Multi‐scale coordinated optimal dispatch method of electricity‐thermal‐hydrogen integrated energy systems

Abstract

To achieve carbon neutrality, renewable energy‐based power systems and hydrogen are increasingly being promoted. A novel electricity‐thermal‐hydrogen integrated energy system that combines new energy generation, multi‐source load, and multiple energy storage is proposed by the authors. To address uncertainties in new energy output, and issues of untimely unit regulation response and large planning tracking errors, a multi‐scale scheduling method based on model predictive control (MPC) was proposed. In the day‐ahead dispatching stage, an optimal economic dispatching model was established with the lowest system operation cost as the optimisation objective. The model considers equipment investment, operation, maintenance, and peak‐to‐valley differences in electricity prices. In the intraday dispatching stage, an MPC‐based intraday rolling optimisation correction strategy was proposed to cope with contact line power fluctuations caused by prediction errors of new energy and multi‐source load. This strategy combines time‐domain rolling and feedback correction of the real‐time system state to eliminate the influence of uncertainty factors in the microgrid. The MPC‐based intraday rolling optimal scheduling model was established in the form of a discrete state space and transformed into a quadratic planning problem to improve the efficiency and accuracy of the model solution. Finally, a typical microgrid was used as an example to verify the effectiveness of the proposed method. Results show that the contact line tracking error can be within 0.025 kW, and the single scheduling time was within 0.14 s.

INTRODUCTION

In the global pursuit of carbon neutrality, the need for renewable energy sources (RES) is rapidly increasing, making RES-based power systems an inevitable trend [1]. However, the inherent randomness and uncertainty associated with RES, such as wind and photovoltaic, make stable grid operation a challenge. To address this issue, an integrated energy system (IES) has emerged as a promising solution and has gained significant attention in recent years. IES leverages spatiotemporal coupling and complementary substitution between various forms of energy [2] to achieve multi-energy complementarity, delivering a sustainable and reliable energy supply [3]. By integrating multiple energy networks to cater to electricity, heating, and natural gas demands [4], IES enhances the flexibility and economy of the overall system operation.

The development and promotion of hydrogen are crucial in achieving green and low-carbon energy systems [5]. Hydrogen fuel cells are known for their high energy density and long equipment run time, emitting no carbon during operation [6]. In recent years, major automobile manufacturers such as Toyota, Honda, and Hyundai have started producing hydrogen fuel cell vehicles to support their sustainability goals [7]. Furthermore, studies have been conducted to integrate hydrogen fuel cells into ship microgrids to reduce greenhouse gas emissions [8]. As the demand for hydrogen in the energy market has been increasing, it is important to consider the challenges associated with transporting hydrogen over long distances. Electrolysis of hydrogen is a promising approach to obtaining hydrogen, especially when renewable energy sources such as photovoltaic and wind power are used, resulting in relatively high energy efficiency (21.9%–29.2%) [9]. Therefore, combining hydrogen production in microgrids is a feasible option. In Ref. [10], the minimum cost combination of hydrogen generation, storage, transmission, and compression facilities was studied to meet hydrogen demand while coupling to the electricity system through tariffs. In Ref. [11], the study focussed on the use of electrolytic hydrogen facilities to supply the natural gas grid, mobile sector, and grid using renewable electricity. Ref. [12] proposed a model for hydrogen and electricity energy sharing in an integrated energy system.

Hydrogen tank energy storage is also a promising technology for grid energy dispatch. While battery energy storage is of great interest due to its high energy density and low maintenance, frequent charging and discharging can lead to wear and tear, reducing the cycle life and storage capacity of batteries, and increasing operating costs [3]. In contrast, hydrogen systems present a broad range of applications due to their high storage efficiency, low emissions, and versatility. High-pressure hydrogen storage tanks are among the most commonly used hydrogen storage devices, capable of increasing the hydrogen pressure from 20 to 45 MPa during the filling process [9]. The use of hydrogen storage tanks can enable flexible and low-cost filling and discharging, making them a high-quality means of energy storage. The stored hydrogen can be subsequently converted to electricity using fuel cells [11].

Various system designs for integrated energy have been developed and matured for different microgrid-specific energy forms. Ref. [3] presented a coupled multi-carrier energy supply framework for biogas-solar-wind hybrid renewable systems, and Ref. [13] designed a micro-energy network based on rural biomass waste energy conversion systems (BWs). In the context of community-integrated energy systems (CIES), Ref. [2] proposed a two-stage multi-timescale scheduling control strategy based on model predictive control, and [14] suggested a flexible load-integrated energy system for coal mines. Ref. [8] proposed a synergistic operation strategy for ship microgrids and hybrid propulsion systems, and Ref. [15] investigated the optimal scheduling strategy for systems that incorporate hydrogen or upgraded biogas as the gas injection gas. Despite the gradual increase in research on energy systems incorporating hydrogen, a coordinated control scheme between an offshore wind farm and a hydrogen management system (HMS) was proposed by Ref. [16] to reduce the adverse effects of wind variability and to enable the coordinated operation of wind power generation by combining electrolytic hydrogen, hydrogen storage tanks, and hydrogen cell fuel.

There are various approaches for synthesising energy system optimisation algorithms, including quadratic programming, stochastic mixed-integer programming, and reinforcement learning. Meta-inspired methods have also been applied in energy scheduling optimisation to find the global optimum. Ref. [17] used meta-inspired ideas to solve scheduling problems, and Ref. [18] used an improved non-dominated ranking genetic algorithm with an adaptive simulated binary crossover to solve a multi-objective optimisation model for integrated energy. Ref. [15] proposed a method and framework for solving the economic scheduling model of REGS using a particle swarm algorithm, and Ref. [19] proposed an improved COOT novel intelligent optimisation algorithm to enhance the convergence performance and solution speed of the solution problem. However, these methods do not consider the stochastic nature of the optimisation operation process, and uncertainty in prediction is also a challenge that needs to be addressed in the scheduling process. Although increasing the system reserve is a traditional solution, it is difficult to determine the exact amount of reserve needed to ensure the safety of the system, and the outcomes tend to be conservative [20].

Scenario generation is a widely adopted approach for addressing uncertainty in power system operation planning. To model the uncertainty of the system, a Monte Carlo simulation is employed to generate a set of possible scenarios in Ref. [21]. In recent research, robust optimisation has emerged as a general direction for achieving robust operation planning of power systems. Ref. [8] proposed a two-stage robust optimisation method for ship microgrid operation planning. Their approach utilised a two-level column constraint generation (C&CG) algorithm to solve the optimisation model. Ref. [22] developed a two-stage distributed robust optimisation model that employs the Wasserstein metric. Ref. [23] transformed the robust optimisation problem into a mixed integer linear programming problem using pairwise theory. For a multi-time robust scheduling system with a rolling scheduling mechanism, Ref. [20] proposed a new framework. Additionally, Ref. [24] proposed a robust energy and reserve scheduling model, while Ref. [25] used a distributed robust optimisation (DRO) approach to evaluate the operating cost expectations affected by renewable energy sources uncertainty.

Some new methods have also been developed in recent years to cope with the uncertainty in the operation of power systems. Ref. [26] proposed a real-time optimisation algorithm based on approximate dynamic programming (ADP) to consider the Markov decision process for the dynamic process of combined cycle gas turbines. Ref. [27] proposed a relaxed depth generative adversarial network method that replaces the traditional combinatorial approach with a multiple time-scale combinatorial framework. Ref. [1] proposed a digital twin (DT)-based data model fusion scheduling strategy for building parameter uncertainty. Model predictive control (MPC), based on the idea of rolling optimisation and feedback correction, can also better solve the optimal control problem with multiple uncertainties and has strong anti-interference capability and robustness; in addition, MPC can realise the simultaneous tracking of multiple optimisation targets, so it is especially suitable for the optimisation of renewable energy output power. In addition, MPC can track multiple optimisation targets simultaneously, so it is especially suitable for microgrid optimisation and dispatching problems that include various uncertainties, such as random fluctuation of renewable energy output power, the uncertainty of load power and fluctuation of the market price. Nowadays, there are also many integrated energy design optimisation systems in which MPC prediction is used. Ref. [2] proposed a two-level multi-timescale scheduling control strategy based on model predictive control, and Ref.[28] proposed a hierarchical UPS scheduling strategy for IDC systems based on model predictive control (MPC). In Ref.[29], the model predictive control method is introduced in the real-time stage to smooth the power fluctuation.

It can be seen from Table 1 that compared with the existing literature, the work in this paper is more comprehensive. Hydrogen was added to the system for energy scheduling, the two-stage MPC method was adopted to solve the prediction uncertainty problem, and the sensitivity analysis of modelling control parameters was carried out.

TABLE 1 Comparison of the proposed approach with the related works.

Ref.	Method	Timescale	Types of energy in the system	Uncertainty modelling	Sensitivity analysis
Electricity	Thermal	Hydrogen
[2]	MPC	Multi-timescale	√	√	×	√	√
[30]	Multi-objective optimal dispatch	Day-head	√	√	√	×	×
[28]	MPC	Multi-timescale	√	√	×	×	×
[31]	Multi-objective optimal dispatch	Multi-timescale	√	√	×	√	×
[32]	MPC	Intraday	√	×	×	√	×
This paper	MPC	Multi-timescale	√	√	√	√	√

Based on the above research, this paper proposes a multi-time-scale coordinated optimal dispatching method for the electricity–thermal hydrogen-integrated energy systems, which combines renewable energy sources such as wind, photovoltaic and various forms of energy storage, and interconnects electricity, thermal power and hydrogen with multiple energy sources. Overall optimisation process is shown in Figure 1. In the day-ahead dispatching stage, an optimal economic dispatching model with the lowest system operation cost as the optimisation objective was established, while the intraday stage combines time-domain rolling and feedback correction of the real-time system status to eliminate the influence of uncertainties in the microgrid to a greater extent and ensure the reasonableness of the day-ahead plan and the stability of system operation.

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The main contributions of this paper are as follows:

• (1)

  In the day-ahead dispatching stage, a detailed mathematical model of electrolytic hydrogen and hydrogen storage tank was established. The hydrogen network was developed, and the optimal dispatching of the system was achieved by combining the thermal network and electric power network which meets the demand for hydrogen and fully utilising the dispatching role of hydrogen.

• (2)

  In the stage of intraday rolling optimisation, the muti-sources storage was utilised to achieve multi-objective tracking of day-ahead contact lines and multi-source state of charges (SOCs) which can eliminate the influence of uncertainties in the day-ahead stage. The model was constructed in the form of a discretised state space, which enhances computational efficiency.

• (3)

  Sensitivity analysis was conducted on electricity-thermal-hydrogen integrated energy systems, aiming to investigate the influence of various system parameters on the scheduling effect and computational efficiency.

The paper is organised as follows: Section 2 introduces the electrolytic hydrogen model, followed by the construction of the day-ahead economic optimal scheduling model in Section 3. In Section 4, the intraday rolling optimisation model is proposed. Simulation and experiment studies are presented in Section 5 to verify the validity and feasibility of the proposed topology. Finally, the findings of this study are summarised in Section 6.

ELECTROLYTIC HYDROGEN MODEL

The electrolysis of hydrogen has emerged as a widely used method of hydrogen production in recent times. With the progress in technology, the investment cost associated with electrolysis hydrogen equipment has witnessed a decline, thereby, increasing the feasibility of large-scale implementation of hydrogen energy. This paper presents the electrolytic hydrogen plant, as depicted in Figure 2, consisting of two components, namely an electrolytic tank and a compressor. To reduce hydrogen loss, the hydrogen produced by the electrolytic tank undergoes compression, which is stored as high-pressure hydrogen in a designated storage tank. Subsequently, the high-pressure hydrogen tank facilitates the extraction of hydrogen, as per the prevailing demand for the same. 1 $${m}_{H}^{t}={P}_{\text{el}}^{t}\ast {\eta }_{H}$$

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Equation (1) shows the amount of hydrogen generated at time t, represented by $${m}_{H}^{t}$$,where the rate of hydrogen production per unit of electricity in an electrolyse is denoted as $${\eta }_{H}$$; the electrical power input to the electrolyse is denoted as $${P}_{\text{el}}^{t}$$.

To facilitate storage, a compressor is required to compress the hydrogen into high pressure hydrogen, and the power consumption during the compression process is as Equation (2). 2 $${P}_{\mathrm{c}\mathrm{o}\mathrm{m}}^{t}=\frac{{m}_{\mathrm{c}\mathrm{o}\mathrm{m}}^{t}{R}_{H}{T}_{in}\kappa }{3600{\eta }_{\mathrm{c}\mathrm{o}\mathrm{m}}(\kappa -1)}\left[{\left(\frac{{P}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{{P}_{\mathrm{i}\mathrm{n}}}\right)}^{\tfrac{\kappa -1}{\kappa }}-1\right]$$ Where $${m}_{\mathrm{c}\mathrm{o}\mathrm{m}}^{t}$$ denotes the flow rate of hydrogen gas from the compressor ($$\mathrm{K}\mathrm{g}/h$$); $${R}_{H}$$ represents the specific heat capacity constant of hydrogen $$\mathrm{K}\mathrm{J}/(\mathrm{k}\mathrm{g}\cdot \mathrm{K})$$, $${T}_{\mathit{i}\mathit{n}}$$ indicates the temperature of the input hydrogen gas (K); $$\kappa $$ represents the isentropic index of hydrogen; $${P}_{\mathrm{o}\mathrm{u}\mathrm{t}}/{P}_{\mathrm{i}\mathrm{n}}$$ is denotes the compression ratio, and $${\eta }_{\text{com}}$$ is conversion efficiency.

The pressure of the hydrogen storage tank indirectly reflects the amount of hydrogen stored in the tank, and the compression process needs to satisfy the following equation: 3 $${P}_{H}^{t}={P}_{H}^{t-1}+\frac{{R}_{H}{T}_{H}}{{V}_{H}\mathrm{m}\mathrm{o}{\mathrm{l}}_{H}}\left({m}_{\mathrm{c}\mathrm{o}\mathrm{m}}^{t}-{L}_{H}^{t}\right){\Delta }t$$ Where $${P}_{H}^{t}$$ is the internal pressure of the hydrogen storage tank at time t(bar); $${T}_{H}$$ represents the internal temperature of the hydrogen tank(K); $${V}_{H}$$ is the volume of the hydrogen storage tank $$\left({\mathrm{m}}^{3}\right)$$; $$\mathrm{m}\mathrm{o}{\mathrm{l}}_{H}$$ represents the molar mass of hydrogen($$\text{Kg}/\text{mol}$$), $${L}_{H}^{t}$$ denotes the hydrogen demand at time t($$\mathrm{K}\mathrm{g}/h$$).

The electrolytic storage hydrogen conversion efficiency can be determined based on the aforementioned variables. This efficiency denotes the amount of hydrogen produced per unit of electrical power, and the calculation process is shown in Equation (4). 4 $${\gamma }_{1}=\frac{{R}_{H}{T}_{H}}{{V}_{H}\mathrm{m}\mathrm{o}{\mathrm{l}}_{H}}\cdot {\eta }_{\mathrm{H}}/{\left(1+\frac{{m}_{\mathrm{c}\mathrm{o}\mathrm{m}}^{t}{R}_{H}{T}_{in}\kappa }{3600{\eta }_{\mathrm{c}\mathrm{o}\mathrm{m}}(\kappa -1)}[\left(\frac{{P}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{{P}_{\mathrm{i}\mathrm{n}}}\right)\right.}^{\tfrac{\kappa -1}{\kappa }}-1])$$

DAY-AHEAD ECONOMIC OPTIMAL DISPATCH MODEL

The proposed structure of the multi-source load and energy storage system is presented in Figure 3. The system consists of renewable energy sources, including photovoltaic power systems (PV) and wind power systems (WT), as well as dispatchable energy conversion devices, such as micro combustion generators (MT), fuel cells (FC), and boilers (Boil), hydrogen fuel cells (HFC), and electrolysers. Energy storage devices include battery energy storage (BES), hydrogen storage tank (HST), and thermal storage tank (TST). The system is designed to meet the electrical load, hydrogen load, and thermal load, which consume electrical energy, hydrogen, and thermal energy, respectively.

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The primary objective of day-ahead optimisation is to plan for dispatchable units, such as micro-combustion engines, fuel cells, and boilers, while minimising overall day-ahead operating costs, taking into account grid power purchases and operational constraints. The day-ahead economic dispatch is optimised in one-hour intervals to achieve the best dispatch plan for the next 24 h. The WT and PV are renewable energy power generation devices that are randomly affected by weather conditions and are uncontrollable power generation devices. The MT is a micro gas turbine for combined heat and power generation, which generates heat and has a fixed thermoelectric ratio, making it a dispatchable power generation device. The FC is a fuel cell for power generation and is also a dispatchable power generation device. The grid is an external source from which the system can take electricity or sell electricity to the grid. The Boil is a heat generating equipment for boilers, which is used to generate heat to supply the heat load and is also a dispatchable heat generating device. The Hess is a thermal energy storage device that can absorb or emit thermal loads. The SH2 is high-pressure hydrogen storage equipment that can absorb or emit hydrogen, while L2H is electrolytic hydrogen equipment that produces hydrogen by electrolysing water. The H2L is a hydrogen fuel cell that uses hydrogen as fuel to generate electricity and heat in a certain range, with an adjustable thermoelectric ratio. Finally, the energy consumption of the system includes electrical load, thermal load, and hydrogen load, defined as load, H_load, and H_2load, respectively.

The objective function for the day-ahead optimal scheduling problem is expressed as follows, where Obj represents the total cost of operating the microgrid over T time periods, the Objective function is represented in Equation (5), The specific formula for each part of Objective function is shown in Equation (6)–(8). 5 $$\min \ \mathrm{O}\mathrm{b}\mathrm{j}=\sum\limits _{t=1}^{T}\sum\limits _{n=1}^{{N}_{1}}{C}_{\mathrm{O}\mathrm{M}}\left({P}_{n}^{t}\right)+\sum\limits _{t=1}^{T}\sum\limits _{n=1}^{{N}_{2}}{C}_{f}\left({P}_{n}^{t}\right)+\sum\limits _{t=1}^{T}\sum\limits _{n=1}^{{N}_{3}}{C}_{\mathrm{e}\mathrm{v}\mathrm{a}}\left({P}_{n}^{t}\right)+\sum\limits _{t=1}^{T}\left[{C}_{\mathrm{b}\mathrm{a}\mathrm{t}}\left({P}_{\mathrm{b}\mathrm{a}\mathrm{t}}^{t}\right)+{C}_{p}^{t}\left({P}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}^{t}\right)\right.-{C}_{{H}_{2}}\left({P}_{H2\text{load}}^{t}\right)]$$ 6 $${C}_{\mathrm{O}\mathrm{M}}\left({P}_{n}^{t}\right)=K{\text{om}}_{n}{P}_{n}^{t}+C{\text{az}}_{n}\mathrm{r}{(1+r)}^{{L}_{n}}\ast \frac{{P}_{n}^{t}}{8760{(1+r)}^{{L}_{n}}-1}$$ Where cost of equipment maintenance and investment for the ith unit is denoted by $${C}_{\mathrm{O}\mathrm{M}}(\cdot )$$, $${P}_{n}^{t}$$ represents the power generated by the equipment (kW), and $${N}_{1}$$ is the number of equipment in the microgrid; $$K{\text{om}}_{n}$$ denotes the maintenance cost factor of unit power equipment, $$C{\text{az}}_{n}$$ is the investment cost of equipment unit capacity, $${L}_{n}$$ denotes the equipment life, $$r$$ is the annual growth rate of depreciation, $$n=\mathrm{W}\mathrm{T},\mathrm{P}\mathrm{V},\mathrm{M}\mathrm{T},\mathrm{F}\mathrm{C},B\mathrm{o}\mathrm{i}\mathrm{l},H\mathrm{e}\mathrm{S}\mathrm{S},L2H,H2L,SH2$$. The fuel consumption cost of the unit is shown in Equation (7), which is applicable to micro gas turbines, fuel cells, and boiler heat generating equipment that consume fuel. $${P}_{n}^{t}$$ represents the power of the equipment (kW), $$\mathrm{n}=\mathrm{MT},\mathrm{FC},B\mathrm{oil}$$, $$K{\mathrm{f}}_{n}$$ is the unit's fuel consumption factor. 7 $${C}_{f}\left({P}_{n}^{t}\right)=K{\mathrm{f}}_{n}{P}_{n}^{t}$$

8 $${C}_{\mathrm{e}\mathrm{a}\mathrm{v}}\left({P}_{n}^{t}\right)=\left(\mathrm{K}{\text{ec}}_{\mathrm{C}{\mathrm{O}}_{2}}{K}_{{\text{FC}}_{\mathrm{C}{\mathrm{O}}_{2}}}+\mathrm{K}{\text{ec}}_{\mathrm{S}{\mathrm{O}}_{2}}{K}_{{\text{FC}}_{\mathrm{S}{\mathrm{O}}_{2}}}+K{\text{ec}}_{\mathrm{N}\mathrm{O}\mathrm{X}}{K}_{{\text{FC}}_{\mathrm{N}\mathrm{O}\mathrm{X}}}\right)\times {P}_{n}^{t}$$ Where $${C}_{\mathrm{e}\mathrm{a}\mathrm{v}}(\cdot )$$ denotes the cost of pollution emissions associated with the operation of the equipment, which includes both the emissions from the fuel equipment and those from the external grid, $${P}_{n}^{t}$$ represents the power generation of the equipment (kW), $$n=\mathrm{M}\mathrm{T},\mathrm{F}\mathrm{C},B\mathrm{o}\mathrm{i}\mathrm{l},\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}$$.The hydrogen fuel cell uses hydrogen from the microgrid as fuel and do not emit polluting gases. $$\mathrm{K}{\text{ec}}_{\mathrm{C}{\mathrm{O}}_{2}},\mathrm{K}{\text{ec}}_{\mathrm{S}{\mathrm{O}}_{2}},\mathrm{K}{\text{ec}}_{\mathrm{N}\mathrm{O}\mathrm{X}}$$ are the three waste treatment cost coefficients, $$K$$ are the unit emission coefficient, and $${K}_{{\text{FC}}_{\mathrm{C}{\mathrm{O}}_{2}}}$$ represents the $$\mathrm{C}{\mathrm{O}}_{2}$$ emission coefficient of FC unit. 9 $${C}_{\mathrm{b}\mathrm{a}\mathrm{t}}\left({P}_{\mathrm{b}\mathrm{a}\mathrm{t}}^{t}\right)=\frac{0.4838{E}_{\mathrm{b}\mathrm{a}\mathrm{t}}\cdot \mathrm{C}\mathrm{a}{\mathrm{z}}_{\mathrm{B}\mathrm{a}\mathrm{S}}\cdot {P}_{\mathrm{b}\mathrm{a}\mathrm{t}}^{t}}{\left(1161.6{E}_{\mathrm{b}\mathrm{a}\mathrm{t}}-1000{P}_{\mathrm{b}\mathrm{a}\mathrm{t}}^{t}\right)}$$

Equation (9) shows the calculation process of the operating cost of electric energy storage, represented as $${C}_{\mathrm{b}\mathrm{a}\mathrm{t}}(\cdot )$$. The equivalent discharge depth of batteries has been determined based on existing literature, and the cost associated with the loss of energy storage life has been estimated by considering the relationship between discharge depth, the number of cycles, and the initial investment in energy storage. $$\mathrm{C}\mathrm{a}{\mathrm{z}}_{\mathrm{B}\mathrm{a}\mathrm{S}}$$ represents the investment cost per unit capacity, $${E}_{\mathrm{b}\mathrm{a}\mathrm{t}}$$ denotes the total capacity of the energy storage battery, and the $${P}_{\mathrm{b}\mathrm{a}\mathrm{t}}^{t}$$ is charging and discharging power of the battery. Equation (10) represents the income or cost function associated with buying and selling electricity, where $${C}_{p}^{t}$$ denotes the electricity price at time t, $${P}_{\mathrm{grid}}^{t}$$ represents the interactive power of the grid at time t. 10 $${C}_{p}^{t}\left({P}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}^{t}\right)={C}_{p}^{t}{P}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}^{t}$$

Equation (11) represents payoff for hydrogen, $${C}_{{H}_{2}}$$ denotes the price of hydrogen, $${P}_{H2\text{load}}^{t}$$ represents the quantity of hydrogen at time t. 11 $${C}_{{H}_{2}}^{}\left({P}_{\mathrm{H}2\mathrm{load}}^{t}\right)={C}_{{H}_{2}}^{}{P}_{\mathrm{H}2\mathrm{load}}^{t}$$

During unit operation, the power network must satisfy the following constraint equation:

Electric network balance constraint

12 $${P}_{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}^{t}+{P}_{L2H}^{t}={P}_{\mathrm{P}\mathrm{V}}^{t}+{P}_{\mathrm{W}\mathrm{T}}^{t}+{P}_{\mathrm{M}\mathrm{T}}^{t}+{P}_{\mathrm{F}\mathrm{C}}^{t}+{P}_{\mathrm{b}\mathrm{a}\mathrm{t}}^{t}+{P}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}^{t}+{P}_{\mathrm{H}\mathrm{L}}^{t}$$ Where the $${P}_{L2H}^{t}$$ represents power generation and total thermal power of hydrogen fuel cell with adjustable heating ratio, and the power generation power is $${P}_{\mathrm{H}\mathrm{L}}^{t}$$, Equation (12) shows that all power generation and consumption as well as charge-discharge capacity of electric storage are balanced.

Thermal network balance constraint

13 $${P}_{H\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}^{t}=\omega {P}_{\mathrm{M}\mathrm{T}}^{t}+{P}_{\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s}}^{t}+{P}_{B\mathrm{o}\mathrm{i}\mathrm{l}}^{t}+{P}_{H2L}^{t}-{P}_{\mathrm{H}\mathrm{L}}^{t}$$

The power balance constraint of the power network is described by Equation (13), which ensures that the heating power of the micro-grid, the thermal power used, and the heat charging and releasing power of the thermal storage tank are in equilibrium. This equation incorporates the thermoelectric ratio of the micro-gas turbine is $$\omega $$

Hydrogen network balance constraint

14 $${g}_{H2\mathrm{L}\mathrm{o}\mathrm{a}\mathrm{d}}^{t}+{S}_{H2}^{t}{E}_{H2}={\gamma }_{1}{P}_{L2H}^{t}-{\gamma }_{2}{P}_{H2L}^{t}$$

The remaining capacity of the hydrogen storage tank is denoted as $${S}_{H2}^{t}$$, $${E}_{H2}$$ represents the total capacity of the energy storage battery, and the hydrogen demand at time t is $${g}_{H2\mathrm{L}\mathrm{o}\mathrm{a}\mathrm{d}}^{t}$$, $${\gamma }_{1}$$ represents the hydrogen electrolytic coefficient per unit electric power, and $${\gamma }_{2}$$ is the hydrogen coefficient required for generating power per unit fuel cell. Based on these variables, Equation (14) indicates that the amount of hydrogen in the microgrid, the amount of electrolytic hydrogen, and the amount of hydrogen charged and discharged in the hydrogen storage tank are balanced.

Power interaction constraints of micro-grid and external power grid

15 $${P}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}^{\min }\le {P}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}^{t}\le {P}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}^{\max }$$

Dispatchable (MT/FC/Boil, H2L, L2H) equipment output constraints

16 $${P}_{n}^{\min }\le {P}_{n}^{t}\le {P}_{n}^{\max }$$

Output power climbing constraint of dispatchable equipment

17 $${\Delta }{P}_{n}^{\min }\le \vert {P}_{n}^{t}-{P}_{n}^{t-1}\vert \le {\Delta }{P}_{n}^{\max }$$

Hydrogen fuel cell thermoelectric ratio constraint

18 $${\gamma }_{3}\le \frac{{P}_{H2L}^{t}-{P}_{\mathrm{H}\mathrm{L}}^{t}}{{P}_{\mathrm{H}\mathrm{L}}^{t}}\le {\gamma }_{4}$$

Constraints on battery energy storage devices

19 $${P}_{\mathrm{b}\mathrm{a}\mathrm{t}}^{\min }\le {P}_{\mathrm{b}\mathrm{a}\mathrm{t}}^{t}\le {P}_{\mathrm{b}\mathrm{a}\mathrm{t}}^{\max }$$

The power constraints for energy storage devices in terms of absorption and generation are directly correlated to the remaining capacity of the energy storage unit. This can be expressed through Equation (19), which represents the output constraints that must be adhered to. 20 $${S}_{B}^{t}={S}_{B}^{t-1}(1-\sigma )+{\eta }_{c}\frac{{P}_{\mathrm{c}\mathrm{h}}^{t}{\Delta }t}{{E}_{\mathrm{b}\mathrm{a}\mathrm{t}}}$$

Equation (20) shows Constraints of energy storage capacity, $${S}_{B}^{t}$$ denotes the remaining capacity of the energy storage device, $$\sigma $$ is the energy storage self-discharge factor, $${\eta }_{c}$$ represents the energy storage charging and discharging efficiency factor, $${E}_{\mathrm{b}\mathrm{a}\mathrm{t}}$$ is the total capacity of the energy storage battery.

The remaining capacity of the energy storage in time period t is show in Equation (21) 21 $${S}_{B}^{\min }\le {S}_{B}^{t}\le {S}_{B}^{\max }$$

In order to enhance the participation of energy storage systems in the dispatch of subsequent cycles, it is essential to ensure that the remaining capacity of the electric energy storage equipment at the end of the operational dispatch of a cycle is equivalent to the initial remaining capacity. 22 $${S}_{B}^{t=0}={S}_{B}^{t=T}$$

Constraints on thermal energy storage devices

23 $${P}_{\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s}}^{\min }\le {P}_{\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s}}^{t}\le {P}_{\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s}}^{\max }$$

The storage of thermal energy is a dynamic process in which the capacity for energy storage is constantly changing as power is applied. The residual capacity of the thermal energy storage device at a given time t can be described using Equation (24). 24 $${S}_{H}^{t}={S}_{H}^{t-1}+\frac{{P}_{\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s}}^{t}{\Delta }t}{{E}_{\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s}}}$$ Where $${S}_{H}^{t}$$ represents the residual capacity of the thermal energy storage device, $${E}_{\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s}}$$ denotes the total capacity of the energy storage battery. 25 $${S}_{H}^{\min }\le {S}_{H}^{t}\le {S}_{H}^{\max }$$ 26 $${S}_{H}^{t=0}={S}_{H}^{t=T}$$

Hydrogen energy storage equipment constraints

27 $${S}_{H2}^{t}={S}_{H2}^{t-1}+\frac{\left({\gamma }_{1}{P}_{L2H}^{t}-{\gamma }_{2}{P}_{H2L}^{t}\right){\Delta }t-{g}_{H2\mathrm{L}\mathrm{o}\mathrm{a}\mathrm{d}}^{t}}{{E}_{H2}}$$ Where $${S}_{H2}^{t}$$ is the remaining capacity of the thermal energy storage equipment, $${E}_{H2}$$ is the total capacity of the hydrogen storage tank, Equation (27) represents the remaining capacity of the hydrogen storage in time t, the remaining capacity of the hydrogen tank energy storage unit should meet the constraints as follows: 28 $${S}_{H2}^{\min }\le {S}_{H2}^{t}\le {S}_{H2}^{\max }$$

At the same time, to enhance the participation of the energy storage system in the scheduling of the next cycle, it is crucial to ensure that the remaining capacity of the hydrogen storage tank is equal to the starting capacity. However, considering the large capacity of the system storage tank and the scheduling flexibility, a threshold value $$\psi $$ is set to optimise the system operation, the final remaining capacity and initial capacity of the cycle scheduling are subject to the following constraints. 29 $$\frac{\vert {S}_{H2}^{t=0}-{S}_{H2}^{t=T}\vert }{{S}_{H2}^{t=0}}\le \psi $$

INTRADAY ROLLING OPTIMIZATION MODEL

The day-ahead optimal scheduling strategy is based on the day-ahead new energy generation forecast. However, the day-ahead short-term new energy generation forecast error typically falls between 10% and 20%, and there is a significant degree of randomness in the electric load and thermal load. Comparatively, the generation forecast error of the intraday ultra-short-term forecast is much more accurate than the day-ahead forecast. Therefore, in the intraday dispatching stage, the ultra-short-term power generation forecast is fully utilised. To eliminate the deviation from the actual intraday plan caused by the large forecast error before the day, the intraday plan is revised on a rolling basis with a 5-min cycle. The ultra-short-term renewable energy and load power forecast information within a period of time after the current time break is considered in each rolling optimisation, without changing the start/stop and energy storage status of the units in the intraday plan. On the premise of not changing the start/stop and charging/discharging status of the units in the previous day's plan and satisfying the constraints of network safety operation, the MPC optimisation is used to obtain the revised plan of all units within this time window. 30 $\begin{align*}x(k+{\Delta }t)=\left[\begin{array}{@{}c@{}}{P}_{\mathrm{M}\mathrm{T}}(k+{\Delta }t)\\ {P}_{\mathrm{F}\mathrm{C}}(k+{\Delta }t)\\ {P}_{\mathrm{b}\mathrm{a}\mathrm{t}}(k+{\Delta }t)\\ {S}_{B}(k+{\Delta }t)\\ {P}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}(k+{\Delta }t)\\ {S}_{H}(k+{\Delta }t)\\ {P}_{B\mathrm{o}\mathrm{i}\mathrm{l}}(k+{\Delta }t)\\ {P}_{\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s}}(k+{\Delta }t)\\ {P}_{L2H}(k+{\Delta }t)\\ {P}_{H2L}(k+{\Delta }t)\\ {S}_{{H}_{2}}(k+{\Delta }t)\\ {P}_{\mathrm{H}\mathrm{L}}(k+{\Delta }t)\end{array}\right]=\left[\begin{array}{@{}cccccccccccc@{}}1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& -{\alpha }_{1}& {\alpha }_{2}& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& -\beta & 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& -{\theta }_{1}& {\theta }_{2}& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1\end{array}\right]\left[\begin{array}{@{}c@{}}{P}_{\mathrm{M}\mathrm{T}}(k)\\ {P}_{\mathrm{F}\mathrm{C}}(k)\\ {P}_{\mathrm{b}\mathrm{a}\mathrm{t}}(k)\\ {S}_{B}(k)\\ {P}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}(k)\\ {S}_{H}(k)\\ {P}_{B\mathrm{o}\mathrm{i}\mathrm{l}}(k)\\ {P}_{\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s}}(k)\\ {P}_{L2H}(k)\\ {P}_{H2L}(k)\\ {S}_{{H}_{2}}(k)\\ {P}_{\mathrm{H}\mathrm{L}}(k)\end{array}\right]\\ +\left[\begin{array}{@{}cccccccc@{}}1& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& -{\alpha }_{1}& 0& 0& 0& 0& 0\\ -1& -1& -1& 0& 0& 1& 0& -1\\ 0& 0& 0& 0& -\beta & 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0\\ -\omega & 0& 0& -1& -1& 0& -1& 1\\ 0& 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& -{\theta }_{1}& {\theta }_{2}& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\end{array}\right]\left[\begin{array}{@{}l@{}}{\Delta }{P}_{\mathrm{M}\mathrm{T}}(k)\\ {\Delta }{P}_{\mathrm{F}\mathrm{C}}(k)\\ {\Delta }{P}_{\mathrm{b}\mathrm{a}\mathrm{t}}(k)\\ {\Delta }{P}_{B\mathrm{o}\mathrm{i}\mathrm{l}}(k)\\ {\Delta }{P}_{H\mathrm{e}\mathrm{s}\mathrm{s}}(k)\\ {\Delta }{P}_{L2H}(k)\\ {\Delta }{P}_{H2L}(k)\\ {\Delta }{P}_{\mathrm{H}\mathrm{L}}(k)\end{array}\right]+\left[\begin{array}{@{}ccccc@{}}0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 1& -1& -1& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 0& 0& {\theta }_{3}\\ 0& 0& 0& 0& 0\end{array}\right]\left[\begin{array}{@{}l@{}}{\Delta }{P}_{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}(k)\\ {\Delta }{P}_{\mathrm{W}\mathrm{T}}(k)\\ {\Delta }{P}_{\mathrm{P}\mathrm{V}}(k)\\ {\Delta }{P}_{H\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}(k)\\ {\Delta }{P}_{H2\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}(k)\end{array}\right]\end{align*}$

In this study, a microgrid model has been developed and an intraday rolling model with model predictive control (MPC) has been utilised to optimise the dispatch of various energy resources. The model considers dispatchable fuel units, storage charging and discharging power, electric storage SOC (state of charge), contact line exchange power between the microgrid and external grid, thermal storage SOC, boiler power, thermal storage charging and discharging power, electrolytic hydrogen power, hydrogen fuel cell power, hydrogen storage SOC, and hydrogen fuel cell transfer power. To achieve the optimal dispatch of energy resources. To achieve optimal dispatch of energy resources, power balance equations and electric storage SOC iterative equations have been formulated for each time period of the microgrid. The state variable vectors are $$x(k)$$,which is as follows: 31 $$x(k)=\left[{P}_{\mathrm{M}\mathrm{T}}(k),{P}_{\mathrm{F}\mathrm{C}}(k),{P}_{\mathrm{b}\mathrm{a}\mathrm{t}}(k),{S}_{B}(k),{P}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}(k),{S}_{H}(k),{P}_{B\mathrm{o}\mathrm{i}\mathrm{l}}(k)\right.{P}_{\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s}}(k),{{P}_{L2H}(k),{P}_{H2L}(k),{S}_{{H}_{2}}(k),{P}_{\mathrm{H}\mathrm{L}}(k)]}^{T}$$ In the context of power system dispatch, intraday rolling is a crucial technique used to balance the forecast errors arising from stochastic factors. The objective of this technique is to dispatch controllable units, including incremental output from dispatchable units and energy storage, to achieve a balance between energy demand and supply. The vector of control variables is denoted as $$u(k)$$ which is as follows: 32 $${u(k)=\left[{\Delta }{P}_{\mathrm{M}\mathrm{T}}(k),{\Delta }{P}_{\mathrm{F}\mathrm{C}}(k),{\Delta }{P}_{\mathrm{b}\mathrm{a}\mathrm{t}}(k),{\Delta }{P}_{B\mathrm{o}\mathrm{i}\mathrm{l}}(k),{\Delta }{P}_{H\mathrm{e}\mathrm{s}\mathrm{s}}(k),{\Delta }{P}_{L2H}(k),{\Delta }{P}_{H2L}(k),{\Delta }{P}_{\mathrm{H}\mathrm{L}}(k)\right]}^{T}$$

The perturbation variables refer to the effects of inaccuracies in forecasting during intraday dispatch. These variables are represented by a perturbation input vector, which comprises ultra-short-term forecasts for power generation from turbines, photovoltaic (PV) panels, and load, as well as short-term forecasts for thermal load power and the difference between hydrogen demand and the day-ahead forecast. The perturbation variables are denoted as $$r(k)$$, which is as follows: 33 $$r(k)={\left[{\Delta }{P}_{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}(k),{\Delta }{P}_{\mathrm{W}\mathrm{T}}(k),{\Delta }{P}_{\mathrm{P}\mathrm{V}}(k),{\Delta }{P}_{H\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}(k),{\Delta }{P}_{H2\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}(k)\right]}^{T}$$

Equation (30) represents the state space equation during operation. Where $${\alpha }_{1}$$ is SOC ratio changes; the detailed calculation of the state-space equation is shown in Equations (34)–(38). 34 $${\alpha }_{1}=\eta {\Delta }\mathrm{t}/{{E}_{B}}_{1}$$ 35 $${\alpha }_{2}=1-\sigma $$ where $$\sigma $$ represents the energy storage self-discharge rate 36 $$\beta ={\eta }_{2}{\Delta }\mathrm{t}/{E}_{H}$$ 37 $${\theta }_{1}={\gamma }_{1}{\Delta }\mathrm{t}/{E}_{{H}_{2}}$$ Where coefficient of electrolysis of hydrogen is $${\theta }_{1}$$ 38 $${\theta }_{2}={\gamma }_{2}{\Delta }\mathrm{t}/{E}_{{H}_{2}}$$ Where $${\theta }_{2}$$ represents the coefficient of hydrogen to electricity and heat; $$\omega $$ denotes thermoelectric ratio of steam turbine combustion engines.

The contact line power is a crucial factor that determines the operational cost of the system. To ensure stable and economically optimal power exchange with the grid, it is essential to maintain the contact line power as close as possible to the previous day's value. However, regulating the state-of-charge (SOC) of the multi-source energy storage is a challenging task as it needs to meet multiple constraints. The SOC of the three storage states is adjusted at the end of the operating cycle to conform to the scheduling plan of the next cycle, which serves as a tracking target. Consequently, a vector composed of the contact line exchange power and the three energy storage SOC states is utilised. $$y(k)={\left[{P}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}(k),{S}_{B}(k),{S}_{H}(k),{S}_{{H}_{2}}(k)\right]}^{T}$$ is the output variable, Then the following multi-input multi-output state space model can be built. 39 $$y(k)=\left[\begin{array}{@{}cccccccccccc@{}}0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0\end{array}\right]x(k)$$

Iterating the state space prediction model for T steps enables the prediction of the vector of contact line power and the output values of the three energy storage state of charges (SOCs) over the prediction time. This is expressed as Equation (40). 40 $${Y}_{g}={\left[\begin{array}{@{}l@{}}{P}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}^{g}(k+{\Delta }t)\ {S}_{B}^{g}(k+{\Delta }t)\ {S}_{H}^{g}(k+{\Delta }t){S}_{{H}_{2}}^{g}(k+{\Delta }t){\cdots}\\ {\cdots}{P}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}^{g}(k+T{\Delta }t)\ {S}_{B}^{g}(k+T{\Delta }t)\ {S}_{H}^{g}(k+T{\Delta }t)\,{S}_{{H}_{2}}^{g}(k+T{\Delta }t)\end{array}\right]}^{T}$$

The planned reference volume before the day is $${Y}_{\mathrm{r}\mathrm{e}\mathrm{f}}$$ 41 $${Y}_{\mathrm{r}\mathrm{e}\mathrm{f}}={\left[\begin{array}{@{}l@{}}{P}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}^{\mathrm{r}\mathrm{e}\mathrm{f}}(k+{\Delta }t)\ {S}_{B}^{\mathrm{r}\mathrm{e}\mathrm{f}}(k+{\Delta }t)\ {S}_{H}^{\mathrm{r}\mathrm{e}\mathrm{f}}(k+{\Delta }t)\,{S}_{{H}_{2}}^{\mathrm{r}\mathrm{e}\mathrm{f}}(k+{\Delta }t){\cdots}\\ {\cdots}{P}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}^{\mathrm{r}\mathrm{e}\mathrm{f}}(k+T{\Delta }t)\ {S}_{B}^{\mathrm{r}\mathrm{e}\mathrm{f}}(k+T{\Delta }t)\ {S}_{H}^{\mathrm{r}\mathrm{e}\mathrm{f}}(k+T{\Delta }t)\ {S}_{{H}_{2}}^{\mathrm{r}\mathrm{e}\mathrm{f}}(k+T{\Delta }t)\end{array}\right]}^{T}$$

To achieve the objective of minimising the error between the estimated output of the contact line power and energy storage state of charge (SOC), while also ensuring that the incremental control regulation of each unit is as small as possible, an intraday rolling optimal scheduling problem can be formulated as a quadratic programming problem in Equation (42). 42 $$\left\{\begin{array}{@{}l@{}}\min \quad {J}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}-\mathrm{d}\mathrm{a}\mathrm{y}}={\left({Y}_{\mathrm{r}\mathrm{e}\mathrm{f}}-{Y}_{g}\right)}^{T}{W}_{E}\left({Y}_{\mathrm{r}\mathrm{e}\mathrm{f}}-{Y}_{g}\right)+{U}^{T}{W}_{u}U\\ \mathrm{s}\mathrm{t}\left\{\begin{array}{@{}l@{}}{\Delta }{P}_{{n}_{1}}^{\min }\le {\Delta }{P}_{{n}_{1}}^{t}\le {\Delta }{P}_{{n}_{1}}^{\max }\\ {P}_{{n}_{1}}^{\min }\le {P}_{{n}_{1}}^{t}\le {P}_{{n}_{1}}^{\max }\\ {n}_{1}=\mathrm{M}\mathrm{T},\mathrm{F}\mathrm{C},\mathrm{b}\mathrm{a}\mathrm{t},B\mathrm{o}\mathrm{i}\mathrm{l},\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s},L2H,H2L,\mathrm{H}\mathrm{L}\end{array}\right.\end{array}\right.$$ 43 $${W}_{E}=\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{g}\left[{W}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}^{k},{W}_{B}^{k},{W}_{H}^{k},{W}_{{H}_{2}}^{k}{\cdots},{W}_{g}^{k+T{\Delta }t},{W}_{B}^{k+T{\Delta }t},{W}_{H}^{k+T{\Delta }t},{W}_{{H}_{2}}^{k+T{\Delta }t}\right]$$

$${W}_{E}$$ represents the weight coefficient matrix of the contact line power tracking error and the energy storage SOC tracking errors, $$U$$ denotes the matrix of control variables, and $${W}_{u}$$ is the matrix of weight coefficients of control quantities.

CASE STUDY

Experimental background and platform

The microgrid system designed for a park was presented as a demonstration of the calculation analysis. The system includes various controllable distributed energy resources, including a micro gas turbine (100 kW), a fuel cell (60 kW), a boiler (200 kW), and a hydrogen fuel cell (100 kW). The system also incorporates new energy sources, such as a wind turbine (80 kW), a photovoltaic power generation system (100 kW), and a hydrogen electrolysis plant (maximum electrolysis power of 150 kW). The energy storage system is comprised of three main components: a battery storage, a heat storage tank, and a high-pressure hydrogen storage tank. The battery storage has a total capacity of 180 kW, with an initial state-of-charge (SOC) of 0.5. The maximum and minimum SOCs for the battery storage were 0.3 and 0.9, respectively. The heat storage tank has a total capacity of 100 kW, with an initial SOC of 0.5. The maximum and minimum SOCs for the heat storage tank were 0.2 and 0.9, respectively. Finally, the high-pressure hydrogen storage tank has a capacity of 35 Mpa and 500 m³, with an SOC of 0.5. The maximum and minimum SOCs for the hydrogen storage tank were 0.2 and 0.9, respectively.

The optimisation model was developed using MATLAB software on a platform. This model was utilised for optimising the operation of a microgrid system in order to cater to the electrical load, thermal load, and hydrogen demand of a park. The power output of each equipment in the microgrid system, along with the interactive power limit with the grid and the climbing limit, are presented in Table 2. Table 3 provides the cost parameters for each equipment, including investment, operation, energy consumption, and emissions.

TABLE 2 Output constraint parameters.

	Technical output/kW
Lower limit	Upper limit	Climbing rate kW/h
Grid	$${\mathrm{P}}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}^{\min }$$: −50	$${\mathrm{P}}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}^{\max }$$: 50	$${\Delta }{\mathrm{P}}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}^{\max }$$: 40
MT	$${\mathrm{P}}_{\mathrm{M}\mathrm{T}}^{\min }$$: 0	$${\mathrm{P}}_{\mathrm{M}\mathrm{T}}^{\max }$$: 60	$${{\Delta }\mathrm{P}}_{\mathrm{M}\mathrm{T}}^{\max }$$: 48
FC	$${\mathrm{P}}_{\mathrm{F}\mathrm{C}}^{\min }$$: 0	$${\mathrm{P}}_{\mathrm{F}\mathrm{C}}^{\max }$$: 40	$${{\Delta }\mathrm{P}}_{\mathrm{F}\mathrm{C}}^{\max }$$: 32
Bat	$${\mathrm{P}}_{\mathrm{b}\mathrm{a}\mathrm{t}}^{\min }$$: −18	$${\mathrm{P}}_{\mathrm{b}\mathrm{a}\mathrm{t}}^{\max }$$: 18	$${{\Delta }\mathrm{P}}_{\mathrm{b}\mathrm{a}\mathrm{t}}^{\max }$$: 18
Boil	$${\mathrm{P}}_{B\mathrm{o}\mathrm{i}\mathrm{l}}^{\min }$$: 0	$${\mathrm{P}}_{B\mathrm{o}\mathrm{i}\mathrm{l}}^{\max }$$: 200	$${{\Delta }\mathrm{P}}_{\mathrm{B}\mathrm{o}\mathrm{i}\mathrm{l}}^{\max }$$: 80
Hess	$${\mathrm{P}}_{\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s}}^{\min }$$: −20	$${\mathrm{P}}_{\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s}}^{\max }$$: 20	$${{\Delta }\mathrm{P}}_{\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s}}^{\max }$$: 20
L2H	$${\mathrm{P}}_{L2H}^{\min }$$: 0	$${\mathrm{P}}_{L2H}^{\max }$$: 150	$${{\Delta }\mathrm{P}}_{\mathrm{L}2\mathrm{H}}^{\max }$$: 100
H2L	$${\mathrm{P}}_{H2L}^{\min }$$: 0	$${\mathrm{P}}_{H2L}^{\max }$$: 150	$${\Delta }{\mathrm{P}}_{\mathrm{H}2\mathrm{L}}^{\max }$$: 60

TABLE 3 Other parameters in the system.

Para	Value	Para	Value	Para	Value
$${E}_{\mathrm{b}\mathrm{a}\mathrm{t}}$$	180 (kW.H)	$${\eta }_{\mathrm{c}\mathrm{o}\mathrm{m}}$$	0.7	$$K{f}_{\mathrm{M}\mathrm{T}}$$	0.38445
$${E}_{H}$$	100 (kW.H)	$${T}_{H}$$	333.15 k	$$K{f}_{\mathrm{F}\mathrm{C}}$$	0.59415
$${E}_{{H}_{2}}$$	350 (kPa)	$${V}_{H}$$	500 m3	$$K{f}_{B\text{oi}\mathrm{l}}$$	0.25
$$\omega $$	2.2	$$\mathrm{m}\mathrm{o}{\mathrm{l}}_{H}$$	0.002 kg/mol	$$\mathrm{K}\mathrm{e}{\mathrm{c}}_{\mathrm{c}{\mathrm{o}}_{2}}$$	0.21
$${R}_{H}$$	14.304	$${\gamma }_{1}$$	64.8091	$$\mathrm{K}\mathrm{e}{\mathrm{c}}_{\mathrm{s}{\mathrm{o}}_{2}}$$	14.842
$${T}_{\mathrm{i}\mathrm{n}}$$	313.15 K	$${\gamma }_{2}$$	59.4	$$\mathrm{K}\mathrm{e}{\mathrm{c}}_{\mathrm{N}\mathrm{O}\mathrm{X}}$$	62.964
$$\kappa $$	1.4	$${\gamma }_{3}$$	0.5	$${K}_{\mathrm{F}{\mathrm{C}}_{\mathrm{C}{\mathrm{O}}_{2}}}$$	498
$${P}_{\mathrm{o}\mathrm{u}\mathrm{t}}/{P}_{\mathrm{i}\mathrm{n}}$$	35/12	$${\gamma }_{4}$$	3	$${K}_{\mathrm{F}{\mathrm{C}}_{\mathrm{S}{\mathrm{O}}_{2}}}$$	0.003
$$\sigma $$	0.01			$${K}_{\mathrm{F}{\mathrm{C}}_{\mathrm{N}\mathrm{O}\mathrm{X}}}$$	0.01
$$\mathrm{K}\mathrm{o}{\mathrm{m}}_{\mathrm{P}\mathrm{V}}$$	0.0096	$$\mathrm{C}\mathrm{a}{\mathrm{z}}_{\mathrm{P}\mathrm{V}}$$	2	$${K}_{\mathrm{M}{\mathrm{T}}_{\mathrm{C}{\mathrm{O}}_{2}}}$$	184
$$\mathrm{K}\mathrm{o}{\mathrm{m}}_{\mathrm{W}\mathrm{T}}$$	0.0296	$$\mathrm{C}\mathrm{a}{\mathrm{z}}_{\mathrm{W}\mathrm{T}}$$	1.2	$${K}_{\mathrm{M}{\mathrm{T}}_{\mathrm{S}{\mathrm{O}}_{2}}}$$	0.001
$$\mathrm{K}\mathrm{o}{\mathrm{m}}_{\mathrm{M}\mathrm{T}}$$	0.041	$$\mathrm{C}\mathrm{a}{\mathrm{z}}_{\mathrm{M}\mathrm{T}}$$	1	$${K}_{\mathrm{M}{\mathrm{T}}_{\mathrm{N}\mathrm{O}\mathrm{X}}}$$	0.619
$$\mathrm{K}\mathrm{o}{\mathrm{m}}_{\mathrm{F}\mathrm{C}}$$	0.0293	$$\mathrm{C}\mathrm{a}{\mathrm{z}}_{\mathrm{F}\mathrm{C}}$$	2.8	$${K}_{\text{Boi}{\mathrm{l}}_{\mathrm{C}{\mathrm{O}}_{2}}}$$	649
$$\mathrm{K}\mathrm{o}{\mathrm{m}}_{B\mathrm{o}\mathrm{i}\mathrm{l}}$$	0.028	$$\mathrm{C}\mathrm{a}{\mathrm{z}}_{B\mathrm{o}\mathrm{i}\mathrm{l}}$$	1.5	$${K}_{\text{Boi}{\mathrm{l}}_{\mathrm{S}{\mathrm{O}}_{2}}}$$	0.002
$$\mathrm{K}\mathrm{o}{\mathrm{m}}_{\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s}}$$	0.01	$$\mathrm{C}\mathrm{a}{\mathrm{z}}_{\mathrm{H}\mathrm{e}\mathrm{s}\mathrm{s}}$$	3	$${K}_{\text{Boi}{\mathrm{l}}_{\mathrm{N}\mathrm{O}\mathrm{X}}}$$	0.01
$$\mathrm{K}\mathrm{o}{\mathrm{m}}_{L2H}$$	0.01	$$\mathrm{C}\mathrm{a}{\mathrm{z}}_{L2H}$$	4	$${K}_{\text{gri}{\mathrm{d}}_{\mathrm{C}{\mathrm{O}}_{2}}}$$	889
$$\mathrm{K}\mathrm{o}{\mathrm{m}}_{H2L}$$	0.02	$$\mathrm{C}\mathrm{a}{\mathrm{z}}_{H2L}$$	3.5	$${K}_{\text{gri}{\mathrm{d}}_{\mathrm{S}{\mathrm{O}}_{2}}}$$	1.8
$${L}_{\mathrm{P}\mathrm{V}}$$	20 (year)	$${L}_{\text{ot}\mathrm{h}\mathrm{e}\mathrm{r}}$$	10	$${K}_{\text{gri}{\mathrm{d}}_{\mathrm{N}\mathrm{O}\mathrm{X}}}$$	1.6

A typical integrated energy microgrid demonstration project in the northern region was selected for the case, where the capacity and unit of each equipment were obtained from the nameplate parameter table of the equipment. Part of the case parameters and power data refer to our previous two works [33–35].

Day-head optimised dispatch experiments

In this paper, an experimental test case utilising 1 day of actual data gathered from a park was presented in this study. Figure 4 shows the predicted wind power generation data and PV power generation data at one-hour intervals before the day based on the predicted electric load, thermal load and hydrogen load, which were obtained by artificial intelligence prediction methods based on historical data and weather forecasts.

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Photovoltaic power generation and wind power generation are both subject to weather conditions, which can be highly unpredictable. In order to thoroughly evaluate the effectiveness and robustness of the optimisation system, this study utilised Monte Carlo sampling to generate 1000 historical training scenarios based on past photovoltaic and wind power generation data. Through the use of clustering methods, three typical power generation scenarios were extracted, as shown in Figures 5 and 6.

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The wind power generation and photovoltaic power generation data from three different scenarios were combined with other load data to construct three simulated scenarios to verify the effectiveness of the optimisation. In order to explore the impact of the addition of a hydrogen system on the economic operation of an electricity-thermal integrated energy systems, the investment cost of hydrogen equipment was considered and the following three system cases were constructed:

$1$

Case

A system with heat and electricity only, without electrolytic hydrogen, hydrogen storage tanks, or hydrogen fuel cells.

$2$

Case

A system with heat and electricity and hydrogen, including the electrolysis of hydrogen and hydrogen storage tanks, but without the process of converting hydrogen into electricity and heat.

$3$

Case

A system with heat and electricity and hydrogen, including the electrolysis of hydrogen, hydrogen storage tanks, and hydrogen fuel cells, with both the electrolysis of hydrogen and the conversion of hydrogen into electricity and heat.

In order to evaluate the impact of integrating hydrogen production equipment and hydrogen fuel cells on microgrid operations, a comparative analysis of operating costs was conducted across various scenarios. Specifically, the costs associated with the addition of hydrogen production equipment alone were compared with those associated with the addition of both hydrogen production equipment and hydrogen fuel cells. To generate data for the analysis, historical data on PV and wind power generation were clustered into three typical scenarios, and the operating costs for a real-life scenario from a selected day were also analysed. The day-ahead optimisation cost in three simulated scenarios and one real scenarios scene are shown in Table 4.

TABLE 4 Day-ahead optimisation cost in different scene.

Scene	Electricity-heat	Electricity-heat-hydrogen	Electricity-heat-hydrogen-electricity
1	1330.2407	1395.2640	1397.4853
2	1146.4840	1325.1763	1325.0012
3	1581.5109	1282.8635	985.6211
Real	2941.4980	2997.3325	2938.7589

Based on the analysis, it can be concluded that the addition of hydrogen production equipment in electricity-thermal-hydrogen systems can result in higher costs when new energy generation is limited and the system consumes more electricity. This is due to the relatively large investment cost of electrolysis of hydrogen, which may result in higher costs in the case of insufficient electricity. However, by incorporating hydrogen fuel cells, the hydrogen to electricity process can help reduce costs.

In contrast, scenarios with high photovoltaic and wind power generation can benefit from the addition of hydrogen production equipment, which can effectively utilise excess electricity and reduce overall operating costs. Therefore, the addition of hydrogen production equipment can meet the system's hydrogen demand while minimising additional costs. Furthermore, incorporating hydrogen fuel cells can better coordinate the system and reduce operating costs in each scenario. Moreover, hydrogen is a non-polluting energy source, which can help achieve environmental protection goals and meet the demand for hydrogen in the park.

By optimising the real scenario that includes electrolytic hydrogen, hydrogen storage tanks, and the hydrogen system objective function, the optimised dispatch power of each dispatchable energy source for the previous 24 h was obtained. Figure 7 displays the results. The diagram indicated that when the electricity price was low and various loads consume less electricity (0–6h in the diagram), the system extracted electricity from the grid at maximum power. Meanwhile, the dispatchable equipment generates electricity to some extent, the electric energy storage equipment starts charging, the thermal storage tank stores heat, and the hydrogen electrolysis equipment operates at higher power to store the hydrogen obtained in the high-pressure hydrogen tank via the compressor.

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During the peak electricity consumption period (10–15h in the diagram), when electricity prices are higher, micro-combustion engines and fuel cells became the main power supply units, electric and thermal energy storage discharges and exerts heat, and hydrogen fuel cells also operate to discharge. In the last phase of dispatch (22–24h), when the electricity and heat demand is relatively low, the electric and thermal energy storage absorb capacity, and the electrolytic hydrogen equipment runs to produce hydrogen to deposit in hydrogen tanks to meet the capacity constraints before and after dispatch of the three storage SOCs.

The three energy storage devices mainly charge and discharge heat during low electricity price hours and discharge and discharge heat during high electricity price hours, effectively playing the role of peak shaving and valley filling of energy storage. The optimised dispatch power of each dispatchable energy source can help balance the energy supply and demand and meet the load requirements, which contributes to the efficient operation of the hydrogen system.

Based on the sensitivity analysis of relevant parameters and the global optimum analysis conducted in Scenario 1, the present study utilised the Sequential Quadratic Programming (SQP) optimisation method to obtain the optimisation results at one initial point. It is important to note that mathematical methods may be localised, and thus different initial points were set to find the global optimum. The accuracy of the optimisation result was verified using the effective set method and the inner point method.

To achieve this, 10 runs were conducted by uniformly selecting 10 different variables from the upper and lower limits of the constraints. The objective function values and running time were recorded and analysed to obtain the optimisation results. The obtained results were validated by comparing the obtained objective function values with the theoretical values of the effective set and the inner point method. The result in Figure 8 and Figure 9 show that the optimisation effect of the SQP method is better and the optimisation efficiency is higher.

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Intraday rolling updates

The ultra-short-term prediction of wind power, photovoltaic (PV) power, and electric load can be achieved using methods such as artificial intelligence. In this study, it was assumed that the ultra-short-term predicted power of wind power, PV, electric load, thermal load, and hydrogen load can be simulated by superimposing the prediction error of normal distribution on their previous day predicted power. The ultra-short-term power generation forecast can predict the future power generation at an interval of 5 min. The rolling optimisation scheduling execution period was established at 5 min, while the forecast duration was set to 2 h, corresponding to 24 forecast time points. The control duration was set to 1 h, which included 12 optimisation control time points. This resulted in a total of 288 rolling optimisation times throughout the day.

Four tracking variables were introduced with weights of (1, 200, 5, 2000). The results are presented in the Figure 10. The findings shows that in the absence of intraday rolling optimisation, the power of the contact line interacting with the external grid fluctuated rapidly, making it challenging to achieve smooth and controllable dispatching of the microgrid access distribution network. After adding the intraday rolling mechanism, the power of the contact line during the day matches the planned value before the day, and the random factors in the process were balanced. Figure 10b–d show the tracking effect of electric energy storage state of charge (SOC), thermal energy storage SOC, and hydrogen energy storage SOC, respectively, on the day-ahead reference. Although there were slight deviations from the day-ahead dispatch, the overall tracking effect was good, and the tracking variables of intraday rolling can better track the day-ahead dispatch command from an overall perspective.

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To maintain synchronisation between the microgrid contact line power and the day-ahead plan value, the intraday dispatch must introduce a certain degree of correction to the day-ahead dispatch plan. After the intraday rolling adjustment, the control variables can be obtained, and the dispatch unit power adjustment is shown in Figure 11.

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Sensitivity analysis

To achieve better tracking of the day-ahead plan, it is necessary to adjust the weight factor of the control variables due to the large difference in their magnitudes. Specifically, the power magnitude of the contact line has little effect on the contact line under different parameter settings, whereas the main effect is on the electric storage SOC. Therefore, the effect of different weight factor matrix settings on electric storage tracking results were investigated. At the same time, the model predictive control time will also affect the optimisation effect and efficiency, because the sensitivity analysis of weight parameters and time parameters can make the system run better, and the system modelling can be applied to other systems by adjusting the parameters, which is conducive to the promotion of the model.

To investigate the effectiveness of different control scales and the computational time required for tracking, three weight factor matrix settings (W1 = [1,200,5,1000], W2 = [1,200,5,2000], W3 = [1,200,50,2000]) were selected and tested in real and simulated scenarios. The mean square error was used as a measure of tracking effectiveness. Figure 12 shows the tracking results with different weighting parameters. And the intraday tracking effect under different parameters are shown in Table 5.

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TABLE 5 Real scene intraday tracking effect.

True	Single planning calculation time	Liaison line error	Electric storage tracking error	Thermal storage error	Hydrogen storage tracking error
Control timescale 24 W1	0.9893	1.3296	0.048	0.0312	0.0093
Control timescale 12 W1	0.1351	1.328	0.0228	0.0304	0.0291
Control timescale 6 W1	0.0242	1.3284	0.0568	0.0241	0.0424
Control timescale 24 W2	0.9731	1.3297	0.0479	0.0312	0.0076
Control timescale 12 W2	0.1337	1.3285	0.0225	0.0304	0.0193
Control timescale 6 W2	0.0238	1.3286	0.0574	0.0241	0.0374
Control timescale 24 W3	0.9964	1.3297	0.048	0.0321	0.0076
Control timescale 12 W3	0.136	1.285	0.0225	0.033	0.0192
Control timescale 6 W3	0.0239	1.3287	0.0572	0.0208	0.0372

Based on the obtained results, it can be deduced that longer control scales result in increased calculation time. Specifically, a control duration of 2 h takes about 9 times the single calculation time compared to a control duration of 1 h, while a control duration of 30 min only required a mere 0.02 s for single calculation time. Regarding the contact line tracking effect, it remains relatively consistent across different control scales. For electric storage SOC tracking effect, a control duration of 1 h achieved the best tracking effect in real scenarios. In terms of thermal energy storage SOC tracking effect, a control duration of 30 min provided the best effect in the scenarios, while a control duration of 2 h offered the best tracking effect for hydrogen energy storage SOC.

During the intraday rolling adjustment process, four variables were tracked, and it may be challenging to consider all four tracking variables simultaneously when their tracking effects differ across various parameter settings. Therefore, the control time parameter of the system was set at 1 h, given its suitable calculation time of 0.2 s, which satisfied the calculation demand while providing a satisfactory tracking effect on electric energy storage SOC. Furthermore, the tracking effect of electric energy storage and hydrogen storage can also meet the standard. This approach strikes an effective balance between calculation time and tracking effects, rendering it a practical solution for the intraday rolling adjustment process.

CONCLUSION

This paper proposes an electricity-thermal-hydrogen integrated energy systems that incorporates hydrogen into the integrated energy dispatching system. To account for prediction errors and stochastic factors in the operation process, this paper proposes a multi-timescale optimal dispatching strategy. In the day-ahead dispatching stage, the dispatching operation cost of the next 24 h was taken as the optimisation target. The day-ahead dispatching strategy was optimised considering the investment, operation, fuel, and sewage costs of various equipment. In the intraday stage, the model prediction control (MPC) method was applied, combined with ultra-short-term generation, and the intraday rolling update was carried out with 5 min as the control scale. This approach effectively achieves the tracking of the planned value of the day-ahead contact line and ensures the tracking of the three energy storage systems. The single operation time of the day is as short as 0.02 s to meet the demand for fast dispatch.

Overall, the proposed electricity-thermal-hydrogen integrated energy systems provides a promising approach for incorporating hydrogen into the integrated energy dispatching system. The multi-timescale optimal dispatching strategy considers prediction errors and stochastic factors and improves the tracking of the planned value of the day-ahead contact line and the three energy storage systems. The proposed approach has potential for practical application and can contribute to the development of efficient and sustainable energy systems.

ACKNOWLEDGEMENTS

This work was supported by National Natural Science Foundation of China (52177124, U2066211), in part by the Youth Innovation Promotion Association CAS (2019143), the Institute of Electrical Engineering, CAS (E155610101), and in part by the DNL Cooperation Fund, CAS (DNL202023).

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

DATA AVAILABILITY STATEMENT

Data available on request due to privacy/ethical restrictions.

References

Song, Y., et al.: A data‐model fusion dispatch strategy for the building energy flexibility based on the digital twin. Appl. Energy 332, [eLocator: 120496] (2023). [DOI: https://dx.doi.org/10.1016/j.apenergy.2022.120496]