Optimal Economic Dispatch of Hydrogen Storage-Based Integrated Energy System with Electricity and Heat

Abstract

To enhance the accommodation capacity of renewable energy and promote the coordinated development of multiple energy, this paper proposes a novel economic dispatch method for an integrated electricity–heat–hydrogen energy system on the basis of coupling three energy flows. Firstly, we develop a mathematical model for the hydrogen energy system, including hydrogen production, storage, and hydrogen fuel cells. Additionally, a multi-device combined heat and power system is constructed, incorporating gas boilers, waste heat boilers, gas turbines, methanation reactors, thermal storage tanks, batteries, and gas storage tanks. Secondly, to further strengthen the carbon reduction advantages, the economic dispatch model incorporates the power-to-gas process and carbon trading mechanisms, giving rise to minimizing energy purchase costs, energy curtailment penalties, carbon trading costs, equipment operation, and maintenance costs. The model is linearized to ensure a global optimal solution. Finally, the experimental results validate the effectiveness and superiority of the proposed model. The integration of electricity–hydrogen coupling devices improves the utilization rate of renewable energy generation and reduces the total system operating costs and carbon trading costs. The use of a tiered carbon trading mechanism decreases natural gas consumption and carbon emissions, contributing to energy conservation and emission reduction.

1. Introduction

Under the global energy transition framework and the “dual carbon” goals, issues such as the depletion of fossil fuels and environmental pollution are becoming increasingly severe. The proportion of renewable energy in power systems continues to rise. However, traditional systems often exhibit a singular focus on energy utilization, limiting the complementary advantages of diverse energy sources. As an innovative energy supply solution, the Integrated Energy System aims to optimize energy structures, improve energy efficiency, and reduce carbon emissions through unified scheduling and coordinated operation of various energy forms. By integrating multiple energy types, the Integrated Energy System (IES) meets the diversified energy demands of various end-users [1,2].

The economic dispatch of integrated energy systems refers to minimizing system operating costs and reducing energy consumption by rationally allocating and scheduling energy equipment while meeting energy demand. Literature [3] proposes a two-stage robust scheduling model for a multi-energy system(MES), considering combined heat and power demand response. This robust optimization model reduces operating costs while satisfying system constraints. Literature [4] develops a mathematical model aimed at minimizing system operating costs and carbon emissions under conditions of wind power uncertainty, verifying its effectiveness. Literature [5] introduces an optimal economic dispatch model that balances combined heat and power (CHP), intermittent renewables like wind and solar power, and battery storage systems. This model, incorporating heat storage tanks and regional heating networks, enhances the flexibility of combined heat and power units and integrates energy more effectively. Literature [6] investigates the potential role of clean hydrogen within energy systems, quantitatively assessing its impact on key metrics and conducting techno-economic optimization for integrated energy systems.

Combined heat and power, a mature and reliable technology, offers high flexibility, efficiency, and minimal environmental impact, making it a significant form of IES [7,8]. Combined heat and power achieve efficient coupling of heat and electricity, supplying heat through waste heat boilers while utilizing waste heat sources such as exhaust gas and wastewater, emerging as a critical development path for future energy systems. An optimized operation model based on nonlinear programming to minimize costs in combined heat and power systems is proposed in [9] to analyze the relationships among energy management, load conditions, and energy costs. However, the CO₂ emissions from combined heat and power systems pose potential environmental threats. To enhance the flexibility and adaptability of combined heat and power, power-to-gas (P2G) technology has gained prominence. By absorbing CO₂ through methanation reactions in a methane reactor (MR), power-to-gas promotes low-carbon emissions and improves wind power utilization. Literature [10] presents an integrated energy system optimization model incorporating power-to-gas and carbon capture, analyzing its electricity, heat, gas, and carbon coupling characteristics to reduce emissions and costs. Literature [11] introduces a joint configuration approach for power-to-gas and photovoltaic equipment while considering the impact of a tiered carbon trading mechanism on optimization results.

Carbon trading is a policy innovation for carbon reduction and a vital tool for achieving the “dual carbon” goals in China [12,13]. It is categorized into two primary mechanisms: the traditional carbon trading mechanism and the tiered carbon trading mechanism. The former uses a fixed carbon price to calculate trading costs, where entities exceeding allocated emission quotas must purchase excess allowances at a set price. While this model reflects environmental and economic benefits, it is relatively simplistic and limited. The latter increases trading costs incrementally with higher emissions, effectively encouraging carbon reduction efforts and promoting green transitions in power generation. Literature [12] proposes an integrated energy system planning scheme based on fluctuating carbon trading prices, demonstrating that an integrated energy system can balance cost-effectiveness and low-carbon goals when price volatility reaches a certain level. Literature [13] incorporates a tiered carbon trading mechanism, proposing an optimized scheduling strategy for a park-based integrated energy system.

Hydrogen energy, as a clean energy source, boasts high energy density, ease of storage and transportation, and renewability, making it a critical component of future energy systems [14,15]. Hydrogen technologies include hydrogen production, hydrogen storage, and hydrogen fuel cells. Renewable energy-based hydrogen production through water electrolysis is a key focus for achieving green hydrogen [16]. By directly converting renewable electricity into hydrogen and water through electrochemical reactions, it enables zero-emission energy utilization [17,18]. Among large-scale hydrogen production methods, this approach demonstrates remarkable potential. Literature [14] develops a hydrogen production model based on offshore wind energy, calculating hydrogen production costs from offshore wind. It shows that integrating electrolysis systems with offshore wind facilities offers cost and economic advantages over traditional onshore methods. Literature [15] investigates wind-to-hydrogen equipment, studying the coupling operation of electrolyzers and wind turbines, and evaluates the working characteristics of four electrolyzer models. Literature [16,17] examines wind-to-hydrogen systems under various hydrogen production modes and demand levels, proposing optimized planning schemes considering economic and environmental benefits. Literature [18] addresses wind turbine output volatility and grid curtailment issues, proposing wind–hydrogen coupled generation systems and energy management strategies under various operating modes. These strategies smooth power output and enhance wind energy utilization.

Large-scale energy storage systems are essential for the economic dispatch of power systems [19,20]. Storage systems balance power loads, smooth peaks and valleys, and mitigate negative impacts from output fluctuations, optimizing overall system efficiency. However, traditional storage systems face limitations for large-scale, long-duration storage. Hydrogen energy storage system (HESS) technology, with its seasonal and regional scalability and large-scale storage advantages, is gaining attention. Literature [19] studies hydrogen storage system applications in renewable-based integrated energy systems, optimizing hydrogen output to shift peak load demand to off-peak periods, thereby reducing overall system costs. Literature [20] explores a long-term hydrogen storage model, analyzing its impact on system planning and operations under temporal constraints. Literature [21] proposes a hybrid energy storage system combining wind turbine (WT), photovoltaic (PV), battery (BT), Electrolyser (EL), fuel cells (FC), and hydrogen storage tank (HST), presenting innovative scheduling strategies to improve system stability and economics. Literature [22] designs an integrated energy system architecture using solar and natural gas energy, including natural gas-to-hydrogen conversion, achieving a coordinated supply of electricity, cooling, heat, and hydrogen.

Hydrogen fuel cells (HFCs), devices that convert chemical energy directly into electricity via electrochemical reactions without combustion, are considered one of the most promising power generation technologies of the 21st century [23]. Compared to internal combustion engines, hydrogen fuel cells offer high efficiency, environmental friendliness, superior reliability, and exceptional flexibility, securing their vital role in hydrogen energy applications. Literature [24] presents case studies on various fuel cell and hydrogen production technologies, showcasing feasible and environmentally acceptable alternatives to fossil fuels.

The referenced literature addresses the integrated utilization of various energy sources but provides insufficient consideration of hydrogen fuel cells and limited application of carbon trading in economic dispatch. To overcome these limitations, this paper starts with the electricity–heat–hydrogen integrated energy system and proposes a joint operation model incorporating hydrogen production via electrolysis, hydrogen energy storage, hydrogen fuel cells, and a combined heat and power system. By considering power-to-gas technology and carbon trading mechanisms, an economic dispatch model for the electricity–heat–hydrogen energy storage system with hydrogen storage is developed, aiming to minimize system operating costs. The economic advantages of the proposed model are verified through case studies.

2. Modeling of an Integrated Electro-Thermal Hydrogen Energy System Considering Hydrogen Energy Storage

A hydrogen energy storage system (HESS) was developed by utilizing the electric–hydrogen–electric intermutability, and the hydrogen storage system mainly consists of three parts: EL, HST, and FC. In Figure 1, the electric boiler is the thermoelectric coupling unit, and the fuel cell and electrolyzer are the electric–hydrogen–thermal coupling unit. WT and PV are the renewable energy generation in the system, which has a certain degree of volatility and stochasticity.

2.1. Modeling of Electrical Heat Coupling Systems

(1)

Gas turbine

Gas turbines operate by combustion of fuel gas, such as natural gas, to form a high-temperature, high-pressure gas, which in turn drives a turbine to rotate and convert into mechanical energy, and are widely used in electric power production and combined-cycle power generation systems [25].

The generating power of a gas turbine can be expressed as follows:

$$P_{\mathrm{GT}}(t)=P_{\mathrm{GT},\mathrm{e}}(t)+P_{\mathrm{GT},\mathrm{h}}(t)$$

(1)

where $P_{\mathrm{GT}}(t)$ represents the total output power of the gas turbine at time period t, while $P_{\mathrm{GT},\mathrm{e}}(t)$ and $P_{\mathrm{GT},\mathrm{h}}(t)$ denote the electrical power and the waste heat power of the gas turbine at time period t, respectively.

The generation power and waste heat power of the gas turbine is modeled as:

$$\left\{\begin{array}{l}{P}_{\mathrm{GT},\mathrm{e}}(t)={\eta }_{\mathrm{GT}}^{\mathrm{e}}{P}_{\mathrm{GT},\mathrm{g}}(t)\\ P_{\mathrm{GT},\mathrm{h}}(t)={\eta }_{\mathrm{GT}}^{\mathrm{h}}{P}_{\mathrm{GT},\mathrm{g}}(t)\end{array}\right.$$

(2)

where $P_{\mathrm{GT},\mathrm{g}}(t)$ represents the amount of gas consumed by the gas turbine during time period t, while ${\eta }_{\mathrm{GT}}^{\mathrm{e}}$ and ${\eta }_{\mathrm{GT}}^{\mathrm{h}}$ represent the electricity generation and heating efficiencies of the gas turbine, respectively.

(2)

Waste heat boiler

Waste heat boilers are devices used to collect waste heat energy from industrial processes and use the process to generate energy in the form of steam or hot water for use.

The relationship between the heat output and heat input of a waste heat boiler is related to its efficiency with the expression:

$$H_{\mathrm{WHB}}(t)={\eta }_{\mathrm{WHB}}{H}_{\mathrm{WHB},\mathrm{in}}(t)$$

(3)

where $H_{\mathrm{WHB},\mathrm{in}}(t)$ and $H_{\mathrm{WHB}}(t)$ represent the input and output heat, respectively, while ${\eta }_{\mathrm{WHB}}$ denotes the efficiency of the waste heat boiler.

(3)

Gas boiler

A gas boiler is a device that uses the combustion of gas to produce heat and plays the role of an auxiliary heat source in the system. The power output of a gas turbine can be expressed as:

$$P_{\mathrm{GB},\mathrm{h}}(t)={\eta }_{\mathrm{GB}}{P}_{\mathrm{GB},\mathrm{g}}(t)$$

(4)

where $P_{\mathrm{GB},\mathrm{h}}(t)$ represents the heat generated by the gas boiler during the time period t, ${\eta }_{\mathrm{GB}}$ denotes the heating efficiency of the gas boiler, and $P_{\mathrm{GB},\mathrm{g}}(t)$ refers to the amount of gas consumed by the gas boiler during the time period t.

(4)

Methane reactor

Methane reactors convert organic matter or gases (such as carbon dioxide and hydrogen) into methane through a catalyst at specific temperatures and pressures for energy conversion or waste utilization. The mathematical model is shown below:

$$\left\{\begin{array}{l}{P}_{\mathrm{MR},\mathrm{g}}(t)={\eta }_{\mathrm{MR}}^{\mathrm{g}}{P}_{{\mathrm{MR},\mathrm{H}}_2}(t)\\ P_{\mathrm{MR},\mathrm{h}}(t)={\eta }_{\mathrm{MR}}^{\mathrm{h}}{P}_{{\mathrm{MR},\mathrm{H}}_2}(t)\\ C_{\mathrm{MR}}(t)=\chi P_{\mathrm{MR},\mathrm{g}}(t)\end{array}\right.$$

(5)

where $P_{{\mathrm{MR},\mathrm{H}}_2}(t)$ is the hydrogen energy input to the MR at time t, ${\eta }_{\mathrm{MR}}^{\mathrm{g}}$ and ${\eta }_{\mathrm{MR}}^{\mathrm{h}}$ are the hydrogen-to-methane conversion efficiency and heat production efficiency of the MR, $P_{\mathrm{MR},\mathrm{g}}(t)$ and $P_{\mathrm{MR},\mathrm{h}}(t)$ are the natural gas power and heat power output at time t, $C_{\mathrm{MR}}(t)$ is the amount of carbon dioxide consumed in the methanation process at time t, and $\chi$ is the calculation coefficient of CO₂.

(5)

Thermal storage tank

A thermal storage tank is a device that can store thermal energy when it is in excess supply and release it when it is needed, thus balancing energy supply and demand, improving energy efficiency, and increasing the flexibility of system operation. It is modeled as follows:

$$\left\{\begin{array}{l}{H}_{\mathrm{TST}}(t)=H_{\mathrm{TST}}^{\mathrm{cha}}(t){\eta }_{\mathrm{TST}}^{\mathrm{cha}}-H_{\mathrm{TST}}^{\mathrm{dis}}(t)/{\eta }_{\mathrm{TST}}^{\mathrm{dis}}\\ S_{\mathrm{H}}(t)=S_{\mathrm{H}}(t-1)+H_{\mathrm{TST}}(t)/H_{\mathrm{TST}}^{\max }\end{array}\right.$$

(6)

where $H_{\mathrm{HST}}(t)$ represents the thermal energy stored in the thermal storage tank during the time period t, ${\eta }_{\mathrm{HST}}^{\mathrm{cha}}$ and ${\eta }_{\mathrm{HST}}^{\mathrm{dis}}$ denote the charging and discharging efficiencies of the thermal storage tank, $H_{\mathrm{HST}}^{\mathrm{cha}}(t)$ and $H_{\mathrm{HST}}^{\mathrm{dis}}(t)$ refer to the total thermal storage power and total heat release power of the tank during the time period t, $S_{\mathrm{H}}(t)$ and $S_{\mathrm{H}}(t-1)$ represent the thermal storage states of the storage device during the time periods t and t − 1, and $H_{\mathrm{HST}}^{\max }$ denotes the maximum storage capacity of the thermal storage tank.

(6)

Battery

A battery is a device that converts electrical energy into chemical energy for storage and reverses the conversion to electrical energy for release when necessary. It is modeled as follows:

$$\left\{\begin{array}{l}{P}_{\mathrm{BT}}(t)=P_{\mathrm{BT}}^{\mathrm{cha}}(t){\eta }_{\mathrm{BT}}^{\mathrm{cha}}-P_{\mathrm{BT}}^{\mathrm{dis}}(t)/{\eta }_{\mathrm{BT}}^{\mathrm{dis}}\\ S_{\mathrm{E}}(t)=S_{\mathrm{E}}(t-1)+P_{\mathrm{BT}}(t)/P_{\mathrm{BT}}^{\max }\end{array}\right.$$

(7)

where $P_{\mathrm{BT}}(t)$ represents the electrical power stored in the energy storage device during the time period t, ${\eta }_{\mathrm{BT}}^{\mathrm{cha}}$ and ${\eta }_{\mathrm{BT}}^{\mathrm{dis}}$ denote the charging and discharging efficiencies of the battery, $P_{\mathrm{BT}}^{\mathrm{cha}}(t)$ and $P_{\mathrm{BT}}^{\mathrm{dis}}(t)$ refer to the charging power and discharging power of the battery during the time period t, $S_{\mathrm{E}}(t)$ and $S_{\mathrm{E}}(t-1)$ represent the state of charge of the energy storage device during the time periods t and t − 1, and $P_{\mathrm{BT}}^{\max }$ denotes the maximum storage capacity of the battery.

(7)

Gas storage tank

A gas storage tank is a key device for storing natural gas, which is applied in this paper to store natural gas produced during the methanation process of a P2G plant. Its mathematical model is as follows:

$$\left\{\begin{array}{l}{P}_{\mathrm{GST}}(t)=P_{\mathrm{GST}}^{\mathrm{cha}}(t){\eta }_{\mathrm{GST}}^{\mathrm{cha}}-P_{\mathrm{GST}}^{\mathrm{dis}}(t)/{\eta }_{\mathrm{GST}}^{\mathrm{dis}}\\ S_{\mathrm{G}}(t)=S_{\mathrm{G}}(t-1)+P_{\mathrm{G}}(t)/P_{\mathrm{G}}^{\max }\end{array}\right.$$

(8)

where $P_{\mathrm{G}}(t)$ represents the gas power stored in the gas storage device during the time period t, ${\eta }_{\mathrm{G}}^{\mathrm{cha}}$ and ${\eta }_{\mathrm{G}}^{\mathrm{dis}}$ denote the charging and discharging efficiencies of the gas storage tank, $P_{\mathrm{G}}^{\mathrm{cha}}(t)$ and $P_{\mathrm{G}}^{\mathrm{dis}}(t)$ refer to the charging and discharging power of the gas storage tank during the time period t, $S_{\mathrm{G}}(t)$ and $S_{\mathrm{G}}(t-1)$ represent the gas storage states of the gas storage device during the time periods t and t − 1, and $P_{\mathrm{G}}^{\max }$ denotes the gas storage capacity limit of the gas storage tank.

2.2. Modeling of Hydrogen Energy Systems

The hydrogen energy system studied in this paper is shown in Figure 2, and the system consists of the fuel cell (FC), heat exchanger (HE), electrolyzer (EL), hydrogen storage tank (HST), water pump (WP), and heat and power grids. Of this, the heat produced by electrolyzer hydrogen and fuel cell electricity can be used for heat loads.

(1)

Modeling of electric hydrogen production

Hydrogen production by water electrolysis is a device that produces hydrogen and oxygen by injecting direct current into an electrolytic cell.

$$\left\{\begin{array}{l}{P}_{\mathrm{EL},\mathrm{e}}(t)=P_{{\mathrm{EL},\mathrm{H}}_2}(t)+P_{\mathrm{EL},\mathrm{h}}(t)\\ P_{\mathrm{EL},\mathrm{e}}(t)=P_{{\mathrm{EL},\mathrm{H}}_2}(t)/{\eta }_{\mathrm{EL}}\\ P_{\mathrm{EL},\mathrm{h}}(t)=P_{{\mathrm{EL},\mathrm{H}}_2}(t)(1-{\eta }_{\mathrm{EL}})/{\eta }_{\mathrm{EL}}\\ P_{{\mathrm{EL},\mathrm{H}}_2}(t)=P_{{\mathrm{HT},\mathrm{H}}_2}^{\mathrm{cha}}(t)+P_{\mathrm{EL},\mathrm{FC}}(t)\end{array}\right.$$

(9)

where ${\eta }_{\mathrm{EL}}$ represents the operating efficiency of the electrolyzer, $P_{\mathrm{EL},\mathrm{FC}}(t)$ denotes the power consumed during the time period t directly used for electricity generation by the fuel cell, and $P_{{\mathrm{HT},\mathrm{H}}_2}^{\mathrm{cha}}(t)$ refers to the power generated by the electrolyzer during the time period t for hydrogen production and storage.

The hydrogen production rate of the electrolytic cell in normal operation can be expressed as:

$$\left\{\begin{array}{l}{n}_{\mathrm{EL}}={\eta }_{\mathrm{EL}}{P}_{\mathrm{EL},\mathrm{e}}(t)/(H_{{\mathrm{HV},\mathrm{H}}_2})\\ {P^{\prime }}_{\mathrm{EL},\mathrm{e}}(t)=P_{\mathrm{EL},\mathrm{e}}(t)/{\eta }_{\text{EL\_DC}}\end{array}\right.$$

(10)

where $n_{\mathrm{EL}}$ represents the hydrogen production efficiency of the electrolyzer, $H_{{\mathrm{HV},\mathrm{H}}_2}$ denotes the higher heating value of hydrogen, and ${\eta }_{\text{EL\_DC}}$ refers to the efficiency of the electrolyzer converter.

The relationship between the electric power P_EL,e provided by the DC bus to the electrolyzer and the power used by the electrolyzer for heat production P_EL,h can be expressed as:

$$P_{\mathrm{EL},\mathrm{h}}(t)=(1-{\eta }_{\mathrm{EL}})P_{\mathrm{EL},\mathrm{e}}(t)$$

(11)

The thermal power output of the electrolyzer to the hot bus P′_EL,h can be expressed as:

$${P^{\prime }}_{\mathrm{EL},\mathrm{h}}(t)={\eta }_{\text{EL\_RE}}{P}_{\mathrm{EL},\mathrm{h}}(t)$$

(12)

where ${\eta }_{\text{EL\_RE}}$ represents the heat transfer efficiency of the fuel cell.

(2)

Modeling hydrogen energy storage

Hydrogen storage tanks are essential to improve economy and flexibility. High-pressure gaseous hydrogen storage technology is favored due to its maturity and cost advantages, so this paper adopts high-pressure energy storage. The specific model is as follows:

$$\left\{\begin{array}{l}{P}_{{\mathrm{HT},\mathrm{H}}_2}(t)=P_{{\mathrm{HT},\mathrm{H}}_2}^{\mathrm{cha}}(t){\eta }_{{\mathrm{HT},\mathrm{H}}_2}^{\mathrm{cha}}-P_{{\mathrm{HT},\mathrm{H}}_2}^{\mathrm{dis}}(t)/{\eta }_{{\mathrm{HT},\mathrm{H}}_2}^{\mathrm{dis}}\\ S_{{\mathrm{H}}_2}(t)=S_{{\mathrm{H}}_2}(t-1)+P_{{\mathrm{HT},\mathrm{H}}_2}(t)/P_{{\mathrm{HT},\mathrm{H}}_2}^{\max }\end{array}\right.$$

(13)

where $P_{{\mathrm{HT},\mathrm{H}}_2}(t)$ represents the hydrogen power stored in the hydrogen storage tank during the time period t, ${\eta }_{{\mathrm{HT},\mathrm{H}}_2}^{\mathrm{cha}}$ and ${\eta }_{{\mathrm{HT},\mathrm{H}}_2}^{\mathrm{dis}}$ denote the charging and discharging efficiencies of the hydrogen storage tank, $S_{{\mathrm{H}}_2}(t)$ and $S_{{\mathrm{H}}_2}(t-1)$ refer to the hydrogen storage states of the storage device during the time periods t and t − 1, and $P_{{\mathrm{HT},\mathrm{H}}_2}^{\max }$ denotes the maximum storage capacity of the hydrogen storage tank.

(3)

Modeling of hydrogen fuel cells

A fuel cell is an energy conversion device that produces electricity through an electrochemical reaction of hydrogen and oxygen. The electric heating power relationship of HFCs can be shown in the following expression:

$$\left\{\begin{array}{l}{P}_{{\mathrm{FC},\mathrm{H}}_2}(t)=P_{\mathrm{FC},\mathrm{e}}(t)+P_{\mathrm{FC},\mathrm{h}}(t)\\ P_{\mathrm{FC},\mathrm{e}}(t)={\eta }_{\mathrm{FC}}{P}_{{\mathrm{FC},\mathrm{H}}_2}(t)\\ P_{\mathrm{FC},\mathrm{h}}(t)=(1-{\eta }_{\mathrm{FC}})P_{{\mathrm{FC},\mathrm{H}}_2}(t)\\ P_{{\mathrm{FC},\mathrm{H}}_2}(t)=P_{{\mathrm{HT},\mathrm{H}}_2}^{\mathrm{diss}}(t)+P_{\mathrm{EL},\mathrm{FC}}(t)\end{array}\right.$$

(14)

where ${\eta }_{\mathrm{FC}}$ represents the operating efficiency of the fuel cell, and $P_{{\mathrm{HT},\mathrm{H}}_2}^{\mathrm{diss}}(t)$ denotes the power obtained by the fuel cell from the hydrogen storage tank during the time period t.

The power transferred by the fuel cell to the DC bus can be expressed as:

$$\left\{\begin{array}{l}{n}_{\mathrm{FC}}=P_{\mathrm{FC},\mathrm{e}}(t)/({\eta }_{\mathrm{FC}}{L}_{{\mathrm{HV},\mathrm{H}}_2})\\ {P^{\prime }}_{\mathrm{FC},\mathrm{e}}(t)={\eta }_{\text{FC\_DC}}{P}_{\mathrm{FC},\mathrm{e}}(t)\end{array}\right.$$

(15)

where $n_{\mathrm{FC}}$ represents the hydrogen consumption efficiency of the fuel cell, $L_{{\mathrm{HV},\mathrm{H}}_2}$ denotes the lower heating value of hydrogen, and ${\eta }_{\text{FC\_DC}}$ refers to the efficiency of the fuel cell converter.

The relationship between the electrical power $P_{\mathrm{FC},\mathrm{e}}$ generated by the fuel cell and the thermal power $P_{\mathrm{FC},\mathrm{h}}$ generated by the fuel cell can be expressed as:

$$P_{\mathrm{FC},\mathrm{h}}(t)=(1-{\eta }_{\mathrm{FC}})P_{\mathrm{FC},\mathrm{e}}(t)/{\eta }_{\mathrm{FC}}$$

(16)

The thermal power P’_FC,h of the fuel cell flowing to the hot bus can be expressed as:

$${P^{\prime }}_{\mathrm{FC},\mathrm{h}}(t)={\eta }_{\text{FC\_RE}}{P}_{\mathrm{FC},\mathrm{h}}(t)$$

(17)

where ${\eta }_{\text{FC\_RE}}$ represents the heat transfer efficiency of the fuel cell.

3. Economic Dispatching Model of Electrothermal Hydrogen Integrated Energy System Under Carbon Trading Mechanism

3.1. Tiered Carbon Trading Scheme

The ladder carbon trading mechanism takes carbon emission rights as a market mechanism for commodity trading, and the actual carbon emission rights trading volume participating in carbon trading is as follows:

$$E_{\mathrm{IES},\mathrm{t}}={E^{\ast }}_{\mathrm{IES}}-E_{\mathrm{IES}}$$

(18)

where $E_{\mathrm{IES},\mathrm{t}}$ represents the carbon emissions trading value of the IES, ${E^{\ast }}_{\mathrm{IES}}$ denotes the actual carbon emissions of the IES, and $E_{\mathrm{IES}}$ refers to the carbon emissions allowance of the IES.

The cost of a stepped carbon trading scheme is expressed in the following expression.

$$f_{{\mathrm{CO}}_2}^{\text{price\_}}=\left\{\begin{array}{l}\lambda E_{\mathrm{IES},\mathrm{t}} E_{\mathrm{IES},\mathrm{t}}\le x\\ \lambda (1+s)(E_{\mathrm{IES},\mathrm{t}}-x)+\lambda x x\le E_{\mathrm{IES},\mathrm{t}}\le 2x\\ \lambda (1+2s)(E_{\mathrm{IES},\mathrm{t}}-2x)+\lambda x(2+s) 2x\le E_{\mathrm{IES},\mathrm{t}}\le 3x\\ \lambda (1+3s)(E_{\mathrm{IES},\mathrm{t}}-3x)+\lambda x(3+3s) 3x\le E_{\mathrm{IES},\mathrm{t}}\le 4x\\ \lambda (1+4s)(E_{\mathrm{IES},\mathrm{t}}-4x)+\lambda x(4+6s) E_{\mathrm{IES},\mathrm{t}}\ge 4x\end{array}\right.$$

(19)

where $\lambda$ represents the base price of carbon trading, $s$ denotes the unit carbon price growth rate, $x$ refers to the carbon emission range, and $f_{{\mathrm{CO}}_2}^{\text{price\_}}$ represents the cost of the tiered carbon trading system.

3.2. Objective Function

To promote the absorption of wind, this paper considers the wind abandonment, light penalty cost, and carbon trading cost in the total operating cost of the system and establishes an economic scheduling model of an electrothermal hydrogen integrated energy system considering hydrogen storage with the minimum daily operating cost of the system as the objective function. Running costs are as follows:

$$F=\min (f_1+f_2+f_3+f_4)$$

(20)

where $F$ represents the total operational cost of the system, $f_1$ denotes the operation and maintenance cost of each device in the system, $f_2$ refers to the energy purchase cost of the system, $f_3$ represents the curtailment cost for wind and solar energy, and $f_4$ denotes the carbon trading cost of the system.

(1)

The operation and maintenance cost of each device in the system f₁

$$f_1={\displaystyle \sum _{t=1}^T[f_{\text{WT\&PV}}(t)+f_{\mathrm{HY}}(t)+f_{\mathrm{ES}}(t)+f_{\mathrm{CHP}}(t)]}$$

(21)

where T represents the scheduling period, $f_{\text{WT\&PV}}$ denotes the operation and maintenance cost of the wind–solar system, $f_{\mathrm{HY}}$ refers to the operation and maintenance cost of the hydrogen energy system, $f_{\mathrm{ES}}$ represents the operation and maintenance cost of the energy storage system, and $f_{\mathrm{CHP}}$ denotes the operation and maintenance cost of the combined heat and power system-related equipment.

$$f_{\text{WT\&PV}}(t)={\lambda }_{\mathrm{WT}}{P}_{\mathrm{WT}}(t)+{\lambda }_{\mathrm{PV}}{P}_{\mathrm{PV}}(t)$$

(22)

$$f_{\mathrm{HY}}(t)={\lambda }_{\mathrm{HL}}{P}_{\mathrm{HL}}(t)+{\lambda }_{\mathrm{FC}}{P}_{\mathrm{FC}}(t)$$

(23)

$$\begin{array}{l}{f}_{\mathrm{ES}}(t)={\lambda }_{\mathrm{HT}}((P_{\mathrm{HT}}^{\mathrm{cha}}(t)+P_{\mathrm{HT}}^{\mathrm{dis}}(t))+{\lambda }_{\mathrm{BT}}((P_{\mathrm{BT}}^{\mathrm{cha}}(t)+P_{\mathrm{BT}}^{\mathrm{dis}}(t))+\\ {\lambda }_{TST}((P_{\mathrm{TST}}^{\mathrm{cha}}(t)+P_{\mathrm{TST}}^{\mathrm{dis}}(t))+{\lambda }_G((P_G^{\mathrm{cha}}(t)+P_G^{\mathrm{dis}}(t))\end{array}$$

(24)

$$f_{\mathrm{CHP}}(t)={\lambda }_{\mathrm{GT}}{P}_{\mathrm{GT}}(t)+{\lambda }_{\mathrm{WHB}}{P}_{\mathrm{WHB}}(t)+{\lambda }_{\mathrm{GB}}{P}_{\mathrm{GB}}(t)+{\lambda }_{\mathrm{MR}}{P}_{\mathrm{MR}}(t)$$

(25)

where ${\lambda }_{\mathrm{WT}}$ and ${\lambda }_{\mathrm{PV}}$ represent the unit power operation and maintenance costs of the WT and PV systems, ${\lambda }_{\mathrm{EL}}$ and ${\lambda }_{\mathrm{FC}}$ denote the unit power operation and maintenance costs of the electrolyzer and fuel cell, ${\lambda }_{\mathrm{HT}},{\lambda }_{\mathrm{BT}},{\lambda }_{\mathrm{TST}}$ and ${\lambda }_{\mathrm{G}}$ refer to the unit power operation and maintenance costs of the hydrogen storage tank, battery, thermal storage tank, and gas storage tank (charging/discharging), ${\lambda }_{\mathrm{GT}},{\lambda }_{\mathrm{WHB}},{\lambda }_{\mathrm{GB}}$ and ${\lambda }_{\mathrm{MR}}$ represent the unit power operation and maintenance costs of the gas turbine, waste heat boiler, gas boiler, and methane reactor, $P_{\mathrm{WT}}$ and $P_{\mathrm{PV}}$ denote the operational power of the WT and PC systems, $P_{\mathrm{EL}}$ and $P_{\mathrm{FC}}$ represent the operational power of the electrolyzer and fuel cell, $P_{\mathrm{HT}}^{\mathrm{cha}}(t)$ and $P_{\mathrm{HT}}^{\mathrm{dis}}(t)$ refer to the charging/discharging power of the hydrogen storage tank during the time period t, $P_{\mathrm{BT}}^{\mathrm{cha}}(t)$ and $P_{\mathrm{BT}}^{\mathrm{dis}}(t)$ represent the charging/discharging power of the battery during the time period t, $P_{\mathrm{TST}}^{\mathrm{cha}}(t)$ and $P_{\mathrm{TST}}^{\mathrm{dis}}(t)$ denote the charging/discharging power of the thermal storage tank during the time period t, $P_{\mathrm{G}}^{\mathrm{cha}}(t)$ and $P_{\mathrm{G}}^{\mathrm{dis}}(t)$ refer to the charging/discharging power of the gas storage tank during the time period t, and $P_{\mathrm{GT}},P_{\mathrm{WHB}},P_{\mathrm{GB}}$ and $P_{\mathrm{MR}}$ represent the operational power of the gas turbine, waste heat boiler, gas boiler, and methane reactor, respectively.

(2)

The purchase cost of the system f₂

$$f_2={\displaystyle \sum _{t=1}^T({\rho }_{\mathrm{e}}{P}_{\mathrm{e},\mathrm{buy}}(t)+{\rho }_{\mathrm{g}}{P}_{\mathrm{g},\mathrm{buy}}(t))}$$

(26)

where ${\rho }_{\mathrm{e}}$ represents the unit price of electricity purchased from the higher-level power grid during the time period t, ${\rho }_{\mathrm{g}}$ denotes the unit price of natural gas purchased from the gas grid, $P_{\mathrm{e},\mathrm{buy}}(t)$ and $P_{\mathrm{g},\mathrm{buy}}(t)$ refer to the amounts of electricity and natural gas purchased during the time period t.

(3)

System of wind, light penalty cost f₃

$$f_3=\delta {\displaystyle \sum _{t=1}^T[}(P_{\mathrm{WT}}^{\max }(t)-P_{\mathrm{WT}}(t))+(P_{\mathrm{PV}}^{\max }(t)-P_{\mathrm{PV}}(t))]$$

(27)

where $\delta$ represents the unit curtailment cost for wind and solar energy, $P_{\mathrm{WT}}^{\max }(t)$ and $P_{\mathrm{PV}}^{\max }(t)$ denote the forecasted values of wind and solar power.

(4)

The carbon trading costs of the system $f_4$ are shown in Equation (19) above.

3.3. Constraint Condition

(1)

Wind–power constraint

$$\left\{\begin{array}{l}0\le P_{\mathrm{WT}}(t)\le P_{\mathrm{WT}}^{\max }(t)\\ 0\le P_{\mathrm{PV}}(t)\le P_{\mathrm{PV}}^{\max }(t)\end{array}\right.$$

(28)

where $P_{\mathrm{WT}}^{\max }(t)$ and $P_{\mathrm{PV}}^{\max }(t)$ represent the upper limits of the wind and solar output power, respectively.

(2)

Electric hydrogen production constraints

$$\left\{\begin{array}{l}{P}_{\mathrm{EL},\mathrm{e}}^{\min }\le P_{\mathrm{EL},\mathrm{e}}(t)\le P_{\mathrm{EL},\mathrm{e}}^{\max }\\ \Delta P_{\mathrm{EL},\mathrm{e}}^{\min }\le P_{\mathrm{EL},\mathrm{e}}(t+1)-P_{\mathrm{EL},\mathrm{e}}(t)\le \Delta P_{\mathrm{EL},\mathrm{e}}^{\max }\end{array}\right.$$

(29)

where $P_{\mathrm{EL},\mathrm{e}}(t)$ represents the electrical energy input to the electrolyzer (EL) during the time period t, $P_{\mathrm{EL},\mathrm{e}}^{\max }$ and $P_{\mathrm{EL},\mathrm{e}}^{\min }$ denote the upper and lower limits of the electrical energy input to the electrolyzer, $\Delta P_{\mathrm{EL},\mathrm{e}}^{\max }$ and $\Delta P_{\mathrm{EL},\mathrm{e}}^{\min }$ refer to the upper and lower limits of the electrolyzer’s ramp-up capacity.

(3)

Hydrogen fuel cell confinement

$$\left\{\begin{array}{l}{P}_{{\mathrm{FC},\mathrm{H}}_2}^{\min }\le P_{{\mathrm{FC},\mathrm{H}}_2}(t)\le P_{{\mathrm{FC},\mathrm{H}}_2}^{\max }\\ \Delta P_{{\mathrm{FC},\mathrm{H}}_2}^{\min }\le P_{{\mathrm{FC},\mathrm{H}}_2}(t+1)-P_{{\mathrm{FC},\mathrm{H}}_2}(t)\le \Delta P_{{\mathrm{FC},\mathrm{H}}_2}^{\max }\\ {\kappa }_{\mathrm{FC}}^{\min }\le P_{\mathrm{FC},\mathrm{h}}(t)/P_{\mathrm{FC},\mathrm{e}}(t)\le {\kappa }_{\mathrm{FC}}^{\max }\end{array}\right.$$

(30)

where $P_{{\mathrm{FC},\mathrm{H}}_2}(t)$ represents the hydrogen energy input to the fuel cell during the time period t, $P_{{\mathrm{FC},\mathrm{H}}_2}^{\max }$ and $P_{{\mathrm{FC},\mathrm{H}}_2}^{\min }$ denote the upper and lower limits of the hydrogen energy input to the fuel cell, $\Delta P_{\mathrm{FC},\mathrm{e}}^{\max }$ and $\Delta P_{\mathrm{FC},\mathrm{e}}^{\min }$ refer to the upper and lower limits of the fuel cell’s ramp-up capacity, ${\kappa }_{\mathrm{FC}}^{\max }$ and ${\kappa }_{\mathrm{FC}}^{\min }$ represents the upper and lower limits of the electric-to-thermal ratio of the fuel cell.

(4)

Methane reactor confinement

$$\left\{\begin{array}{l}{P}_{{\mathrm{MR},\mathrm{H}}_2}^{\min }\le P_{{\mathrm{MR},\mathrm{H}}_2}(t)\le P_{{\mathrm{MR},\mathrm{H}}_2}^{\max }\\ \Delta P_{{\mathrm{MR},\mathrm{H}}_2}^{\min }\le P_{{\mathrm{MR},\mathrm{H}}_2}(t+1)-P_{{\mathrm{MR},\mathrm{H}}_2}(t)\le \Delta P_{{\mathrm{MR},\mathrm{H}}_2}^{\max }\end{array}\right.$$

(31)

where $P_{{\mathrm{MR},\mathrm{H}}_2}(t)$ represents the hydrogen energy input to the methane reactor during the time period t, $P_{{\mathrm{MR},\mathrm{H}}_2}^{\max }$ and $P_{{\mathrm{MR},\mathrm{H}}_2}^{\min }$ denote the upper and lower limits of the hydrogen energy input to the methane reactor, $\Delta P_{{\mathrm{MR},\mathrm{H}}_2}^{\max }$ and $\Delta P_{{\mathrm{MR},\mathrm{H}}_2}^{\min }$ refer to the upper and lower limits of the gas boiler ramp-up capacity.

(5)

Energy storage constraint Energy storage constraint

$$\left\{\begin{array}{l}0\le P_{\mathrm{ES},n}^{\mathrm{cha}}(t)\le B_{\mathrm{ES},n}^{\mathrm{cha}}(t)P_{\mathrm{ES},n}^{\max }\\ 0\le P_{\mathrm{ES},n}^{\mathrm{dis}}(t)\le B_{\mathrm{ES},n}^{\mathrm{dis}}(t)P_{\mathrm{ES},n}^{\max }\\ S_n(1)=S_n(\mathrm{T})\\ B_{\mathrm{ES},n}^{\mathrm{cha}}(t)+B_{\mathrm{ES},n}^{\mathrm{dis}}(t)=1\\ S_n^{\min }\le S_n(t)\le S_n^{\max }\end{array}\right.$$

(32)

where $P_{\mathrm{ES},n}^{\mathrm{cha}}$ and $P_{\mathrm{ES},n}^{\mathrm{dis}}$ represent the charging and discharging power of the n n-th type of energy storage device (hydrogen storage, thermal storage, battery storage, gas storage), $P_{\mathrm{ES},n}^{\max }$ denotes the maximum charging and discharging power for the n-th energy storage device during one cycle, $B_{\mathrm{ES},n}^{\mathrm{cha}}(t)$ and $B_{\mathrm{ES},n}^{\mathrm{dis}}(t)$ are binary variables that indicate the charging and discharging states of the n-th energy storage device during the time period t, where $B_{\mathrm{ES},n}^{\mathrm{cha}}(t)=0$ and $B_{\mathrm{ES},n}^{\mathrm{dis}}(t)=1$ represents the discharging state. $S_n(t)$ refers to the capacity of the n-th energy storage device during the time period t, $S_n^{\max }$ and $S_n^{\min }$ represent the upper and lower limits of the capacity of the n-th energy storage device, respectively.

(6)

CHP constraint

$$\left\{\begin{array}{l}{P}_{\mathrm{CHP},\mathrm{e}}={\eta }_{\mathrm{CHP}}^{\mathrm{e}}{P}_{\mathrm{CHP},\mathrm{g}}(t)\\ P_{\mathrm{CHP},\mathrm{h}}={\eta }_{\mathrm{CHP}}^{\mathrm{h}}{P}_{\mathrm{CHP},\mathrm{g}}(t)\\ 0\le P_{\mathrm{CHP}}(t)\le P_{\mathrm{CHP}}^{\max }\\ \Delta P_{\mathrm{CHP}}^{\min }\le P_{\mathrm{CHP}}(t+1)-P_{\mathrm{CHP}}(t)\le \Delta P_{\mathrm{CHP}}^{\max }\\ {\kappa }_{\mathrm{CHP}}^{\min }\le P_{\mathrm{CHP},\mathrm{h}}(t)/P_{\mathrm{CHP},\mathrm{e}}(t)\le {\kappa }_{\mathrm{CHP}}^{\max }\end{array}\right.$$

(33)

where $P_{\mathrm{CHP},\mathrm{g}}(t)$ represents the amount of natural gas consumed by the CHP system during the time period t, $P_{\mathrm{CHP},\mathrm{e}}$ and $P_{\mathrm{CHP},\mathrm{h}}$ denote the electrical and thermal power inputs to the CHP system during the time period t, ${\eta }_{\mathrm{CHP}}^{\mathrm{e}}$ and ${\eta }_{\mathrm{CHP}}^{\mathrm{h}}$ refer to the electricity generation and heating efficiencies of the CHP system, $P_{\mathrm{CHP}}^{\max }$ represents the maximum output power of the CHP system, $\Delta P_{\mathrm{CHP}}^{\max }$ and $\Delta P_{\mathrm{CHP}}^{\min }$ denote the upper and lower limits of the ramp-up capacity of the CHP system, ${\kappa }_{\mathrm{CHP}}^{\max }$ and ${\kappa }_{\mathrm{CHP}}^{\min }$ represent the upper and lower limits of the electricity-to-thermal ratio of the CHP system.

(7)

Gas boiler confinement

$$\left\{\begin{array}{l}{P}_{\mathrm{GB},\mathrm{g}}^{\min }\le P_{\mathrm{GB},\mathrm{g}}(t)\le P_{\mathrm{GB},\mathrm{g}}^{\max }\\ \Delta P_{\mathrm{GB},\mathrm{g}}^{\min }\le P_{\mathrm{GB},\mathrm{g}}(t+1)-P_{\mathrm{GB},\mathrm{g}}(t)\le \Delta P_{\mathrm{GB},\mathrm{g}}^{\max }\end{array}\right.$$

(34)

where $P_{\mathrm{GB},\mathrm{g}}(t)$ represents the natural gas power input to the gas boiler during the time period t, $P_{\mathrm{GB},\mathrm{g}}^{\max }$ and $P_{\mathrm{GB},\mathrm{g}}^{\min }$ denote the upper and lower limits of the natural gas power input to the gas boiler, $\Delta P_{\mathrm{GB},\mathrm{g}}^{\max }$ and $\Delta P_{\mathrm{GB},\mathrm{g}}^{\min }$ refer to the upper and lower limits of the gas boiler’s ramp-up capacity.

(8)

Power balance constraint of the power grid

$$\left\{\begin{array}{l} P_{\mathrm{e},\mathrm{buy}}(t)+P_{\mathrm{WT}}(t)+P_{\mathrm{PV}}(t)+P_{\mathrm{FC},\mathrm{e}}(t)+P_{\mathrm{CHP},\mathrm{e}}(t)\\ =P_{\text{e\_load}}(t)+P_{\mathrm{EL},\mathrm{e}}(t)+P_{\mathrm{EB},\mathrm{e}}(t)+P_{\mathrm{ES}}^{\mathrm{e}}(t)\\ 0\le P_{\mathrm{e},\mathrm{buy}}(t)\le P_{\mathrm{e},\mathrm{buy}}^{\max }\end{array}\right.$$

(35)

where $P_{\text{e\_load}}(t)$ represents the electrical load during the time period t, $P_{\mathrm{e},\mathrm{buy}}^{\max }$ denotes the maximum power purchased from the higher-level power grid, and $P_{\mathrm{ES}}^{\mathrm{e}}(t)$ refers to the power input to the electrical storage during the time period t.

(9)

Power balance constraint of heat supply network

$$P_{\mathrm{FC},\mathrm{h}}(t)+P_{\mathrm{CHP},\mathrm{h}}(t)+P_{\mathrm{GB},\mathrm{h}}(t)+P_{\mathrm{EB},\mathrm{h}}(t)+P_{\mathrm{MR},\mathrm{h}}(t)=P_{\text{h\_load}}(t)+P_{\mathrm{ES}}^{\mathrm{h}}(t)$$

(36)

where $P_{\text{h\_load}}(t)$ represents the thermal load during the time period t, $P_{\mathrm{MR},\mathrm{h}}(t)$ denotes the reaction heat of the P2G system during the time period t, and $P_{\mathrm{ES}}^{\mathrm{h}}(t)$ refers to the power input to the thermal storage during the time period t.

(10)

Hydrogen power balance constraints

$$P_{{\mathrm{EL},\mathrm{H}}_2}(t)=P_{{\mathrm{FC},\mathrm{H}}_2}(t)+P_{\mathrm{ES}}^{{\mathrm{H}}_2}(t)$$

(37)

where $P_{\mathrm{ES}}^{{\mathrm{H}}_2}(t)$ represents the power input to the hydrogen storage during the time period t.

(11)

Power balance constraint of the gas network

$$\left\{\begin{array}{l}{P}_{\mathrm{g},\mathrm{buy}}(t)+P_{\mathrm{P}2\mathrm{G},\mathrm{g}}(t)=P_{\mathrm{GB},\mathrm{g}}(t)+P_{\mathrm{CHP},\mathrm{g}}(t)+P_{\mathrm{ES}}^{\mathrm{g}}(t)\\ 0\le P_{\mathrm{g},\mathrm{buy}}(t)\le P_{\mathrm{g},\mathrm{buy}}^{\max }\end{array}\right.$$

(38)

where $P_{\mathrm{ES}}^{\mathrm{g}}(t)$ represents the power input to the gas storage during the time period t.

3.4. Model Linearization Processing and Solving

The model constructed in this paper further introduces integer constraints on the basis of linear programming and includes nonlinear expressions such as high-order functions and variable products. It is a mixed integer nonlinear model. Because its solution efficiency is not high and it is easy to fall into the problem of local optimal solution, the model is converted into a linear form. Through this conversion, the feasibility of the model solution is ensured, and the solution efficiency is also improved so that the model can better meet the needs of actual economic dispatch calculations.

The model in this paper is built in the Matlab R2019a software environment with the help of the YALMIP toolbox for the system scheduling model. In the solution process, the CPLEX commercial solver is used to solve the model. The YALMIP toolbox integrates a variety of external optimization solvers, providing a consistent programming platform for model construction and solutions. In particular, CPLEX has significant advantages in flexibility, calculation speed, and reliability of results when dealing with linear programming problems.

(1)

Gas turbine linearization process

The problem of mixed integer nonlinear programming optimization for gas turbines of cogeneration units is solved by implementing piecewise linearization and piecewise averaging of the cogeneration model of gas turbines.

Linearization of thermal efficiency of gas turbines:

Step 1: reigning load rate $v={\displaystyle \frac{P_{\mathrm{GT},\mathrm{h}}(t)}{P_{\mathrm{GT},\mathrm{hN}}(t)}}, 0\le v\le 1$.

Step 2: The formula of heat production efficiency is transformed by piecewise linearization and simplified to a function form.

$${\eta }_{\mathrm{GT}}^{\mathrm{h}}(t)={\alpha }_{i}v, v_i\le v\le v_{i+1}=\left\{\begin{array}{l}{\alpha }_{1}v, v_1\le v\le v_2\\ {\alpha }_{2}v, v_2\le v\le v_3\\ ⋮ ⋮\\ {\alpha }_{n}v, v_n\le v\le v_{n+1}\end{array}\right.$$

(39)

In this process, the number of segments has a significant impact on the accuracy of the calculation: the more segments, the higher the accuracy of the calculation results, and the accuracy of the calculation mainly depends on the interval divided by the cubic function.

Step 3: In each segment interval, the efficiency value corresponding to the average load rate in the interval is selected as the representative value of the heat production efficiency of the internal combustion gas turbine in the interval, namely:

$${\eta }_{\mathrm{GT}}^{\mathrm{h}}(t)={\alpha }_i{\displaystyle \frac{v_i+v_{i+1}}{2}}, v_i\le v\le v_{i+1}$$

(40)

Through the above treatment, the simplified expression of gas turbine heat production efficiency is obtained, which effectively reduces the complexity of calculation. Similarly, the electricity generation efficiency of a gas turbine is as follows:

$${\eta }_{\mathrm{GT}}^{\mathrm{e}}(t)={\alpha }_i{\displaystyle \frac{v_i+v_{i+1}}{2}}, v_i\le v\le v_{i+1}$$

(41)

(2)

The actual carbon emission model linearization process

Using piecewise linearization:

Step 1 The original function is divided into n segments whose segment points are [r₁, r_2, … r_n+1].

Step 2 Continuous variables [w₁, w_2, … w_n+1] and 0–1 variables [z₁, z_2, … z_n] are introduced, and the following equation is satisfied.

$$\left\{\begin{array}{l}{w}_1+w_2+\cdots +w_{n+1}=1\\ z_1+z_2+\cdots +z_n=1\\ w_1\ge 0,w_2\ge 0,\cdots w_{n+1}\ge 0\\ w_1\le z_1,w_2\le z_1+z_2,\cdots ,w_{n+1}\le z_n\end{array}\right.$$

(42)

Step 3 The nonlinear function can be expressed in the linearized form of the following formula.

$$\left\{\begin{array}{l}{P}_{\mathrm{e},\mathrm{buy}}={\displaystyle \sum _{i=1}^{n+1}{w}_i{r}_i}\\ E_{\mathrm{e},\mathrm{buy},\mathrm{a}}={\displaystyle \sum _{i=1}^{n+1}{w}_i{E}_{\mathrm{e},\mathrm{buy},\mathrm{a}}(r_i)}\end{array}\right.$$

(43)

Formula (19) cascade carbon trading model is itself a piecewise function, so step 1 can be omitted and linearized in combination with step 2 and step 3.

Finally, using CPLEX version 12.10.0 solver to solve in MATLAB environment, the economic scheduling results can be obtained.

4. Case Study

In this chapter, the benefits of carbon trading mechanism, hydrogen energy technology, cogeneration system, and electric–gas coupling element are analyzed and verified in detail by a series of examples. The carbon trading mechanism promotes emission reductions by incentivizing cleaner technologies. Hydrogen energy technology offers a sustainable fuel alternative, aiding decarbonization. The cogeneration system enhances energy efficiency by producing both electricity and heat. The electric–gas coupling element fosters integration between power and gas networks, improving system flexibility and reliability.

4.1. System Data

With 24 h as a dispatching cycle, the gas purchase price is 0.35 (CNY/kW·h), and the cost coefficient of wind abandonment and light is 0.5 (CNY/kW·h). The parameters of the main equipment in the system are listed in

Table 1. Equipment parameter.

Equipment	Capacity/kW	Efficiency	Climbing Constraint	O and m Cost Factor Element/(kw·h)
Wind turbine	-	-	-	0.018
Photovoltaic	-	-	-	0.008
Electrolyser	500	87%	20%	0.016
Fuel cell	250	95%	20%	0.0128
Electric boiler	800	80%	20%	0.011
Gas boiler	800	95%	20%	0.025
Combined heat and power	600	92%	20%	0.04
Methane reactor	250	60%	20%	0.016

, the parameters of the energy storage equipment are listed in

Table 2. Energy storage parameter.

Equipment	Capacity/kW	Capacity Lower Bound	Upper Capacity Constraint	Climbing Constraint	O and m Cost Factor Element/(kw·h)
Hydrogen storage tan	200	10%	90%	20%	0.016
Thermal storage tan	500	10%	90%	20%	0.016
Air storage tank	150	10%	90%	20%	0.016
Battery	450	10%	90%	20%	0.018

, the parameters of the TOU are listed in

Table 3. Time-of-use tariff.

Period Type	Time Frame	Electricity Price/ [CNY(kW·h)−1]
Valley interval	01:00—07:00, 23:00—24:00	0.38
Meantime segment	08:00—11:00, 15:00—18:00	0.68
Peak hour	12:00—14:00, 19:00—22:00	1.20

, the parameters of the actual carbon emission model are listed in

Table 4. Actual carbon emission model parameters.

Power Consumption Type			Gas-Consuming Type
a1	b1	c1	a2	b2	c2
36	−0.38	0.0034	3	−0.004	0.001

, and the parameters of the carbon trading model are listed in

Table 5. Parameters of ladder carbon trading model.

Parameter	Numerical Value
Carbon trading base price	250 CNY/t
Length of the carbon trading band	2 t
Carbon trading growth rate	0.25

.

The forecast curves of wind–power output and various loads are shown in Figure 3 [7,8].

4.2. Case 1: Benefit Analysis of Carbon Trading Mechanism

4.2.1. Scenario Configuration and Analysis of Case 1

This section discusses the impact of the carbon trading mechanism on the system. To verify the effectiveness of this mechanism, on the premise of establishing an economic scheduling model, the following three scenarios are set for research:

Scenario 1: Carbon trading schemes are not considered.

Scenario 2: Consider traditional carbon trading schemes.

Scenario 3: Consider a tiered carbon trading scheme.

According to

Table 6. Scheduling results of each scenario of Case 1.

Cost/CNY	Scenario 1	Scenario 2	Scenario 3
Total cost	14,757.94	12,065.80	11,456.83
Operation and maintenance cost	1087.13	1048.20	1104.50
Power purchase cost	1646.50	2254.21	2514.25
Gas purchase cost	6170.48	6024.92	5525.2
Abandonment cost	0	0	0
Carbon trading cost	5853.83	2738.47	2312.88

, in Scenario 1, the cost of carbon trading is most significant because in most time slots during the dispatch cycle, the price of natural gas is lower than the price of electricity, so the system tends to maximize the purchase of natural gas to improve the efficiency of combined heat and power generation units. However, the high output of combined heat and power generation units will cause the system’s carbon emissions to rise significantly, resulting in the system’s carbon emission quota falling far short of the current carbon emission standards, thereby pushing up the cost of carbon trading. In Scenario 2, compared with the savings in gas purchase substitution for electricity purchase in the traditional carbon trading system, the cost of carbon trading is higher. The system adopts the strategy of increasing electricity purchases to reduce carbon trading costs. This shows that the cost of gas purchase is lower than in Scenario 1, but the cost of electricity purchase has increased, which to some extent controls carbon emissions. This mechanism uses a base price to calculate the cost of carbon trading, so the cost of carbon trading is smaller than in Scenario 3, and its total operating cost is the lowest among the three scenarios. In Scenario 3, a tiered carbon trading mechanism results in a lower total cost compared to both Scenarios 1 and 2. Under the traditional carbon trading scheme of Scenario 3, the carbon trading costs are higher than the savings from substituting gas for electricity purchases. As a result, the system responds by increasing electricity purchases to reduce carbon trading expenses. This strategy leads to lower gas costs compared to Scenarios 1 and 2 but incurs higher electricity costs. Nevertheless, this shift in energy procurement helps to control carbon emissions to a certain extent.

4.2.2. Parameter Sensitivity Analysis of Cascade Carbon Trading Mechanism

In this simulation, a stepped carbon trading price system is adopted when implementing carbon emission rights trading, with a base price of 250 CNY/t and an interval length of 2 t. The growth rate of the price is set at 0.25. Then, the impact of the carbon trading base price, interval length, and price growth rate on the system’s total cost and carbon emissions is analyzed in detail. By comprehensively analyzing and optimizing these parameters, it is hoped that a more economical and environmentally friendly IES operation mode can be found to better adapt to the future development needs of the energy system.

According to Figure 4, as the base price of the step-by-step carbon trading mechanism rises, the system’s total cost generally shows an upward trend, while the corresponding carbon emissions show a gradual reduction trend. Specifically, when the carbon trading base price is below approximately 260 CNY/t, the rise in the base price directly raises the cost weight of carbon emissions, thereby enhancing the cost effect of carbon trading. Due to the consideration of carbon trading costs, the system needs to reduce carbon emissions to lower the overall cost and thus achieve a gradual reduction in carbon emissions. However, when the carbon trading base price breaks through the threshold of 260 CNY/t, as the price continues to rise, the system’s energy output allocation will tend to stabilize, thereby making the carbon emissions level also reach a relatively stable state. Therefore, in this stage, the sensitivity of carbon emissions to changes in the base price of carbon trading is significantly reduced.

According to Figure 5, as the interval length increases, carbon emissions grow proportionally, while the total system cost shows a decreasing trend. When the interval range of the stepped carbon trading is set to [0.5, 2], the total system cost is relatively high due to the tight supply of carbon quotas, and the carbon emission level remains at a low level. This is because the system needs to purchase more carbon quotas to maintain operation, resulting in a greater impact of the stepped carbon trading mechanism on HEES’s carbon emission right trading. As the interval range expands to [2, 4), the length of the stepped carbon trading mechanism increases, and the system obtains more free carbon quotas accordingly. This leads to a reduction in the high-priced carbon emission quotas that need to be purchased, thereby weakening the carbon trading mechanism’s constraint on carbon emissions. However, when the interval range further expands to [4, 8), carbon emissions trading is mainly determined by the base price and low-priced quotas. At this point, the impact of interval length on carbon emissions becomes smaller and smaller, and carbon emissions tend to stabilize. This shows that in a larger interval range, the carbon trading mechanism’s regulation of carbon emissions gradually weakens.

According to Figure 6, when the price growth rate is between [0, 0.35), as the price growth rate of the stepwise carbon trading system increases, carbon emissions decrease while system operating costs rise. This is because the carbon trading price increases, and to ensure the economic feasibility of the system, the system will limit the output of carbon-emitting units, thereby reducing carbon emissions. When the price growth rate is between [0.35, 8), as the carbon emission cost gradually rises, the output of each power generation unit begins to show a stable trend. In this process, carbon emissions are effectively reduced, but the total cost shows a trend of continuously rising and eventually stabilizing.

Based on the analysis of Figure 7, Figure 8 and Figure 9, the following conclusions can be drawn: When conducting carbon emission right allocation trading, a higher carbon trading base price, a higher carbon trading price growth rate, and a smaller step interval length should be adopted. However, although this strategy can effectively improve the energy efficiency and carbon emission control level of IES, it inevitably leads to an increase in the total operating cost of IES. Therefore, when considering using the carbon trading mechanism to optimize the low-carbon and economic dispatch of IES, a reasonable and feasible carbon trading base price, stepwise trading interval length, and carbon trading price growth rate must be formulated, and the optimal balance point must be found to achieve the goal of environmentally friendly and economical energy utilization.

4.3. Case 2: Benefit Analysis of Hydrogen Technology and Cogeneration System

4.3.1. Scenario Configuration and Analysis of Case 2

To reflect the scheduling advantages of hydrogen energy storage technology and cogeneration system, the following three operating scenarios are set up:

Scenario 4: Hydrogen-free technology with cogeneration system.

Scenario 5: Hydrogen technology without CHP system.

Scenario 6: Hydrogen technology, cogeneration system.

According to

Table 7. Scheduling results of each scenario of Case 2.

Cost/CNY	Scenario 4	Scenario 5	Scenario 6
Total cost	20,230.94	16,521.44	15,627.83
Operation and maintenance cost	1073.05	1023.76	1104.50
Power purchase cost	4258.47	3941.51	3514.25
Gas purchase cost	5594.44	5701.57	5696.20
Abandonment cost	54.55	17.55	0
Carbon trading cost	9250.43	5837.06	5312.88

, in Scenario 4, due to the lack of P2G, the system relies entirely on external gas networks to meet the gas load demand, which increases the actual carbon emission burden and increases the carbon trading cost. In Scenario 5, the hydrogen energy storage device reduces the amount of wind power curtailment, reducing the carbon trading cost and total cost relative to Scenario 4. In Scenario 6, during the peak heat load period, the hydrogen fuel cell will perform heat generation operations, which reduces the amount of natural gas consumed by the combined heat and power unit for heat generation, thereby reducing the gas purchase volume, reducing the gas purchase cost and carbon trading cost. At the same time, this measure also effectively reduces carbon emissions, making it an effective means of achieving the lowest carbon trading cost and total cost.

After comparing and analyzing, it was observed that the introduction of hydrogen equipment in Scenarios 5 and 6 not only effectively promoted the utilization of wind power but also significantly reduced the total operating cost and carbon emissions of the system. These improvements made the system operation more economical and efficient and also achieved more environmentally friendly operation goals. Compared with Scenario 5 and Scenario 4, it can be seen that the total operating cost of the system decreased by 18.3%, and the carbon trading cost decreased by CNY 3413.37, a reduction of 36.9%. The comparison between Scenario 6 and Scenario 4 shows that the total operating cost of the system decreased by 22.8%. Among them, the procurement cost decreased by CNY 744.22, a reduction of 17.5%; the carbon trading cost decreased by CNY 3937.55, a reduction of 42.6%. It is worth noting that the cost of wind power curtailment was significantly reduced, reflecting a reduction in wind curtailment and a substantial increase in energy utilization efficiency, making the system operation more economical and environmentally friendly.

4.3.2. Analysis of Scenery Absorption Ability

The economic dispatch model in Scenario 4 does not include hydrogen technology-related equipment in consideration of its optimal layout and deployment strategy during the IES operation. In contrast, Scenario 6 represents the integrated economic dispatch model constructed in this paper that incorporates hydrogen energy technology. The PV output is free from the phenomenon of abandoned light during the peak electric load hours.

The power conditions of the three scenario WTGs in actual operation are shown in Figure 7, where the predicted power of the turbines is higher than the actual during the periods 01:00 to 08:00 and 21:00 to 24:00. This is since electricity demand is not high at this time, but the electric storage is full, and it is difficult to connect to the wind power, which leads to severe wind abandonment. Hydrogen technology is better able to cope with the instability of wind energy and is more effective in absorbing wind energy than CHP systems.

4.3.3. Analysis of System Power Scheduling Results in Different Scenarios

Figure 8a shows the electric power balance for Scenario 4. During the low electric load hours, the system mainly relies on wind and CHP units to meet the power demand; however, when the power generated by wind power exceeds the actual demand, the electric storage units reach saturation, resulting in a large amount of wind power being abandoned. During peak electrical load hours, the system relies on external power purchases to make up for the shortfall in supply as the wind and PV capacity is insufficient to meet the load demand, which may increase the system operating costs and pose a challenge to the stability and reliability of the energy supply. Figure 8b shows the thermal power balance for Scenario 4, especially during 02:00–07:00 and 15:00–20:00, when thermal loads are high, and the system needs more thermal energy to meet the demand. CHP improves energy efficiency by generating both electricity and heat simultaneously, and the gas boiler acts as a backup thermal device to provide thermal support when needed to ensure the system supply and demand balance.

A power balance diagram for Scenario 5 is shown in Figure 9. In terms of the power balance, the electrolyzer can convert excess power in the low valley into hydrogen energy, thus enabling efficient storage of surplus wind power. During 15:00–20:00 h, the power demand peaks, and a large amount of power is purchased from the higher grid to maintain the supply–demand balance. In terms of heat balance, especially at the peak of heat load, hydrogen fuel cells share part of the heat load by discharging, thus effectively reducing the burden of heat output from gas boilers.

Scenario 6 electrical power balance is shown in Figure 10a. The electrical energy required by the system’s electrical loads and power-consuming equipment mainly comes from purchased electricity, CHP, PV, WT, and hydrogen FC and BT devices. In this paper, EL is introduced to realize the conversion of electric energy to hydrogen energy, and the converted hydrogen energy has two application pathways: part of it is converted to natural gas through the reaction of MR with carbon dioxide, and the other part is stored or directly converted to heat and electricity through the hydrogen FC. The remaining hydrogen energy is safely stored in the HST for future use. Therefore, electrical energy can be converted and stored under the premise of peak wind power output and meeting the power demand of the system, which in turn enhances the efficiency of renewable energy utilization. However, during the hours of 07:00–09:00 and 15:00–20:00, the power generation drops while the power demand climbs, resulting in the power supply from the HFC and storage devices not being able to fully satisfy the demand, and therefore, the power needs to be purchased from the grid to fill the power gap. To balance the power demand and supply, the system uses CHP for power supply at the right time to ensure the stable operation of the power system.

Scenario 6 thermal power balance is shown in Figure 10b. To meet the system’s thermal energy demand, CHP, GB, and TST work together. The system thermal load demand is low at 13:00–15:00, and the TST stores heat to reduce energy abandonment. At 02:00–09:00 and 18:00–22:00, the CHP takes part in the thermal load. Especially at 01:00–02:00 and 23:00–24:00, the system heat load demand is high; at this time, the hydrogen FC is exothermic to meet the system heat power balance demand. It is worth noting that the direct generation of electricity and heat by the hydrogen fuel cell, compared with the generation of natural gas by MR and then electricity by CHP and GB, significantly reduces the loss of energy in the process of gradient utilization, which in turn improves the overall efficiency of energy utilization.

4.4. Case 3: Benefit Analysis of P2G Coupling Elements

4.4.1. Scheduling Results of Each Scenario of Case 3

Scenario 7: Electricity-to-gas equipment not considered.

Scenario 8: Conventional P2G equipment without consideration of refining it into two stages.

Scenario 9: P2G refined into a two-stage operation with a combination of electrolyzer, hydrogen fuel cell, and methane reactor considered.

According to the analysis of the scheduling results in

Table 8. Scheduling results of each scenario.

Cost/CNY	Scenario 7	Scenario 8	Scenario 9
Total cost	20,230.94	19,712.61	15,627.83
Operation and maintenance cost	1073.05	1098.28	1104.50
Power purchase cost	4258.47	4704.97	3514.25
Gas purchase cost	5594.44	5391.30	5696.20
Abandonment cost	54.56	0	0
Carbon trading cost	9250.43	8518.06	5312.88

, compared to Scenario 7, the conventional P2G equipment is introduced in Scenario 8, and the results show the positive effect of this equipment in optimizing the system operation and reducing the cost of carbon trading. In addition, the P2G equipment converts the excess electricity generated from wind and light energy into H2 through the electrolysis of water and generates natural gas in the methane reactor to supply gas equipment, which promotes energy saving and emission reduction of the system and enhances the capacity of renewable energy consumption.

In Scenario 9, the conventional P2G equipment in Scenario 8 is replaced with a two-stage P2G technology. Scenario 9 shows a reduction in both total cost and carbon trading cost compared to Scenario 7. This is because the HFC can efficiently utilize the hydrogen produced when the system is rich in electrical energy for electrical energy production, which in turn achieves a significant reduction in the cost of purchased electricity. At the same time, HST enhances the flexibility of hydrogen utilization, further contributing to the low-carbon and economic operation of the system. In the end, the total operating cost of Scenario 9 becomes the lowest among the three scenarios, with a reduction of 22.8 percent compared to Scenario 7 and 21.8 percent compared to Scenario 8.

4.4.2. Analysis of System Power Scheduling Results in Each Scenario

Scenario 7, Scenario 8, and Scenario 9 electric power balance diagrams are shown in Figure 10a and Figure 11a,b. The following conclusions are drawn from the analysis: in Scenario 7, the system electrical load is low during the night time from 0:00 to 7:00 h since no P2G device is incorporated. In this case, even though part of the wind power is stored in the energy storage device, a large amount of wind power load cannot be consumed by the system, resulting in a serious wind abandonment phenomenon, which makes Scenario 7 have the highest wind abandonment cost among the three scenarios. In contrast, Scenario 8 and Scenario 9 have significantly higher wind power utilization. The P2G device allows excess electricity to be converted into natural gas, which can be supplied to the GT for consumption as well as stored in the storage facility, which not only reduces the loss of natural gas during transportation but also reduces the cost of energy purchased by the IES, thus further optimizing the total cost structure of the system.

5. Conclusions

Firstly, starting with the IES of electricity, heat, and hydrogen, a coordinated operation model encompassing power-to-hydrogen, hydrogen storage, HFC, and CHP systems is established to achieve multi-energy coupling and complementarity. By leveraging the synergy between hydrogen storage units and the CHP system, wind curtailment and carbon trading costs are effectively reduced, significantly enhancing the system’s economic benefits and environmental value. Secondly, the introduction of P2G technology facilitates the efficient utilization of renewable energy. The P2G operational process is analyzed in stages, further improving energy conversion efficiency and promoting energy conservation and emissions reduction. Lastly, a parametric analysis of the tiered carbon trading mechanism is conducted. Scientifically and reasonably setting relevant parameters helps achieve the dual goals of efficient energy utilization and environmental protection. When exploring optimization pathways for the tiered carbon trading mechanism, P2G equipment is considered a critical carbon absorption unit. This not only significantly reduces system operating costs but also minimizes carbon trading expenses, thereby enhancing the environmental friendliness and sustainability of the entire system.