Risk Assessment of Grid-Integrated Energy Service Projects: A Hybrid Indicator-Based Fuzzy-Entropy-BP Evaluation Framework

Abstract

Grid-integrated energy service (GIES) projects are characterized by strong cross-energy coupling and long investment horizons, resulting in multidimensional and nonlinear risk profiles. To address these challenges, this study develops an indicator-based risk evaluation framework by integrating an entropy–back-propagation (BP) combined weighting method with fuzzy matter-element theory. A 30-indicator system covering economic, environmental, and safety and reliability dimensions is constructed to support systematic risk assessment. The entropy–BP scheme combines data-driven objectivity with nonlinear correction, producing stable and interpretable indicator weights, as confirmed through robustness tests based on indicator removal and data perturbation. A real-world GIES project in East China is used as a case study. The results show clear risk grade differentiation among alternative scenarios and identify key risk drivers related to renewable energy integration, investment structure, and energy supply reliability. The proposed framework provides effective decision support for GIES project planning and risk management.

1. Introduction

With the rapid evolution of the energy internet and the implementation of the “Dual Carbon” strategy, power grid enterprises are transforming from traditional electricity transmission and distribution providers into integrated energy service providers [1]. GIES projects feature diversified investment entities, cross-disciplinary technological integration, and long investment cycles, resulting in risks that are highly diverse, dynamic, and interrelated, as well as inherently nonlinear [2,3]. Therefore, establishing a scientific, transparent, and systematic risk evaluation framework is essential for ensuring the sustainable and healthy development of such projects.

Existing studies have evaluated investment and operational risks of GIES from multiple perspectives. Investment-oriented research has developed a range of methods for risk characterization. Ref. [4] developed an investment risk assessment model grounded in mean–variance theory. Ref. [5] proposed a Monte Carlo–based modeling framework to capture randomness in renewable energy outputs. Ref. [6] introduced a three-dimensional risk investment evaluation model for energy projects using a multi-attribute decision-making (MADM) approach, enabling comprehensive risk quantification. Ref. [7] adopted the analytic hierarchy process (AHP) to develop an investment risk evaluation system for GIES projects, showing its effectiveness in small-scale decision scenarios with limited indicators. Ref. [8] applied the fuzzy analytic hierarchy process (FAHP) to rank risks in regional distributed energy projects. With respect to operational risk, ref. [9] established a conditional value-at-risk (CVaR)-based modeling framework for quantifying tail-risk behavior. Ref. [10] constructed a multi-energy flow coupling model to represent cross-energy interactions. Ref. [11] presented a stochastic dispatch framework under uncertainty to analyze risk propagation across operational scenarios. Moreover, refs. [12,13] showed that conventional entropy weight methods often underrepresented nonlinear interactions among indicators, while BP neural networks suffered from instability, sensitivity to initialization, and limited interpretability.

Despite these advancements, most existing approaches still exhibit three major limitations, which restrict the applicability of existing risk evaluation frameworks to real-world GIES projects.

• Existing studies predominantly focus on either economic or environmental dimensions and do not provide a unified life-cycle-oriented risk evaluation system, leading to static assessments that inadequately capture dynamic risk evolution throughout the project life cycle.
• Existing methods remain overly reliant on traditional evaluation tools, including the AHP, FAHP, and matter-element extension, which are limited in effectively modeling complex nonlinear interdependencies in high-dimensional indicator systems.
• Existing entropy–fuzzy hybrid models [14,15] rely on static weights and thus fail to capture dynamic nonlinear risk interactions, while BP-based fuzzy methods [16,17] suffer from initialization sensitivity, causing unstable weight allocation in high-dimensional GIES systems.

To address these gaps, an enhanced multidimensional GIES risk evaluation framework was developed by coupling an improved BP network with entropy-based weighting and fuzzy evaluation, enabling nonlinear risk modeling and adaptive weight adjustment. The framework is tailored to GIES projects through three key designs: indicator customization using GIES-specific metrics to capture multi-energy coupling risks; life-cycle-adaptive weighting to adjust risk priorities across project stages; and GIES-oriented fuzzy calibration based on domain standards and carbon targets.

The main contributions are as follows:

• Section 2.1 establishes a unified hierarchical risk evaluation system integrating economic, environmental, and safety dimensions to characterize the multi-faceted and high-dimensional risk profile of GIES beyond traditional single-dimension and static assessments.
• Section 2.2 develops a life-cycle dynamic hybrid evaluation approach that combines entropy-based weighting, BP networks, and fuzzy matter-element theory to address weight rigidity and capture nonlinear risk interactions in high-dimensional GIES risk evaluation.
• Section 3 validates the proposed model using a regional GIES case study, showing its capability to identify dominant risk factors, discriminate risk levels among competing scenarios, and maintain high predictive accuracy.

The remainder of this paper is organized as follows: Section 2 presents the construction of the enhanced multidimensional risk evaluation index system and the proposed hybrid modeling framework. Section 3 conducts a comprehensive case study of a regional GIES project, covering data preprocessing, indicator weighting, fuzzy risk evaluation, robustness verification, and result interpretation. Section 4 summarizes the main findings, discusses practical implications, and outlines future research directions.

2. Multidimensional Risk Evaluation Framework for GIES Projects

2.1. Multidimensional Risk Evaluation Index System

The 2024 risk white paper on the integrated energy service industry released by the China Electricity Council reports that financial, technical, operational, and policy risks account for 32%, 28%, 20%, and 20% of risk, respectively. Moreover, a representative case in Jiangsu province [18] demonstrated that reliance on a single-dimensional economic risk model led to an underestimation of wind power curtailment impacts, resulting in a 23% reduction in net present value. Taken together, these findings motivate the development of a multidimensional and nonlinear risk evaluation system tailored to GIES projects.

Based on risk management theory and aligned with existing GIES studies and national standards [19,20], this study developed an indicator-based, multilevel risk evaluation system for GIES projects. The system comprises three primary dimensions—economic, environmental, and safety & reliability risks—with indicators mapped to project life-cycle stages according to their occurrence characteristics. Here, risk denotes potential adverse impacts on project objectives, safety focuses on accident prevention, and reliability emphasizes stable energy supply. Specifically, economic risk indicators (A1) capture project costs, revenue potential, and long-term development capability; environmental risk indicators (A2) reflect pollutant emissions, renewable energy penetration, and clean energy utilization; and safety risk indicators (A3) describe energy supply reliability, equipment loading constraints, and outage risks. For indicator types, higher values of benefit-type indicators diminish project risk, while higher values of cost-type indicators escalate it. By systematically integrating these dimensions within a life-cycle perspective, the proposed indicator system enhances the ability to capture key operational and market-related uncertainties inherent in real-world GIES projects. The detailed indicator hierarchy is summarized in

Table 1. Hierarchical risk evaluation indicator system for GIES projects.

Primary Indicators	Secondary Indicators	Third-Level Indicators
		Indicator Names	Indicator Types	Indicator Label
Economic risk: A1	Cost risk: B1	Initial investment (×104 $)	Cost	C1
		Annualized total cost (×104 $/year)		C2
		Annual energy cost (×104 $/year)		C3
		Investment cost per unit load ($/kW×year)		C4
		Cost per unit load ($/kW×year)		C5
	Revenue risk: B2	Annual profit (×104 $/year)	Benefit	C6
		Present value of total revenue (×104 $)		C7
		Cost-to-revenue ratio (%)	Cost	C8
		Net profit margin (%)	Benefit	C9
	Long-term development risk: B3	Internal rate of return (%)		C10
		Payback period (Years)	Cost	C11
		Annual return on investment (%)	Benefit	C12
Environmental risk: A2	Pollutant emission risk: B4	Total pollutant equivalent (×104 kg/year)	Cost	C13
		Emission intensity per unit load (kg/kW)		C14
		Pollutant emission reduction rate (%)	Benefit	C15
	Renewable energy integration risk: B5	Renewable energy penetration rate (%)		C16
		Share of renewable installed capacity (%)		C17
		Total renewable energy generation (×104 kWh/year)		C18
		Total installed renewable capacity (kW)		C19
		Share of clean energy consumption (%)		C20
Safety & reliability risk: A3	Energy supply reliability: B6	Energy self-sufficiency rate (%)		C21
		Share of imported electricity (%)	Cost	C22
		Energy supply adequacy (%)	Benefit	C23
		Maximum electricity supply capacity (kW)		C24
		Maximum heating/cooling supply capacity (kW)		C25
	Energy supply safety: B7	Loss-of-load probability (%)	Cost	C26
		Maximum grid load factor (%)		C27
		Maximum heating/cooling network load factor (%)		C28
	Grid operational safety: B8	Maximum peak-shaving capability (kW)	Benefit	C29
		Maximum valley-filling capability (kW)		C30

Notes: Unit explanation: All monetary indicators use “×10⁴ $” (10,000 $); “kW” = kilowatt, “kg” = kilogram, “year” = year, “%” = percentage. Risk correlation: For “Cost” type indicators, higher values mean higher risk; for “Benefit” type indicators, higher values mean lower risk.

.

2.2. Hybrid Entropy-BP-Based Risk Evaluation Model

2.2.1. Integrated Risk Evaluation Methods Overview

This subsection summarizes the established methods adopted in this study and presents only the core formulations required for the proposed framework. For clarity and consistency, the main notations used throughout this section are summarized in

Table 2. Symbol description.

Symbols	Explanation
$x_{ij}$	Original value of the $j\text{-}th$. indicator for the $i\text{-}th$ sample
$x_{ij}^{\prime }$	Standardized value of the $j\text{-}th$ indicator for the $i\text{-}th$ sample
$p_{ij}$	Proportion of the $j\text{-}th$ indicator for the $i\text{-}th$ sample
${\omega }_{\mathrm{entropy},j}$	Entropy-based weight of the $j\text{-}th$ indicator
${\omega }_{BP,j}$	Weight of the $j\text{-}th$ indicator obtained from the BP neural network
${\omega }_j$	Comprehensive weight of the $j\text{-}th$ indicator
$C_j$	Compensation constant
$c_j$	$j\text{-}th$ evaluation indicator
$e_j$	Information entropy of the $j\text{-}th$ indicator
$v_j$	Value of indicator $c_j$
$K_k(c_j)$	Correlation degree of indicator $c_j$ with respect to the $k\text{-}th$ risk grade
$K_k(N)$	Comprehensive correlation degree of project $N$ with respect to the $k\text{-}th$ risk grade
$N$	Evaluated GIES project
$n$	Number of samples
$m$	Number of evaluation indicators

.

(i) Entropy weight method

The entropy weight method [21,22] determines objective indicator weights based on data dispersion. The main computational steps are summarized as follows.

First, indicators are classified as benefit-type or cost-type according to their risk implications to ensure rational standardization. The data are then standardized to eliminate dimensional differences.

$$x_{ij}^{\prime }={\displaystyle \frac{{(-1)}^{k_j}{x}_{ij}+C_j}{\max (x_j)-\min (x_j)}}$$

(1)

where $k_j$ indicates the indicator type, with $j=0$ for benefit-type indicators ($C_j=-\min (x_j)$) and $j=1$ for cost-type indicators ($C_j=\max (x_j)$); $\max (x_j)$ and $\min (x_j)$ are the maximum and minimum values of the $j\text{-}th$ indicator across all samples.

The information entropy of the $j\text{-}th$ indicator is then calculated as

$$e_j=-{\displaystyle \frac{1}{\ln n}}{\displaystyle \sum _{i=1}^n{p}_{ij}}\ln p_{ij}$$

(2)

When $p_{ij}={\displaystyle \frac{x_{ij}^{\prime }}{{\displaystyle {\sum }_{i=1}^n{x}_{ij}^{\prime }}}}$, $p_{ij}=0$ is treated as zero by taking the limit.

Finally, the entropy-based weight is obtained as

$${\omega }_{\mathrm{entropy},j}={\displaystyle \frac{1-e_j}{{\displaystyle {\sum }_{j=1}^m(1-e_j)}}}$$

(3)

The entropy weight vector ${\Omega }_{\mathrm{entropy}}$ is denoted as

$${\Omega }_{\mathrm{entropy}}=[{\omega }_{\mathrm{entropy},1},{\omega }_{\mathrm{entropy},2},\dots ,{\omega }_{\mathrm{entropy},m}]$$

(4)

(ii) BP neural network

The BP neural network [23,24] is adopted to model nonlinear dependencies among risk indicators in GIES projects. Model robustness is ensured through systematic parameter settings and training strategies, as described below.

(1) Dataset and input–output definition

The BP network takes as input the standardized values of 30 tertiary risk indicators $[N,30]$. The training target is the entropy-based comprehensive risk score, providing an objective, data-driven reference that matches the nonlinear mapping capability of the BP network and avoids subjective target specification.

(2) Structure and training rules

The hidden-layer output $h_k$ is expressed as

$$h_k=f({\displaystyle \sum _{i=1}^m{\omega }_{ik}{x}_i}-b_k)$$

(5)

where $f(\cdot )$ is the Sigmoid activation function; ${\omega }_{ik}$ is the connection weight between the input and hidden layers; $b_k$ is the hidden-layer bias.

The output layer $y_l$ is defined as

$$y_l=g\left({\displaystyle \sum _{k=1}^t{\omega }_{kl}{h}_k}-b_l\right)$$

(6)

where $g(\cdot )$ is the linear activation function; ${\omega }_{kl}$ is the connection weight between the hidden and output layers; $t$ is the number of hidden-layer neurons; $b_l$ is the output layer bias.

The training error $E$ and weight update rules are given by

$$E={\displaystyle \frac{1}{2}}{\displaystyle \sum _{l=1}^q(d_l-y_l)}$$

(7)

$$\left\{\begin{array}{c}\Delta {\omega }_{kl}=\eta {\displaystyle \frac{\mathsf{\partial }E}{\mathsf{\partial }{\omega }_{kl}}}\\ \Delta {\omega }_{ik}=\eta {\displaystyle \frac{\mathsf{\partial }E}{\mathsf{\partial }{\omega }_{ik}}}\end{array}\right.$$

(8)

where $d_l$ is the target output; $q$ is the number of output neurons; $\eta$ is the learning rate, set to 0.01 [25].

(3) BP weight extraction

After training convergence ($E<0.001$), the BP weights ${\omega }_{BP,j}$ are given as follows:

According to Equations (5) and (6), output sensitivity $S_j$ with respect to the input indicators is evaluated.

$$\left\{\begin{array}{c}{S}_j={\displaystyle \frac{\mathsf{\partial }{y}_l}{\mathsf{\partial }{x}_{ij}}}={\displaystyle {\sum }_{h=1}^t({\omega }_{kl}{f}^{\prime }(z_k){\omega }_{ik})}\\ z_k={\displaystyle {\sum }_{j=1}^{30}({\omega }_{ik}{x}_{ij}+b_k)}\end{array}\right.$$

(9)

where $f^{\prime }(\cdot )$ is the derivative of the activation function in the hidden layer; $z_k$ is the weighted input sum of the $k\text{-}th$ hidden neuron.

The normalized BP weights are obtained accordingly.

$${\omega }_{BP,j}={\displaystyle \frac{\left|S_j\right|}{{\displaystyle {\sum }_{j=1}^{30}\left|S_j\right|}}}$$

(10)

(iii) Fuzzy matter-element theory

Fuzzy matter-element theory is adopted to map quantitative indicators to discrete risk grades. Its fuzzy elements include membership functions and fuzzified expert scores for qualitative indicators, while deterministic elements comprise grade interval thresholds, quantitative indicators, and a three-dimensional matter-element matrix of objects, indicators, and grades.

The matter-element matrix $R$ is defined as

$$R=(N,c_j,v_j)$$

(11)

The correlation degree of indicator $c_j$ with respect to the $k\text{-}th$ risk grade is calculated as

$$K_k(c_j)=\left\{\begin{array}{c}{\displaystyle \frac{\left|x_j^{\prime }-a_j^k\right|}{b_j^k-a_j^k}},x_j^{\prime }\in \left[a_j^k,b_j^k\right]\\ {\displaystyle \frac{\left|x_j^{\prime }-a_p^k\right|}{b_p^k-a_p^k}},x_j^{\prime }\notin \left[a_j^k,b_j^k\right]\end{array}\right.$$

(12)

where $a_j^k$ and $b_j^k$ are the standardized bounds of the classical domain; $a_p^k$ and $b_p^k$ are the bounds of the nodal domain.

The entropy–BP combined weights $K_k(N)$ are obtained by weighting the original grade correlations of each indicator and synthesizing them into an extension index, integrating indicator importance with grade relevance.

$$K_k(N)={\displaystyle \sum _{j=1}^m{\omega }_j}{K}_k(c_j)$$

(13)

2.2.2. Hybrid BP–Entropy Weighting Model

The BP–entropy combined weighting strategy, deeply integrated with fuzzy matter-element theory, enables the proposed framework to fuse objective data dispersion with nonlinear feature learning, thereby overcoming the limitations of traditional single-weighting methods.

The comprehensive indicator weight is defined as

$${\omega }_j=\alpha {\omega }_{BP,j}+(1-\alpha ){\omega }_{\mathrm{entropy},j}$$

(14)

where $\alpha$ is the weight allocation coefficient; $\alpha \in \left[0,1\right]$ is adaptively adjusted based on the nonlinear behavior of the indicators.

Compared with entropy weighting and BP weighting alone [21,23], the parameter $\alpha$ in Equation (14) is calibrated using five-fold cross-validation. For strongly coupled indicators (e.g., C19 and C29), $\alpha$ is set to 0.3 to emphasize BP-based nonlinear weighting, whereas for relatively independent indicators (e.g., C1), $\alpha$ is set to 0.7 to retain entropy-based objectivity. This adaptive scheme balances data objectivity with nonlinear feature representation.

2.2.3. Overall Risk Evaluation Procedure

Based on the above framework, the overall risk evaluation process is summarized into five steps to ensure clarity and practical implementation, as shown in Figure 1.

(1) Data preparation. 30 indicators are collected for each of the three schemes and standardized using Equation (1). Minimum risk values are assigned to benefit-type indicators, whereas maximum risk values are assigned to cost-type indicators. The resulting dimensionless input matrix is $X^{\prime }={(x_{ij}^{\prime })}_{3\times 30}$.

(2) Dual weight calculation. Entropy-based weights are derived using Equations (2)–(4). The standardized matrix $X^{\prime }$ is used as input, and BP-based weights are obtained via network training following Equation (10). Risk grade scores calibrated to T/CESS 104-2022 serve as target values, enabling the extraction of inter-indicator relationships and improved weight interpretability.

(3) Comprehensive weight determination. Integrated weights are computed using Equation (14) to balance the objectivity of entropy-based weights and the nonlinear sensitivity of BP-based weights, emphasizing key risk factors.

(4) Fuzzy risk assessment. The classical and node domains are established according to national standards. The correlation degree is computed using Equation (12), and the comprehensive risk index $K_k(N)$ is derived using Equation (13) within the range of 0–1, where higher values indicate lower risk and greater project feasibility.

(5) Risk classification and validation. The risk grade is assigned according to the maximum correlation degree, and robustness is validated through five-fold cross-validation using the mean squared error (MSE) on 90 samples [26]. Moreover, the framework supports out-of-sample performance evaluation under limited samples, consistent with practical GIES planning conditions. The use of externally defined risk grades that are independent of the model construction ensures that the validation reflects genuine model performance rather than internal fitting. The resulting model provides a transparent and reproducible decision-support tool for feasibility screening and risk-informed planning.

3. Case Study

3.1. GIES Project Description and Data Configuration

(i) Case description

This section describes a case study on the planning and construction of a GIES project in an emerging eco-tourism area in East China [27]. The system integrates photovoltaic units, wind turbines, gas boilers, and energy storage. Pollutant emissions are calculated according to GB 13223-2011 [28], with 2024 as the cost base year and a discount rate of 8%. Industrial and residential loads are assumed to operate for 8000 and 3000 h per year, respectively, and annual load profiles are generated using HOMER Pro [29,30]. The simulated annual electrical, heating, and cooling load profiles are illustrated in Figure 2a–c. In accordance with the “14th Five-Year Plan” land use classification, heating demand is mainly attributed to residential, hotel, and medical areas, while cooling demand shows pronounced seasonal variations due to the subtropical monsoon climate.

(ii) Meteorological data and climate-driven uncertainties

The National Aeronautics and Space Administration Prediction of Worldwide Energy Resources (NASA POWER) dataset, Version 3, is employed as the meteorological data source [31]. It provides daily solar radiation expressed in kilowatt-hours per square meter and daily mean wind speed expressed in meters per second. The data are compiled at a daily resolution for the East China Ecotourism Region (30.5–31.5° N, 120.5–121.5° E) over the period 2019–2023 and were accessed on March 15, 2024. The study region receives approximately 2200–3000 h of annual sunshine, with an average annual solar radiation of 1427.15 kilowatt-hours per square meter, and exhibits annual wind speeds ranging from 3.5 to 6.0 m per second.

Driven by the monsoon climate, wind energy resources exhibit pronounced seasonal variability, characterized by stronger intensity in winter, moderate levels in spring and autumn, and weaker conditions in summer. In addition, frequent monsoon-induced typhoons and extreme weather events impose stringent requirements on the structural and foundation design of wind power systems. These factors not only increase construction and maintenance costs but also intensify environmental disturbance, thereby introducing additional technical and investment risks to renewable energy deployment in the project area.

(iii) GIES-specific risk identification and mapping

Considering the GIES-specific risk sources of the case project, namely, cross-energy coupling, long investment cycles, policy uncertainty, and operational risks, the associated indicators are listed in

Table 3. GIES risk–indicator mapping.

GIES-Specific Risks	Risk Manifestations	Associated Indicators
Cross-energy coupling	Demand–generation mismatch across electricity, heating, and cooling	C19; C23; C29
Long investment cycles	Long-term revenue uncertainty due to policy and market fluctuations	C10; C11; C12
Policy uncertainties	Changes in carbon policy constraints on emissions and renewable subsidies	C15; C17; C20
System operation	Typhoon-driven operational risks	C26; C27

.

(iv) BP model configuration and sample construction

Based on the indicator dimension, the BP network was configured with 30 input neurons, 18 hidden neurons, and one output neuron. A Sigmoid activation function was used in the hidden layer, while a linear activation function was applied in the output layer. The model was trained using gradient descent with the MSE loss for 1000 epochs under a random seed of 2025, with L2 regularization (coefficient = 0.001) introduced to suppress overfitting in small-sample scenarios.

The data were derived from two sources: preliminary feasibility study reports of GIES projects in East China, providing technical schemes, investment estimates, energy demand forecasts, and pollutant emission data, and simulation outputs from HOMER Pro, generating renewable energy production, grid interaction power, and system operational efficiency under different operating scenarios. Each sample represented a complete risk profile of a specific GIES operating scenario and consisted of all 30 third-level risk indicators listed in Table 1. Three schemes were considered for model validation and robustness testing, with 30 independent samples generated for each scheme by varying key parameters, yielding a total of 90 samples. Latin hypercube sampling (LHS) was employed to ensure uniform coverage of the parameter space, while physically infeasible or policy-inconsistent parameter combinations were excluded.

3.2. Evaluation Results and Model Validation

3.2.1. Indicator Data Description

The data used in this section are derived from the original data of the project’s preliminary feasibility study report. The indicator dataset reflects the projected performance of three alternative implementation scenarios, as summarized in

Table 4. Raw data of 30 indicators for different scenarios.

Evaluation Factors	Indicators	Scenario 1	Scenario 2	Scenario 3
Cost risk: B1	C1 (×104 $)	36,410.15	26,105.41	26,575.20
	C2 (×104 $/year)	6647.93	5885.61	6055.32
	C3 (×104 $/year)	3671.93	3817.40	3942.85
	C4 ($/kW×year)	6.83	6.27	6.41
	C5 ($/kW×year)	0.1514	0.1278	0.1382
Revenue risk: B2	C6 (×104 $/year)	4784.23	3998.88	3838.89
	C7 (×104 $)	44,056.28	31,587.54	32,155.99
	C8 (%)	30.91	25.05	28.83
	C9 (%)	13.37	16.92	15.52
Long-term development risk: B3	C10 (%)	6.91	7.32	7.08
	C11 (Years)	8.9	7.98	8.5
	C12 (%)	13.14	15.32	14.45
Pollutant emission risk: B4	C13 (×104 kg/year)	365.56	299.86	330.28
	C14 (kg/kW)	0.2652	0.2176	0.2396
	C15 (%)	17.97	24.02	19.65
Renewable energy integration risk: B5	C16 (%)	16.87	21.04	19.16
	C17 (%)	23.19	26.22	24.71
	C18 (×104 kWh/year)	332.52	389.99	364.09
	C19 (kW)	1500	2300	2100
	C20 (%)	32.03	40.91	38.72
Energy supply reliability: B6	C21 (%)	38.48	46.40	41.20
	C22 (%)	61.52	53.60	58.80
	C23 (%)	1.52	1.47	1.49
	C24 (kW)	16,000	14,800	15,500
	C25 (kW)	9000	9200	8500
Energy supply safety: B7	C26 (%)	0.0001	0.0001	0.0001
	C27 (%)	37.29	42.01	41.84
	C28 (%)	35.43	39.91	39.75
Grid operational safety: B8	C29 (kW)	6200	5900	5500
	C30 (kW)	6500	7600	7200

. These indicators form the basis for risk-level evaluation and comparative analysis, thereby supporting quantitative investment decisions.

3.2.2. Risk Level Classification Scheme

Based on the comprehensive risk indicator system for grid-integrated energy service projects, project risks are classified into four levels, namely, Grades I–IV. Grade I indicates acceptable risk ($K_k(N)\in [0.8,1.0]$), Grade II conditionally acceptable risk ($K_k(N)\in [0.6,0.8]$), Grade III undesirable risk ($K_k(N)\in [0.3,0.6]$), and Grade IV unacceptable risk ($K_k(N)\in [0,0.3]$). Following indicator standardization and in accordance with relevant national policies and project construction requirements [32], the grade ranges of the indicators are summarized in

Table 5. Risk grade classification criteria for third-level indicators.

Third-Level Indicators		Risk Intervals by Grade				Sources of Threshold Values
Names	Types	Grade I	Grade II	Grade III	Grade IV
Initial investment: C1 (×104 $)	Cost	0–3000	3000–3500	3500–4000	>4000	DL/T 2443-2021 [33]: Investment upper limits for gas-fired distributed energy stations
Annualized total cost: C2 (×104 $/year)		0–800	800–850	850–900	>900	GB/T 39775-2021 [34]: Operating cost control criteria
Annual energy cost: C3 (×104 $/year)		0–520	520–540	540–560	>560	TCET 103-2024 [35]: Energy consumption benchmarking criteria
Investment cost per unit load: C4 ($/kW×year)		0–0.9	0.9–0.93	0.93–0.96	>0.96	DL/T 2443-2021 [33]: Unit investment criteria for distributed energy systems
Cost per unit load: C5 ($/kW×year)		0–0.13	0.13–0.14	0.14–0.15	>0.15	Industry specification for distributed energy cost accounting (2025)
Annual profit: C6 (×104 $/year)	Benefit	>600	550–600	500–550	<500	Industry benchmarks for economic evaluation of integrated energy projects
Present value of total revenue: C7 (×104 $)		>5000	4000–5000	3500–4000	<3500	GB/T 50866-2013 [36]: Extended economic analysis criteria
Cost-to-revenue ratio: C8 (%)	Cost	0–26	26–29	29–32	>32	Industry thresholds for energy project revenue risk control
Net profit margin: C9 (%)	Benefit	>16	14–16	12–14	<12	Industry standards for profitability evaluation of distributed energy projects
Internal rate of return: C10 (%)		>7.2	7–7.2	6.8–7	<6.8	Benchmark IRR reference for distributed energy industry
Payback period: C11 (Years)	Cost	0–8	8–8.5	8.5–9	>9	Payback period benchmarks for PV projects
Annual return on investment: C12 (%)	Benefit	>15	14–15	13–14	<13	Industry benchmarks for investment returns of integrated energy projects
Total pollutant equivalent: C13 (×104 kg/year)	Cost	0–300	300–330	330–360	>360	GB 13223-2011 [28]: Special emission limits for thermal power plants
Emission intensity per unit load: C14 (kg/kW)		0–0.22	0.22–0.24	0.24–0.27	>0.27	GB 13223-2011 [28]: Emission limit conversion for gas turbine units
Pollutant emission reduction rate: C15 (%)	Benefit	>23	20–23	17–20	<17	14th FYP target for 18% reduction in CO2 emissions per unit GDP
Renewable energy penetration rate: C16 (%)		>20	18–20	16–18	<16	Renewable energy configuration standards for zero-carbon parks
Share of renewable installed capacity: C17 (%)		>26	24–26	22–24	<22	Renewable energy share requirements for energy transition
Total renewable energy generation: C18 (×104 kWh/year)		>380	350–380	320–350	<320	Generation evaluation criteria for distributed PV systems
Total installed renewable capacity: C19 (kW)		>2200	1900–2200	1600–1900	<1600	GB/T 32900-2025 [37]: Supporting capacity criteria for PV stations
Share of clean energy consumption: C20 (%)		>40	37–40	34–37	<34	Optimization standards for zero-carbon energy consumption structure
Energy self-sufficiency rate: C21 (%)		>45	40–45	37–40	<37	Industry requirements for energy network self-sufficiency rate
Share of imported electricity: C22 (%)	Cost	0–55	55–59	59–63	>63	Threshold criteria for energy supply security
Energy supply adequacy: C23 (%)	Benefit	>1.5	1.48–1.5	1.46–1.48	<1.46	Reliability evaluation criteria for integrated energy systems
Maximum electricity supply capacity: C24 (kW)		>15,500	15,000–15,500	14,500–15,000	<14,500	Industry standards for regional load supply assurance
Maximum heating/cooling supply capacity: C25 (kW)		>9000	8700–9000	8400–8700	<8400	Configuration standards for CCHP systems
Loss-of-load probability: C26 (%)	Cost	<0.00008	0.00008–0.00010	0.000010–0.00012	>0.00012	Four-level risk classification criteria for power grid security
Maximum grid load factor: C27 (%)		41–45	39–41	37–39	<37	Safety and stability thresholds for power grid operation
Maximum heating/cooling network load factor: C28 (%)		39–43	37–39	35–37	<35	Industry standards for heating and cooling network efficiency
Maximum peak-shaving capability: C29 (kW)	Benefit	>6000	5700–6000	5400–5700	<5400	Peak-regulation capability requirements for new-type power systems
Maximum valley-filling capability: C30 (kW)		>7500	7000–7500	6500–7000	<6500	Technical specifications for power grid valley-filling operation

.

3.2.3. Indicator Weight Determination

Establishing an appropriate indicator system is essential for comprehensive project risk evaluation. Given the multifactorial nature of project risks, the evaluation criteria encompassed cost-related, revenue-related, and long-term development indicators, as well as pollutant emission equivalents, renewable energy penetration, energy supply reliability and security, and power grid security. A total of thirty indicators were selected, including initial investment, annualized cost, annual energy consumption cost, and investment per unit capacity. Indicator weights were determined using the hybrid BP–entropy weighting method described in Section 2.2.2, and the resulting weight distribution is illustrated in Figure 3.

Figure 3 directly indicates that the total renewable energy installed capacity (C19) had the highest weight at 0.154698, reflecting its critical role in GIES cross-energy coupling, where the integration scale of wind, photovoltaic, and conventional energy sources governs multi-energy coupling complexity. With a ±5% perturbation applied to the indicator data of the three scenarios, C19 exhibited a weight fluctuation of only 1.5%, confirming the stability of the proposed weighting method.

This was followed by initial investment, the present value of total income, and the pollutant emission reduction rate, with weights of 0.123537, 0.123537, and 0.075522, respectively. Accordingly, cost-related, revenue-related, and pollutant emission indicators were the dominant factors influencing the project’s comprehensive risk level. Further analysis demonstrated that the proposed framework captured coupled risk effects, identifying C19 and maximum grid load factor (C27) as dominant typhoon-related risk factors with a combined weight of 0.278, consistent with on-site reinforcement requirements.

3.2.4. Indicator Relevance Analysis

The correlation degree of each evaluation indicator reflected the extent to which the assessed object belonged to a given risk level. The correlation degree was evaluated using the extension correlation coefficient across Grades I-IV. Taking Scenario 1 as an example, the results are summarized in

Table 6. Indicator–grade correlation degrees under Scenario 1 and corresponding indicator risk grades across different scenarios.

Correlation Degree	Scenario 1				Grades
	Grade I	Grade II	Grade III	Grade IV	Scenario 1	Scenario 2	Scenario 3
C1	−0.08731	−0.06920	−0.01487	0.01486	IV	I	I
C2	−0.0077	−0.00467	0.00438	−0.00268	III	II	I
C3	−0.00059	0.00178	−0.00077	−0.00160	II	II	III
C4	−0.0034	−0.00178	0.00305	−0.00159	III	II	III
C5	−0.01457	−0.00987	0.00420	−0.00311	III	I	III
C6	−0.03053	−0.02220	0.002768	−0.00248	III	I	I
C7	0.01486	−0.06920	−0.01487	−0.08731	I	IV	II
C8	−0.01238	1.33402	−6.7 × 10−17	−0.01238	II	I	I
C9	−0.02302	0.01165	−0.01472	−0.01709	II	I	I
C10	0.00037	−0.00139	−0.00053	−0.00158	I	I	I
C11	−0.00443	−0.00169	0.00339	−0.00281	III	III	II
C12	0.00391	−0.00982	−0.00560	−0.00875	I	I	I
C13	−0.01661	−0.00861	0.01535	−0.00791	III	II	II
C14	−0.01661	−0.00861	0.01535	−0.00791	III	II	II
C15	7.56 × 10−5	−0.00012	−0.01893	−0.03022	I	III	II
C16	−0.02014	0.00982	−0.01269	−0.01542	II	I	I
C17	−0.00625	0.00223	−0.00331	−0.00599	II	I	I
C18	−0.01053	0.00428	−0.00608	−0.00925	II	I	I
C19	−0.07735	0.05678	−0.05500	−0.0145	II	I	I
C20	−0.0169	−0.02620	0.01357	−0.01907	III	I	I
C21	0.00670	−0.01511	−0.00913	−0.01246	I	I	I
C22	−0.00932	−0.00591	0.00429	−0.0028	III	II	II
C23	3.85 × 10−5	−0.00047	−0.00059	−0.00071	I	I	I
C24	0.00016	−0.00254	−0.00382	−0.00424	I	II	II
C25	0.00029	−0.00274	−0.00325	−0.004	I	I	II
C26	−0.00037	0.00068	0.00023	−0.00023	II	II	II
C27	−0.00222	0.00665	−0.00263	−0.0056	II	I	II
C28	−0.00222	0.00665	−0.00263	−0.0056	II	I	II
C29	0.00108	−0.00597	−0.00602	−0.008	I	II	II
C30	−0.01030	0.00447	−0.00728	−0.00175	II	I	II

.

As shown in Table 6, the initial investment of Scenario 1 was assessed as Grade IV. The annualized cost, annual energy consumption cost, investment per unit capacity, cost per unit capacity, payback period, emissions per unit energy, pollutant emission reduction rate, proportion of clean energy consumption, and proportion of external power were classified as Grade III. These results indicate that cost reduction and improvements in energy cleanliness should be prioritized to mitigate the overall risk of Scenario 1.

Figure 4 illustrates the correlation degree distributions of the three scenarios under different risk grades. As shown in Figure 4a, the correlation degrees of Scenario 1 corresponding to Grade I fell within the range of [−0.09, 0.015], those for Grade II within [−0.07, 0.06], and those for Grade III within [−0.06, 0.016], with relatively small fluctuations, while the correlation degrees for Grade IV lay in the same range as Grade I, namely, [−0.09, 0.015]. Figure 4b shows that, for Scenario 2, the correlation degrees corresponding to Grade I ranged from [−0.05, 0.009] with limited variation; those for Grade II fell within [−0.08, 0.007], for Grade III within [−0.14, 0.025], and for Grade IV within [−0.15, 0.007]. As illustrated in Figure 4c, the correlation degrees of Scenario 3 spanned [−0.01, 0.02] for Grade I, [−0.08, 0.035] for Grade II, and [−0.10, 0.005] for Grade III, whereas the values for Grade IV were markedly lower, falling within [−0.12, −0.0002].

3.2.5. Comprehensive Risk Level Evaluation

Taking Scenario 1 as an example, the comprehensive correlation degrees of the secondary-level indicators for each scenario were calculated, and the results are presented in

Table 7. Factor-grade correlation degrees under Scenario 1 and corresponding risk grades across different scenarios.

Evaluation Factors	Scenario 1				Grades
	Grade I	Grade II	Grade III	Grade IV	Scenario 1	Scenario 2	Scenario 3
B1	−0.11358	−0.08376	−0.00399	0.005887	IV	I	II
B2	−0.11857	−0.11443	−0.02682	−0.01708	IV	I	II
B3	−0.00014	−0.01292	−0.00273	−0.01314	I	II	II
B4	−0.03314	0.269489	−0.24875	−0.1283	II	II	IV
B5	0.086702	−0.62609	0.773287	0.524869	III	IV	IV
B6	−0.00212	−0.02679	−0.0125	−0.02421	I	I	II
B7	−0.0058	0.006283	−0.00641	−0.01086	II	III	III
B8	0.005554	−0.01627	−0.0133	−0.00975	I	I	I

.

Table 7 reports the comprehensive correlation degrees corresponding to the four risk grades, which were −0.11358, −0.08376, −0.00399 and 0.005887, respectively. Accordingly, the cost-related indicators were classified as Grade IV, while the revenue-related indicators, with a maximum correlation degree of −0.01708, were also assigned to Grade IV. The development-related indicators, pollutant emission equivalent, renewable energy proportion, energy supply assurance, energy supply security, and power grid security exhibited maximum correlation degrees of −0.00014, 0.269489, 0.773287, −0.00212, 0.006283, and 0.005554, corresponding to Grades I, II, III, I, II, and I, respectively.

Figure 5a–c illustrate that the correlation degrees of Scenarios 1–3 varied across the four risk levels. For Scenario 1, the values ranged from −0.12 to 0.09 (Grade I), −0.63 to 0.27 (Grade II), −0.25 to 0.78 (Grade III), and −0.13 to 0.53 (Grade IV). For Scenario 2, the corresponding ranges were [−0.047, 0.012], [−0.14, 0.16], [−0.21, 1.96], and [−0.17, 3.36]. For Scenario 3, they were [−0.03, 0.034], [−0.31, 0.004], [−0.11, 0.73], and [−0.12, 1.09]. Overall, Scenarios 2 and 3 showed wider fluctuations at higher risk levels, indicating greater instability in their correlation characteristics.

Across the three GIES scenarios, development-related indicators, energy supply assurance, and grid security were mainly rated at Grade II or above, accounting for 37.5% of all indicators. This suggests that, although the scenarios are generally feasible, substantial room remains for improvement in cost control, revenue performance, emission reduction, renewable energy penetration, and supply security.

Table 8. Comprehensive correlation degrees and final risk grades of different scenarios.

Scenarios	Grade I	Grade II	Grade III	Grade IV	Evaluation Grade	Extension Index
Scenario 1	−0.17974	−0.39869	−0.14680	−0.17975	III	2.68255647
Scenario 2	−0.02715	−0.24494	−0.42520	−0.57900	I	1.61715564
Scenario 3	−0.18200	−0.00042	−0.28093	−0.50744	II	1.73510216

presents the comprehensive risk correlation degrees of each scenario and their corresponding evaluation grades. Scenario 1 is classified as Grade III, Scenario 2 as Grade I, and Scenario 3 as Grade II. Notably, the comprehensive correlation degree of Scenario 3 at Grade II is −0.00042, indicating that its risk performance is close to the threshold of Grade I and therefore exhibits potential for further improvement.

A leave-one-indicator-out analysis was performed on the ten highest-weighted indicators identified in Figure 3 to assess robustness against missing key inputs. Each indicator was removed in turn, after which the comprehensive weights and risk grades were updated. The results show that the scenario ranking remained unchanged, with the corresponding risk grades reported in Table 8. Moreover, the Pearson correlation coefficient between the reduced and full indicator systems exceeded 0.96 in all cases, confirming strong robustness.

3.3. BP-Based Model Performance Validation

(i) Fitting, generalization, and benchmarking analysis

The BP neural network performance was analyzed as a validation tool for the proposed model, as depicted in Figure 6.

Figure 6 shows that the correlation coefficients $R$ were close to unity, demonstrating high fitting accuracy and supporting the reliability of the proposed weighting scheme. Five-fold cross-validation was conducted based on the MSE using 90 samples from three cases, as illustrated in Figure 6a,b. The MSE difference between the training and validation sets was 0.0005, with a validation-to-training MSE ratio of 1.06, indicating that the model did not exhibit overfitting. Compared with the AHP benchmark, the scheme weights obtained by the proposed combined method (0.82, 0.70, and 0.55) showed improved discrimination relative to those derived from AHP (0.78, 0.75, and 0.52).

(ii) Ablation analysis

To evaluate the effectiveness of the combined method, Scenario 2 was selected as a representative case, and the ablation results were quantified using the root mean squared error (RMSE) and mean absolute error (MAE), as summarized in

Table 9. Ablation analysis results of different weighting methods.

Method Types	Risk Weights	RMSE	MAE
Entropy method-only	0.68	0.041	0.035
BP-only	0.72	0.038	0.032
BP-entropy combined method	0.70	0.023	0.018

.

As shown in Table 9, the proposed combined method achieved consistently lower RMSE and MAE than the single-method counterparts, indicating enhanced robustness through the integration of entropy-based objectivity and BP-driven nonlinear feature learning.

4. Conclusions

This study developed a comprehensive risk evaluation framework for GIES projects by integrating an entropy–BP combined weighting method with fuzzy matter-element theory. A 30-indicator evaluation system spanning technical, economic, environmental, and social dimensions was constructed to enable systematic risk assessment. With standards-based thresholds and traceable data, the entropy–BP scheme yields stable and interpretable weights by integrating data-driven objectivity and nonlinear correction. Stability tests based on indicator removal and data perturbation showed only minor weight variation, suggesting the robustness of the proposed method. In the fuzzy matter-element evaluation, the combined weights transformed correlation degrees into weighted extension indices, enabling joint consideration of indicator importance and grade relevance. Application to three GIES scenarios yielded clear risk grade differentiation from Grade I to Grade III, supporting the practical applicability of the framework within the adopted threshold and data assumptions.

Nevertheless, the evaluation index system did not explicitly incorporate dynamic external factors, such as policy adjustments and extreme climate events, which may affect adaptability under evolving conditions. In addition, validation was conducted on three project scenarios, and broader generalizability would benefit from additional cases covering diverse regions and scales. Membership function parameters in the fuzzy matter-element model were determined empirically and may be improved through adaptive optimization. Future research will focus on enhancing index system dynamicity, expanding sample coverage, and optimizing model parameters using machine learning techniques. Moreover, incorporating contingency analysis to characterize system resilience under rare events and refining the coupling representation among multi-energy subsystems are expected to further improve the accuracy and practical relevance of the framework.