Optimal Operation Strategy of PV-Charging-Hydrogenation Composite Energy Station Considering Demand Response

Abstract

Traditional charging stations have a single function, which usually does not consider the construction of energy storage facilities, and it is difficult to promote the consumption of new energy. With the gradual increase in the number of new energy vehicles (NEVs), to give full play to the complementary advantages of source-load resources and provide safe, efficient, and economical energy supply services, this paper proposes the optimal operation strategy of a PV-charging-hydrogenation composite energy station (CES) that considers demand response (DR). Firstly, the operation mode of the CES is analyzed, and the CES model, including a photovoltaic power generation system, fuel cell, hydrogen production, hydrogen storage, hydrogenation, and charging, is established. The purpose is to provide energy supply services for electric vehicles (EVs) and hydrogen fuel cell vehicles (HFCVs) at the same time. Secondly, according to the travel law of EVs and HFCVs, the distribution of charging demand and hydrogenation demand at different periods of the day is simulated by the Monte Carlo method. On this basis, the following two demand response models are established: charging load demand response based on the price elasticity matrix and interruptible load demand response based on incentives. Finally, a multi-objective optimal operation model considering DR is proposed to minimize the comprehensive operating cost and load fluctuation of CES, and the maximum–minimum method and analytic hierarchy process (AHP) are used to transform this into a linearly weighted single-objective function, which is solved via an improved moth–flame optimization algorithm (IMFO). Through the simulation examples, operation results in four different scenarios are obtained. Compared with a situation not considering DR, the operation strategy proposed in this paper can reduce the comprehensive operation cost of CES by CNY 1051.5 and reduce the load fluctuation by 17.8%, which verifies the effectiveness of the proposed model. In addition, the impact of solar radiation and energy recharge demand changes on operations was also studied, and the resulting data show that CES operations were more sensitive to energy recharge demand changes.

1. Introduction

The consumption of oil resources by traditional vehicles accounts for 60% of the total consumption [1]. In addition, considering that China proposes to achieve a carbon peak by 2030 and carbon neutrality by 2060, the development of NEVs with low power consumption and pollution-free characteristics is an effective way to reduce dependence on oil resources and improve environmental pollution. It is also an inevitable trend in the future development of the automotive industry.

NEVs mainly include EVs, HFCVs, etc. While new energy vehicle energy stations provide convenient and safe energy supply services for NEVs, their construction and operation also restrict the further increase in the number of NEVs [2]. At present, the large-scale use of energy stations in the market mainly comprises electric vehicle charging stations, but there are some problems, as follows: the charging station obtains electricity via one route, and the main source is the AC power distribution network [3]. Large-scale EV access will bring risks to the safe operation of the power grid, causing the voltage to exceed the limit [4], and increases in the load peak-to-valley difference [5], etc. At the same time, charging stations do not consider the hydrogenation demand of HFCVs. If renewable energy power generation systems, fuel cells (FC), hydrogen production, hydrogen storage, and hydrogenation equipment are added to the charging station, on the one hand, it can promote the local consumption of renewable energy and improve the renewable energy utilization efficiency of the system [6,7]. Coordinated and optimized operation between subsystems can also reduce operating costs and grid load peak-to-valley differences [8]. On the other hand, it is also conducive to promoting the development of the HFCV industry and realizing low-carbon travel. Therefore, it is necessary to conduct in-depth research on the optimal operation of new energy vehicle energy stations.

Recently, some scholars have studied the optimal operation of integrated renewable energy in new energy vehicle energy stations. The authors in [9] proposed an operation framework of a centralized charging station integrating photovoltaic and battery cascade utilization systems and established a multi-objective operation model of the centralized charging station based on a rolling optimization method to maximize resource utilization. The authors in [10] improved the profitability of quick charging stations and reduced the cost of electricity purchase during peak charging demand with a charging station model including wind power, photovoltaic power generation, and battery energy storage. The genetic algorithm was adopted to solve the model, and the best cost-effectiveness scheme was obtained. The authors in [11] proposed a life-cycle optimization operation method for optical storage charging stations based on deep reinforcement learning, given the complex operation characteristics of the energy storage system and the uncertainty of photovoltaic power generation and EV charging load. The authors in [12] proposed a day-ahead operation strategy of an integrated charging station for PV and storage considering carbon emissions, which can effectively alleviate the impact of large-scale EV charging on the power grid and reduce the cost of carbon emissions. The main limitation of previous studies [9,10,11,12] is that they primarily consider the integration of renewable energy power generation systems into charging stations that cannot provide hydrogen refueling services for HFCVs, and most of the energy storage devices constructed are lithium batteries. Lithium batteries have a self-discharge rate, which increases the energy loss of the system during operation, and the excessive use of lithium battery energy storage in renewable energy sources may lead to a short-term mineral supply shortage in the battery industry. As a green, non-polluting gas, hydrogen can be stored for a long time and has a high energy density. It has developed rapidly in recent years. Renewable energy, hydrogen storage tanks (HSTs), and fuel cells can form a green hydrogen storage system. While providing hydrogen energy supply for HFCV, it can also promote the development of the hydrogen energy industry and reduce carbon emissions. In the research field of absorbing renewable energy, the authors in [13] proposed a capacity allocation method for using a hydrogen production system to absorb wind power. By analyzing the capacity allocation example of the hydrogen production system in single and multiple wind farms, the optimal configuration scheme of the hydrogen production system was obtained. The authors in [14] proposed a two-stage energy management model for a sustainable wind power–photovoltaic–hydrogen storage microgrid based on receding horizon optimization. Through day-ahead and real-time operation strategies, it can effectively eliminate the influence of uncertain factors, improve system operation stability, and reduce operating costs. The authors in [15] designed an off-grid hybrid photovoltaic–diesel–battery system; while effectively solving the energy supply problem in rural areas, this can achieve the lowest net present cost, levelized cost of energy, and CO₂ emission in the system.

As regards the participation of NEVs in the field of DR, if the economic potential of DR can be brought into full play, it will help to realize the complementation advantages of source-load resources [16]. The authors of [17] developed a charging optimization strategy to improve the comprehensive benefits of EVs and charging stations using electricity price incentives and constructed a dual optimization target model with the optimal comprehensive cost of EVs and the optimal comprehensive benefits of charging stations, thus greatly improving the operating benefits of charging stations. The authors in [18] aimed at minimizing the overall operating cost of optical storage and charging stations, whereby PV, energy storage, EVs, and other facilities were controlled by polymerization to participate in DR. In this way, the utilization rate of renewable resources was improved. The authors in [19,20] optimized the charging process and vehicle-to-grid (V2G) interaction process in photovoltaic charging stations, respectively, using real-time electricity prices, effectively improving the economic benefits of the DR strategy. The authors in [21] proposed an optimal charging and discharging scheduling strategy for charging station G2V/V2G and a battery energy storage system (BESS). The charging and discharging conversion efficiencies of electric vehicles under different loads were considered in the scheme based on price demand response in order to maximize profits for charging stations and energy storage systems. The above studies [17,18,19,20,21] mainly considered price-based demand response but ignored the fact that considering incentive-based demand response at the same time can also reduce operating costs.

The current research mainly focuses on charging stations that can only provide charging services for EVs, and there are few studies that consider both EV charging demand and HFCV hydrogenation demand. The authors in [22,23] integrated electrolyzers and HSTs into the charging station, which can meet the energy supply demands of EVs and HFCVs but does not reasonably predict these demands and consider the economic benefits brought by DR. In addition, the optimal operation objective of grid-connected charging stations usually considers economics but does not consider the load fluctuation caused by the tie-line when the renewable energy power generation system and large-scale charging load are connected, which will affect the safe and stable operation of the power grid.

The contribution of this study can be summarized as follows:

(1)

A CES model, including photovoltaic, hydrogen production, hydrogen storage, fuel cells, hydrogenation, and charging, has been established, which can provide energy supply services for EV and HFCV at the same time;

(2)

Based on the analysis of the travel rules of EV and HFCV, the charging demand of EV and hydrogenation demand distribution of HFCV are reasonably predicted by the Monte Carlo method, which is helpful for CES to formulate an operation strategy;

(3)

The two kinds of demand responses are considered at the same time—one is the charging load demand response based on the price elasticity matrix, and the other is the interruptible load demand response based on incentive. A multi-objective operation model considering demand response is also proposed, which is conducive to reducing the comprehensive operation cost and load fluctuation of CES;

(4)

The multi-objective function is transformed into a linear weighted single objective function through the max–min method and analytic hierarchy process, and the improved moth fire-fighting algorithm is used to solve the problem, which has a stronger search ability and obtains the optimal operation strategy with fewer iterations.

2. CES Operation Mode and Structure Composition

2.1. CES Operation Mode

In this paper, a CES model including photovoltaic, charging, and hydrogenation is proposed, which aims to provide energy supply for EV and HFCV at the same time. Its structure mainly includes PVs and fixed loads such as air conditioning lighting, an electrolyzer, HST, FC, a hydrogen dispenser, and a charging pile. The system structure is shown in Figure 1.

In this application scenario, the electricity generated by PV is mainly used for EV charging, hydrogen production from electrolyzers, and daily electricity consumption in the station. Considering that the output power of PV does not match the power required for CES operation, the operation strategy of CES is proposed as follows: When the energy supply demand of EV and HFCV and the fixed load in the station can be met, the remaining output power of the PV will be used for hydrogen production in the electrolyzer. When the HFCV hydrogenation demand can be met but the EV charging demand and fixed load cannot be met, the lack of electric energy is first supplemented by fuel cell power generation. If it still cannot be satisfied, electric energy needs to be purchased from the grid. When the EV charging demand and fixed load can be met but the HFCV hydrogenation demand cannot be met, the PV surplus power is used for hydrogen production, and the shortfall is supplemented by the grid. When all three cannot be satisfied, CES considers the operating economy to reasonably distribute the remaining hydrogen of the HST and the output power of the PV, and then the shortfall of electricity is supplemented by the grid. Due to the existence of peak–valley electricity prices in the power grid, CES should formulate reasonable energy management strategies to reduce operating costs while meeting the charging demand, hydrogenation demand, and fixed load.

2.2. CES Structure Composition

2.2.1. PV Generation Model

The role of the PV generation system in CES is to provide electrical energy for charging piles and electrolyzers. The output power is mainly related to the area of the photovoltaic array, the radiation intensity of the sun, and the ambient temperature. The PV generation model can be expressed as follows:

$$P_t^{PV}=\frac{R_t·{\eta }_{PV}·S}{1000}·\left[1-0.005·\left(C_t^{out}-25\right)\right]$$

(1)

where $P_t^{PV}$ is the PV output power at time $t$; $R_t$ is the solar radiation intensity at time $t$; ${\eta }_{PV}$ is the efficiency of converting light energy into electrical energy; $S$ is the area of the constructed photovoltaic array; $C_t^{out}$ is the ambient temperature at time $t$.

2.2.2. Hydrogen Production and Hydrogen Storage System Model

The main equipment included in the hydrogen production and storage system are electrolyzers, HSTs, and FCs. The function of the electrolyzer is to use electricity to electrolyze water into hydrogen and oxygen, and then compress the hydrogen into high-pressure gaseous hydrogen through a compressor and store it in HST. The HST can supply hydrogen to the HFCV through the hydrogen dispenser, or to the FC, to generate electricity.

(1)

Electrolyzer model

At present, the electrolyzers on the market are mainly alkaline and proton exchange membrane electrolyzers (PEM). The electrolyzer selected in this paper is a proton exchange membrane electrolytic cell, which has the advantages of higher conductivity and lower ohmic loss, and the working efficiency is about 85% [24]. The electrolyzer model is as follows:

$$P_t^{ELE}=\frac{2v^{ELE}F}{{\eta }^{COM}{T}_C}{M}_t^{ELE}$$

(2)

where $P_t^{ELE}$ represents the input power of the electrolytic cell at time $t$; $v^{ELE}$ is the cell operating voltage of the electrolyzer; $F$ is the Faraday constant; ${\eta }^{COM}$ is the energy conversion efficiency of the compressor; $T_C$ is the time constant; $M_t^{ELE}$ is the amount of hydrogen produced by the electrolyzer at time $t$.

(2)

FC model

Considering the intermittent nature of PV power generation, when the PV output power cannot meet the charging demand, the FC can meet this part of the charging demand by consuming the remaining hydrogen to generate electricity. This paper considers the use of a PEM fuel cell [25], and its model is the following:

$$P_t^{FC}=\frac{2.96{\eta }^{FC}{\eta }^{FC,con}F}{T_C}{M}_t^{FC}$$

(3)

where $P_t^{FC}$ represents the output power of the FC at time $t$; ${\eta }^{FC}$ is the efficiency of the FC; ${\eta }^{FC,con}$ is the energy conversion efficiency between the FC and the charging pile; $M_t^{FC}$ is the amount of hydrogen consumed by the FC at time $t$.

(3)

HST model

The hydrogen produced by the electrolyzer cannot be consumed by HFCVs in real time. Therefore, the construction of the HST in the CES station can store excess hydrogen to meet the hydrogen refueling demand in the next moment [26]. The HST model can be expressed as follows:

$$V_t^{TANK}=V_{t-1}^{TANK}+\frac{R{T}^{TANK}}{P^{TANK}}(M_t^{ELE}-M_t^{FC})-V_t^{HFCV}$$

(4)

where $V_t^{TANK}$ and $V_{t-1}^{TANK}$ represent the hydrogen storage volume in the HST at time $t$ and time $t-1$, respectively; $R$ is the gas constant; $T^{TANK}$ is the temperature of the HST; $P^{TANK}$ is the pressure of the HST; $V_t^{HFCV}$ is the hydrogen refueling demand of the HFCVs at time $t$.

3. EV Charging and HFCV Hydrogenation Demand Forecast

The Monte Carlo method is a random sampling statistical method. The charging demand generated by EVs and the hydrogenation demand generated by HFCV are independent and random, but the energy supply demand generated by their large-scale travel conforms to a certain probability distribution. Therefore, the Monte Carlo method can be used to simulate a large number of such events to obtain reasonable predictive values.

3.1. EV and HFCV Daily Travel Distance Probability Distribution

According to the current development of EV and HFCV in the Chinese market [27], the main research objects of this paper are electric private vehicles and hydrogen fuel cell logistics vehicles. Through the analysis of the statistical data of electric vehicle travel, the daily mileage generated by large-scale EV travel conforms to a certain probability distribution, which can be represented by the log-normal distribution function shown in Equation (5). Since HFCV is not widely used at present, and there is a lack of corresponding actual data, this paper assumes that the probability distribution of its daily mileage is the same as that of electric logistics vehicles, and the daily mileage can be calculated by the log-normal distribution function shown in Equation (6) [28]. Then,

$$f_{EV}(x)=\frac{1}{x{\sigma }_{EV}\sqrt{2\pi }}\exp \left[-\frac{{\left(\ln x-{\mu }_{EV}\right)}^2}{2{\sigma }_{EV}^2}\right]$$

(5)

$$f_{HFCV}(x)=\frac{1}{{\sigma }_{HFCV}\sqrt{2\pi }}\exp \left[-\frac{{\left(x-{\mu }_{HFCV}\right)}^2}{2{\sigma }_{HFCV}^2}\right]$$

(6)

where ${\sigma }_{EV}$ and ${\sigma }_{HFCV}$ are the average daily mileage of EV and HFCV, respectively; ${\mu }_{EV}$ and ${\mu }_{HFCV}$ are the variance of daily mileage of EV and HFCV, respectively. By referring to the research in reference [29], this paper takes ${\sigma }_{EV}=0.8$, ${\sigma }_{HFCV}=130$, ${\mu }_{EV}=3.2$ and ${\mu }_{HFCV}=20$.

3.2. Demand Prediction for Charging and Hydrogenation Based on Monte Carlo

We divide a day into $T=24$ periods, each period $\Delta t=1$ h, and use the Monte Carlo method to simulate the EV charging demand and HFCV hydrogenation demand in each period. The simulation flow chart is shown in Figure 2, and the specific steps are as follows:

Step 1: Initialization parameters. Initialize the number of EVs W and the number of HFCVs G, and use the Monte Carlo method to randomly generate the daily travel mileage $L_{d,g}^{EV}$ of the gth EV, the initial battery capacity, the battery capacity threshold that generates charging demands, the daily travel mileage $L_{d,w}^{HFCV}$ of the wth HFCV, the initial hydrogen storage capacity, and the hydrogen storage threshold that generates hydrogen refueling demand.

Step 2: Determination of charging and hydrogenation time. The generation of EV charging demand is mainly related to the initial battery capacity, daily mileage, and power consumption per kilometer of driving. Therefore, the distance $L_g$ traveled by the gth EV from the start of driving to the charging event in one day can be expressed by Equation (7). Similar to the process of EV generation in charging demand, the distance $L_w$ traveled by the wth HFCV from the start of driving to the generation of hydrogenation demand can be expressed by Equation (8) as follows:

$$\{\begin{array}{l}{L}_g=\frac{(Ca{p}_{0,g}^E-Ca{p}_{d,g}^E)}{B_{EV}}\\ L_g=L_{d,g}^{EV}{\displaystyle \sum _{t=1}^{t_g}{f}_{EV}(t)}\end{array}$$

(7)

$$\{\begin{array}{l}{L}_w=\frac{(Ca{p}_{0,w}^H-Ca{p}_{d,w}^H)}{H_{HFCV}}\\ L_w=L_{d,w}^{HFCV}{\displaystyle \sum _{t=1}^{t_w}{f}_{HFCV}(t)}\end{array}$$

(8)

where $Ca{p}_{0,g}^E$ and $Ca{p}_{d,g}^E$ are the battery capacity of the gth EV at the initial driving time of the day and the battery capacity threshold that generates the charging demand, respectively; $B_{EV}$ is the electric power consumption of the EV per 1 km of travel; $t_g$ is the time at which the charging of the gth EV occurs; $f_{EV}(t)$ is the percentage of the EV’s mileage in each period out of the daily mileage; $Ca{p}_{0,w}^H$ and $Ca{p}_{d,w}^H$ are the hydrogen storage capacity of the wth HFCV at the initial driving time of the day and the minimum hydrogen storage capacity used to generate hydrogen refueling demand, respectively; $H_{HFCV}$ is the hydrogen consumption per 1 km of HFCV driving; $t_w$ is the time at which the demand for hydrogenation of the wth HFCV arises; $f_{HFCV}(t)$ it is the percentage of the mileage of the HFCV in each period to the daily mileage. The first row and the second row in Equations (7) and (8) can be combined to obtain the timing of the EV-generated charging demand and the HFCV-generated hydrogenation demand.

Step 3: Accumulation charging load and hydrogenation demand. Assuming the EV fills the battery with every charge, the HFCV fills up the HST every time it refuels. According to the time and amount of charging demand generated by the EV and the time and amount of hydrogen charge generated by the HFCV, we superimpose each period to obtain the total charging amount $Q_t^{EV}$ and the hydrogenation demand $V_t^{HFCV}$ in each period, as shown in Equations (9) and (10) as follows:

$$Q_t^{EV}={\displaystyle \sum _{g=1}^{G_t}(B_r-Ca{p}_{t_g,g}^E)}$$

(9)

$$V_t^{HFCV}={\displaystyle \sum _{w=1}^{W_t}(V_r-Ca{p}_{t_w,w}^H)}$$

(10)

where $G_t$ and $W_t$ are the number of vehicles generating charging demand and hydrogen refueling demand at the time $t$; $B_r$ and $V_r$ are the rated battery capacity of EV and the rated hydrogen storage capacity HFCV, respectively; $Ca{p}_{t_g,g}^E$ is the remaining battery capacity of the gth EV that generates the charging demand at time $t_g$; $Ca{p}_{t_w,w}^H$ is the remaining hydrogen when the wth HFCV generates hydrogen demand at time $t_w$.

3.3. CES Demand Response Model

DR means that users can actively change their original electricity consumption behavior according to price signals or incentive mechanisms. The response methods can be divided into price-based DR and incentive-based DR [30]. This paper mainly considers price-based DR based on charging price and interruptible load based on incentives. For HFCV, since HFCV does not directly participate in the power exchange, it can flexibly adjust the hydrogen production state of the electrolyzer through internal decision-making to optimize operation. For EVs, dynamic charging prices are used, and the CES needs to consider its own operating costs and formulate an optimal charging price plan according to PV power generation, stored energy, and charging load to guide users to transfer charging periods and their needs so that they can appropriately reduce/increase charging capacity during high/low electricity price periods, thereby improving the economics and flexibility of CES operations. In this paper, the electricity price elasticity matrix D is used to describe the response quantity of the charging load [31]. Then,

$$D=\left[\begin{array}{cccc}{\epsilon }_{11}& {\epsilon }_{12}& \cdots & {\epsilon }_{1t^{\prime }}\\ {\epsilon }_{21}& {\epsilon }_{22}& \cdots & {\epsilon }_{2t^{\prime }}\\ ⋮& ⋮& \ddots & ⋮\\ {\epsilon }_{t1}& {\epsilon }_{t2}& \cdots & {\epsilon }_{t{t}^{\prime }}\end{array}\right]$$

(11)

$${\epsilon }_{t{t}^{\prime }}=\frac{\Delta P_t^{EV}}{P_t^{EV}}/\frac{\Delta {\lambda }_{t^{\prime }}^{\mathrm{s}}}{{\lambda }_{t^{\prime }}^{\mathrm{s}}}$$

(12)

where ${\epsilon }_{t{t}^{\prime }}$ is the elastic coefficient, which, when $t=t^{\prime }$, is the self-elastic coefficient, referring to the impact of price changes in a certain period. When $t\ne t^{\prime }$, this gives the mutual elasticity coefficient, and refers to the influence of price changes in one period on other periods. $\Delta P_t^{EV}$ and $P_t^{EV}$ are the changes in the charging power after DR and the charging power before DR at time $t$, respectively. $\Delta {\lambda }_{t^{\prime }}^{\mathrm{s}}$ and ${\lambda }_{t^{\prime }}^{\mathrm{s}}$ are the amounts of electricity price change after DR and the electricity price before DR.

Then, according to Equations (11) and (12), the change in the charging load after DR is the following:

$$\Delta P_t^{EV}={\displaystyle \sum _{t^{\prime }=1}^T\frac{{\epsilon }_{t{t}^{\prime }}\Delta {\lambda }_{t^{\prime }}^{\mathrm{s}}}{{\lambda }_{t^{\prime }}^{\mathrm{s}}}}{P}_t^{EV}$$

(13)

It should be noted that this paper only considers EV charging and does not consider EV discharging to the grid.

There is daily electrical equipment, such as lighting and air conditioners, inside CES. Assuming that these loads are interruptible, interruptions can be made at appropriate times to respond to the CES’s operational needs and relieve the operating pressure of CES during peak load hours, but this will incur certain load interruption costs, the actual amount of which can be determined by the CES internal operation strategy. As a whole, CES coordinates various resources, implements optimized operation strategies through its energy management system, and makes full use of demand-side response resources, thereby realizing the safe, economical, and efficient operation of CES.

4. CES Multi-Objective Optimization Operation Model Considering Demand Response

After simulating the charging and hydrogenation demands of each period based on the Monte Carlo method, a multi-objective operation optimization objective function of CES considering the DR is established, including the minimum comprehensive operation cost of CES and the minimum load fluctuation.

4.1. Objective Function

4.1.1. CES Comprehensive Operating Cost

The FC operation will cause voltage decay during starting, stopping, light loading, load changes, and heavy loading, resulting in a corresponding degradation cost [32]. Therefore, the comprehensive operating cost $f_1$ of the CES during the operation period includes the operation and maintenance cost $f_{op}$ of each component, the cost of power purchased from the grid, $f_{gr}$ and the degradation cost $f_{de}$ caused by the FC in different operating states. The mathematical model is as follows:

$$\min f_1=f_{op}+f_{gr}+f_{de}$$

(14)

$$f_{op}={\displaystyle \sum _{t=1}^T(k_P{P}_t^{PV}+k_C{P}_t^{EV}}+k_E{P}_t^{ELE}+k_F{P}_t^{FC}+k_V{V}_t^{TANK}+k_{DR}\Delta P_t^{EV}+k_{IL}\Delta P_t^{\mathrm{IL}})$$

(15)

$$f_{gr}={\displaystyle \sum _{t=1}^T{P}_t^{GR}{p}_t^{in}}$$

(16)

$$f_{de}={\displaystyle \sum _{t=1}^T(n_t^s{V}_1+n_t^c{V}_2+l_t{U}_1+h_t{U}_2)}·c_d$$

(17)

where $k_P$, $k_C$, $k_E$, $k_F$, and $k_V$ are the operation and maintenance cost coefficients of photovoltaics, charging piles, electrolyzers, FCs, and HSTs, respectively; $k_{DR}$ and $k_{IL}$ are the charging load DR cost coefficient and interruptible load cost coefficient, respectively; $\Delta P_t^{\mathrm{IL}}$ is the interruptible load; $P_t^{GR}$ is the transmission power between the CES and the grid; $p_t^{in}$ is the price of purchasing electricity from the grid at time t. $n_t^s$ and $n_t^c$ are the times of the starting and stopping and load changes of the FC at time t, respectively; V₁ and V₂ are the voltage attenuations caused by start-stop and load changes, respectively; U₁ and U₂ are the voltage attenuations caused by the fuel cell working under light load and heavy load, respectively; $l_t$ and $h_t$ are the light load running time and the heavy load running time, respectively; $c_d$ is the cost coefficient of voltage attenuation.

4.1.2. CES System Load Fluctuation

The accumulation of charging loads and hydrogenation loads in a certain period will cause the charging piles and electrolyzers to work at high power, forming a new load peak; if the PV output power is insufficient at this time, CES will have to buy a lot of electricity through the tie-line, which will have an impact on the safe operation of the grid. Therefore, this paper introduces the load mean square variance into the objective function to reduce the load fluctuation of CES. Then,

$$\min f_2={\left[\frac{1}{T}{\displaystyle \sum _{t=1}^T{\left(P_t^{GR}-P_{\mathrm{av}}\right)}^2}\right]}^{1/2}$$

(18)

$$P_{\mathrm{av}}=\frac{1}{T}{\displaystyle \sum _{t=1}^T{P}_t^{GR}}$$

(19)

where $P_{\mathrm{av}}$ is the average load curve of CES during operation.

The optimization operation objective function is a multi-objective function. After normalization by the maximum and minimum methods, [33], the values of each sub-objective function will be in the same order of magnitude, and then the multi-objective function is transformed into a multi-objective evaluation index F after linear weighting. The processed objective function can be expressed as follows:

$$\min F={\lambda }_1\frac{f_1-f_{1,\min }}{f_{1,\max }-f_{1,\min }}+{\lambda }_2\frac{f_2-f_{2,\min }}{f_{2,\max }-f_{2,\min }}$$

(20)

where $f_{1,\min }$ and $f_{1,\max }$ are the minimum and maximum values of the comprehensive operating cost recorded in the optimization process, respectively; $f_{2,\min }$ and $f_{2,\min }$ are the minimum and maximum values of the load fluctuation recorded in the optimization process, respectively; ${\lambda }_1$ and ${\lambda }_2$ are the weight coefficients of the sub-objective function, satisfying ${\lambda }_1+{\lambda }_2=1$. This paper considers the use of the AHP and combines the importance of the two sub-objective functions to determine the weight coefficient [34], as shown below as follows:

$${\lambda }_i=\sqrt[m]{{\displaystyle \prod _{j=1}^m{a}_{ij}}}/{\displaystyle \sum _{i=1}^m\sqrt[m]{{\displaystyle \prod _{j=1}^m{a}_{ij}}}},(i=1,2,\cdots ,m)$$

(21)

where ${\lambda }_i$ is the weight coefficient of the ith sub-objective function; $m$ is the order of the matrix; $a_{ij}$ is the result of a comparison of the importance between element i and element j in the AHP judgment matrix. In this paper, the sub-objective functions are scaled as 3 and 2 based on AHP, and ${\lambda }_1=0.6$ and ${\lambda }_2=0.4$ are obtained after calculation.

4.2. Constraint Condition

4.2.1. PV Output Power Constraint

The PV output power cannot exceed the limit, then

$$0\le P_t^{PV}\le P_{\max }^{PV}$$

(22)

where $P_{\max }^{PV}$ is the maximum output power of the PV.

4.2.2. Hydrogen Production and Hydrogen Storage System Constraints

The constraints of the hydrogen production and storage system include the power constraint of the electrolyzer, the power constraint of the FC, and the capacity constraint of the HST, as shown in the following formula:

$$\{\begin{array}{l}{P}^{ELE,\min }\le P_t^{ELE}{\eta }_t^{ELE}\le P^{ELE,\max }\\ P^{FC,\min }\le P_t^{FC}{\eta }_t^{FC}\le P^{FC,\max }\\ V^{TANK,\min }\le V_t^{TANK}\le V^{TANK,\max }\\ V_{24}^{TANK}=V_{init}^{TANK}\\ {\eta }_t^{ELE}+{\eta }_t^{FC}\le 1\\ \mathrm{Equations} (2)\text{–}(4)\end{array}$$

(23)

where $P^{ELE,\min }$ and $P^{ELE,\max }$ are the minimum and maximum working powers of the electrolyzer, respectively; $P^{FC,\min }$ and $P^{FC,\max }$ are the minimum and maximum working powers of the FC; $V^{TANK,\min }$ and $V^{TANK,\min }$ are the minimum and maximum storage capacities of the HST; $V_{init}^{TANK}$ represents the initial hydrogen storage capacity of the HST. The fourth line of Formula (23) ensures that the hydrogen storage capacity of the HST at the last moment of the day is equal to the initial quantity of hydrogen; ${\eta }_t^{ELE}$ and ${\eta }_t^{FC}$ are the binary variables of the working state of the electrolyzer and the FC at time t, respectively; when ${\eta }_t^{ELE}=1$ or ${\eta }_t^{FC}=1$, this indicates that the electrolyzer or FC is working at time t; when ${\eta }_t^{ELE}=0$ or ${\eta }_t^{FC}=0$, this indicates that the electrolyzer or FC is not working at time t. It should be noted that if both the electrolyzer and the FC work at time t, the FC will generate electricity by consuming hydrogen, and the electrolyzer will also produce hydrogen by consuming the electricity provided by the FC. Such repeated operations will greatly increase the energy loss and operation cost of the system. Therefore, line five ensures that the electrolyzer and FC cannot be run at the same time. The HST can supply hydrogen to the HFCV through the hydrogen dispenser while supplying hydrogen to the FC.

4.2.3. Tie-Line Power Constraint

If the transmission power of the tie-line between the CES and the power grid cannot exceed its capacity limit, then

$$0\le P_t^{GR}\le P_{l,\max }$$

(24)

where $P_{l,\max }$ is the maximum capacity of the tie line between the CES and the power grid.

4.2.4. Charging Demand Constraint

This paper assumes that the EV is charged with constant power, and the energy provided by the CES to the EV in each period should be equal to the charging demand generated by it, as follows:

$$Q_t^{EV}=P_t^{EV}·\Delta t$$

(25)

4.2.5. Hydrogenation Demand Constraint

The hydrogen stored in the HST should meet the hydrogenation demand of HFCV in each period as follows:

$$V_t^{HFCV}\le V_t^{TANK}$$

(26)

4.2.6. DR Constraints

In addition to meeting the constraints of Equations (11)–(13), when the charging load participates in the price type DR, it should meet the constraints of the change rate in the electricity price and the degree of change in the charging load. Charging load has the characteristics of time sequence translation, and the total degree of change in the whole operation cycle should be 0. Then,

$$\Delta {\lambda }_t^{\min }\le \Delta {\lambda }_t^{\mathrm{s}}\le \Delta {\lambda }_t^{\max }$$

(27)

$$\Delta P_{\min }^{EV}\le \Delta P_t^{EV}\le \Delta P_{\max }^{EV}$$

(28)

$${\displaystyle \sum _{t=1}^T\Delta P_t^{EV}}=0$$

(29)

where $\Delta {\lambda }_t^{\min }$ and $\Delta {\lambda }_t^{\max }$ are the minimum and maximum values of electricity price change, respectively; $\Delta P_{\min }^{EV}$ and $\Delta P_{\max }^{EV}$ are the minimum and maximum values of EV charging power variation, respectively.

The constraint of the interruptible load is the following:

$$0\le \Delta P_t^{\mathrm{IL}}\le {\lambda }_{\mathrm{IL}}{P}_t^L$$

(30)

where $\Delta P_t^{\mathrm{IL}}$ is the interruption load at time t; ${\lambda }_{\mathrm{IL}}$ is interruptible load factor; $P_t^L$ is the fixed electricity load of CES at time t.

4.2.7. Power Balance Constraint

The sum of the power of charging piles, electrolyzers, charging power transfer, fixed load, and interruptible load power in each period during operation should be equal to the sum of the photovoltaic output power, the electricity purchased from the grid, and the FC output power,

$$P_t^{EV}+P_t^{ELE}+\Delta P_t^{EV}+P_t^L-\Delta P_t^{\mathrm{IL}}=P_t^{PV}+P_t^{FC}+P_t^{GR}$$

(31)

5. Solving Algorithm and Process

5.1. Improved Moth–Flame Optimization Algorithm

The moth–flame optimization (MFO) algorithm is a swarm intelligence optimization algorithm proposed by Mirjalili by simulating the flight trajectory of moths [35]. The CES operation problem considering DR proposed in this paper is a multi-variable, multi-objective complex optimization problem in which the objective function includes comprehensive operating costs and load fluctuation indicators. Considering the influence and constraints of DR, the amount of calculation is large, and the conventional mathematical method is difficult to solve, so this paper solves the running model with the help of the MFO algorithm. Compared with the traditional particle swarm algorithm, the results obtained using MFO are better. However, when using the MFO algorithm to solve the running model, in the later stage of the iteration, the difference in the fitness value of the objective function is small, and it is easy to fall into the local optimum. Therefore, this paper introduces an improved MFO [36], which updates the positions of moths by introducing dynamic inertia weights, and generates mutated moths to expand the search range, such that the algorithm can optimally solve the model. The moth position update formula is as follows:

$$M_k=\omega ·D_k·e^{b·\theta }·\cos (2\pi t)+(1-\omega )·F_z$$

(32)

$$\omega =2\times (1-\sin (0.5\times \pi \times \frac{t_b}{t_{\max }}))\times \partial$$

(33)

where $M_k$ is the position of the kth moth; $F_z$ represents the position of the zth flame; $D_k$ represents the distance between the kth moth and the zth flame, namely, $D_k=|F_z-M_k|$; $b$ is the logarithmic spiral constant greater than 0; $\theta$ is a random number between −1 and 1; $\omega$ is the inertia weight; $t_b$ represents the current number of iterations; $t_{\max }$ is the maximum number of iterations.

By introducing a mutation strategy to generate mutant moths, the search range of the algorithm can be expanded, and the diversity of the population can still be maintained at the later stage of the iteration to escape the local optimal solution. Assuming that $(x_{1j},x_{2j},···,x_{nj})$ represents the value of n moths in the jth dimension, the center of gravity $Z_j$ of the population in the jth dimension is the following:

$$Z_j=\frac{x_{1j}+x_{2j}+\cdots +x_{nj}}{n}$$

(34)

If we let $x_i=\left(x_{i1},x_{i2},\cdots ,x_{id}\right)$ represent the ith moth with dimension j, and the selected variation dimension is the jth dimension, then the inverse solution of the center of gravity corresponding to the moth is $x_{op,i}=(x_{op,i1},x_{op,i2},···,x_{op,id})$, which is calculated as follows:

$$x_{op,i}=2\times \alpha \times Z_j-x_i$$

(35)

where $\alpha$ is the contraction factor, $\alpha \in [0,1]$. In the calculation process, the moth selects a certain dimension j for mutation and compares it with the position of the previous iteration, in order to retain better mutation.

5.2. Solving Process

The solution flow of the CES optimization operation model based on the IMFO algorithm is shown in Figure 3.

Step 1: Divide the running time of a day into 24 periods, each of which is 1 h. According to the simulation results using the Monte Carlo method, the charging demand of an EV and the hydrogenation demand of HFCV in each period are input. The output power $P_t^{EV}$ of the photovoltaic system in each period is obtained according to the illumination data of a typical day. Enter the fixed load $P_t^L$ for CES.

Step 2: Initialize the algorithm parameters. Input constraints such as hydrogen production, hydrogen refueling, hydrogen storage systems, DR, power balance, power grid tie-line power capacity, etc., randomly generate moth positions within the constraints and compile variables such as $P_t^{ELE}$, $P_t^{FC}$ and $P_t^{PV}$ into moth position dimensions.

Step 3: According to Equations (14)–(21), take the optimization operation objective function of CES as the fitness value of the algorithm, calculate the fitness value of each moth, arrange them in increasing order, and assign them to the flame as the location of the first-generation flame.

Step 4: Formulas (32) and (33) were used to update the current positions of moths, and Formulas (34) and (35) were used to reverse the center of gravity variation of moths. The fitness values of the updated moth position and the flame position were reordered, and the space position with the better fitness values was selected as the next-generation flame position.

Step 5: Reduce the number of flames through the following adaptive mechanism:

$$flame.no=round\left(N-t_b\ast \frac{N-1}{t_{\max }}\right)$$

(36)

where N represents the number of flames.

Step 6: If the termination condition of the iteration is not reached, return to step 3; if the termination condition is reached, output the optimal result and record it.

6. Case Analysis

6.1. Basic Parameters

Assuming that CES provides energy supply services for 800 EVs and 80 HFCVs in the area, the constructed photovoltaic array area is 34,000 m², and the solar radiation intensity and ambient temperature on a typical day are shown in Figure 4, along with the PV conversion efficiency ${\eta }_{PV}=20\%$. The relevant parameters of the hydrogen production system are shown in

Table 1. Related parameters of the hydrogen production system.

Parameter	Value	Parameter	Value
$v^{ELE}$	2 V	${\eta }^{FC}$	47%
$F$	96,485 C·mol−1	${\eta }^{FC,con}$	95%
${\eta }^{COM}$	95%	$R$	0.008314 MPa·mol−1
$T_H$	3600	$T^{TANK}$	273 K
$P^{ELE,\min }$	0	$P^{TANK}$	20 MPa
$P^{ELE,\max }$	5000 kW	$V^{TANK,\min }$	0
$P^{FC,\min }$	0	$V^{TANK,\max }$	4800 N/m3
$P^{FC,\max }$	600 kW	$U_1$	8.66 μV/h
$V_1$	13.79 μV/time	$U_2$	10 μV/h
$V_2$	0.42 μV/time	-	-

[23], and the initial hydrogen quantity of the HST is set as 380 N/m³. According to the analysis of NHTS statistics [37], the travel proportions of EV and HFCV in each period are shown in

Table A1. Percentage of EV mileage in each period to daily mileage.

Period	1	2	3	4	5	6	7	8	9	10	11	12
Percentage/%	0.44	0.21	0.11	0.07	0.19	0.81	2.54	6.13	7.69	5.61	6.45	6.57
Period	13	14	15	16	17	18	19	20	21	22	23	24
Percentage/%	6.51	6.91	6.98	7.21	8.78	9.05	5.28	4.41	2.78	2.06	1.95	1.26

and

Table A2. Percentage of HFCV mileage in each period to daily mileage.

Period	1	2	3	4	5	6	7	8	9	10	11	12
Percentage/%	0.54	0.41	0.31	0.27	0.19	0.81	2.54	3.01	4.21	5.61	7.81	8.70
Period	13	14	15	16	17	18	19	20	21	22	23	24
Percentage/%	6.68	5.22	5.20	5.83	5.32	5.68	6.25	8.18	7.56	5.56	2.85	1.26

in Appendix A, respectively. The battery capacity of the EV is 55 kWh, the power consumption is 0.18 kWh/km, the initial battery capacity is evenly distributed among $[0.6B_r,B_r]$, and the minimum battery capacity required to generate charging demand is $Ca{p}_d^E=0.2B_r$. The initial amount of hydrogen is uniformly distributed within $[0.6V_r,V_r]$, and the minimum amount of hydrogen required to generate hydrogenation is $Ca{p}_d^H=0.1V_r$.

The upper limit of the transmission power of the tie-line is 2000 kW. The operation and maintenance cost coefficients $k_P=0.01$, $k_C=0.1$, $k_E=0.25$, $k_F=0.087$, and $k_V=0.085$. The price of purchasing electricity from the grid in the CES is the time-of-use electricity price. The peak periods are 9:00–11:00 and 18:00–21:00, and the electricity price is 1.1 CNY/kWh; the valley period is from 1:00 to 6:00, and the electricity price is 0.49 CNY/kWh. The normal periods are 7:00–8:00, 12:00–17:00, and 22:00–24:00, and the electricity price is 0.83 CNY/kWh. Considering EV participation in DR, the self-elasticity coefficient is −0.35, and the mutual elasticity coefficient is −0.063; the fixed loads, such as air conditioning and lighting in the CES station, are shown in Figure 5; the coefficient of the interruptible load is 0.3, and the interruption cost is 0.9 CNY/kW. The initial charging electricity price of the EV is 1.8 CNY/kWh, the charging load change is limited to 400 kW, the load transfer cost is 0.25 CNY/kW, and the charging electricity price change is limited to 0.8 CNY/kWh. The FC degradation cost is $c_d$ = 0.9 CNY/μV.

6.2. Analysis of Simulation Results

6.2.1. Charging and Hydrogen Demand Results

The charging demand of an EV at each period and the hydrogenation demand of HFCV under standard atmospheric pressure are simulated by the Monte Carlo method, as shown in Figure 6.

As can be seen from Figure 6, the EV charging demand and the HFCV hydrogenation demand are both large in the daytime because a large amount of travel during this period consumes more electric energy and hydrogen energy, which thus necessitates timely charging in order to meet the travel demand during the next period. At night, the demand for both will gradually decay, and it will remain at a lower level during the period from 24:00 to 6:00. From the point of view of the charging time, there will be two obvious peaks in the charging demand and the hydrogenation demand on a single day. The difference is that the charging peaks of the two do not fall within the same period. The peak EV charging demand periods are 9:00–10:00 in the morning and 17:00–19:00 in the evening. These two periods are also CES power purchases. During the electricity price peak period, if the photovoltaic output cannot meet the charging demand during this period, CES will purchase a large amount of electricity from the grid, which will increase the operating cost while also putting pressure on the safe and stable operation of the grid. Therefore, CES needs to formulate a reasonable operation strategy according to the charging timing distribution of EVs and HFCVs in order to provide safe and efficient charging services to EVs and HFCVs while reducing their operating costs.

6.2.2. CES Operation Result Analysis

According to the time-series distribution of charging and hydrogenation demands, the CES power balance results relating to DR are shown in Figure 7, and the hydrogen storage state is shown in Figure 8.

As can be seen from Figure 7 and Figure 8, in periods 1–4, since the output power of the photovoltaic is 0, the CES needs to purchase electric energy from the grid in order to meet the EV charging demand and the fixed load in the CES. At the same time, the hydrogen storage capacity of the HST gradually decreased since there was no hydrogen production in the electrolyzer during this period, and the hydrogenation demand of the HFCV was mainly met by the initial hydrogen capacity of the HST.

During periods 5–16, the photovoltaic output power can meet the operating requirements of the CES; the remaining photovoltaic output power will be used for hydrogen production in the electrolyzer. Since this part of the hydrogen production volume is greater than the hydrogenation demand of HFCV, excess hydrogen will be stored. In HST, the hydrogen storage capacity of the HST gradually increased, and it reached its highest peak in the 15th period. In the 17th period, the photovoltaic output can just meet the fixed load and EV charging demand in the station, and the remaining hydrogen in the HST can also meet the hydrogen refueling demand during this period, so there is no need to purchase electricity from the grid.

During the period from 18 to 24, the electricity purchase price is high, and the charging demand of EVs and the hydrogenation demand of HFCV are still relatively large. The remaining hydrogen of the HST is used to meet the hydrogenation demand during this period, and the hydrogen storage capacity is continuously reduced. The photovoltaic output cannot meet the charging needs of CES, so a large amount of electricity needs to be purchased from the grid during this period. To reduce the power purchase cost of CES, the FC consumes the remaining hydrogen of HST to provide part of the electricity to the charging piles during the 18–19 period; at the same time, during the power purchase period, the EV charging load transfers part of the load via price guidance. During peak pricing periods 18–21, when the load interruption cost is lower than the electricity price cost, CES reduces the operating costs by interrupting part of the fixed load.

Figure 9 shows the optimal charging price scheme after considering DR and the charging price before DR.

As can be seen from Figure 9, during periods 5–16, the charging price after considering DR is reduced, while the charging price in other periods is increased. The reason is that CES needs to consider its own operation costs and load fluctuations to adjust the charging price. When the sum of the output and stored energy of PV is greater than the energy consumed by operation, the charging degree of EV during this period can be increased by reducing the charging price. When the energy is insufficient, to avoid the necessity for a large number of power purchases from the grid that will increase the operating costs and load fluctuations on the tie-line, the charging amount during this period is reduced by increasing the price. This also illustrates the effectiveness of using dynamic charging prices to change the load response.

6.2.3. Analysis of CES Operation Results under Different Scenarios

To verify and consider the impact of DR on the economic operation of CES, this paper sets the following four scenarios with the same basic parameters:

• Scenario 1: DR is not considered;
• Scenario 2: Considering only interruptible load DR;
• Scenario 3: Considering only price-based DR;
• Scenario 4: Considering both interruptible load and price-based DR—the method proposed in this paper.

The four scenarios are solved separately, and the respective interruptible load costs, load transfer costs, comprehensive operating costs, and load fluctuations are shown in

Table 2. Comparative analysis of operating costs in different scenarios.

Scenario	Interruptible Load Cost (CNY)	Charge Power Transfer Cost (CNY)	Comprehensive Operating Cost (CNY)	Load Fluctuation (kW)
1	-	-	24,132.14	525.43
2	240.02	-	24,079.13	503.77
3	-	772.73	23,249.06	480.50
4	240.02	893.70	23,080.64	446.06

.

As can be seen from Table 2, Scenario 2 and Scenario 3 are compared with Scenario 1. Although Scenario 2 increases the cost of interruptible load and Scenario 3 increases the cost of load transfer, the comprehensive operating costs of both CESs are reduced by 21.66 kW and 44.93 kW, respectively, and the load fluctuates. This is because, in Scenario 2, the interruption fee of the interruptible load during the peak period is lower than the electricity purchase price, so the CES-interrupting part of the fixed load during the peak period can improve the economic benefits. In Scenario 3, part of the charging load is transferred from the peak period to the flat valley period and the peak period of the photovoltaic output through price guidance, which leads to a reduction in the charging quantity in the peak period of power purchase, reduced comprehensive operation cost, and reduced load fluctuation. Scenario 4 considers both price-type and interruptible-load DR. Compared with scenario 1, which does not consider DR, the comprehensive operating cost is reduced by 1051.5 CNY, and the load fluctuation is significantly reduced, which is conducive to giving full play to the economic potential of CES demand response. This shows the effectiveness of the model proposed in this paper.

6.2.4. Algorithm Performance Analysis

In order to further evaluate the effectiveness of the IMFO algorithm in solving the CES optimization operation problem, the optimization of the IMFO algorithm, the MFO, and the PSO algorithm were compared and analyzed. The parameters of the algorithm are set as follows: for the logarithmic helical constant $b=1$ of the IMFO algorithm, the dynamic inertia weight $w$ is used; for the logarithmic helical constant $b=1$ of the MFO algorithm, there is no dynamic inertial weight; the inertial weight of the PSO algorithm $w=0.9$, the individual learning factor $c_1=2.0$, and the global learning factor $c_2=2.0$. For fairness of comparison, the number of iterations set for the three algorithms is 300, the population size is 30, and each is run 100 times. Figure 10 shows the iterative curve used for each algorithm to obtain the optimal fitness value.

It can be seen from Figure 10 that within the range of 300 iterations, the IMFO achieves effective convergence earlier than MFO and PSO, and the obtained objective function value is also smaller than in MFO and PSO. In order to better compare the performances of different algorithms, the results of 100 runs were counted using boxplots, as shown in Figure 11, and the average values obtained are shown in

Table 3. Average of 100 runs of different algorithms.

Algorithm	PSO	MFO	IMFO
Comprehensive operating cost average (CNY)	23,088.02	23,086.75	23,084.23
Load fluctuation average (kW)	453.28	450.01	448.82

.

According to Figure 11 and Table 3, compared with the other two algorithms, the IMFO algorithm has a smaller median and average results after 100 runs, and the distance between the median and the lower quartile and lower edge is closer, indicating that the consistency of the results calculated by the IMFO algorithm is higher, the robustness of the algorithm is the best, and the probability of obtaining smaller comprehensive operating costs and load fluctuations during calculation is also higher.

6.2.5. Influence of Elasticity Coefficient

The above research considers a dynamic charging price. In the case of a given elasticity coefficient, the price elasticity matrix is used to describe the impact of the change in the charging price on the load response. This subsection will discuss the effect of different elastic coefficients on the comprehensive operating cost and load fluctuation as shown in Figure 12.

In Figure 12, three elastic coefficients are given, which are reduced once and twice compared to the original elastic coefficient $({\epsilon }_{t{t}^{\prime }}=-0.35,{\epsilon }_{tt}=-0.063)$. Different elasticity coefficients also imply different impacts of price changes on load response. With the reduction in the elasticity coefficient, both the comprehensive operating cost and the load fluctuation are reduced to different degrees. Compared with the original elasticity coefficient, the operating cost is reduced by CNY 446.61, and the load fluctuation is reduced by 11.2 kW when the elasticity coefficient is reduced twice, indicating the effectiveness of establishing a price-based demand response through the price elasticity matrix.

6.2.6. Sensitivity Analysis

The size of each component of CES is fixed; therefore, changes in solar radiation and changes in NEV energy supply requirements will affect the operation of CES. This subsection presents two sensitivity analyses, namely, the impacts of changes in solar radiation between −10% and 10%, and of changes in charging and hydrogenation demand between −10% and 10%, on the comprehensive operating costs and load fluctuations of CES. The results are shown in Figure 13 and Figure 14, respectively.

It is certain that with the increase in solar radiation, the power generation of PV will also increase. Therefore, as can be seen in Figure 13, with the increase in solar radiation, the comprehensive operation cost and load fluctuation both decrease. The operating cost changed the most when the solar radiation was −10%, with a change of +8.87%. When the solar radiation was +10%, the load fluctuation was the largest, at −35.4%. However, when the solar radiation varied between 0% and 10%, the reduction in operating cost was not obvious, indicating that the operating cost was not sensitive to changes in solar radiation at this time.

In Figure 14, as the demand for charging and hydrogenation varies between −10% and 10%, the comprehensive operation cost and load fluctuation of CES both show a rapid upward trend, indicating that the operation of CES is more sensitive to these two types of demands. When the demand is +10%, the operating cost changes the most, by 16.32%. Load fluctuation undergoes the largest change when the demand is −10%, at −43.24%.

7. Conclusions

This paper firstly constructs a CES model including photovoltaics, FCs, hydrogen production, hydrogen storage, hydrogen refueling, and charging, and then establishes a CES demand response model based on the time-series forecast of EV charging demand and HFCV hydrogenation demand. A multi-objective optimization operation strategy of CES considering DR is proposed with the minimum comprehensive operating cost and load fluctuation of CES, and this is solved by an improved moth–fire algorithm, which verifies the validity of the proposed model. The simulation example is analyzed, and the conclusions are as follows:

(1)

The energy supply demand of EV and HFCV will show two peak periods in a day. The use of price guidance can transfer part of the charging power to the peak period of photovoltaic output and formulate a reasonable hydrogen production plan, which can promote photovoltaic consumption, achieve source–load resource complementarity, and reduce electricity purchases during peak electricity price periods;

(2)

Comparative analysis shows that considering both price-based DR and interruptible load resources can greatly reduce the comprehensive operating cost of CES and can effectively improve load fluctuations;

(3)

The proposed model is solved by the improved moth–flame algorithm, which is superior to the PSO and MFO algorithms in terms of both algorithm performance and results;

(4)

Sensitivity analysis research shows that compared with the change in solar radiation in the range of −10–10%, the change in energy supply demand in this range has a greater impact on the operation of CES.

Although the proposed CES operation strategy considering demand response can effectively reduce the impact of operation cost and load fluctuation on the tie-line, this paper studies the day-ahead operation strategy. In the real-time operation process, there are uncertainties in the solar radiation and energy supply demand, which will cause errors in the operation results. In future research, on the one hand, a multi-timescale scheduling strategy will be considered for CES operation, and more refined and accurate results will be achieved by combining day-ahead and real-time operation strategies. Meanwhile, conditional value-at-risk is introduced to quantify the uncertainty risk. On the other hand, users’ satisfaction with the demand response is considered in the CES operation to provide better energy supply services.