A Power-to-Gas Model Considering the Waste Heat Compensation for Power System Application

Power-to-Gas (P2G) technology is a crucial enabler for the new energy-based power system. In this study, a daily economic dispatch model is proposed for the power system operation with P2G units. It incorporates collecting and utilizing waste heat generated by the methanation plant and connected with the Proton exchange membrane (PEM) electrolysis. The simulation results demonstrate that the proposed model achieves a 1.1% decrease in power system operation costs compared to the conventional P2G model. This paper provides valuable insights into the power systems optimization with P2G units for more efficient and cost-effective renewable energy integration into the power grid.


Introduction
China has been constructing a new power system with the critical objective of enhancing the consumption capability of renewable energy.However, these renewable energy sources exhibit strong stochastic characteristics, making energy storage technology critical to achieving this objective.Powerto-Gas (P2G) technology has attracted considerable attention among various energy storage technologies due to its unique advantages [1].P2G refers to using electricity to produce hydrogen via water electrolysis and applying hydrogen to produce methane.Meanwhile, it provides a safe way for utilizing hydrogen [2], enabling the use of existing natural gas pipelines for transporting methane products [3].Hence, the introduction of P2G in the power system is beneficial for fully utilizing existing infrastructure to integrate renewable energy and promoting an environmentally friendly and low-carbon power system's growth.
The most widely used technologies for water electrolysis include Alkaline Electrolytic Cells (AEC), Proton Exchange Membrane (PEM) Electrolyzer Cells, and Solid Oxide Electrolytic Cells (SOEC) [4].SOEC is a high-temperature electrolysis technology that requires a significant amount of external thermal energy.AEC and PEM are two types of low-temperature water electrolysis technologies.AEC possesses the most mature technical foundation, but it suffers from low efficiency and purity in hydrogen production, as well as limitations in its working load range and response speed.PEM electrolysis has the advantages of fast response time, good start-stop performance, high scalability, and significant potential for future development [5].However, the heat generated solely by the electrolysis is not sufficient to maintain the PEM electrolyzer at the ideal electrolysis temperature [6].Energy complementarity between nuclear reactors and high-temperature electrolysis cells has been proposed in [7], providing inspiration for us to consider thermal energy complementarity in P2G units of the power system.This is because the methanation reaction is exothermic [8], providing ample thermal energy that can be utilized.
Before the research, we reviewed existing P2G studies.We found that Toro and Sciubba [9] proposed a heat exchange network design method for P2G, and Ancona et al. [10] proposed a P2G model including the high-temperature electrolyzer, the empirical methanation modeling, and their heat utilization.In [11][12][13][14], similar methods that consider heat compensation between low-temperature electrolysis and methanation equipment were proposed.Both low-temperature and high-temperature electrolysis are endothermic processes, but the principle of heat recovery is different.High-temperature electrolysis usually requires an external heat source, and typically waste heat is from the electrolysis process.By contrast, heat compensation is a process that utilizes waste heat from methanation plants to supply electrolyzers for low-temperature electrolysis.
However, these references only consider the benefits from the P2G unit perspective without evaluating the impact of considering heat recovery from the perspective of the entire power system.Besides, the existing P2G model includes many factors coupled with the power system, leading to a high computational burden.Meanwhile, existing studies on P2G in the power system have mostly focused on the integrated energy system, with P2G only serving as an energy conversion unit [15].The P2G internal energy coupling relationships, such as heat exchange, are not properly considered.
In this paper, we propose a daily economic dispatch model for the power system that incorporates thermal energy compensation between the methanation plant and the PEM electrolyzer.The test conducted on the IEEE 118-bus system indicates that the inclusion of waste heat utilization in the model leads to a 1.1% reduction in net generation cost compared to traditional P2G modeling approaches [16].Furthermore, this model better satisfies the practical requirements of the industry.

Model of the Power-to-Gas Units
The overall model structure, as depicted in Figure 1, encompasses both the electric power system and the internal parts of P2G units.In this section, we will focus on the P2G model.
The CO2 methanation reaction is a strongly exothermic reaction with many complex side reactions, as can be seen from Equation (1).To ensure product quality, the input gas ratio must be strictly controlled during the actual reaction.However, in practical processes, the volume of methane gas output can account for more than 96% of the total volume.Therefore, we simplify the problem by neglecting the equilibrium constant of the chemical reaction so that it can be coupled with the water electrolysis module.

t k c
V is the total incoming gas flow rate (in Nm 3 /h) of the k th P2G unit's methanation plant at time t, which involves the entry of CO2 and H2 in a stoichiometric ratio.The incoming CO2 flow rate is 2 , , is the methane (SNG) output flow rate (in Nm 3 /h) at time t of the k th P2G unit, which can be directly injected into the natural gas pipeline.1  represents the methane conversion rate of the P2G reaction.
Equation ( 4) represents the heat production constraint of the methanation plant. , Q is the amount of waste heat collected at time t from the k th P2G unit methanation reaction; 2  represents the waste heat recovery efficiency., , , 0 Equation ( 5) constrains the methane production within the rated capacity, and is the rated natural gas output (in Nm 3 /h) of a single P2G unit.
Due to its strong exothermic characteristics, the coupling between the methanation unit and the power system is relatively simple.During the steady state, the main power load is the compressor motor.The compressor is used to maintain the gas pressure in the methanation plant and to drive the reaction gas flow. ,c t k P (in MW) represents the power of the compressor for the k th P2G unit at time t, and , c N P (in MW) is the rated power of the compressor in a single methanation unit.

Model of H2 Storage
The geometric volume of a high-pressure hydrogen storage tank remains constant, and hydrogen is stored by changing the pressure.To ensure safe operation, the storage tank has a maximum allowable pressure.The pressure constraints of the hydrogen storage tank can be converted into constraints on the storage volume of hydrogen under standard conditions as follows: Equation ( 9) describes the dynamic balance of the hydrogen storage tank, where the gas inventory at this time plus the hydrogen produced by the electrolysis module minus the hydrogen consumed by the methane production unit equals the gas inventory at the next hour.It is assumed that the initial hydrogen storage is zero by Equation (10) and that the supply of CO2 meets the demand of the methanation process in real time.

Simplified Model of the PEM Electrolysis Module
Based on the characteristics of the PEM electrolyzer, it is assumed that the electrolytic cell needs to operate at the rated temperature and the relationship between the electrolysis power and the output is described by a linear equation: , , , where , t k e P represents the total operating power (in MW) of the electrolytic cells in the k th P2G unit at time t; , e N P represents the rated total operating power (in MW) of the electrolytic cells in a single P2G unit; 2 , , represents the total hydrogen production rate (in Nm 3 /h) in the k th P2G unit at time t; 2 , H N V represents the rated gas production rate (in Nm 3 /h) of hydrogen in a single P2G unit., , ,0} 10 Maintaining the PEM electrolytic cell at its rated operating temperature requires heating the circulating water using an electric heater, and the waste heat recovered from the methanation plant can replace part of the heater's role.As can be seen in equation ( 13), , t k h P represents the power (in MW) of the electric heater in the k th P2G unit at time t. 3  is the heat transfer loss coefficient.0 T is the equivalent inlet temperature of the circulating water. 1 T is the rated operating temperature of the electrolyzer.The specific heat capacity of water, denoted as C, is measured in units of J/(kg•℃).
is the mass of water (in kg) that can be heated from 0 T to 1 T , using the waste heat recovered from the methanation plant at time t in the k th P2G unit.Due to the density of water, the mass of water (in kg) is equal to its volume (in L).  is the flow rate of circulating water required per standard cubic meter of hydrogen produced in L/Nm 3 .h  is the efficiency of the electric heater.T is the time interval of 1 hour or 3600 seconds.The max function ensures that the electric heater is not operated when the waste heat is sufficient to heat the whole inlet water to the rated temperature.

Constraints of the Power System
In addition to the operational constraints of the aforementioned devices, the daily economic dispatch model considering the thermal compensation between the methanation plant and the PEM electrolyzer in the power grid has other constraints as follows.From the perspective of the internal power consumption of the P2G equipment, Equation (14) shows that the power consumption of the entire P2G unit is determined by the combined power usage of the electrolyzer, electric heater, and compressor.
From the perspective of external power supply, the total power consumption of P2G units is represented by the sum of the power output from the grid, as shown in Equation (15) Equation ( 17) represents the output constraint of generators.
,max i gen P and P i gen,min represent the upper limit and the lower limit of the power output of generator i. Equation ( 18) represents the matrix equation of the DC power flow constraint, where t gen p is a column vector composed of , t i gen P , t loads p is a vector composed of , t j loads P , and branch,max p is a column vector composed of branch power upper limits.

Objective Function
The model's objective function is designed to describe the minimum daily net cost S , which is the difference between the daily total generation cost t gen S  and the daily total economic benefit of the products t SNG S  , as shown in Equation (19).
24 24 where t SNG S equals the yield of natural gas multiplied by its price.Given the significant fluctuations in the international natural gas market, the price has a significant impact on the economic benefits of P2G.The generation cost t gen S is applied to the polynomial in the case study.4 , , )

Case Setting
The modeling method proposed in the above section was tested on the IEEE 118-bus system to demonstrate its effectiveness [17].We implemented it in MATLAB, and the Gurobi solver was used for optimization.The parameters of the case study were presented in Table 1.The simulations were executed on a computer featuring an Intel(R) Core (TM) i7-10875H CPU operating at a frequency of 2.30 GHz and 16 GB of RAM.The single-day dispatch results were obtained using three different models for comparison: M0 represents the case where the Power-to-Gas (P2G) Units are not in operation.M1 assumes that the P2G Units are in operation but does not consider the dispatch method with the methanation plant's waste heat collection.
M2, which is the subject of this paper, introduces a power grid operation model that considers the complementary heat relationship between the methanation plant and the PEMEC.
The P2G Units were located at the nodes specified in

Proposed Method Evaluation
The objective function results obtained from solving M1 and M2 can be presented in Table 3:  in methods M1 and M2, it can be demonstrated that by considering the complementary relationship between the methanation plant and the PEMEC, it is possible to increase natural gas production while reducing generation costs.Matching the corresponding methane production capacity, electrolytic hydrogen production consumes much more electricity than methane equipment.Thus, the hydrogen production in the figures almost corresponds linearly with the power consumption.To enable the P2G units to achieve greater efficiency, further development of hydrogen production technology is needed in the future.
2) During the off-peak hours, the P2G units have high power outputs, and the total power generation cost will not become unacceptable.1) The collection of waste heat from methanation plants makes the net electricity generation cost more stable.Especially in the midday when the electricity demand is low, the economic benefits are most apparent.
2) Waste heat utilization from methanation plants can offset the heating energy required for circulating water in the original electrolytic hydrogen production process.So, the methanation plants in our model always operate continuously after considering waste heat collection.In actual operation, this is more in line with industrial needs than frequent start-stop cycles.

Conclusion
This paper presents a daily economic dispatch model for power systems considering the thermal compensation of methanation reactors and PEM electrolyzers in P2G units.Compared with the traditional model without considering thermal energy complementarity, our model decreased the daily net electricity generation cost by 1.1% in the case study.The benefits of thermal complementarity will become more apparent as the installed capacity of PEM electrolyzers continues to increase in the future.The significant fluctuations in natural gas prices caused by changes in the international situation have an important impact on the economic benefits of P2G.Future research should focus on the transient characteristics of P2G units interacting with the power system, particularly on whether P2G units can play a certain role during power system faults and the transient impact on the power system from internal faults in P2G units.

Figure 1 .
Figure 1.Schematic diagram of energy flow in the model

4. 3 .
Comparison ResultFirstly, as shown in Figure2, our case study is based on the multi-time period load in M0 when the Power-to-Gas units are not in operation.The data in Figure2represents the sum of loads at all nodes in the IEEE 118 system for each hour, based on the Elia grid load on Sept. 1, 2022[19].

Figure 2
Figure 2 M0 total load per hour

Table 1 .
Parameters of the case study

Table 3 .
Results of the objective function

Table 3
demonstrates that: 1) By comparing the total objective function of M1 and M2, it can be seen that the system's daily net cost is reduced by 1.1% when waste heat collection is considered.
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