Research on the Development Potential of a Hybrid Energy Electric–Hydrogen Synergy System: A Case Study of Inner Mongolia

Abstract

The utilization of hydrogen energy presents new opportunities for renewable energy integration, and the hybrid electricity–hydrogen synergy system exhibits significant potential for renewable energy accommodation and multi-scenario applications. To comprehensively explore the potential of such systems, this study proposes a two-stage design methodology that integrates HOMER simulation with multi-criteria decision-making (MCDM). Using Baotou, Inner Mongolia as a case study, HOMER is employed for simulation and optimization, and a comprehensive evaluation index system encompassing energy, economic, and environmental dimensions is established to assess the potential Cases and identify the optimal one. This study proposes an innovative weighting model combining CRITIC, Grey-DEMATEL, and Huber loss function. The model effectively resolves conventional methods’ deficiencies in balancing subjective–objective factors. Furthermore, an enhanced GRA-VIKOR model is developed to overcome the inherent constraints of conventional VIKOR approaches, particularly their excessive dependence on indicator weights and decision-maker preferences. The experimental results reveal that systems with 50% wind power integration demonstrate the optimal comprehensive development potential, while the developed MCDM framework successfully confines indicator weight deviations within the range of 0.016–0.019.

1. Introduction

The accelerated evolution of power systems has introduced multifaceted challenges to modern energy infrastructures [1]. Cost-effectively, reliably, and efficiently addressing escalating electricity demand constitutes a persistent challenge in energy provisioning [2]. Hybrid electricity–hydrogen integrated systems effectively mitigate energy intermittency through hydrogen-based energy conversion and storage mechanisms [3,4]. These integrated systems demonstrate synergistic improvements in energy economics, the reliability of supply, and environmental sustainability.

System optimization necessitates the simultaneous consideration of multiple competing objectives. However, configurations generally demonstrate Pareto optimality—no single Case outperforms the others on all criteria. Instead, they provide specific trade-offs between conflicting objectives. This necessitates the data-driven comparative analysis of system alternatives to determine Pareto-optimal configurations. Current evaluation frameworks lack robust mechanisms for objective weighting and multi-criteria performance benchmarking, hindering the systematic comparison of alternative Cases. Therefore, developing advanced multi-criteria decision-making (MCDM) frameworks for hybrid electricity–hydrogen systems holds critical importance for optimizing infrastructure planning, enhancing operational efficiency, and achieving decarbonization goals.

Optimal decision-making is contingent upon rigorous data evaluation, whose foundational element resides in precisely quantifying indicator weights. Existing indicator weighting methodologies can be classified into two categories:

• Objective Perspective: For example, reference [5] employs the Anti-Entropy Weights (AEWs) method to determine indicator weights, while reference [6] utilizes the CRITIC method to evaluate photovoltaic energy system indicators. While deriving their weights from inherent data patterns, these approaches do not systematically account for decision-makers’ preferences in the weighting calculus.
• Subjective Perspective: Reference [7] combines the Grey Decision-Making Trial and Evaluation Laboratory (Grey-DEMATEL) method with the Fuzzy Analytic Hierarchy Process (Fuzzy-AHP) to determine indicator weights. Similarly, reference [8] uses cloud models and fuzzy techniques to rank the importance of the indicators. Although anchored in expert judgments, such subjective methods’ absence of data-driven validation could compromise decision robustness due to cognitive bias propagation.

Recent advances have focused on hybrid weighting frameworks that synthesize subjective and objective methodologies, seeking to reconcile their respective limitations through systematic integration. For instance, reference [9] proposed a model combining Nash equilibrium with the Technique for Order Preference by Similarity to Ideal Case (TOPSIS), which incorporates participants’ opinions while ranking the alternatives based on objective distances. Similarly, reference [10] employed Fuzzy Analytic Hierarchy Process (Fuzzy-AHP) and Anti-Entropy Weights (AEWs) to calculate subjective and objective weights, respectively, and used a weighted approach to derive the final weights. However, these methods fail to account for the adaptability of the approach to specific scenarios. When cognitive preferences diverge substantially from empirical evidence, existing frameworks exhibit polarization tendencies—either overemphasizing subjective judgments or disproportionately weighting objective data—thus subverting the fundamental rationale for hybrid weighting.

The Huber loss function—a robust statistical estimator—implements an adaptive penalty mechanism that differentially treats small and large deviations through piecewise linear optimization. In this study, the Huber loss function is utilized to manage the deviations between subjective and objective weights. The proposed framework synergistically couples Huber-based robust optimization with stochastic gradient descent, where

• Huber-adapted gradients dynamically modulate the update magnitudes;
• Iterative refinement converges to consensus weights through error-adaptive learning.

This methodology establishes a theoretically rigorous weighting paradigm particularly suited for multi-criteria decision conflicts where subjective preferences and objective evidence exhibit non-negligible discordance.

After comprehensively evaluating the system, selecting the optimal Case based on the evaluation results is another critical step. Due to the diverse characteristics of different indicators—some performing better when larger and others more favourable when smaller—it is challenging to simultaneously optimize all indicators, necessitating a scientific approach for trade-offs. Numerous scholars have conducted relevant research in this area. For instance, reference [11] employed the Type-2 Fuzzy TOPSIS method to screen energy storage technologies. Reference [12] combined the Fuzzy Analytic Hierarchy Process (Fuzzy-AHP) with the CRITIC method to determine indicator weights and utilized the Triangular Fuzzy VIKOR method to provide decision-making recommendations for commercial energy system selection. Reference [13] applied the AHP-TOPSIS method for decision-making in hydrogen energy system selection. Reference [14] adopted the Grey Relational Analysis (GRA) method to establish a carbon quota correlation model for energy parks, offering decision-making guidance for carbon emission allocation at various levels.

Currently, single decision-making methods such as TOPSIS, VIKOR, and GRA are predominantly used. However, the inherent limitations of these single methods restrict their effectiveness in practical applications. VIKOR method: This approach ranks alternatives based on decision-maker preferences by considering both group utility and individual regret values. It is computationally simple and offers a high reCase [15]. However, it faces two significant issues: 1. It relies heavily on decision-maker preferences. 2. It requires precise weight allocation for the group utility and individual regret of each indicator. These limitations result in the traditional VIKOR method underutilizing sample data and yielding less accurate results [16]. GRA method: This method can fully leverage sample information; nevertheless, it suffers from low discriminative power in analyzing information [17].

Therefore, this study proposes an integrated GRA-VIKOR model to address these limitations. The model leverages Grey Relational Analysis (GRA) to determine the ideal degree of each alternative, which is then used to establish decision-maker preferences. Simultaneously, the indicator weights obtained through the combined weighting method are applied to calculate the group utility and individual regret values in VIKOR. This approach not only enhances the discriminative power of GRA but also resolves the issues of VIKOR’s reliance on decision-maker preferences and precise weight allocation. By integrating these methods, the model maximizes the utilization of sample data information, providing a more robust and accurate decision-making framework.

In summary, this study focuses on the design and optimization of a hybrid electricity–hydrogen synergy system, using Inner Mongolia as a case study. The research employs HOMER to simulate and generate feasible system configurations for Baotou, Inner Mongolia. A comprehensive three-dimensional evaluation framework encompassing economic, technical, and environmental dimensions is established for systematic system assessment. The methodology integrates CRITIC, Grey-DEMATEL, and Huber loss functions to balance subjective and objective indicator weights, while the proposed GRA-VIKOR synthesis maximizes sample information utilization for optimal decision-making.

2. Materials and Methods

This study constructs a hybrid electricity–hydrogen synergy system based on real load scenarios in Inner Mongolia. The system employs HOMER ×64 3.14.2 (Pro Edition) for cost-minimized optimization design, yielding nine feasible Cases with varying wind power proportions to form a candidate Case set. Technical, economic, and environmental performance indicators are quantified for each configuration. Subsequently, by evaluating the indicator performance and collecting expert opinions, an enhanced MCDM method is applied to conduct multi-criteria decision-making on the nine Cases, identifying the one with the greatest potential. The load data, model construction, and simulation results are presented in Appendix A.

2.1. Construction of Hybrid Energy Electric–Hydrogen Collaborative System

The traditional hybrid electricity–hydrogen synergy system, as illustrated in Figure 1, primarily consists of three key components: the energy supply section, responsible for converting various energy sources into electricity and managing energy acquisition and initial power conversion, which includes wind power, photovoltaic systems, and diesel generators; the energy conversion section, dedicated to transforming electrical energy into hydrogen energy, comprising rectifiers, inverters, hydrogen production modules, and energy storage modules; and the energy demand section, which involves the utilization of the system’s energy products and directly influences the design scale of the system [18], encompassing electrical loads and hydrogen loads.

2.2. Index Evaluation System

The inherent volatility of renewable energy significantly impacts the system’s supply performance. Hydrogen energy supplementation can effectively mitigate the resource waste caused by renewable curtailment, thereby enhancing the overall energy utilization efficiency. System power supply reliability is defined as the ratio of supplied load to the total load demand. The excess electricity fraction, calculated as the ratio of total surplus electricity to total electricity production, quantifies the system’s “efficiency loss”. Consequently, energy-related metrics include power supply reliability, renewable energy penetration rate [19], excess electricity fraction, and system-wide electrical efficiency.

Although renewable energy generation costs persistently decrease [2], numerous projects remain subsidy-dependent. The Internal Rate of Return (IRR) is employed to evaluate the profitability of different configurations [20], while the Annualized Return on Investment (AROI) reflects the economic viability of projects [21]. Additionally, the Levelized Cost of Electricity (LCOE) and Net Present Cost (NPC) are calculated under varying wind–solar capacity ratios to assess system-wide economic performance.

The substitution of diesel generation with renewable energy sources achieves significant pollutant emission reductions. Using a baseline scenario where all electricity is grid-supplied, the system’s annual carbon emissions are quantified to derive the relative carbon emission reduction rate, thereby evaluating its decarbonization benefits. The carbon emission intensity per unit of energy output is also calculated. Traditional diesel generators primarily emit sulphur dioxide (SO₂), nitrogen oxides (NO_x), carbon monoxide (CO), unburned hydrocarbons (UHC), and particulate matter [22]. The Photochemical Ozone Creation Potential (POCP) measures the relative capacity of volatile organic compounds to generate ground-level ozone. Since CO and UHC are key precursors for ozone formation, POCP intensity per unit of electricity is calculated based on these pollutants. The Acidification Potential (AP) intensity per unit of electricity is determined using SO₂ and NO_x emissions, as these acidic substances induce soil and atmospheric acidification, posing ecological risks.

Based on the contribution of the indicators to the system, they are classified into cost-type and benefit-type indicators. The constructed evaluation index system and corresponding symbol table are shown in

Table 1. Benefit evaluation index system.

Criteria		Indicator	Type	Calculation Formula	Unit
Technical perspective	c11	power supply reliability	Benefit	${\eta }_e=1-{\displaystyle \frac{L_{\mathrm{umet}}}{L_{demand}}}$	%
	c12	renewable energy penetration rate	Benefit	$f_{re}={\displaystyle \frac{E_{re}}{E_p}}\times 100\%$	%
	c13	excess electricity fraction [23]	Cost	$f_{excess}={\displaystyle \frac{E_{excess}}{E_p}}\times 100\%$	%
	c14	system-wide electrical efficiency	Benefit	${\mu }_e={\displaystyle \frac{E_c}{E_p}}\times 100\%$	%
Economic perspective	c21	IRR	Benefit	$NPV={\displaystyle {\sum }_{t=1}^n\frac{C_t}{{(1+IRR)}^t}}-C_0=0$	%
	c22	AROI	Benefit	$AROI={({\displaystyle \frac{C_t}{C_{tac}}})}^{{\displaystyle \frac{1}{n}}}-1$	%
	c23	COE [24]	Cost	$COE={\displaystyle \frac{C_{tac}}{E_p}}$	CNY/kWh
	c24	NPC	Cost	$NPC={\displaystyle \frac{C_{\mathrm{tac}}\left[{(1+r)}^n-1\right]}{r{(1+r)}^n}}$	million CNY
Environmental perspective [20]	c31	carbon emission intensity	Cost	$C_{E,P}={\displaystyle \frac{C_{GP}}{E_P}}$	kg/kWh
	c32	decarbonization benefits	Benefit	$R={\displaystyle \frac{C_{baseline}-C_{project}}{C_{baseline}}}\times 100\%$	%
	c33	POCP	Cost	$POCP=(C_{CO}\times {\beta }_{CO}+C_{HC}\times {\beta }_{HC})/E_p$	10−3 kg C2H4/MWh
	c34	AP	Cost	$AP=(C_{S{O}_2}\times {\beta }_{S{O}_2}+C_{N{O}_X}\times {\beta }_{N{O}_X})/E_p$	10−3 kg SO2/MWh

. To ensure a fair comparison of Cases, hypothetical conditions and calculation scenarios are established. The assumptions for this study are presented in

Table 2. Meanings of variables and values.

Variable	Meaning	Unit	Value	Variable	Meaning	Unit	Value
Lumet	Unmet load	kWh	HOMER simulation results	CGP	Carbon emission	kg	HOMER simulation results
Ldemand	Demand load	kWh	HOMER simulation results	Cbasline	Carbon emissions in baseline scenario	kg	HOMER simulation results
Ere	Renewable electricity	kWh	HOMER simulation results	Cproject	Carbon emissions in project scenario	kg	HOMER simulation results
Ep	System electricity production	kWh	HOMER simulation results	CCO	Carbon monoxide emissions	kg	HOMER simulation results
Eexcess	Excess power	kWh	HOMER simulation results	βCO	Carbon monoxide equivalent factor	/	0.3
Ec	Load electricity consumption	kWh	HOMER simulation results	CHC	Unburned hydrocarbon emissions	kg	HOMER simulation results
Ct	Cash flow in year t	CNY	HOMER simulation results	βHC	Unburned hydrocarbons equivalent factor	/	1
C0	Capital cost	CNY	HOMER simulation results	CSO2	SO2 emission	kg	HOMER simulation results
Ctac	Total cost of system	CNY	HOMER simulation results	βSO2	SO2 equivalent factor	/	1
t	Project time	year	25	CNox	NOx emission	kg	HOMER simulation results
r	Discount rate	%	5	βNOx	NOx equivalent factor	/	0.7

.

2.3. Comprehensive Benefit Evaluation Model

The MCDM method in this study is divided into two stages:

Stage 1: Indicator Weight Determination. This stage integrates subjective and objective methods to determine indicator weights. First, the CRITIC method is employed to establish the objective weights of the indicators. The CRITIC method not only considers the volatility of the data themselves but also introduces indicator correlation as a criterion for judgement [6]. Second, the subjective weights of the indicators are calculated by combining grey number theory [25] with the DEMATEL method. Finally, the Huber loss function [26] is utilized to balance the subjective and objective weights, yielding the comprehensive weights of the indicators.

Stage 2: Multi-Criteria Decision Ranking (MCDA). In complex decision-making environments, MCDA ranks a set of alternatives based on multiple attributes, facilitating effective and optimized decision-making [27]. GRA is used to reveal the degree of ideality among the alternatives. The VIKOR method ranks the decisions by simultaneously considering the costs and benefits [28]. The flowchart of the overall evaluation model is illustrated in Figure 2.

2.3.1. Subjective Evaluation Based on CRITIC Method

The CRITIC method posits that criteria with higher volatility and lower correlation provide more valuable information for decision-making [29]. The key steps [30] are as follows:

Step 1: Information Quantification. For each criterion j, its information content C_j is calculated. The greater the information content of the j-th criterion, the more significant its role in the evaluation system, and thus, the higher its corresponding weight.

$$C_j={\sigma }_j\times R_j$$

(1)

Step 2: Calculation of Objective Weights $𝒲$_1j. The objective weight of each criterion is determined by normalizing its information content, where ∑C_j represents the total information content of all criteria.

$$w_{1j}={\displaystyle \frac{C_j}{{\displaystyle {\sum }_{j=1}^n{C}_j}}}$$

(2)

2.3.2. Objective Evaluation Based on GREY-DEMATEL Method

The GREY-DEMATEL method is capable of handling systems with incomplete information and high uncertainty. The key steps [23] are as follows:

Step 1: Calculation of Centrality M_i and Causality N_i. Centrality reflects the importance of an indicator, while causality indicates whether the indicator primarily influences other indicators (positive value) or is primarily influenced by other indicators (negative value).

$$M_i=f_i+e_i$$

(3)

$$N_i=f_i-e_i$$

(4)

In the formula, f_i and e_i represent the influencing degree and influenced degree of indicator i, respectively.

Step 2: Calculation of Subjective Weights $𝒲$_2j. Based on the formula, the subjective weights $𝒲$_2j are calculated for each indicator.

$$w_{2i}={\displaystyle \frac{M_i}{{\displaystyle \sum _i{M}_i}}}$$

(5)

2.3.3. Comprehensive Evaluation Based on Conflict Scenarios

This study innovatively treats subjective and objective weights as competing parties with differing preferences, aiming to determine an ideal weight that falls within an acceptable range for both sides. The Huber loss function employs linear loss iteration for weights with significant discrepancies and square loss iteration for weights with minor discrepancies, thereby reducing the impact of outliers on the model. By incorporating the Huber loss function, the MCDM model’s ability to handle outliers is enhanced, particularly in scenarios where significant conflicts exist between weights derived from subjective and objective methods, making this approach especially suitable.

The Case process is as follows: For the i-th indicator, an initial weight and gradient are randomly generated. The deviations between this weight and the subjective/objective weights are then calculated. Next, based on whether the deviation exceeds a predefined threshold, the method for updating the gradient is determined, and the weight is adjusted using the updated gradient, completing one iteration. This process is repeated multiple times until the error of the i-th indicator converges. Finally, the procedure is applied to all 12 indicators to obtain the final results. The calculation flow is illustrated in Figure 3, and the formulas used are provided as follows [24]:

$$L_{\delta }(y_i,y)=\left\{\begin{array}{l}{(y_i-y)}^2\left|y_i-y\right|\le \delta \\ 2\delta \left|y_i-y\right|-{\delta }^2\left|y_i-y\right|\ge \delta \end{array}\right.$$

(6)

$$\nabla (i+1)=\nabla (i)+L_{\delta }(y_i,y)$$

(7)

$$w(i+1)=w(i)+\mathcal{l}·\nabla (i+1)$$

(8)

$$errors\_w_{1i}=\max \left[MAE\_w_{1i},RMSE\_w_{1i}\right]$$

(9)

$$errors\_w_{2i}=\max \left[MAE\_w_{2i},RMSE\_w_{2i}\right]$$

(10)

$$MAE={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N\left|w(i)-w\right|}$$

(11)

$$RMSE=\sqrt{{\displaystyle \frac{1}{N}}{{\displaystyle \sum _{i=1}^N\left|w(i)-w\right|}}^2}$$

(12)

$$\begin{array}{c}{f}_1={{\displaystyle {\sum }_{i=1}^{12}\max \left[errors\_w_{1i},errors\_w_{2i}\right]}}^{(1)}\\ f_2={{\displaystyle {\sum }_{i=1}^{12}\max \left[errors\_w_{1i},errors\_w_{2i}\right]}}^{(2)}\\ \dots \\ f_n={{\displaystyle {\sum }_{i=1}^{12}\max \left[errors\_w_{1i},errors\_w_{2i}\right]}}^{(n)}\end{array}$$

(13)

$$\min \left[f_1,f_2,\dots ,f_n\right]$$

(14)

$$s.t.{\displaystyle \sum _{i=1}^{n}w(i)}=1$$

(15)

where (y_i − y) represents the error between the comprehensive weight and the subjective/objective weights, y is the true value, y_i is the predicted value, δ denotes the threshold that determines whether square loss or linear loss is applied, ∇ represents the gradient, ℓ is the learning rate, $𝒲$(i) indicates the weight value of the indicator, and Ν represents the number of indicators.

2.3.4. Scheme Ranking Method Based on GRA-VIKOR

This study proposes a multi-criteria decision-making method combining GRA and VIKOR, with the specific steps outlined as follows [31]:

Step 1: Data Preprocessing. Min-max normalization is performed on the data.

$$x_{nor}={\displaystyle \frac{x-x_{\min }}{x_{\max }-x_{\min }}}$$

(16)

Here, x_min and x_max represent the minimum and maximum values of each column in the data matrix, respectively.

Step 2: Construct the Ideal Case. For cost-type indicators, the minimum valueis selected, and for benefit-type indicators, the maximum value is selected as the optimal value for each indicator. The Case composed of these optimal values is referred to as the “ideal Case”.

Step 3: Calculate Correlation Degrees and Classify Them. First, calculate the distance β of each indicator relative to its optimal value. Using the reCase coefficient ρ and β, compute the correlation degree matrix ξ between each Case and the ideal Case. Finally, determine the average correlation degree χ_i for all indicators of each Case.

$$\xi ={\displaystyle \frac{{\beta }_{\min }+\rho \cdot {\beta }_{\max }}{\beta +\rho \cdot {\beta }_{\max }}}$$

(17)

$${\chi }_i={\displaystyle \frac{1}{n}}{\displaystyle \sum _{j=1}^n{\xi }_{ij}}$$

(18)

where ξ_ij is the correlation degree value of the i-th Case for the j-th indicator, and n is the total number of indicators. The nine Cases are ranked in descending order based on their correlation degree values. The top three Cases are classified as high-ideal Cases, where decision-makers prioritize individual losses (p = 0.4). The bottom three Cases focus on group benefits (p = 0.6), while the remaining Cases tend toward a compromise-based decision (p = 0.5).

Step 4: Based on the weights of the 12 indicators calculated earlier, the S value and R value are computed for each Case. For each Case, the S value represents the sum of the weighted differences across all indicators, reflecting the group benefit of the Case. The R value is the maximum weighted difference, reflecting the individual loss within the Case

$$S_i={\displaystyle \sum _{j=1}^n\frac{w_j(f_j^{\max }-f_{ij})}{f_j^{\max }-f_j^{\min }}}$$

(19)

$$R_i=\underset{j=1}{\overset{n}{\max }}\left\{\left.{\displaystyle \frac{w_j(f_j^{\max }-f_{ij})}{f_j^{\max }-f_j^{\min }}}\right\}\right.$$

(20)

In the formula, $𝒲$_j represents the comprehensive weight of each indicator, and f_j^min and f_j^max denote the minimum and maximum values of the i-th Case for the j-th indicator, respectively.

Step 5: The comprehensive utility value Q for each Case is calculated using the weight p determined by GRA. The Q value incorporates different weights to reflect decision-maker preferences, with the GRA-determined weight p providing a criterion for judging how close a Case is to the ideal Case.

$$Q_i=p\times S_i+(1-p)\times R_i$$

(21)

Finally, rank the alternative Cases based on their comprehensive utility values.

3. Example Calculation and Result Analysis

3.1. Example Information

This study establishes a wind–solar proportion analysis framework under Baotou’s typical operational scenarios. Nine gradient Cases (1–9) with wind power capacity ratios spanning from 10% to 90% (10% increments) are systematically configured. Second, while keeping the load demand (electric load: 174,583.2 kWh/day, hydrogen load: 500 kg/day), equipment parameters, and meteorological data (obtained from the NASA database) constant, simulation results are obtained using HOMER, as shown in

Table 3. Simulation results of examples.

	Case 1	Case 2	Case 3	Case 4	Case 5	Case 6	Case 7	Case 8	Case 9
PV capacity (MW)	53.10	33.00	23.80	18.00	13.60	10.30	7.07	4.44	2.11
Wind capacity (MW)	5.90	8.25	10.20	12.00	13.60	15.50	16.50	17.75	18.95
Wind proportion (%)	10	20	30	40	50	60	70	80	90
LOLP (%)	0.93	1.18	1.50	1.58	1.58	1.38	1.56	1.60	1.67
Power generation (×103 MWh)	121.71	97.16	90.12	88.18	87.75	90.52	89.43	90.49	91.91
Power consumption (×103 MWh)	70.26	68.96	68.53	68.46	68.43	68.80	68.41	68.36	68.32
Carbon emission (×103 kg/yr)	314.58	524.03	741.96	794.52	808.03	685.85	763.84	758.12	787.40
Carbon monoxide (kg/yr)	1983	3303	4677	5008	5093	4323	4815	4779	4963
Unburned hydrocarbons (kg/yr)	87	144	204	219	222	189	210	209	217
SO2 (kg/yr)	770	1283	1817	1946	1979	1679	1870	1856	1928
NOx (kg/yr)	1863	3103	4394	4705	4785	4061	4532	4489	4663

, along with the calculated 12 evaluation indicators presented in

Table 4. Index values of each Case.

	Indicator	Case 1	Case 2	Case 3	Case 4	Case 5	Case 6	Case 7	Case 8	Case 9
Technical	power supply reliability (%)	99.07	99.82	98.50	98.42	98.42	98.62	98.44	98.40	98.33
	renewable energy penetration rate (%)	99.3	98.8	98.3	98.2	98.1	98.4	98.2	98.2	98.2
	excess electricity fraction (%)	37.0	23.6	18.6	16.9	16.4	18.2	17.4	18.1	19.0
	system electrical efficiency (%)	57.73	70.97	76.04	77.64	77.98	76.02	76.51	75.55	74.34
Economy	IRR (%)	6.6	7.5	8.1	8.5	9.8	9.2	9.1	9.3	9.8
	AROI (%)	4.88	5.08	5.30	5.56	5.40	5.39	5.48	5.53	5.66
	COE (CNY/kWh)	0.455	0.377	0.353	0.338	0.327	0.317	0.311	0.306	0.304
	NPC (million CNY)	503	416	388	371	359	349	342	336	333
Environment	carbon emission intensity (kg/kWh)	0.26	0.54	0.82	0.90	0.92	0.76	0.85	0.84	0.86
	decarbonization benefits (%)	99.62	99.21	98.79	98.68	98.66	98.89	98.75	98.78	98.75
	POCP (10−3 kg C2H4/MWh)	1.20	2.50	3.82	4.19	4.27	3.52	3.96	3.89	3.98
	AP (10−3 kg SO2/MWh)	0.017	0.0356	0.0543	0.0594	0.061	0.050	0.056	0.055	0.056

. The profit interest rate, unit fuel cost, and environmental emission coefficients are set to be consistent across all scenarios.

3.2. Homer Simulation Result

Among all configurations, Case 1 demonstrates the highest power supply reliability at 99.07%, while Case 9 exhibits the lowest (98.33%). Off-grid systems need to balance renewable energy output with load, including hydrogen production, so a system reliability higher than 98% is considered acceptable.

All configurations achieve renewable energy penetration rates exceeding 98%. However, excessive renewable integration does not inherently enhance load supply capability. Conversely, it may induce surplus power curtailment and compromise system-wide electrical efficiency. The load supply profile of Case 1 is illustrated in Figure 4. As indicated in Table 3, Case 1 features the largest PV installed capacity (53.1 MW), with wind power (5.9 MW) constituting 10% of the total capacity. This yields an exceptional renewable energy penetration rate of 99.3%, though its overall energy utilization efficiency remains suboptimal at 57.73%.

Excess electricity fraction refers to generated power that neither serves load demand nor qualifies for storage within each discrete time step. Regarding excess electricity metrics, Case 5 generates only 16.4% surplus power, whereas Case 1 suffers a substantial curtailment rate of 37%. While increasing wind power proportion initially reduces the excess electricity fraction, surpassing 50% wind penetration triggers volatility dominance in wind-driven systems. This regime shift induces renewed growth in excess electricity.

System electrical efficiency is defined as the ratio of load-serving electricity to the total generation output, serving as a critical metric for energy utilization effectiveness. Figure 5 reveals that Case 5 achieves superior system-wide energy utilization efficiency (77.98%) through temporal complementarity between its hydrogen production module and electrical load supply module. This peak-shaving strategy optimizes energy scheduling, contrasting sharply with Case 1’s efficiency of 57.73%.

The IRR and AROI quantify system economic vitality through long-term viability and short-term operational efficiency perspectives, respectively. The COE measures the electricity production cost per unit, whereas the NPC represents the discounted aggregate lifecycle expenditures. Case 9 demonstrates the optimal performance across all four economic metrics. Notably, it shares the top rank with Case 5 in IRR (9.8%), indicating a robust profitability potential, while its 5.66% annualized return on investment further validates its economic competitiveness. Although Case 9 features a 90% wind power capacity ratio, its total generation-side installed capacity remains substantially lower than Case 1. As shown in Figure 6, photovoltaic costs constitute over 60% of Case 1’s total system expenditures, primarily driving its highest overall costs. Both COE (Cost of Energy) and NPC exhibit declining trends with increasing wind power penetration rates.

Carbon emission intensity is defined as the CO₂ equivalents emitted per kWh generated. Decarbonization benefits are computed by comparing operational emissions with a baseline scenario where grid electricity fully meets demand. This metric evaluates decarbonization effectiveness against conventional power supply paradigms. POCP and AP constitute dual-axis environmental impact metrics. POCP quantifies ozone-forming precursors (CO, UHC), while AP evaluates acid deposition contributors (SO₂, NO_x), both normalized per MWh electricity output. Case 1 outperforms all others across four environmental metrics, while Case 5 lags behind environmentally. Case 1 achieves the lowest carbon intensity (0.26 kg/kWh), contrasting sharply with Case 5’s highest emission level of 0.92 kg/kWh. Regarding carbon reduction efficiency, Case 1 demonstrates superior performance at 99.62%, whereas Case 5 registers the minimum value of 98.66%. All environmental metrics exhibit an initial increase followed by a gradual decline with rising wind power penetration rates.

3.3. Indicators’ Weight Results

First, the judgments of five experts in the field are collected as subjective criteria, while the objective criteria are derived from the indicator values calculated using the formulas, as shown in Table 4. Next, the subjective and objective weights of the indicators are calculated using the GREY-DEMATEL and CRITIC methods, respectively. Following the process outlined in Figure 3, the comprehensive weights of the indicators are computed, with the weight calculation results presented in

Table 5. Index weight calculation results.

Perspective	c11	c12	c13	c14	c21	c22	c23	c24	c31	c32	c33	c34
Objective	0.027	0.041	0.107	0.089	0.130	0.053	0.128	0.122	0.077	0.050	0.070	0.106
Subjective	0.082	0.099	0.062	0.090	0.125	0.039	0.101	0.080	0.153	0.050	0.030	0.062
Comprehensive	0.0532	0.0715	0.093	0.09	0.136	0.041	0.112	0.099	0.108	0.05	0.052	0.0923

.

3.4. GRA-VIKOR Ranking Results

With the Case coefficient ρ = 0.5, the correlation degree between each Case and the ideal Case is calculated and classified to determine the VIKOR weight p. The benefit ratios Q for all Cases are then computed and ranked, as shown in

Table 6. Calculation results of GRA-VIKOR.

CASE	χi	Classification	p	Q	Ranking
CASE1	0.6249	Type 1	0.4	0.2788	2
CASE2	0.5252	Type 3	0.6	0.3406	5
CASE3	0.5386	Type 3	0.6	0.3661	8
CASE4	0.6085	Type 2	0.5	0.3171	4
CASE5	0.6408	Type 1	0.4	0.2666	1
CASE6	0.5342	Type 3	0.6	0.3762	9
CASE7	0.5682	Type 2	0.5	0.3413	6
CASE8	0.5665	Type 2	0.5	0.3442	7
CASE9	0.6092	Type 1	0.4	0.2915	3

.

4. Discussion

4.1. Validation of Model

The combined weighting model’s calculation results for the indicator weights are illustrated in Figure 7. This model demonstrates robustness against extreme values during weight processing, and as a hybrid weighting method that integrates both subjective and objective perspectives, it proves particularly suitable for decision-making scenarios with significant opinion conflicts. Compared with alternative weighting approaches, the Huber loss function offers enhanced flexibility in handling weight deviations while maintaining true impartiality in balancing subjective and objective opinions. The model exhibits distinct advantages over linear weighting methods and equal weighting approaches, as these conventional methods inherently manifest subjective tendencies when dealing with objective–subjective weight relationships. Specifically, they either assign equal importance to subjective and objective opinions (equal weighting) or impose linear proportionality between them (linear weighting)—both of which essentially constitute subjective judgments in themselves.

To validate the harmonizing effect of the Huber loss function on indicator weights, two general-purpose MCDM studies are selected for a comparison with the results of this study [23,32], as illustrated in Figure 8. Conventional MCDM models exhibit pronounced deviations between composite and objective weights, with evident subjective–objective weight imbalances dominated by decision-maker preference. In contrast, the MCDM models yield substantially reduced weight allocation errors (0.016–0.019).

To validate the robustness of GRA-VIKOR model calculation results, this section conducts a consistency verification of scenario rankings under perturbation conditions. The ranking outcomes are analyzed using the following three similarity coefficients for quantitative evaluation: the Pearson correlation coefficient, Spearman’s rank correlation coefficient, and Kendall’s Tau coefficient. The computational formulas are specified below:

$$r_{\mathrm{p}}={\displaystyle \frac{{\displaystyle \sum (x_i-\stackrel{-}{x})(y_i-\stackrel{-}{y})}}{\sqrt{{\displaystyle \sum {(x_i-\stackrel{-}{x})}^2{(y_i-\stackrel{-}{y})}^2}}}}$$

(22)

$$r_{\mathrm{s}}=1-{\displaystyle \frac{6{\displaystyle \sum {d_i}^2}}{n(n^2-1)}}$$

(23)

$$\tau ={\displaystyle \frac{2(S-n(n-1)/4)}{n(n-1)/2}}$$

(24)

where x_i/y_i denote the specific values of the first/second sequence; $\overline{x}$/$\overline{y}$ represent the mean values of the first/second sequence; d_i indicates the ranking discrepancy between two ordered sets; n represents the sample size; and S represents the difference between concordant and discordant pairs in the sequence comparisons.

In the construction of the GRA-VIKOR methodology, the distinguishing coefficient ρ of the GRA algorithm is set to 0.5, indicating equivalent weighting of differentiation and association across all alternatives. The parameter ρ operates within the interval [0, 1], where larger values increasingly emphasize inter-alternative disparities. This investigation systematically evaluates ρ across 10 equidistant values (0.1–1.0), computing corresponding alternative rankings and their correlation coefficients, as detailed in

Table 7. Ranking consistency of GRA-VIKOR across distinguishing coefficient values.

ρ	Ranking Results	rp	rs	τ
0.1	5 > 1 > 9 > 4 > 2 > 7 > 8 > 3 > 6	1.00	1.00	1.000
0.2	5 > 1 > 9 > 4 > 2 > 7 > 8 > 3 > 6	1.00	1.00	1.000
0.3	5 > 1 > 9 > 4 > 2 > 7 > 8 > 3 > 6	1.00	1.00	1.000
0.4	5 > 1 > 9 > 4 > 2 > 7 > 8 > 3 > 6	1.00	1.00	1.000
0.5	5 > 1 > 9 > 4 > 2 > 7 > 8 > 3 > 6	1.00	1.00	1.000
0.6	5 > 1 > 9 > 4 > 2 > 7 > 8 > 3 > 6	1.00	1.00	1.000
0.7	5 > 1 > 9 > 4 > 2 > 7 > 8 > 3 > 6	0.95	0.95	0.944
0.8	5 > 4 > 1 > 9 > 2 > 7 > 8 > 3 > 6	0.95	0.95	0.944
0.9	5 > 4 > 1 > 9 > 2 > 7 > 8 > 3 > 6	0.95	0.95	0.944
1	5 > 4 > 1 > 9 > 2 > 7 > 8 > 3 > 6	0.95	0.95	0.944

. All three correlation metrics consistently exceed 0.9 under experimental conditions, demonstrating a strong agreement between computational outcomes across parametric variations. These results conclusively validate the model’s robust insensitivity to fluctuations in the distinguishing coefficient ρ.

In comparison with conventional decision-making methodologies such as TOPSIS and VIKOR, the GRA-VIKOR approach demonstrates fundamental superiority through its transcendence of the static positive/negative ideal solution paradigm. By systematically incorporating decision-makers’ preference dynamics across alternative evaluations, it establishes a refined decision architecture with adaptive granularity. As evidenced in Table 7, the model exhibits exceptional stability under parametric variations in distinguishing the coefficients ρ. This methodological advancement not only proves effective for energy system optimization in the Inner Mongolia region but ultimately constitutes a generalizable framework for complex decision scenarios involving competing priorities in energy infrastructure planning.

4.2. Case Disparity Analysis

According to Table 6, in terms of comprehensive benefits, Case 5 performs the best, while Case 6 performs the worst. Although the wind power proportions of the two Cases are very close, they exhibit significant differences under this decision-making framework. Therefore, this study further conducts a comprehensive comparative analysis of all indicators for Case 5 and 6 to explain the ranking differences, and calculates the differences in the contributions of each indicator for the two Cases using the following formula:

$$\Delta =\left(I_5-I_6\right)\times {\eta }_I$$

(25)

In the formula, I₅ and I₆ represent the normalized values of Case 5 and Case 6 for the I-th indicator, respectively, and η_I denotes the weight of the I-th indicator. For benefit indicators, a positive value indicates that Case 5 outperforms Case 6; for cost indicators, a positive value indicates that Case 6 outperforms Case 5. The comprehensive comparison of all indicators for the two Cases is presented in

Table 8. Comparison of indicators of Case 5 and Case 6.

Indicator	Type	Weight	Winner	Contribution
power supply reliability	Benefit	0.0532	Case 6	−0.0107
renewable energy penetration rate	Benefit	0.0715	Case 6	−0.0238
excess electricity fraction	Cost	0.093	Case 5	0.0090
system-wide electrical efficiency	Benefit	0.09	Case 5	0.0089
IRR	Benefit	0.136	Case 5	0.0236
AROI	Benefit	0.041	Case 5	0.0002
COE	Cost	0.112	Case 6	−0.0083
NPC	Cost	0.099	Case 6	−0.0064
carbon emission intensity	Cost	0.108	Case 6	−0.0121
decarbonization benefits	Benefit	0.05	Case 6	−0.0056
POCP	Cost	0.052	Case 6	−0.0174
AP	Cost	0.0923	Case 6	−0.0180

.

Under the assumption of equal weighting across all indicators, the aggregate contribution differential between the two alternatives totals −0.044, indicating the superior performance of Case 6. However, in practical decision-making contexts, Case 5 demonstrates marked advantages in four high-priority metrics: system-wide electrical efficiency, IRR, COE, and excess electricity fraction. Notably, it achieves a substantial positive contribution differential of 0.0236 in the IRR metric, thereby magnifying its group effect S-value. Furthermore, comparative analysis reveals that Case 5’s weakest metric AP exhibits a relative performance deficit of R_AP = 0.126, whereas Case 6 manifests a more significant deficiency in its critical metric (R_IRR = 0.246).

The analysis demonstrates that the GRA-VIKOR framework emphasizes both the “benefit” and “loss” trade-offs among indicators, prioritizing performance on high-weight metrics while rigorously evaluating deficiencies in weak-point indicators. Key system metrics—including excess electricity fraction, system-wide electrical efficiency, IRR, COE, NPC, carbon emission intensity, and AP—critically influence rankings. Significant advantages in these metrics substantially enhance system competitiveness. Concurrently, if a case’s weak-point indicator demonstrates marked inferiority compared to its counterparts in that metric, the system categorizes it as having a “significant deficiency”, leading to lower rankings. Therefore, Case 5 is identified as being optimal due to achieving significant leads in four critical metrics while maintaining a minimal gap in its disadvantaged AP indicator. In contrast, Case 6, despite demonstrating advantages in more metrics, exhibits neither substantial superiority in its strong indicators nor acceptable performance in its critical weak-point indicator, consequently being ranked last due to the absence of decisive strengths coupled with evident deficiencies.

4.3. Analysis of Simulation Results

Among the nine Cases, the configurations with 10%, 50%, and 90% wind power proportions exemplify three distinct structural paradigms: (1) solar-dominant/low-wind, (2) wind–solar balanced, and (3) wind-dominant/low-solar. These configurations occupy the top three positions in comprehensive benefit rankings, demonstrating Q values of 0.2788 (10%), 0.2666 (50%), and 0.2915 (90%), respectively. The differences among them are analyzed as follows:

Case 1 (10% wind power proportion): Except for power supply reliability, it achieves the best performance in renewable energy penetration and all four environmental indicators. This demonstrates Case 1’s environmental advantages, where the 53.1 MW photovoltaic capacity constitutes the majority of the system’s power output, significantly reducing diesel generator usage. This results in both a high renewable energy penetration rate and superior environmental benefits. However, the exclusive deployment of large-scale renewable energy also introduces the challenges of resource wastage and increased system costs; it performs the worst in all other indicators. Case 1 simultaneously exhibits the highest surplus electricity and lowest energy utilization efficiency. This is primarily attributable to the photovoltaic panels’ near-zero power output during nighttime hours, while the load profile (Figure A1a) maintains substantial nighttime demand. Consequently, the system must rely exclusively on energy storage facilities to meet nighttime loads, incurring additional costs. Furthermore, the energy conversion processes involved inevitably result in efficiency losses. Overall, Case 1 exhibits a typical “eco-prioritized but economically constrained” profile, ultimately ranking second.

Case 5 (50% wind power proportion): This Case performs best in excess electricity, electrical efficiency, and IRR indicators, while maintaining moderate standings elsewhere. The ranking results of Case 5 demonstrate GRA-VIKOR’s capability in balancing “benefits versus losses” across the system. Its dominance in high-weight critical indicators (IRR, excess electricity) drives its premier ranking position. Case 5 can supply loads during both daytime and nighttime, which reduces the system’s reliance on energy storage facilities. Compared to Case 1, Case 5 has a significantly smaller installed capacity and generates the least surplus electricity. However, it is noteworthy that surplus electricity does not exhibit a monotonic trend relative to either system scale reduction or increased wind power penetration. Despite having the smallest scale and highest wind power ratio, Case 9 unexpectedly shows elevated surplus electricity levels. Another characteristic of Case 5 is that its performance on disadvantageous metrics does not significantly lag behind other Cases, and these metrics have lower weights. Specifically, the four environmental indicators have a combined weight of only 0.262, which minimizes the impact of these disadvantages on its final ranking.

Case 9 (90% wind power proportion): An interesting observation is that Case 9 exhibits opposite performance characteristics compared to Case 1; in contrast to Case 1, it achieves the best performance in all four economic indicators but lacks advantages in the remaining eight indicators, representing an “economically optimized but sustainability-compromised” configuration, ultimately ranked third. The 90% wind power proportion ensures 24 h effective supply, with the system’s surplus electricity fraction and electrical efficiency outperforming Case 1. Case 9 meets load demands with the smallest installed capacity, significantly reducing system costs, achieving a 33% lower NPC compared to Case 1. However, wind power variability introduces negative effects: Case 1 gains cost advantages at the expense of power supply reliability, where diesel generators’ compensatory role proves both limited and environmentally detrimental.

Figure 9 illustrates the variation trends of several key indicators with respect to wind proportion, with the 50% mark identified as a critical inflection point. This observation further validates the robustness of the GRA-VIKOR computational results while highlighting the inherent complexity of energy system performance, underscoring the necessity for more comprehensive decision-making methodologies.

5. Conclusions

This research progresses through three sequential phases. Firstly, it conducts system optimization design for the Inner Mongolia hybrid electricity–hydrogen synergy system using HOMER, with comprehensive three-dimensional benefit quantification. Secondly, it develops a novel method integrating CRITIC and GREY-DEMATEL to balance subjective and objective decision-making preferences in indicator weighting. Finally, it constructs a hybrid GRA-VIKOR ranking model to perform three-dimensional benefit evaluation on systems with different power generation structures, thereby identifying critical threshold points in system design.

The results indicate that IRR, COE, NPC, and the system carbon emission indicator exert the most substantial influence on comprehensive system benefits, with respective contribution weights of 13.6%, 11.2%, 9.9%, and 10.8%. The Huber loss function establishes an innovative methodological framework for multi-criteria decision analysis. In conflict scenarios, the adaptive mechanism uses gradient descent with composite penalty. It limits weight deviations to 0.016–0.019. This shows better error control than linear weighting methods

The GRA-VIKOR methodology incorporates differential decision-making preferences across alternatives, exhibiting robust performance in complex decision-making environments. Under varying distinguishing coefficients ρ, the minimum Kendall’s Tau coefficient is 0.944, demonstrating exceptional result stability throughout parametric sensitivity analyses. The hybrid energy system with a 50% wind power proportion in Inner Mongolia is identified as the most promising, ranking first with Q = 0.2788. The system achieves an excess electricity fraction of 16.4%, a peak system electrical efficiency of 77.98%, and an IRR of 9.8%. Additionally, the comparison of Cases 1, 5, and 9 reveals the complexity of comprehensive decision-making in energy systems. Superior performance in either economic, environmental, or technical dimensions can render Cases extremely competitive. Case 1 achieves a 99.07% power supply reliability, a 99.3% renewable energy penetration rate, and the lowest emission levels. However, this configuration demonstrates the poorest economic performance, with maximal resource wastage. Conversely, Case 9 attains optimal economic competitiveness by outperforming in all four economic metrics, though this is achieved through substantial compromises in technical performance and environmental sustainability. Ultimately, Case 5 achieves a slight lead (4.6% over Case 1 and 9.3% over Case 9) through dominant advantages in critical high-weight indicators.

The comprehensive evaluation of diverse power generation configurations in Inner Mongolia ultimately reveals that a 50% wind power penetration rate constitutes the critical threshold for systemic benefit transitions. At this juncture, multiple indicators—including excess electricity fraction, system electrical efficiency, and POCP—reach inflection points, beyond which their evolutionary trajectories exhibit marked transitions.

However, this study does not delve into the technical implementation of the system, and the impacts of market environments and policies on the model remain to be explored. Future research could expand in the following directions: (1) Investigating the influence of market environments and policies on the comprehensive benefits of systems in different regions. (2) While this study does not address the quantitative relationships among the three perspectives, future work could employ relevant tools to quantitatively analyze the mutual influences of indicators. (3) While this investigation primarily focuses on the Inner Mongolia context, future research should validate the method’s general applicability across regions with diverse energy profiles.