{(1+r_0)}^{t_{10kVml}}-1}}\right]{\displaystyle \sum _{i=1}^{N+M}{\displaystyle \sum _{j=1}^m{d}_{ij}{l}_{ij}}}+{\alpha }_{LINE10kV}\epsilon {\displaystyle \sum _{i=1}^{N+M}{\displaystyle \sum _{j=1}^m(\frac{q_j}{n_j})d_{ij}{l}_{ij}}}$$

(12)

where β_LINE110kV and β_LINE10kV represent the investment cost per unit length of the 110 kV line and 10 kV line. t_110kVml and t_{10k ml} represent the depreciation life of the 110 kV line and 10 kV line. ${\alpha }_{LINE10kV}$ represents the network loss conversion factor of the 10 kV line. ε represents the zigzag coefficient of the evolved area. m represents the equivalent nodes. l_110kV represents the total length of all 110 kV lines. q_j represents the load of the jth equivalent load node, and n_j represents the number of 10 kV main supply lines of the jth equivalent load node. l_ij, d_ij are (N + M) × m matrices, l_ij represents the length of the 10 kV line between substation i and the equivalent load node j, and d_ij represents the connection relationship between substation i and the equivalent load node j, which is 1 or 0.

3.2. The Constraints

Real-world power systems typically mandate standardized configuration requirements across all voltage levels, with particular emphasis on distribution network topology. This paper considers two primary interconnection architectures for the 110 kV transmission network: loop network configuration and the ‘3T’ connection scheme. For the 10 kV distribution network connection mode, the model employs an (n + 1) redundancy configuration, comprising n main supply feeders with one dedicated standby feeder.

The integrated planning model for the multi-voltage level grid incorporates several constraints, including the following: capacity-to-load ratio constraints within the planning region, substation loading limitations, 10 kV primary feeder capacity constraints, 110 kV transmission line routing constraints, and 110 kV line loading constraints. The specific formulations of these constraints are as follows.

(1)

The 110 kV substation loading constraints:

$$n_j={\displaystyle \sum _{i=1}^{N+M}{d}_{ij},j=1,2,\dots ,m}$$

(13)

$$p_i={\displaystyle \sum _{j=1}^m\frac{q_j{d}_{ij}}{n_j},i=N+1,N+2,\dots ,N+M}$$

(14)

$$p_i<=s_i\eta \cos \phi ,i=N+1,N+2,\dots ,N+M$$

(15)

where p_i represents the actual load of the ith 110 kV substation. η represents the maximum allowable loading rate. cosφ represents the system power factor. When the loading of the ith 110 kV substation remains below the rated capacity, this substation can accommodate load transfers from delayed or deferred substations. Conversely, if capacity constraints are violated, the affected loads must be redistributed to alternative 110 kV substations with available capacity.

(2)

The 10 kV primary feeder capacity constraints:

$$w_i\le n_j\sqrt{3}{I}_{\max }U\cos \phi ,j=1,2,\dots ,m$$

(16)

where I_max represents the maximum safe operating current of the feeder. U represents the current voltage level. To maintain all 10 kV feeders within operational constraints, additional feeder circuits are automatically provisioned when thermal limits are exceeded, ensuring adequate capacity and system reliability.

(3)

The 110 kV transmission line routing constraints:

As shown in Figure 1, the 110 kV transmission line routing planning incorporates both the loop network configuration and the ‘3T’ connection scheme—the development to accurately represent real-world grid expansion scenarios. Here, 1 and 2 represent node 1 and node 2 respectively. In this framework, the 110 kV network employs the ‘3T’ connection configuration as illustrated in the diagram, with breakout connections evolving from the existing 110 kV network infrastructure. The specific routing constraints for 110 kV lines are as follows:

$$l_{110kV}=3{\displaystyle \sum _{i=1}^{N+M}{\displaystyle \sum _{j=1}^{N+M}{D}_{ij}{L}_{ij}}}+3{\displaystyle \sum _{i=1}^{N+M}{\displaystyle \sum _{j=1}^h{D}_{ij}^{\prime }}}{L}_{ij}^{\prime }$$

(17)

$${\displaystyle \sum _{i=1,i\ne j}^{N+M}{D}_{i,N+k}}+{\displaystyle \sum _{j=1}^h{D}_{k{j}^{\prime }}}=1,k=1,2,\dots ,M$$

(18)

$${\displaystyle \sum _{i=1,i\ne j}^{N+M}{D}_{N+k,j}}+{\displaystyle \sum _{j=1}^h{D}_{k{j}^{\prime }}}=1,k=1,2,\dots ,M$$

(19)

$$D_{ij},D_{ij}^{\prime }\in \left\{0,1\right\}$$

(20)

$$u_j\ge u_i-(D_{ij}-1)M+1,1\le i\ne j\le M$$

(21)

where D_ij, L_ij are (N + M) × (N + M) matrices. D_ij represents the unidirectional connection relationship between substation i and substation j. L_ij represents the length of the 110 kV line between substation i and substation j, where 1 ≤ i, j ≤ N denotes a 220 kV substation, and N + 1 ≤ i, j ≤ N + M denotes a 110 kV substation. $D_{ij}^{\prime }$, $L_{ij}^{\prime }$ are M × h matrices representing the connection relationship between 110 kV substation i and 110 kV line j. $L_{ij}^{\prime }$ represents the shortest distance length between 110 kV substation i and 110 kV line j. h represents the number of existing 110 kV lines in the current grid. u_i is an auxiliary series of length M. Equation (21) refers to the constraints of the traveler’s problem, ensuring that the 110 kV network maintains a radial configuration without forming closed loops in dual-supply arrangements. These constraints guarantee that each load point receives power through exactly two independent supply paths while preventing inadvertent loop formation that could compromise system protection coordination. When the optimization algorithm detects potential loop closure, the routing logic automatically reassigns line connections to alternative substations, maintaining the desired radial dual-supply topology.

(4)

The 110 kV line loading constraints:

As illustrated in Figure 2, the maximum line loads in each two-terminal 110 kV power supply network are concentrated in sections 1a and 2k. Here, 1 and 2 represent node 1 and node 2 respectively. Neglecting reactive loads, the loading constraints for these critical transmission sections (1a and 2k) are as follows:

$$P_{1a}={\displaystyle \frac{{\displaystyle {\sum }_{j=1}^k{P}_j{L}_j}}{L_{\sum }}}\le \sqrt{3}{I}_{\max }U\cos \phi$$

(22)

$$P_{2k}=={\displaystyle \frac{{\displaystyle {\sum }_{j=1}^k{P}_j{L}_j^{\prime }}}{L_{\sum }}}\le \sqrt{3}{I}_{\max }U\cos \phi$$

(23)

where P_1a represents the active power flow through section 1a of the line. P_2k represents the active power flow through section 2k of the line. P_j represents the actual load of the jth 110 kV substation within the dual-supply network. L_j and $L_j^{\prime }$ represent the transmission distance from the 220 kV substations to the jth substation in the network, and L_Σ represents the transmission distance between the 220 kV substations. When the loading rate of the 110 kV transmission line exceeds the specified constraint, the optimization algorithm automatically initiates load transfer procedures to alternative substations with available capacity.

(5)

The 220 kV substation loading constraints:

For each 220 kV substation, the loading constraints are as follows.

$$P_i={\displaystyle \sum _{j=1}^m\frac{q_j{d}_{ij}}{n_j}},i=1,2,\dots ,M$$

(24)

$$P_i+{\displaystyle \sum _{j\in J_j}{P}_{ij}^{\prime }}\le S_i\eta \cos \phi ,i=1,2,\dots ,N$$

(25)

where P_i represents the 10 kV load connected to the ith 220 kV substation. J_j represents the set of lines of the jth 220 kV substation, and $P_{ij}^{\prime }$ represents the load carried by the jth line of the ith substation. When the loading rate of the ith 220 kV substation remains within the specified constraint, the substation can accommodate additional 10 kV distribution loads. Conversely, if the capacity constraint is violated, the existing 10 kV loads must be transferred to alternative substations with available capacity.

3.3. Algorithms for Solving Evolutionary Models of Multi-Voltage Level Grids

A genetic algorithm is employed to solve the aforementioned programming model. In this approach, the x and y coordinates of both 220 kV and 110 kV substations are encoded as 2 × (N + M) gene sequences within the evolutionary area. The 110 kV network topology is determined by M gene sequences, each specifying the upstream connection for a new 110 kV substation, which can be either a 220 kV substation or another 110 kV substation. Given the complex constraints of the multi-voltage level grid evolution model, the solution space may not cover the entire problem space. Therefore, when candidate solutions fail to satisfy the model constraints, a substantial penalty cost is applied to the fitness function, ensuring its elimination during the genetic selection process and effectively enforcing the constraints. The genetic algorithm parameters are configured as follows: maximum generations set to 200, population size (INDIVIDUAL_NUM) set to 800, enhanced crossover operation with crossover probability (CROSS_RATE) of 0.5, and the mutation probability (UPTATE_RATE) of 0.5.

4. Case Study Analysis

To investigate the identification of critical substations and analyze the impact of delayed commissioning, a case study was conducted utilizing the planning-phase (2017–2020) grid construction program and medium-to-long-term (2021–2035) load forecast data from a regional power grid. The study comprised two key components: first, identifying critical substations among newly commissioned facilities during the planning period; second, performing grid evolution simulations to quantify the investment implications resulting from commissioning delays of these substations.

4.1. Introduction of the Power Grid

The planning scheme evaluated in this study utilized 2020 as the baseline year. Figure 3 depicts the spatial distribution of electrical loads throughout the region, along with the geographic coordinates of the power grid infrastructure. Each load zone is represented by a circle, where the pink centroid indicates the location of the equivalent load node, and the color intensity corresponds to the local load density. The power system under examination comprises 220 equivalent load nodes with an aggregate demand of 2013.74 MW as measured in the base year 2020.

The planned network topology for the regional power grid in 2020 consists of 5220 kV substations, 12,110 kV substations, 18,110 kV transmission lines, and 51,610 kV distribution feeders, as illustrated in Figure 4a,b. Among these facilities, six new 110 kV substations (labeled 1–6 in Figure 4) are scheduled for commissioning during the 2017–2020 planning period. These newly planned substations constitute the focus of the criticality assessment. Through evolutionary simulation, the impact of commissioning delays for these substations on the regional grid development trajectory is evaluated over a 5–15 years planning horizon.

The grid evolution simulation conducted by the algorithm establishes two evolutionary planning horizons: 2025 and 2035. The forecasted load demand reaches 2734.83 MW and 3316.22 MW for these respective years, representing a growth rate of 35.81% during the initial five-year period (2020–2025) and 21.26% over the subsequent decade (2025–2035). This substantial load growth trajectory through 2025 provides an ideal analytical framework for evaluating how commissioning delays affect multi-voltage level grid development.

The baseline scenario assumes that all six planned substations (numbered 1–6) are commissioned on schedule prior to 2020. Based on this assumption, the evolutionary simulation algorithm generates optimal network expansion plans for 2025 and 2035 using the initial topology shown in Figure 4a,b. The resulting target network configurations for these planning horizons are illustrated in Figure 4c–f, which represent the benchmark for subsequent delay scenario comparisons.

4.2. Importance Assessment of Planned Substations Considering the Impact of Delayed Commissioning

The evaluation indicators for the six new 110 kV substations within the 2020 network configuration are presented in

Table 4. Evaluation indicators of 110 kV substation.

Substation Serial Number	Substation Load Level (MW)	Influence of Substation on Low-Voltage Level Grid (Article)	Substation Power Supply Coverage (km)	Spatial Influence of the Substation (km)	Load Density (km)
1	100.71	35	5.59	98.02	2.80
2	97.96	24	4.03	53.34	2.22
3	105.05	24	3.57	44.15	1.84
4	126.12	41	3.07	68.21	1.66
5	109.25	26	4.88	75.19	2.89
6	106.78	17	3.86	31.07	1.83

:

By applying the criticality assessment methodology defined in Equation (6) and (7), the importance scores for the six substations can be calculated, as illustrated in Table 4.

As demonstrated in

Table 5. Evaluation of the importance of 110 kV substation.

Substation Serial Number	1	2	3	4	5	6
score	0.2035	0.1544	0.1443	0.1705	0.1905	0.1367

, the importance of substations to the power grid can be effectively quantified using the assessment methodology. By selecting substations with both higher and lower importance scores for delayed commissioning scenarios, a comprehensive investigation of the differential impacts resulting from commissioning delays of substations with varying criticality levels can be conducted.

4.3. Experimental Analysis of Crucial Substationscommissioning Delays

The substations with high importance scores are classified as critical substations. As shown in Table 5, substation No. 1 is identified as a critical substation, whereas substation No. 6 exhibits a relatively lower importance score. In this section, substations No. 1 and No. 6 are selected for evolutionary simulation analysis of delayed commissioning to comparatively analyze their impacts on the long-term integrated grid investment, thereby validating the substation importance assessment methodology.

It is assumed that the commissioning of substations No. 1 and No. 6, originally scheduled for 2020, is postponed until 2025. The multi-stage grid construction planning is implemented for 2025 and 2035 based on load power supply requirements and grid reliability criteria.

The evolution model incorporates the following operational constraints: maximum substation loading factor of 75%, maximum safe operating current of 552A for 10 kV feeders, and maximum safe operating current of 718A for 110 kV transmission lines.

Figure 5 illustrates the simulated grid evolution resulting from the delayed commissioning of substation No. 1, which has a high importance score.

Figure 6 illustrates the simulated grid evolution resulting from the delayed commissioning of substation No. 6, which exhibits a lower importance score.

Based on the evolutionary simulation results, the annual investments for each delayed commissioning scenario are discounted to the initial planning year using a discount rate of 8%.

Table 6. Comparison between the investment cost of each part of the delayed commissioning experiment and the original planning scheme.

Programmatic	Particular Year	220 kV Substation (million CNY)	110 kV Substation (million CNY)	110 kV Line (million CNY)	10 kV Line (million CNY)	Converted Total (million CNY)	Total Incremental Costs
Original planning program	2020	160.992	135.4968	307.23	722.089	1325.808	/
	2025	0	22.5828	26.5151	87.5153	136.6132
	2035	32.1984	11.2914	19.6928	97.414	160.5966
Experiment of delayed commissioning of No. 1 substation	2020	160.992	124.2054	305.771	774.9868	1365.955	3.95%
	2025	0	22.5828	25.0989	100.1114	147.7931
	2035	32.1984	11.2914	22.7972	107.1074	173.3944
Experiment of delayed commissioning of No. 6 substation	2020	160.992	124.2054	308.2488	744.6078	1338.054	1.63%
	2025	0	33.8742	29.0456	87.5097	150.4295
	2035	32.1984	11.2914	20.0824	97.3834	160.9556

presents a comparison of these results with the original planning scheme.

The impact of delayed substation commissioning on the total incremental cost is calculated using the following formula: (cumulative annual converted total for the delayed substation scenario — cumulative annual converted total for the baseline planning scheme)/cumulative annual converted total for the baseline planning scheme.

As demonstrated in Table 6, following the delayed commissioning of substation No. 1, which has a high importance score, the increased load in this area must be supplied by substations in other areas through 10 kV feeders. Due to the high load density in this region, most existing 10 kV feeders already operate at relatively high-capacity factors; therefore, additional 10 kV feeders are required, resulting in increased investment and operating costs. Overall, from 2020 to 2035, the total construction investment in the local power grid increases by 3.95%. In contrast, the delayed commissioning of substation No. 6, which has a low importance score, generates a smaller incremental demand for the 10 kV feeders due to its low load density and limited power supply coverage area. Although this scenario ultimately causes a 1.63% increase in comprehensive grid investment, the increase is significantly lower than that caused by the delayed commissioning of substation No. 1.

The delayed commissioning of substation No. 1 exhibits pronounced effects on the temporal distribution of the investment impact. In 2020, numerous new loads in the target area can only be served by distant substations, necessitating substantial investment in 10 kV feeder construction. This impact persists through 2035, affecting deferred 10 kV grid investments in the target area. The delayed commissioning of substation No. 6 follows a similar pattern, albeit with considerably lower incremental investment in the 10 kV grid. Notably, the delayed commissioning of substation No. 1 also affects the 110 kV target grid. Despite load decentralization to other substations via long-distance 10 kV lines, the number of new 110 kV substations and the investment in the 2025 target grid are comparatively lower than in other scenarios. Nevertheless, the total investment across the multi-voltage level grid is highest due to excessive investment in the 10 kV grid.

Compared to substation No. 1, which has a higher importance score, the delayed commissioning of substation No. 6 involves smaller load transfers, fewer lines requiring transfer to other substations, and shorter transfer distances for affected feeders. Consequently, the incremental cost relative to the baseline planning scheme is lower. Given constraints on land availability and investment resources, when substation commissioning delays are unavoidable, prioritizing the postponement of lower-importance substations such as No. 6 is recommended. This strategy minimizes system disruption while ensuring that critical substations with higher importance scores can proceed according to the original schedule.

Based on the above analysis, when power grid operators must accommodate delayed commissioning of planned substations, priority should be given to deferring substations with lower importance assessment scores. This approach effectively minimizes the adverse impacts associated with substation commissioning delays on overall system performance and economics.

4.4. Correlation Analysis of Incremental Costs Resulting from the Delayed Commissioning of Substations with Varying Importance and Grid Construction

To further validate the reliability of the planned substation importance scores described in Section 2, comprehensive planning evolution simulations were conducted for all six planned substations under scenarios with deferred commissioning. The objective was to evaluate whether a strong monotonic correlation exists between substation importance scores and the incremental grid construction costs resulting from commissioning delays.

In these experiments, the commissioning of each of the six substations are deferred individually to the subsequent planning period. The evolutionary simulation generated grid evolution scenarios and construction investment projections for three planning years: 2020, 2025, and 2035.

Table 7. Comparison between the importance scores of each substation and the incremental costs brought by delayed commissioning to the power grid.

Delayed Commissioning Substation Serial Number	None	1	2	3	4	5	6
score	/	0.2035	0.1544	0.1443	0.1705	0.1905	0.1367
Total cost up to 2035 (million CNY)	1623.02	1687.14	1662.45	1646.7	1665.38	1691.79	1649.44
Incremental cost	/	3.95%	2.43%	1.46%	2.61%	4.24%	1.63%

presents a comparison between each substation’s importance score and the incremental grid cost resulting from its delayed commissioning.

Figure 7 displays a scatter plot with substation score on the x-axis and incremental costs on the y-axis. In Figure 7b, the solid line is the fitted line of the scatter points, and the dashed lines represent the distances from each scatter point to the fitted line.

Linear regression analysis of the substation scores and incremental costs reveals a significant linear relationship between the importance assessment scores presented in this paper and the incremental costs incurred due to delayed commissioning of the corresponding substations. This demonstrates that substations with higher importance scores are associated with more substantial economic losses to the grid when their commissioning is deferred. In some instances, such delays can lead to heavy loading or even overloading of specific lines and substations, thereby compromising power system stability and reliability.

Considering the weighting coefficients assigned in the substation importance assessment, it is evident that the expected substation load level constitutes the primary factor influencing overall multi-voltage level grid construction. This is followed by the influence of substations on the low-voltage level grid and the load density. Through evolutionary simulation modeling of multi-voltage level grid development under delayed commissioning scenarios, the analysis reveals that the incremental costs caused by delayed commissioning of substations No. 1 and No. 5 are the highest. According to Table 5, these substations exhibit relatively high loading levels, strong influence on the distribution grid, and high load density. Calculations confirm that their importance scores are correspondingly the highest. In grid planning scenarios where delayed substation commissioning is unavoidable, planners should prioritize avoiding delays for substations with high values in these critical indicators. Conversely, the spatial influence of substations has a relatively lower impact on overall grid construction and can be considered a secondary factor in the planning process.

5. Discussion

This paper proposes a comprehensive set of evaluation indicators and scoring methods for assessing the importance of newly planned substations, which effectively identifies critical substations whose delayed commissioning significantly impacts the overall investment in multi-voltage level power grids. A development and evolution model for multi-voltage level power grids is constructed, covering the collaborative optimization of substation siting and grid architecture across three voltage levels: 220 kV, 110 kV, and 10 kV. This model enables rolling expansion planning over multiple planning horizons while intelligently generating evolution schemes and construction investment projections for multi-voltage level power grids.

Within the development and evolution simulation framework, a specialized function is designed to generate power grid planning schemes for the intelligent connection of new substations at breakpoints of double-ended supply feeders, incorporating real-world operational constraints. This enhancement ensures that the simulated grid structure evolution closely aligns with the actual power grid development patterns. Finally, through a real-world power grid case study, the potential impacts of commissioning time uncertainties for planned substations on overall grid construction in areas experiencing rapid load growth were analyzed and discussed. Future research should incorporate additional influencing factors to further enhance the evaluation framework.

6. Conclusions

This research investigated the implications of substation commissioning delays on multi-voltage level grid construction and developed assessment methodologies for this purpose. A comprehensive set of substation importance assessment indices was established and a scoring method capable of efficiently identifying critical substations where commissioning delays would have significant impacts presented. Additionally, an effective simulation model for multi-voltage level grid evolution is proposed, which enables quantitative analysis and evaluation of how delayed commissioning affects medium- and long-term comprehensive investment in regional grid construction, including the temporal distribution of investment changes. Through experiments and simulations based on actual grid planning calculations, the consequences of substation commissioning delays were quantitatively assessed, yielding the following key conclusions:

(1)

The methodology for assessing substation importance plays a crucial role in grid planning. The primary factor influencing a substation’s grid importance is its expected load level, followed by its impact on the lower grid (quantified as the sum of distances from the substation to lower loads) and the degree of load concentration. Comparatively, the number of 10 kV line returns and a substation’s maximum power supply range have relatively less impact on the overall economic efficiency of grid construction. The application of hierarchical analysis methodology enables the formulation of scores representing substation importance, providing a scientific foundation for rational allocation of power grid resources and informed decision-making in grid planning.

(2)

A linear correlation exists between substation importance and economic losses incurred due to delayed commissioning. The findings demonstrate that as a substation’s importance evaluation score increases, the associated economic loss intensifies correspondingly. Consequently, in power grid planning and construction, enhanced monitoring of construction progress for substations with higher evaluation scores is essential to avoid economic losses.

(3)

The research findings presented in this study hold significant reference value for power grid planning and operational decision-making. In scenarios where resources for actual grid construction are constrained, prioritizing the construction of substations with higher importance scores, as determined by our assessment methodology, can help mitigate economic losses resulting from delayed commissioning. Furthermore, the multi-voltage level grid evolution model serves as a valuable tool for grid planning, offering reference and guidance for the optimization and construction of grid structures.

In future research, we will continue to conduct comprehensive studies on the impacts of delayed commissioning of planned substations on power grid performance and economics. We will incorporate additional influencing factors (such as DC feeder integration) into the quantitative assessment framework to achieve a more holistic evaluation. Furthermore, we will explore mitigation strategies to minimize the economic impacts when specific substation commissioning delays are unavoidable.