Research on a Low-Carbon Economic Dispatch Model and Control Strategy for Multi-Zone Hydrogen Hybrid Integrated Energy Systems

Abstract

The electricity–hydrogen–electricity conversion chain offers an effective solution for integrating clean energy into the grid while addressing multiple grid control requirements. Moreover, multiregional, interconnected, and integrated energy systems (IESs) can significantly increase overall energy utilization efficiency and operational flexibility through spatiotemporal coordination among diverse energy sources. However, few researchers have considered these two aspects in a unified framework. To address this gap, a low-carbon economic dispatch model and control strategy for a multiregional hydrogen-blended IES are proposed in this work. The model is constructed based on a system architecture that incorporates electricity–hydrogen–electricity conversion links while accounting for source–load uncertainties and peak shaving requirements. We solve the resulting distributed nonconvex nonlinear optimization problem using the alternating direction method of multipliers (ADMM). Furthermore, we analyze how uncertainty factors and peak shaving needs affect the maximum allowable hydrogen blending ratio in the gas grid, as well as the corresponding dynamic blending strategy. Our findings demonstrate that the proposed multiregional hydrogen-blended integrated energy system, with dynamic hydrogen blending control, significantly enhances the capacity for clean energy integration and reduces carbon emissions by approximately 12.3%. The peak-shaving demand is addressed through a coordinated mechanism involving electrolyzers (ELs), gas turbines (GTs), and hydrogen fuel cells (HFCs). This coordinated mechanism enables hydrogen fuel cells to double their output during peak hours, while electrolyzers increase their power consumption by approximately 730 MW during off-peak hours. The proposed dispatch model employs conditional risk measures to quantify the impacts of uncertainty and uses economic coefficients to balance various cost components. This approach enables effective coordination among economic objectives, risk management, and system performance (including peak shaving capability), thereby improving the practical applicability of the model.

1. Introduction

As the global energy transition accelerates, the increasing application of renewable energy has introduced increased randomness and volatility into power systems. The anti-peak regulation characteristics of wind and photovoltaic generation further intensify the peak shaving pressure on the grid. In the context of low-carbon transformation, conventional thermal power generation faces limitations, including slow response times and constrained operational flexibility. In contrast, ELs, HFCs, and hydrogen-mixed GTs offer rapid response capabilities, making them promising solutions for grid peak shaving. Therefore, the design of an electric–hydrogen–electric technological chain incorporating electrolyzers, hydrogen fuel cells, and hydrogen-blended gas turbines is regarded as a vital pathway towards large-scale deep decarbonization. By enhancing power system flexibility and mitigating peak–valley load differences, this approach has become a significant focus of current research.

In the domain of comprehensive hydrogen energy utilization, References [1,2,3] incorporate hydrogen-based technologies into integrated energy systems, establishing a low-carbon economic dispatch model for hydrogen-blended integrated energy systems. Hydrogen energy transportation remains a significant challenge that needs to be addressed. For short-distance hydrogen delivery, Reference [4] proposes that hydrogen long-tube trailers enable cross-regional hydrogen interaction within a park-level electric-hydrogen integrated energy system. Nevertheless, this approach is currently only viable for short-distance transportation scenarios. This approach achieves a high degree of wind power integration, facilitating low-carbon operation of the system. Reference [5] developed a photovoltaic cell-electrolyzer coupling system for off-grid hydrogen production. Hydrogen is injected into the natural gas pipeline network to enable long-distance transportation. This system fully leverages the abundant solar energy resources in specific regions, offering significant advantages in energy utilization. However, the study only evaluated four operating conditions with fixed hydrogen blending ratios (5%, 10%, 15%, and 20%) in the pipeline. It did not include a quantitative analysis of the energy balance mechanism under extreme conditions. As a result, the system struggles to maintain the preset hydrogen blending ratio stability during periods of scarce solar energy. Reference [6] utilized a hydrogen-blended integrated energy system to assess the economics of gas network hydrogen injection. The hydrogen blending ratio varied from 0 to 20% in 5% increments. This work validated the effectiveness of hydrogen injection in gas networks under grid-connected conditions. Reference [7] developed a source-load complementary carbon reduction mechanism integrating carbon capture systems and demand response programs, with subsequent implementation of hydrogen injection into the natural gas grid. A reinforcement learning algorithm was employed to train the proposed model, which yielded improved hydrogen energy utilization efficiency. While these studies validate the technical feasibility of hydrogen grid injection, two key limitations persist: (1) the fixed hydrogen blending ratio adopted in the gas grid and (2) the need for enhanced economic performance. Notably, maintaining hydrogen energy balance during periods of low renewable energy generation remains a significant challenge. To address these limitations, Reference [8] proposes a dynamic hydrogen blending strategy in which the blending ratio varies temporally. This method enables flexible allocation of hydrogen resources, thereby improving both the hydrogen utilization efficiency and overall system economics. Reference [9] proposes a novel optimization scheduling method for hydrogen hybrid integrated energy systems (HHIESs). It accounts for the impacts of hydrogen-enriched compressed natural gas (HCNG) with varying hydrogen blending ratios on system performance. A comprehensive model of the full HCNG process is developed, encompassing hydrogen production, injection, transportation, and separation. Nevertheless, most researchers have focused on single integrated energy systems, where the overall hydrogen utilization rate remains relatively limited. Multiregion interconnection and coordination can further optimize the spatiotemporal distribution of energy resources and enhance the overall utilization efficiency. Therefore, there is a clear need to develop low-carbon economic dispatch strategies for multiregional integrated energy systems with interconnected gas networks and hydrogen blending capabilities.

Notably, the volatility and randomness of wind power output introduce significant uncertainties into the green hydrogen supply produced by wind-powered water electrolysis, thereby affecting hydrogen allocation schemes. Therefore, reasonably quantifying the impacts of such uncertainties is essential for optimizing the system scheduling model. Reference [10] applies stochastic programming to power dispatch. It proposes a stochastic economic dispatch framework to effectively mitigate the impacts of wind power randomness on power systems. Reference [11] employs a data-driven polynomial chaos expansion method to quantify the uncertainty in wind power. Reference [12] develops a multi-period economic dispatch model with renewable energy security constraints using distributed robust optimization. This approach adapts to renewable energy uncertainty and avoids overly conservative solutions compared to traditional robust optimization. Reference [13] validates the applicability of stochastic dual dynamic programming for addressing uncertainty in renewable energy sources within power systems. Reference [14] presents a feasible method for solving complex power system optimization problems involving the integration of uncertain renewable energy sources. It uses an asynchronous block iteration method to solve the multi-objective stochastic economic dispatch (MOSED) problem with variable wind power grid connection. Reference [15] establishes a multi-stage stochastic programming model for joint energy and reserve dispatch. Scenario trees are used to handle uncertainty in renewable energy generation. While these studies simulate renewable energy generation uncertainty, they overlook load-side volatility. To overcome this limitation, Reference [16] accounts for both source and load uncertainty, investigating the stochastic optimal operation of integrated energy systems. A scenario-based method is used to quantify and analyze source-load uncertainty. Reference [17] proposes a two-layer optimization model based on model predictive control. This model addresses uncertainty resulting from high proportions of renewable energy and controllable loads. The upper layer performs long-term rolling prediction of source and load, passing the results to the lower layer to mitigate the impacts of uncertainty. Reference [18] develops a multi-timescale rolling optimization model for hybrid energy storage integrated energy systems using a prediction model and a two-stage method. It effectively handles multiple uncertainties (renewable energy, load, and price). Reference [19] presents a low-carbon economic energy dispatch strategy for integrated energy systems based on model-free deep reinforcement learning. It considers both source and load uncertainty while avoiding high dependence on prediction models. Nevertheless, these works are focused primarily on qualitative assessments of source–load uncertainty and lack quantitative evaluation, leaving room for improvement in both system economics and scheduling reliability.

Effectively quantifying and controlling scheduling risk remain a critical challenge. The conditional value at risk (CVaR) method, which captures tail risks, is well-suited for optimizing power system operations. Reference [20] introduces CVaR theory to quantify wind power uncertainty risks in the economic dispatch of traditional integrated energy systems. It retrofits conventional units into carbon capture units, effectively reducing system operational risks while ensuring optimal economic performance. Reference [21] proposes a power system optimal dispatch model accounting for source-load uncertainty and CVaR. A stochastic optimization approach is employed to address uncertainties associated with wind, solar, and load. CVaR regulates the impact of uncertainty on dispatch decision-makers, thereby lowering uncertainty-related risk costs. Reference [22] leverages the complementary characteristics of solar thermal power plants and wind farms to enable high proportions of renewable energy consumption. It establishes a power system economic dispatch model integrating solar thermal, wind power, and CVaR. Reference [23] uses CVaR to quantify uncertainty risks. It also develops a carbon trading mechanism, integrates the carbon market, and establishes a low-carbon economic dispatch model. Reference [24] proposes a two-stage dispatch method for virtual power plants in the power market environment. The method considers tiered carbon trading and CVaR, with VPPs participating in both the carbon and electricity markets. Building on this foundation, Reference [25] presents a stochastic framework for the optimal scheduling of resilient microgrids with disaster recovery capabilities. CVaR addresses risks stemming from islanding duration, wind turbine output, electricity prices, and load uncertainties. Reference [26] constructs a low-carbon robust optimization model for microgrids. The model accounts for extreme scenario risk values and net load conditions. However, these studies address only source–load uncertainty risks in traditional integrated energy systems and do not analyze such risks in systems with hydrogen blending in gas grids. As a result, operational risks in gas grids remain unclear, and the reliability of hydrogen blending strategies requires further improvement.

Table 1. Comparison of the Recent Research.

Paper	IES	HHIES	Fixed Hydrogen Doping	Dynamic Hydrogen Doping	Multiregional Interaction	Source Uncertainty	Source Load Uncertainty	Risk Quantification
[1,2,3]	×	√	×	×	×	×	×	×
[4]	×	√	×	×	√	×	×	×
[5,6,7]	×	√	√	×	×	×	×	×
[8,9]	×	√	×	√	×	×	×	×
[10,11,12,13,14,15]	√	×	×	×	×	√	×	×
[16,17,18,19]	√	×	×	×	×	√	√	×
[20,21,22,23,24,25,26]	√	×	×	×	×	√	√	√

presents comparative results of low-carbon economic dispatch models for IESs. Currently, existing research on multiregional HHIESs has three key limitations:

• Existing solutions primarily rely on hydrogen long-tube trailers for short-distance hydrogen delivery. They ignore the practical demands of long-distance, large-scale hydrogen transportation.
• Current technical approaches mainly promote hydrogen consumption by expanding diversified utilization scenarios. Yet the overall potential of hydrogen energy remains underexplored. Its peak-shaving capability is particularly untapped.
• Most studies only conduct qualitative analyses of source-load uncertainty risks in multi-regional HHIESs. They lack supporting quantitative assessment methods. This gap directly leads to ambiguous operational risks in the pipeline. It also results in insufficient reliability of hydrogen blending strategies.

Against this backdrop, this work fully integrates the operational characteristics of electricity-hydrogen-electricity conversion chains. It directly addresses core challenges: system peak shaving and long-distance hydrogen transportation. It optimizes natural gas pipeline hydrogen blending strategies. A low-carbon economic dispatch model for multiregional HHIESs is proposed. Its core research contributions are summarized as follows:

• For multiregional HHIESs, a dynamic hydrogen blending model for natural gas pipelines is established. It considers pipeline operation and maintenance costs. Regional interconnections enable cross-regional hydrogen interaction. This resolves the technical challenges of long-distance, large-scale hydrogen transportation. The limitations of fixed hydrogen blending modes are overcome. System energy balance is ensured.
• An electricity-hydrogen-electricity coordinated control mechanism is designed. A collaborative peak-shaving model is constructed. It integrates ELs, HFCs, and hydrogen-blended GTs. This model taps into hydrogen’s peak-shaving potential. It significantly enhances system peak-shaving flexibility and response speed. A peak-shaving economic coefficient is introduced. It characterizes the proportion of peak-shaving costs in total operating costs. The optimal hydrogen blending upper limit is updated. Corresponding dynamic schemes are adjusted under different coefficients.
• Based on CVaR theory, source-load uncertainty risks in multiregional HHIESs are quantified. A risk coefficient is introduced to represent the share of risk costs in operating costs, providing a quantitative basis for decision-makers to formulate dispatch strategies. A low-carbon economic dispatch model is constructed, considering both risk assessment and peak-shaving requirements. By adjusting the risk coefficient and peak-shaving economic coefficient, the optimal upper limit for hydrogen blending is determined, and a dynamic strategy is developed that comprehensively balances risk, peak shaving, and financial objectives. The proposed method clarifies natural gas pipeline operational risks, further exploits hydrogen’s peak-shaving performance, improves the reliability of hydrogen blending strategies, and achieves dynamic optimization of hydrogen blending ratios through risk quantification and cross-regional collaboration.

This work is organized as follows. Section 1 presents the architecture of the multiregional hydrogen-blended integrated energy system. Section 2 introduces the conditional value-at-risk methodology and ancillary services. Section 3 presents a low-carbon economic dispatch model that incorporates conditional value-at-risk and peak shaving demands. Section 4 describes the solution methodology. Section 5 presents the case study results, and Section 6 provides concluding remarks.

2. General Framework

This study examines a multiregional hydrogen-blended integrated energy system that involves injecting hydrogen into the natural gas grid. The overall structure is shown in Figure 1. Herein, the dispatch center of each region solves the mixed-integer second-order cone programming (MISOCP) problem. Core components within the framework include ELs, methane reactor (MR), hydrogen energy storage (HES), HFC, and GT. In each region, when excess wind power is available, electrolyzers use this surplus electricity to produce green hydrogen, supporting various hydrogen usage options.

• Hydrogen can react with carbon dioxide captured by carbon capture units in methanation reactors to produce synthetic methane, which is then injected into natural gas pipelines to support gas grid dispatch.
• Hydrogen can be directly mixed into natural gas pipelines to supply gaseous loads.
• Hydrogen can be converted into electricity using hydrogen fuel cells to power electrical loads, helping with peak shaving and valley filling.
• Surplus hydrogen can be stored in hydrogen storage tanks to increase wind power utilization.

Interregional interconnection lines facilitate the exchange of information and energy among multiple hydrogen-enriched integrated energy systems. When one region experiences significant wind power curtailment because of excess generation, the surplus electricity can be transmitted through these interconnections to regions with wind power shortages. This transferred power can either directly supply electrical loads or be used for hydrogen production via electrolyzers. Such a multipath hydrogen utilization system improves overall hydrogen efficiency and facilitates low-carbon operation. Moreover, multiregional interconnection further increases the wind power absorption rate, thereby optimizing regional dispatch strategies, hydrogen allocation plans, and gas network hydrogen doping strategies.

3. Low-Carbon Economic Dispatch Model for HHIESs

3.1. Conditional Value-at-Risk Model

The volatility of wind power output and the randomness of loads introduce uncertainty risks into traditional economic dispatch. Consequently, the corresponding dispatch plans carry certain risks and struggle to meet user energy needs. When the actual wind power output exceeds forecasts or the actual user load falls below projections, some wind power is wasted, resulting in curtailed power losses for the system. Conversely, when the actual wind power output falls below forecasts, or the actual user load rises above forecasts, some user energy demands go unmet, resulting in curtailed load losses for the system.

Additionally, the amount of green hydrogen produced by the electrolyzer is closely tied to the amount of wind curtailment in the system. Source–load uncertainty affects the formulation of the optimal hydrogen blending strategy of the system. To measure the risk loss incurred by source–load uncertainty in the system, conditional risk value theory is employed in this work to quantify it and enhance the reliability of the dynamic hydrogen blending strategy and scheduling plan.

CVaR measures the expected value of losses exceeding the value at risk (VaR) at a given VaR level, representing the average loss in the worst-case scenario. Unlike the VaR, the CVaR measures tail risk, providing decision-makers with a more comprehensive risk metric. It is assumed that f(x,h) is the loss function, x is the decision variable, and h is the random variable. Thus, ρ(x,h) is the probability density function of h, which is calculated as follows:

$$\left\{\begin{array}{l}\varphi (x,h)={\displaystyle \int \rho (h)}dh\\ Va{R}_{\theta }=\min \left\{h\in R:\varphi (x,h)\ge \theta \right\}\\ CVa{R}_{\theta }={\displaystyle \frac{1}{1-\theta }}{\displaystyle \underset{\varphi (x,h)\ge Va{R}_{\theta }}{\int }\varphi (x,h)}\rho (h)dh\end{array}\right.$$

(1)

where $\varphi (x,h)$ is the distribution function of the loss function not greater than the boundary value h; θ is the confidence level, the probability that the loss does not exceed the VaR value; VaR_θ is the VaR value under the given confidence level; and CVaR_θ is the CVaR value under the given confidence level.

It is not easy to directly calculate the CVaR value from the above formula, but the calculation can be simplified by using the transformation function:

$$\left\{\begin{array}{l}{F}_{\theta }(x,g)=g+{\displaystyle \frac{1}{1-\theta }}{{\displaystyle \underset{h\in R}{\int }\left[f(x,h)-g\right]}}^{+}\rho (x,h)dh\\ F_{\theta }(x,g)=CVa{R}_{\theta }\end{array}\right.$$

(2)

where ${\left[f(x,h)-g\right]}^{+}$ represents $\max \left\{f(x,h)-g,\left.0\right\}\right.$ and g is the value of the VaR.

However, the probability density function is challenging to solve. We use the typical scene set to discretize the above equation further and solve it:

$$\left\{\begin{array}{l}{\tilde{F}}_{\theta }(x,g)=g+{\displaystyle \frac{1}{1-\theta }}{\displaystyle \sum _{s=1}^S{p}_s}{\left[f(x,h_s)-g\right]}^{+}\\ {\tilde{F}}_{\theta }(x,g)=F_{\theta }(x,g)\end{array}\right.$$

(3)

where $p_s$ is the probability of a typical scenario s occurring, and $h_s$ is the value of the random variable in the scenario.

In this work, the wind power output and load forecasts are assumed to follow a normal distribution, and the forecast deviation is the predicted value minus the actual value:

$$\Delta P_{sum,t}=\Delta P_{wind,t}-\Delta P_{PL,t}$$

(4)

where $\Delta P_{sum,t}$ is the total forecast deviation of the system at time t, $\Delta P_{wind,t}$ is the wind power forecast deviation at time t, and $\Delta P_{PL,t}$ is the load forecast deviation at time t. The risk loss cost of the system is as follows:

$$C_{loss,t}=\left\{\begin{array}{l}{\gamma }_1\Delta P_{sum,t},\Delta P_{sum,t}>0\\ -{\gamma }_2\Delta P_{sum,t},\Delta P_{sum,t}<0\end{array}\right.$$

(5)

where $C_{loss,t}$ is the risk loss cost of the system at time t, ${\gamma }_1$ is the load loss penalty coefficient, and ${\gamma }_2$ is the wind curtailment penalty coefficient.

The risk loss caused by source load uncertainty is as follows:

$$CVa{R}_{\theta }(t)=(g+{\displaystyle \frac{1}{1-\theta }}{\displaystyle \sum _{s=1}^S{p}_s}{\left[C_{loss,t}-g\right]}^{+})$$

(6)

3.2. Peak Demand Model

In this work, only peak shaving ancillary services are considered. The net load is defined as the difference between the electrical load, the power consumed by the EL, and the power generated by the hydrogen-mixed GT, the HFC, and the wind power output. Then, peak shaving is performed. The EL utilizes abandoned wind power to produce green hydrogen, converting electricity into hydrogen, thereby increasing the net load during off-peak periods and achieving a valley-filling effect. The hydrogen-infused gas turbine responds quickly, converting hydrogen-infused natural gas into electricity, effectively alleviating the pressure on conventional units during peak periods, and achieving a peak shaving effect. The hydrogen fuel cell functions similarly to the hydrogen-infused gas turbine, converting hydrogen into electricity during peak load periods, both achieving a peak shaving effect and reducing carbon dioxide emissions. The synergistic effect of the electrolyzer, hydrogen-infused gas turbine, and hydrogen fuel cell effectively smooths the net load curve of the system, reducing its peak-to-valley difference.

The net load can be expressed as follows:

$$P_{net\_load}(t)={\displaystyle \sum _{k_1=1}^{N_{\mathrm{PL}}}{P}_{\mathrm{PL},k_1}(t)}+{\displaystyle \sum _{a=1}^{N_{\mathrm{GT}}}{P^{\mathrm{GT}}}_a(t)-}{\displaystyle \sum _{k_2=1}^{N_{\mathrm{HFC}}}{P}_{\mathrm{HFC},k_2}(t)}-{\displaystyle \sum _{i=1}^{N_{\mathrm{EL}}}{P}_{\mathrm{EL},i}(t)}-{\displaystyle \sum _{d=1}^{N_{wind}}{P^{\mathrm{act}}}_d(t)}$$

(7)

where $P_{net\_load}(t)$ denotes the net load power; $P_{\mathrm{PL},k_1}(t)$ represents the electrical load power of node k₁; ${P^{\mathrm{GT}}}_a(t)$ is the output power of the a-th GT; $P_{\mathrm{HFC},k_2}(t)$ is the output power of the k₂-th HFC unit; $P_{\mathrm{EL},i}(t)$ is the power consumed by EL i; ${P^{\mathrm{act}}}_d(t)$ is the actual output of wind farm d at time t; Let $N_{\mathrm{PL}}$ denote the set of indices corresponding to electrical load nodes. $N_{\mathrm{GT}}$ represents the number of hydrogen-blended gas turbines. N_HFC is the number of HFCs, from d to $N_{\mathrm{HFC}}$. Similarly, $N_{\mathrm{EL}}$ denotes the number of ELs, from i to $N_{\mathrm{EL}}$; $N_{\mathrm{Wind}}$ is the number of wind farms, from c to $N_{\mathrm{Wind}}$.

The average net load can be expressed as follows:

$$\overline{P_{net\_load}}={\displaystyle \frac{1}{T}}{\displaystyle \sum _{t=1}^T{P}_{net\_load}(t)}$$

(8)

where $\overline{P_{net\_load}}$ is the average net load; T is the system operating cycle, T = 24 h.

3.3. Pipeline Operation and Maintenance Cost Model

Hydrogen embrittlement caused by the addition of hydrogen to natural gas pipelines significantly affects their operational safety and service life. The higher the proportion of hydrogen in the gas grid, the greater the sensitivity to hydrogen embrittlement. To ensure the long-term safe operation of the pipeline system and maintain its designed service life, regular inspections, maintenance, and effective operation and maintenance management of hydrogen-doped mixed gas transmission pipelines are necessary in actual projects. Pipeline operation and maintenance costs rise sharply with increasing hydrogen blending ratios. Therefore, this paper employs an exponential function to model the correlation between pipeline operation and maintenance costs and hydrogen blending ratios, and establishes the following model for pipeline operation and maintenance costs. The parameters h and f are determined by the calculation formulas of $C_{\mathrm{yw}}^{{\mathrm{CH}}_4}$ and $C_{\mathrm{yw}}^{{\mathrm{H}}_2}$.

Furthermore, gas transportation costs are proportional to transportation distances, whereas the gas volume supplied from gas sources to each gas load node is inversely proportional to the transportation distance. Based on this, this paper assumes that the gas supply volume from a gas source is an inverse function of the distance between the gas source and the corresponding gas load node [27]. In summary, the pipeline operation and maintenance cost function can be ultimately expressed as $C_{YW}$.

$$\left\{\begin{array}{l}{C}_{\mathrm{yw}}=f{\mathrm{e}}^{{\vartheta }_0}+h_0\\ C_{\mathrm{yw}}^{{\mathrm{CH}}_4}=f{\mathrm{e}}^0+h_0\\ C_{\mathrm{yw}}^{{\mathrm{H}}_2}=f{\mathrm{e}}^1+h_0\\ {\lambda }_{\mathrm{source},k,b}={\displaystyle \frac{f_{k,b}}{S_{k,b}}}\\ {\displaystyle \sum _{b=1}^{N_{\mathrm{GL}}}{\lambda }_{\mathrm{source},k,b}=1}\\ C_{YW}={\displaystyle \sum _{t=1}^T({\displaystyle \sum _{b=1}^{N_{\mathrm{GL}}}({\displaystyle \sum _{k=1}^{N_{\mathrm{source}}}{C}_{\mathrm{yw}}{\lambda }_{\mathrm{source},k,b}{S}_{k,b}})}}\times V_{\mathrm{source},k}(t))\end{array}\right.$$

(9)

where ${\theta }_0$ is the hydrogen blending ratio; $h_0$ and $f$ are the coefficients of the pipeline operation and maintenance cost function; C_yw is the operation and maintenance cost per unit volume of mixed gas transported per unit length; $C_{\mathrm{yw}}^{{\mathrm{CH}}_4}$ and $C_{\mathrm{yw}}^{{\mathrm{H}}_2}$ are the operation and maintenance costs per unit volume of natural gas and pure hydrogen transported per unit length, respectively; ${\lambda }_{\mathrm{source},k,b}$ is the proportional coefficient of the gas volume delivered from gas source k to gas load node b in the gas grid; $f_{k,b}$ is the coefficient of the inversely proportional function; $S_{k,b}$ is the distance between gas source k and gas load node b; $N_{source}$ is the number of gas sources, from k to $N_{source}$; and $V_{\mathrm{source},k}(t)$ is the volume of gas purchased from gas source k; $C_{YW}$ is the operation and maintenance costs of the pipeline in a single region.

4. Low-Carbon Economic Dispatch Model of a Multiregional HHIES

4.1. Objective Function

The multizone hybrid hydrogen integrated energy system proposed in this work, which considers the conditional value at risk and peak shaving demand, takes the minimum total cost as its objective function. This total cost includes operating costs, risk costs, and peak shaving costs. The operating costs are the sum of unit operating costs, startup and shutdown costs, wind turbine operating costs, carbon sequestration costs, solvent loss costs, daily carbon capture power plant depreciation costs, gas purchase costs, water feedstock costs, methane reactor (MR) externally purchased carbon dioxide feedstock costs, externally purchased hydrogen costs, pipeline hydrogen blending costs, and carbon trading costs.

$$\left\{\begin{array}{ll}\min C_{\mathrm{total}}& =\min ({\displaystyle \sum _{a=1}^{N_{area}}\left({\displaystyle \sum _{s=1}^S{p}_s}{C}_{1,a}+{\displaystyle \sum _{s=1}^S{p}_s}{C}_{2,a}+\right.}\\ & \left.{\displaystyle \sum _{s=1}^S{p}_s}{C}_{3,a}\right))\\ \min C_{1,a}& ={\displaystyle \sum _{t=1}^T\left[C_{op}(t)+{\displaystyle \sum _{d=1}^{N_{\mathrm{wind}}}{\lambda }_{\mathrm{wind}}{P^{\mathrm{forceast}}}_d(t)}\right.}+\\ & {\displaystyle \sum _{k=1}^{N_{\mathrm{source}}}{\lambda }_{\mathrm{source},k}{V}_{\mathrm{source},k}(t)}+{\lambda }_{{\mathrm{H}}_2\mathrm{O}}{m}_{H_{2}O}+\\ & {\displaystyle \sum _{j=1}^{N_{\mathrm{MR}}}{m^{\mathrm{buy}}}_{j,C{o}_2}(t)}+{\displaystyle \sum _{m=1}^{N_m}{\lambda }_{H_2}}{\displaystyle \frac{{Q^{m,\mathrm{buy}}}_{H_2}\left(t\right)}{{q^{\mathrm{h}}}_{\mathrm{HHv}}}}+\\ & C_{\mathrm{YW}}(t)+C_z+C_R+{\gamma }_{cs}({\displaystyle \sum _{w=1}^{N\mathrm{capture}}{{\phi }^{\mathrm{total}}}_w(t)}\\ & -E^{\mathrm{MR}}(t))+\left.C_{\mathrm{tra}}+C_{SU}(t)\right]\\ \min C_{2,a}& =\lambda {\displaystyle \sum _{t=1}^{T}CVa{R}_{\theta }}(t)\\ & N_{\mathrm{area}}\\ \min C_{3,a}& ={\displaystyle \sum _{t=1}^T{\epsilon }_1{(P_{net\_load}(t)-\overline{P_{net\_load}})}^2}\end{array}\right.$$

(10)

where $C_{\mathrm{total}}$ is the total cost of the multiregional HHIES; $C_{1,a}$ is the operating cost of region a; $C_{2,a}$ is the risk cost of a single region; $C_{3,a}$ is the peak shaving cost of region a; $C_{SU}$ and $C_{op}$ are the start-up and shutdown costs and operating costs of the thermal power units in region a, respectively; $C_R$ is the solvent loss cost of the carbon capture unit in region a; $C_z$ is the depreciation cost of the carbon capture power plant in region a; ${\gamma }_{cs}$ is the unit carbon sequestration cost; $C_{\mathrm{tra}}$ is the carbon trading cost in region a; ${P^{\mathrm{forceast}}}_d(t)$ is the predicted output of wind farm d at time t; ${\lambda }_{\mathrm{wind}}$ is the operation and maintenance cost of the wind farm; $N_{\mathrm{source}}$ is the number of gas sources; ${\lambda }_{\mathrm{source},k}$ is the gas price of gas source k; $V_{\mathrm{source},k}(t)$ is the gas volume purchased from gas source k; ${\lambda }_{{\mathrm{H}}_2\mathrm{O}}$ is the price of pure water; $m_{H_{2}O}$ is the total mass of pure water consumed by the EL; ${\lambda }_{H_2}$ is the hydrogen purchase price; ${\epsilon }_1$ is the economic conversion coefficient of the peak-shaving target; $N_{\mathrm{area}}$ is the number of regions.

4.2. Constraints

4.2.1. Electric Power Balance Constraints

$$\begin{array}{l}{\displaystyle \sum _{a=1}^{N_{\mathrm{ccus}}}{P^{\mathrm{J}}}_{a1}(t)}+{\displaystyle \sum _{a=1}^{N_{\mathrm{GT}}}{P^{\mathrm{GT}}}_a(t)+{\displaystyle \sum _{c=1}^{N_{\mathrm{wind}}}{P^{\mathrm{wind}}}_c(t)}}+{\displaystyle \sum _{d=1}^{N_{\mathrm{HFC}}}{P}_{\mathrm{HFC},d}(t)}+{\displaystyle \sum _{e=1}^{N_{\mathrm{EES}}}{P^{\mathrm{dis}}}_{\mathrm{EES},e}(t)}+{\displaystyle \sum _{g=1}^{N\mathrm{area}}{P^{\mathrm{ch}}}_{\mathrm{lianluo},g1}(t)}=\\ {\displaystyle \sum _{e=1}^{N_{\mathrm{EES}}}{P^{\mathrm{ch}}}_{\mathrm{EES},e}(t)}+{\displaystyle \sum _{i=1}^{N_{\mathrm{EL}}}{P}_{\mathrm{EL},i}(t)+}{\displaystyle \sum _{k_1=1}^{N_{\mathrm{PL}}}{P}_{\mathrm{PL},k1}(t)}+{\displaystyle \sum _{g=1}^{N\mathrm{area}}{P^{dis}}_{\mathrm{lianluo},g1}(t)}\end{array}$$

(11)

where ${P^{\mathrm{J}}}_{a1}(t)$ is the net output power of carbon capture unit a; ${P^{\mathrm{wind}}}_c(t)$ is the power generated by wind farm c; $P_{\mathrm{HFC},d}(t)$ is the power output by HFC d; ${P^{\mathrm{dis}}}_{\mathrm{EES},e}(t)$ and ${P^{\mathrm{ch}}}_{\mathrm{EES},e}(t)$ are the power output and stored by energy storage e, respectively; ${P^{dis}}_{\mathrm{lianluo},g1}(t)$ and ${P^{\mathrm{ch}}}_{\mathrm{lianluo},g1}(t)$ are the power transmitted and received through the interconnection line, respectively; $N_{\mathrm{ccus}}$ is the number of carbon capture units; $N_{\mathrm{EES}}$ is the number of energy storage.

4.2.2. Constraints on Natural Gas Grid Hydrogen Blending

The hydrogen produced by EL can be directly injected into natural gas pipelines. After the hydrogen is mixed with natural gas, it provides energy for gas grid scheduling. The formula for calculating the calorific value of the mixed gas and the maximum hydrogen blending constraint in the gas grid is as follows:

$$\left\{\begin{array}{l}{q}_{\mathrm{mix}}(t)=\alpha (t)q^{{\mathrm{H}}_2}+\left(1-\alpha (t)\right)q^{{\mathrm{CH}}_4}\\ 0\le \alpha (t)\le {\alpha }_{\max }\end{array}\right.$$

(12)

where $q_{\mathrm{mix}}(t)$ is the calorific value of the mixed gas at time t; $\alpha (t)$ is the volumetric ratio of hydrogen doping in the gas grid; $q^{{\mathrm{H}}_2}$ and $q^{{\mathrm{CH}}_4}$ are the volumetric calorific values of hydrogen and methane, respectively; and ${\alpha }_{\max }$ is the maximum hydrogen doping ratio in the gas grid.

4.2.3. Tie Line Constraints

$$\left\{\begin{array}{l}{\displaystyle \sum _{t=1}^T{P}_{\mathrm{lianluo},g1}\left(t\right)=P_{g1}}\\ -{P^{\min }}_{\mathrm{lianluo},g1}\le P_{\mathrm{lianluo},g1}\left(t\right)-P_{\mathrm{lianluo},g1}\left(t-1\right)\le {P^{\max }}_{\mathrm{lianluo},g1}\\ {\mu }_{g1}\left(t\right)\left(1-\beta \right){\displaystyle \frac{P_{\mathrm{g}1}}{T}}\le P_{\mathrm{lianluo},g1}\left(t\right)\le {\mu }_{g1}\left(t\right)\left(1+\beta \right){\displaystyle \frac{P_{\mathrm{g}1}}{T}}\\ {\chi }_{g1}\left(t\right)-{\nu }_{g1}\left(t\right)={\mu }_{g1}\left(t\right)-{\mu }_{g1}\left(t-1\right)\\ {\chi }_{g1}\left(t\right)+{\nu }_{g1}\left(t\right)\le 1\\ {\displaystyle \sum _{t=1}^T{\chi }_{g1}\left(t\right)+{\nu }_{g1}\left(t\right)\le {\psi }_{g1}}\end{array}\right.$$

(13)

where T is the scheduling period; P_g1 is the total transaction volume of the g₁-th tie-line; ${P^{\max }}_{\mathrm{lianluo},g1}$ and ${P^{\min }}_{\mathrm{lianluo},g1}$ are the maximum and minimum values, respectively, of the tie-line power; ${\mu }_{g1}\left(t\right)$ is the state variable of the g₁-th tie-line at time t; β is the peak-to-valley difference rate of the tie-line power; ${\chi }_{g1}\left(t\right)$ and ${\nu }_{g1}\left(t\right)$ are the start-stop state variables of the g₁-th tie-line at time t; and ${\psi }_{g1}$ is the start-stop number limit of the g₁-th tie-line.

5. Model Solution

The ADMM algorithm has good convergence performance while ensuring the privacy of each region. The ADMM algorithm is implemented within MATLAB R2020a, and CPLEX 12.10 is invoked in MATLAB to solve the numerical optimization problem and obtain the final solutions. The specific solution steps are as follows:

Step 1. The number of iterations and the algorithm multiplier, k₀ = 1, ${\lambda }_{g_1}^0$, ${\stackrel{-}{P}}_{g_1}^0$, and ${\tilde{P}}_{g_1}^0$ are initialized. Concurrently, construct the augmented Lagrangian function $L_a$ for Region A, which serves as the objective function for the optimization problem corresponding to Region A.

$$L_a=\min \left(C_a+{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{g=1}^l{\lambda }_{g_1}^{k_0}\left({\stackrel{-}{P}}_{g_1}^{k_0+1}\left(t\right)-{\tilde{P}}_{g_1}^{k_0}\left(t\right)\right)}}+\right.\left.{\displaystyle \frac{\xi }{2}}{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{g=1}^l{‖{\stackrel{-}{P}}_{g_1}^{k_0+1}\left(t\right)-{\tilde{P}}_{g_1}^{k_0}\left(t\right)‖}_2^2}}\right)$$

(14)

where T denotes the system operating cycle, with T = 24 h; l represents the index of connecting lines, ranging from g to l; ${\lambda }_{g_1}^{k_0}$ is the Lagrange multiplier to the g₁-th tie-line after k₀ iterations; ${\stackrel{-}{P}}_{g_1}^{k_0+1}\left(t\right)$ stands for the regional interaction variable of the g₁-th tie-line after k₀ + 1 iterations; ${\tilde{P}}_{g_1}^{k_0}\left(t\right)$ denotes updated regional interaction variables; and $\xi$ is penalty coefficient.

Step 2. The mixed-integer second-order cone programming problem in the region that participates in power interaction through the tie line is solved. The objective is to minimize operating costs within the region while updating regional interaction variables and Lagrange multipliers simultaneously. The regional interaction variables and Lagrange multipliers ${\stackrel{-}{P}}_{g_1}^{k_0+1}\left(t\right)$ and ${\lambda }_{g_1}^{k_0}$ are updated and passed to the adjacent regions.

$${\stackrel{-}{P}}_{g_1}^{k_0+1}\left(t\right)=\arg \min L_a\left({\lambda }_{g_1}^{k_0},{\stackrel{-}{P}}_{g_1}^{k_0}\left(t\right),{\tilde{P}}_{g_1}^{k_0}\left(t\right)\right)$$

(15)

Equation (15) solves for the corresponding regional interaction variables and Lagrange multipliers by minimizing the value of the single-region Lagrange function.

Step 3. In the adjacent region, the updated variable values for solving the MISOCP problem in the region are used. Upon solving this problem, the regional interaction variable ${\tilde{P}}_{g_1}^{k_0+1}\left(t\right)$ is updated, and the values are passed to the adjacent region.

$${\tilde{P}}_{g_1}^{k_0+1}\left(t\right)=\arg \min L_a\left({\lambda }_{g_1}^{k_0},{\stackrel{-}{P}}_{g_1}^{k_0}\left(t\right),{\tilde{P}}_{g_1}^{k_0}\left(t\right)\right)$$

(16)

Step 4. After all the regions are solved, whether this iteration meets the convergence conditions is determined:

$${\displaystyle \sum _{t=1}^T{\displaystyle \sum _{g=1}^l‖{\stackrel{-}{P}}_{g_1}^{k_0+1}\left(t\right)-{\tilde{P}}_{g_1}^{k_0}\left(t\right)‖}}\le \varpi$$

(17)

If the convergence condition is met, the solution is considered complete. If not, the Lagrange multiplier is updated, and the k₀ + 1th iteration is continued until the convergence condition is met. The updated Lagrange multiplier is calculated as follows:

$${\lambda }_{g_1}^{k_0+1}={\lambda }_{g_1}^{k_0}+\xi \left({\stackrel{-}{P}}_{g_1}^{k_0+1}\left(t\right)-{\tilde{P}}_{g_1}^{k_0+1}\left(t\right)\right)$$

(18)

6. Case Analysis

6.1. Basic Data

This case study is based on a coupled system consisting of an IEEE 39-node power grid and a 20-node Belgian natural gas network. The system comprises three interconnected regions that exchange both information and energy through bidirectional interconnection lines. Region 1 is wind-rich, whereas Regions 2 and 3 are wind-poor.

In each regional subsystem, the power system is equipped with three wind turbines, two hydrogen-enriched gas turbines, two electrical energy storage units, and eight thermal power units, which are retrofitted as carbon capture power plants. The natural gas system includes four gas sources, two electrolyzers, two methanation reactors, and two hydrogen storage units. Surplus wind power is used to produce hydrogen through electrolysis, which is then injected into the natural gas pipeline, forming a hydrogen-blended gas network that enables coordinated energy management within the region. Key parameters of the electricity–hydrogen–electricity conversion chain and operational settings for all units are all referenced in Appendix B 

Table A1. Parameters of Electro-gas Conversion Equipment.

Power Grid Number	Equipment Type	Conversion Efficiency	Output Upper Limit/MW	Lower Limit of Output/MW
1	8000	0.74	270	0
5	6900	0.74	300	0
8	7300	0.6	120	0
14	7600	0.65	150	0

,

Table A2. Gas Turbine Parameters.

Carbon Emission Coefficient/(MW·h)	Startup Costs/Yuan	Shutdown Costs/Yuan	Output Upper Limit/MW	Lower Limit of Output/MW	Gas Network Number
0.4	80	60	820	0	23
0.4	80	60	820	0	15

,

Table A3. Thermal Power Unit Parameters.

Unit Number	Maximum Contribute/MW	Minimum Contribute/MW	Start-Stop Cost/Yuan	Minimum Start-Stop Time/h	Unit Climbing Slope/(MW/15 min)	Carbon Emission Intensity/(t/(MW·h))
1	1100	200	35,000	10/10	50	1.06
2	1100	200	35,000	10/10	50	1.06
3	580	150	6300	6/6	25	0.92
4	580	150	6300	6/6	25	0.92
5	580	150	6300	6/6	25	0.92
6	455	100	3920	5/5	18	0.9
7	455	100	3920	5/5	18	0.9
8	455	100	3920	5/5	18	0.9

and

Table A4. Carbon Capture Unit Parameters.

Name	Numerical Values
Carbon capture efficiency	0.9
Maximum operating condition coefficient	1.05
Energy consumption per unit carbon capture/((MW·h)/t)	0.269
Fixed energy consumption (MW·h)	5
Total cost of carbon capture equipment (in ten thousand yuan)	165,159.4
Carbon capture equipment depreciation period/year	15
Discount rate for carbon capture power plant projects	8%
Depreciation period of solution storage devices (years)	5
Ethanolamine solvent cost coefficient (yuan/kg)	8.2
Solvent operating loss coefficient (kg/t)	1.5

, and the natural gas source data are referenced in Appendix B 

Table A5. Natural Gas Source Parameters.

Gas Network Number	Gas Price/(Yuan·Mm3)	Upper Limit of Gas Production/Mm3	Lower Limit of Gas Production/Mm3
1	8000	6.5	0
5	6900	3.6	0
8	7300	5.5	0
14	7600	4.6	0

.

The electricity load, wind power profile, and natural gas load for the three regions are presented in Figure 2 and Figure 3.

In this study, four cases are established for comparative analysis to validate the effectiveness of the proposed methodology:

• Case 1: No wind power interaction among the three hydrogen-blended integrated energy systems (HHIESs)
• Case 2: With wind power interactions among the three HHIES
• Case 3: Based on Case 2 with additional consideration of CVaR
• Case 4: Simultaneous consideration of wind power interaction, CVaR, and peak shaving demand

6.2. Algorithm Convergence Analysis

The three regions exchange energy through interconnection lines. The amount of wind power transferred between regions is determined once the proposed algorithm has converged. The convergence curves of the total cost for each region are shown in Figure 4. The algorithm achieves convergence within 69 iterations, demonstrating satisfactory computational performance.

6.3. Uncertainty Risk Analysis

6.3.1. Comparative Analysis of the Low-Carbon and Economic Benefits of Wind Power Interactions Under Multiregional Coordinated Dispatch

Compared with Case 1, Case 2 achieves a carbon emission reduction of approximately 21.5% and a total cost reduction of approximately 19.8%. Considering Region 1 as an example, we compare the wind power interaction outcomes among the HHIESs.

Table 2. Comparison of Results in Various Cases.

Case	Total Cost/(10,000 Yuan)	Carbon Emissions/(Tons)
Case 1	4420.1	51,368.2
Case 2	3908.4	48,579.1
Case 3	3033.1	46,879.0
Case 4	2800.3	45,060.0

presents a summary of the results for the Cases. Compared with Case 1, Case 2 achieves a carbon reduction of approximately 5.4% and a total cost of approximately 11.5%. The implementation of interconnection lines can promote the wind power consumption and reduce the output of the thermal power units. This achieves emission reduction on one hand and reduces system operating costs on the other. Therefore, compared to independent operation in a single region, the wind power interaction among HHIGEs can promote system carbon emission reduction and improve system economics.

Compared with Case 2, Case 3 achieves a carbon emission reduction of approximately 3.4% and a total cost reduction of approximately 22.3%. In Case 3, the introduction of CVaR effectively quantifies the source-load uncertainty and optimizes the scheduling of conventional units. This approach significantly reduces system carbon emissions and operational costs. The results confirm that CVaR is a valuable tool for risk quantification and emission reduction.

Compared with Case 3, Case 4 achieves a carbon emission reduction of approximately 3.9% and a total cost reduction of about 7.6%. This improvement is largely attributable to addressing wind power’s “anti-peak-shaving” characteristic. During peak demand periods when the wind output is minimal, the conventional generators must increase their output to meet the load. Conversely, during off-peak hours when wind generation peaks, the output from conventional units is often sufficient, leading to wind curtailment. The electricity-hydrogen-electricity conversion process mitigates this issue by supplying power during peak hours (reducing conventional generation and costs) and consuming excess wind power for hydrogen production during off-peak hours. Therefore, by leveraging the peak-shaving capability of this conversion, overall operating costs are effectively reduced.

6.3.2. Impacts of the Risk Coefficients on the Economic Performance of the Hydrogen Blending System

The confidence level θ ∈ [0, 1], should balance risk representation accuracy and model computational efficiency. An excessively high value significantly increases the volume of extreme scenario simulations. An excessively low value fails to accurately characterize the system’s tail risks. To fully cover actual high-loss scenarios and avoid risk overestimation or underestimation, this paper sets the confidence level to 0.95.

The risk coefficient balances system operating costs and risk costs. Its value reflects the decision-maker’s preference for risks induced by source-load uncertainties and directly affects system scheduling outcomes. This paper defines its range as [0, 1], with distinct implications for risk preferences: a value of 0 means the model ignores risk costs, a value of 1 prioritizes risk avoidance and yields the most conservative scheduling scheme; an intermediate value balances economic benefits and risk resilience.

The risk coefficient reflects the attitudes of the decision-makers towards uncertainties in source–load variability. The value of this coefficient directly influences system scheduling decisions. In this analysis, the risk coefficient is increased from 0 to 0.4 in increments of 0.05, and its effects on both operating costs and total risk costs are evaluated. The corresponding results for the three regions are presented in Figure 5, Figure 6 and Figure 7.

As shown in Figure 7, when the risk coefficient is set to 0—i.e., potential risks from source–load uncertainty are entirely ignored—the system achieves the lowest operating cost. However, owing to the neglect of uncertainty-related risks, the total risk cost remains high. When risk is considered, the operating cost increases significantly as the risk coefficient increases, whereas the total risk cost decreases sharply before eventually stabilizing.

The risk factor reflects the decision-maker’s tolerance toward source-load uncertainty and significantly influences both the economic performance and security level of system operation. As shown in Figure 7, when the risk factor is 0, the total operating cost of the system is the lowest, whereas the total risk cost is the highest. As the risk factor increases, the operating cost rises and the risk cost declines, with both undergoing the most pronounced changes near the inflection point (risk factor = 0.1). Beyond this inflection point, both curves enter a saturated region, where their values show only minor fluctuations with further increases in the risk factor and overall tend to stabilize.

From the perspective of system operation and optimization, this inflection point indicates that risk-regulation measures have reached their effective limit. At this stage, the dispatchable resources that can be economically utilized to cope with uncertainty (e.g., conventional units) have approached their output saturation, and most of the marginal risk that could be mitigated through scheduling has already been avoided. The remaining risk primarily consists of inherent uncertainties that cannot be further mitigated under the current framework. Mathematically, this corresponds to the solution of the optimization problem entering the boundary of the feasible region, where the objective function becomes insensitive to further changes in the risk factor.

Therefore, this inflection point essentially identifies the optimal trade-off between economy and security achievable under the given system structure and resource constraints, providing a critical reference for setting risk preferences in the low-carbon economic dispatch of integrated energy systems. In practical operation, setting the risk factor around the inflection point can maintain the system’s ability to withstand uncertainty at an acceptable cost while avoiding unnecessary economic penalties caused by excessive conservatism, thereby achieving coordinated optimization of economy and security under low-carbon objectives.

6.4. Analysis of Peak Shaving Performance

To increase operational flexibility and achieve effective peak shaving and valley filling, ELs, GTs, and HFCs are incorporated into the peak shaving process. Taking Region 1 as an example, Figure 8 compares the outputs of flexible resources with and without peak shaving integration. During the low-load period (00:00–08:00), the output of ELs in Case 4 is significantly higher than that in Case 3, presenting a total increase of 730 MW. By participating in valley-filling operations, ELs increase the net load during off-peak hours, which promotes wind power consumption and mitigates the anti-peak-regulation characteristics of renewables.

In Case 3, GT operation is concentrated mainly between approximately 13:00 and 14:00, with a relatively low output. In contrast, Case 4 extends the gas turbine operation from 13:00 to 18:00, with a significantly higher output. Similarly, the HFC output in Case 3 remains low and is distributed mainly between 05:00 and 20:00, whereas in Case 4, both the operating period (05:00–23:00) and the total output approximately double.GT converts natural gas into electricity, whereas HFCs generate power from hydrogen. Their coordinated operation reduces the net load during peak hours, achieving a clear peak shaving effect. Together with ELs, these assets smooth net load fluctuations, enabling the system to realize effective peak shaving and valley filling.

6.5. Analysis of Hydrogen Blending Strategies in Gas Grids Based on Multi-Zone Operation

6.5.1. Impact of the Peak Shaving Economic Coefficient on the Cost of Hydrogen Blending in the Gas Grid

Based on Case 4, we investigate the impact of the economic coefficient on system operating costs and hydrogen blending strategies in the context of peak shaving. The economic coefficient varies from 0.1 to 0.7 in increments of 0.3. For each given economic coefficient, the upper limit of the hydrogen blending ratio in the gas grid is increased from 0.01 to 0.24 in steps of 0.01, and the resulting changes in operating costs across the three regions are analyzed.

For Region 1, the economic coefficients of 0, 0.1, 0.4, and 0.7 are tested. The corresponding variations in operating cost under different hydrogen blending ratio limits for each coefficient are shown in Figure 9, Figure 10 and Figure 11. As shown in Figure 9 and Figure 10, when the economic coefficient is greater than zero and held constant, the system operating cost first decreases but then stabilizes as the hydrogen blending limit increases. Injecting green hydrogen produced from surplus wind power into the gas grid displaces natural gas to meet gaseous load requirements. This process reduces the volume of natural gas purchases, thereby lowering the total cost of the integrated electricity–gas–hydrogen system. As the allowable hydrogen blending limit increases, both the production of green hydrogen and its injection into the grid increase, further reducing gas procurement costs.

However, hydrogen blending introduces additional operation and maintenance costs for the pipeline network, which increase exponentially with the blending limit. When the blending limit is relatively low, the combined costs of peak shaving and blending remain lower than the savings from reduced gas purchases. Therefore, the total system cost decreases as the blending limit increases. As the blending limit continues to increase, the marginal cost savings gradually diminish. Once the cumulative blending-related costs equal the gas cost savings, the total system cost stabilizes. The corresponding hydrogen blending limit at this point represents the economic inflection point, where the system achieves its minimum operating cost.

To clarify the impact of the peak-shaving economic coefficient on the cost of hydrogen blending in the gas grid and its engineering implications, this work conducts an analysis based on Case 4. The economic coefficient is varied from 0.1 to 0.7 in increments of 0.3, and for each coefficient value, the upper limit of hydrogen blending in the gas grid is increased from 1% to 24% in increments of 1%.

For different peak-shaving economic coefficients, the total system cost exhibits a similar pattern as the upper blending limit rises: when the blending limit is below a certain inflection point, the total cost gradually decreases with the increase in the limit; beyond this inflection point, the total cost remains essentially stable without significant further change.

This behavior can be explained by the following mechanism. Injecting green hydrogen produced from surplus wind power into the gas grid can replace a portion of the natural gas, thereby reducing both the volume and cost of gas purchases. As the blending limit increases, more hydrogen is injected into the gas grid, resulting in a further reduction in gas purchase costs. However, the operation and maintenance costs of hydrogen-blending pipelines grow exponentially with the blending limit. When the blending limit is relatively low, the sum of peak-shaving cost and hydrogen-blending cost is smaller than the saved gas purchase cost; therefore, the total system cost decreases as the blending limit rises. As the blending limit continues to increase, the difference between the two gradually narrows. When the cumulative peak-shaving and blending costs equal the cost of the saved gas purchase, the total system cost reaches a minimum and enters a stable plateau. The corresponding blending limit at this point is the inflection point for that economic coefficient, which represents the near-optimal value of the gas-grid hydrogen-blending upper limit under the given coefficient.

Specifically, the inflection points and cost variation characteristics corresponding to each coefficient are as follows: The peak-shaving economic coefficient equals 0 (Figure 9). The cost decreases gradually within the blending upper limit range of 1–11%, then stabilizes beyond 11%. The inflection point is 11%. Peak-shaving economic coefficient = 0.1 (Figure 9): The cost decreases over the range of 1–13%, stabilizing thereafter. The inflection point is 13%. Peak-shaving economic coefficient = 0.4 (Figure 10): The cost declines between 1% and 15%, remaining stable above 15%. The inflection point is 15%. Peak-shaving economic coefficient = 0.7 (Figure 11): The cost decreases up to 18%, after which it stabilizes. The inflection point is 18%.

The results indicate that, for each specific economic coefficient, the system possesses an optimal hydrogen-blending operating point that minimizes the total cost. This regularity provides direct guidance for practical dispatch: in actual operation, the hydrogen-blending upper limit can be set near its corresponding inflection point, according to the system’s peak-shaving requirements and cost structure, thereby meeting peak-shaving demands while minimizing total system cost.

To evaluate the sensitivity of the peak-shaving economic coefficient on system cost optimization, a sensitivity analysis was conducted for Region 1. The results reveal that as the coefficient increases from 0.1 to 0.4 (a 300% relative change), the system’s cost-saving rate rises from 1.9% to 3.5% (an 84.21% relative change), yielding a sensitivity coefficient of 0.28. A further increase from 0.4 to 0.7 (a 75% relative change) results in only a slight decrease of 5.71% in the cost-saving rate, with a sensitivity coefficient of 0.08. Both sensitivity coefficients are below 0.3, indicating that the system cost optimization effect is insensitive to variations in the peak-shaving economic coefficient. This low sensitivity is actually desirable from an engineering perspective, as it indicates that the economic benefits of the proposed strategy are robust and do not rely on a precise estimation of this coefficient, enhancing the practicality and reliability of the approach for real-world applications.

For Regions 2 and 3, under a given peak-shaving economic coefficient, the variation trend of system cost is similar to that observed in Region 1. The corresponding inflection-point values of the gas-grid hydrogen-blending upper limit are summarized in

Table 3. Inflection-point Values of the Gas Grid Hydrogen-blending Upper Limit in Regions 2 and 3 Under Different Peak-shaving Economic Coefficients.

Peak-Shaving Economic Coefficient	Region 2 Inflection Point	Region 3 Inflection Point
0	13% (Appendix A Figure A1(a1))	14%(Appendix A Figure A1(b1))
0.1	18% (Appendix A Figure A1(a1)	17% (Appendix A Figure A1(b1))
0.4	20% (Appendix A Figure A1(a2)	19% (Appendix A Figure A1(b2))
0.7	21% (Appendix A Figure A1(a3))	22% (Appendix A Figure A1(b3))

.

Comparing the results for an economic coefficient of 0 (no peak shaving) and 0.1 (with peak shaving), the overall system-cost trends are largely similar. The key difference lies in the timing of the inflection point: it occurs earlier when peak shaving is inactive. Once peak shaving is engaged, a higher economic coefficient results in a gradual increase in the inflection-point value across all regions.

This shift occurs because when ELs, HFCs, and other devices participate in peak shaving, a larger economic coefficient raises the weight of the peak-shaving objective in the total cost. This improves peak-shaving and valley-filling performance, enhances hydrogen-energy flexibility, and increases the hydrogen-blending ratio in the gas grid—all of which contribute to reducing the total system cost. The inflection point corresponds to the condition where the reduction in gas-purchase cost balances the cumulative increase in peak-shaving cost and hydrogen-blending cost. Compared with the non-participation case, the additional revenue from gas grid hydrogen blending induced by peak shaving offsets the rising blending cost. As the economic coefficient increases, green-hydrogen production rises, further boosting blending revenue and thereby shifting the inflection point to higher values.

6.5.2. Impacts of Peak Shaving Economic Coefficients on the Hydrogen Blending Strategy of the Gas Grid Based on Multizone Operation

For Region 1, the inflection point of the upper limit for hydrogen blending in the gas grid is affected by whether the electricity-hydrogen-electricity conversion chain participates in grid peak shaving. When it does not participate in peak shaving (i.e., the peak shaving economic coefficient is 0), the upper limit for hydrogen blending in the gas grid is 11%; while when it participates in peak shaving (economic coefficients of 0.1, 0.4, and 0.7, respectively), the upper limit for hydrogen blending can be increased to 13%, 15%, and 18%, respectively (see Figure 12 for the corresponding dynamic hydrogen blending strategy).

The hydrogen blending strategies differ markedly between the two scenarios, primarily due to shifts in the allocation of hydrogen flow. Between 00:00 and 08:00, participation in peak shaving increases EL output to meet grid demand, thereby enhancing hydrogen production. As a result, more hydrogen is injected into the gas grid, leading to a higher blending ratio compared to the scenario without participation. Between 13:00 and 19:00, peak shaving requires higher output from HFCs and hydrogen-blended GTs, which consume more hydrogen. Consequently, less hydrogen is allocated to the gas grid, resulting in a lower blending ratio compared to the scenario without peak shaving.

Figure 12 further shows that when the electricity-hydrogen-electricity conversion chain participates in peak shaving, the variations in the dynamic hydrogen blending strategy under different peak-shaving economic coefficients generally follow the same trend: Between 01:00 and 06:00, low electricity load and surplus wind power allow sufficient hydrogen production from electrolyzers, keeping the hydrogen blending ratio in the gas network high. Between 07:00 and 11:00, as the electricity load rises and the wind surplus decreases, EL hydrogen production declines, resulting in a decrease in the blending ratio. Between 12:00 and 19:00, a high electricity load and limited wind output reduce EL hydrogen production. Hydrogen is prioritized for HFCs, resulting in a low blending ratio in the gas grid. Between 20:00 and 24:00, the electricity load decreases, wind output increases, and the gas grid load remains low. EL hydrogen production rises, causing the blending ratio to increase again.

For Region 2, as the peak-shaving economic coefficient rises from 0 to 0.1, 0.4, and 0.7, the corresponding upper-limit inflection points for hydrogen blending in the gas grid increase to 13%, 18%, 20%, and 21%, respectively. The associated dynamic hydrogen blending strategies are presented in Figure 13.

Similarly to Region 1, the variation in hydrogen blending levels is primarily driven by whether the system participates in peak shaving, which alters the allocation of hydrogen flow. Between 00:00 and 07:00, the blending ratio is generally lower, without peak shaving. Participating in peak shaving increases EL output and hydrogen production, thereby raising the blending level. Between 14:00 and 18:00, the blending ratio is higher without peak shaving. When peak shaving is active, HFCs and hydrogen-blended GTs operate at higher outputs, diverting more hydrogen away from the gas grid and reducing the blending ratio.

When the electricity-hydrogen-electricity conversion chain participates in peak shaving, the overall trend of the dynamic blending strategy remains consistent across different economic coefficients. The time intervals in Region 2 are more segmented, reflecting its distinct energy supply–demand dynamics: Between 01:00 and 02:00, gas load increases, leading to a decrease in the hydrogen blending ratio. Between 02:00 and 04:00, higher wind power output increases EL-based hydrogen production, resulting in increased green hydrogen injection into the gas grid and, consequently, a higher blending ratio. From 05:00 to 10:00, sustained high wind output supports sufficient EL hydrogen production, keeping the blending ratio at an elevated level. Between 11:00 and 16:00, a high electricity load and low wind output reduce EL hydrogen production, causing hydrogen to be preferentially directed to HFCs, which lowers the gas grid blending ratio. Between 17:00 and 24:00, the electricity load declines while wind output rises, boosting EL hydrogen production and gas grid hydrogen injection, which in turn raises the blending ratio again.

For Region 3, the upper-limit inflection points for hydrogen blending in the gas grid correspond to 14%, 17%, 19%, and 22% under peak-shaving economic coefficients of 0, 0.1, 0.4, and 0.7, respectively. The corresponding dynamic hydrogen blending strategies are illustrated in Figure 14. As shown in the figure, the trends of the dynamic hydrogen blending strategies remain generally consistent across different economic coefficients. Given that both Region 2 and Region 3 are low-wind areas, their wind power output patterns and load profiles are similar, resulting in comparable distributions of hydrogen blending strategies. Consequently, the variation trend observed in Region 3 aligns closely with that of Region 2.

The findings of this study provide clear guidance for hydrogen-blending projects in gas grids. In actual operation, an appropriate peak-shaving economic coefficient can be selected according to the system’s peak-shaving requirements and economic objectives. The corresponding upper-limit inflection point for hydrogen blending in the gas grid can then be determined through calculation, and a dynamic hydrogen-blending strategy can be formulated accordingly. This method organically couples gas-grid hydrogen blending with grid peak-shaving needs through the economic coefficient, providing a clear and operational dispatch basis for project implementation. Such a coupling approach not only leverages the flexible regulation capability of the hydrogen system but also enhances the peak-shaving capacity and stability of the power grid, thereby helping to ensure safe system operation while improving the overall economic efficiency of energy utilization.

7. Conclusions

In this work, the low-carbon economic dispatch of a multiregional HHIES is studied. This dispatch promotes wind power consumption through interregional coordination, quantifies the risks from source–load uncertainty using CVaR, and incorporates the electricity–hydrogen–electricity regulation link into grid peak shaving. Based on this, a dispatch model that considers the effects of both uncertainty and peak shaving demand is proposed.

• With respect to the system structure, the multiregional system established in Case 4 demonstrates significant advancements over Case 1. The implementation of dynamic hydrogen blending control reduces carbon emissions by approximately 12.3%, effectively enhancing the system’s decarbonization capability. Furthermore, by leveraging a coordinated operation mechanism among ELs, GTs, and HFCs, the system’s peak-shaving and valley-filling performance is substantially improved. Specifically, during peak load periods, the power output of hydrogen fuel cells in Case 4 is approximately twice that in Case 3. During off-peak load periods, the power output of electrolyzers in Case 4 exceeds that in Case 3 by about 730 MW.
• With respect to dispatch model optimization, we use the CVaR to quantify uncertainty and economic coefficients to adjust cost proportions. This process achieves synergy among the economy, risk, and system performance, thus improving the applicability of the model.
• With respect to operational decisions, the upper limit of hydrogen blending exhibits economic coefficient-dependent inflection points. Dynamic adjustment of this limit alongside elevated economic coefficients identifies optimal blending thresholds; subsequent optimization of hydrogen allocation strategies enhances peak-shaving capability. Consequently, the rational dispatch of EL output further reduces operating costs. An analysis of Region 1 verifies this effect: setting peak-shaving economic coefficients to 0, 0.1, 0.4, and 0.7 lowers system operating costs by 1.8%, 1.9%, 3.5%, and 3.3%, respectively.

This work focuses primarily on the core issues of regulation and optimization for HHIESs, without incorporating an analysis of the impact of market-based trading on system scheduling. The next step is to consider the impact of market-based trading on optimized scheduling, focusing on multiple types of trading instruments across various market types. This extension will further refine the economic viability and adaptability analysis of HHIESs in market environments.