Hierarchical Stochastic Optimal Scheduling of Electric Thermal Hydrogen Integrated Energy System Considering Electric Vehicles

Abstract

After a large number of electric vehicles (EVs) are connected to the integrated energy system, disorderly charging and discharging of EVs will have a negative impact on the safe and stable operation of the system. In addition, EVs’ uncertain travel plans and the stochastic fluctuation of renewable energy output and load power will bring risks and challenges. In view of the above problems, this paper establishes a hierarchical stochastic optimal scheduling model of an electric thermal hydrogen integrated energy system (ETH-IES) considering the EVs vehicle-to-grid (V2G) mechanism. The EVs charging and discharging management layer aims to minimize the variance of the load curve and minimize the dissatisfaction of EV owners participating in V2G. The multi-objective sand cat swarm optimization (MSCSO) algorithm is used to solve the proposed model. On this basis, the daily stochastic economic scheduling of ETH-IES is carried out with the goal of minimizing the operation cost. The simulation results show that the proposed strategy can better achieve a win-win situation between EV owners and microgrid operators, and the operation cost of the proposed strategy is reduced by 16.55% compared with that under the disorderly charging and discharging strategy, which verifies the effectiveness of the proposed model and algorithm.

1. Introduction

With the increasing energy crisis and environmental problems, the implementation of a green and sustainable development strategy is becoming more and more important. In order to solve the problem of environmental pollution, electric vehicles (EVs) have been quickly developed in recent years. As a mobile load connected to the power grid, EVs also have the characteristics of energy storage [1]. The direct connection of EVs to the power grid cannot achieve low carbon in the true sense, and large-scale access may also cause the increase of peak load, which in turn has a negative impact on the safe and stable operation of the system [2]. In order to give full play to its energy storage characteristics, in recent years, the vehicle-to-grid (V2G) mode of EVs has been proposed [3], that is, when the vehicle is not traveling, it is always connected to the charging pile, which makes each EV a rechargeable energy storage device. By formulating a reasonable energy management strategy, EVs can be charged and discharged in an orderly fashion. Indeed, ensuring the charging demand of EV users and the satisfaction of participating in V2G could improve the operating economy of the system and reduce the power supply pressure during peak load periods.

With the wide application of hydrogen energy, the electric thermal hydrogen coupling device has gradually become an important part of the integrated energy system [4,5]. References [4,5] introduce the hydrogen energy system into the microgrid, but only considering the electric-hydrogen mutual conversion; the electric thermal hydrogen coupling characteristic of fuel cells and electrolyzers is ignored. Reference [6] considers the thermal characteristics of the electrolyzer during hydrogen production in the coupling system of the active distribution network and the central heating network, which effectively improves the operation efficiency of the electrolyzer and significantly reduces the operation cost of the system. Reference [7] establishes a multi-objective optimal scheduling model in the joint system of electricity, hydrogen and heat, aiming at minimizing the operation cost and maximizing the consumption of wind power. Reference [8] proposes an energy management method of a hybrid system based on photovoltaic, fuel cell and various energy storage devices. Reference [9] considers the cogeneration characteristics of fuel cells and electrolyzers, establishes the hydrogen to electricity and heat model of fuel cells, and the electricity to hydrogen and heat model of electrolyzers. It also introduces the thermal storage tank and studies the optimal scheduling problem of the cogeneration microgrid. When solving the optimal scheduling problem of an integrated energy system, the above literatures adopt deterministic scheduling strategies, without considering the uncertainty of renewable energy output and load power. The predicted power error brings great challenges to the stability and economy of the system in actual operation.

In recent years, there are many studies on the optimal scheduling strategy of the microgrid considering EV charging and discharging. Reference [10] establishes an economic scheduling model of a new energy microgrid with EVs, and proposes a solution method based on an improved genetic algorithm. The results show that EVs’ orderly charging and discharging can not only reduce the power supply burden at peak load, but also achieve good environmental benefits. Reference [11] proposes a fuzzy control algorithm to realize the charging management of electric vehicles based on the real-time data such as the current load state and the charging demand of EVs. The proposed strategy does not depend on the prediction data and has good real-time performance, but it is difficult to find the global optimal scheduling strategy in online real-time control. In addition, it only considers the charging effect of EVs, and ignores that EVs can also be used as distributed power sources. Reference [12] proposes a multi-objective hierarchical economic scheduling model of load level, source load level and source network load level, which was solved by a multi-objective particle swarm optimization algorithm. This strategy considers the output characteristics of scheduling units in each level and has a good effect. The above literatures are all from the perspective of microgrid operators, and improve the operation economy of the microgrid by managing EV charging and discharging. However, it is worth noting that microgrid operators and EV owners belong to different stakeholders, so it is necessary to consider the satisfaction of EV owners when formulating EV charging and discharging plans.

In the latest research, some scholars have considered EV charging and discharging management and the optimal scheduling of a new energy microgrid hierarchically [13]. The EV layer maximizes the comprehensive satisfaction of vehicle owners, and the microgrid layer minimizes the overall operating cost and fluctuation of tie-line power. On this basis, a multi-objective hierarchical optimization scheduling model was established, and it was proved that the layered architecture has better performance than non-layered architecture. However, the degradation cost modeling of EV batteries is relatively rough in ref. [13], and this study adopts a deterministic optimization method, which does not consider the uncertainty of EVs’ travel, renewable energy output and load power. Reference [14] establishes a multi-objective optimization model considering economy and user load consumption satisfaction and quantifies the uncertainty with the conditional value-at-risk of relative disturbance. However, it only considers the optimal scheduling of the electric-thermal coupling system and ignores the effect of EVs. Reference [15] comprehensively considers the economic and environmental aspects of optimal scheduling, but when solving, it uses the weight coefficient to convert it into one objective function. Its essence is single objective optimization, so it is difficult to obtain the optimal Pareto frontier. In ref. [16], a robust optimal power management system is developed for a hybrid ad/dc microgrid. However, it only considers the power load supply, and the robust optimization is too conservative for the actual operation. Reference [17] establishes an optimal scheduling method using game theory for the multi-energy hub system, but hydrogen energy is not considered in its system.

Metaheuristic algorithms have good performance in solving mixed integer nonlinear programming problems. Such methods use less computational cost to find the optimal solution and are not easy to fall into local optimum. Meta-heuristic algorithms are usually divided into evolutionary algorithms (EA), physics-based algorithms, and swarm-intelligence (SI) algorithms. The genetic algorithm (GA) [18] and differential evolution (DE) [19] are well-known algorithms in EA species. The physics-based algorithm acts randomly according to the assumed physical events. Among this kind of algorithm, the gravitational search algorithm (GSA) [20] and the black hole (BH) algorithm [21] are more popular. In general, the inspiration of the SI method comes from the social behaviors of animals in nature that live in groups, captivity and flocks. Particle swarm optimization (PSO) [22], grey wolf optimization (GWO) [23] and the whale optimization algorithm (WOA) [24] are famous algorithms in this category. Although the above algorithms improve the solution accuracy in different extent, they all have the disadvantages of too many parameters and easily falling into local optimum.

The sand cat swarm optimization (SCSO) is a recently proposed meta-heuristic algorithm that mimics the behavior of sand cats in nature [25]. Through the benchmark function test, the algorithm has good convergence and global search ability. On this basis, this paper introduces a fast non-dominated sorting strategy, an elite strategy, and a crowding degree and crowding degree comparison operator, which makes it have the ability of multi-objective optimization, so as to solve the multi-objective mixed integer nonlinear programming problem.

To sum up, this paper establishes a hierarchical stochastic optimization model combining the management of EVs charging and discharging and the optimal scheduling of ETH-IES. The EVs charging and discharging management layer aims to minimize the variance of the load curve and minimize the dissatisfaction of EV owners participating in V2G. The V2G load is obtained by solving the proposed model using the MSCSO algorithm and transmitted to the ETH-IES optimization layer. On this basis, the daily stochastic economic scheduling of ETH-IES containing a PEMFC, an electrolyzer and a hydrogen storage tank is carried out with the goal of minimizing the operation cost. Finally, the effectiveness of the proposed model and algorithm is verified by the comparative analysis of simulation results.

The rest of the study proceeds as follows: Section 2 introduces the hierarchical stochastic optimization strategy; Section 3 introduces the ETH-IES equipment model in detail; Section 4 presents the hierarchical stochastic optimization model of ETH-IES with EVs. In Section 5, the multi-objective sand cat swarm optimization algorithm is proposed. Section 6 discusses the results of the optimal scheduling and the effects of current density of PEMFC on the optimal scheduling. Finally, Section 7 summarizes the main outcome of this paper.

2. Hierarchical Stochastic Optimization Strategy of ETH-IES Considering Electric Vehicles

As shown in Figure 1, the main equipment in the ETH-IES includes a micro gas turbine unit, absorption refrigeration unit, ground source heat pump unit, wind turbine unit, photovoltaic, battery and thermal storage device, as well as a proton exchange membrane fuel cell (PEMFC), hydrogen storage tank and electrolyzer. At the same time, the system is connected with the power grid, which can purchase electricity at a low price and sell electricity to the power grid at a high price. In the hierarchical stochastic optimization framework proposed in this paper, firstly, the EV charging and discharging management layer generates a variety of scenarios by the Monte Carlo simulation method according to the historical habit data of EV owners. Taking the minimum EV owners’ dissatisfaction and the minimum variance of the load curve after superposition of V2G equivalent load as objective functions, EV charging and discharging optimization in V2G mode is carried out, and the SOC changes and charging and discharging power of each EV in each scenario are obtained. Then, the expected V2G load is sent to the ETH-IES optimization layer. Based on the collected information of the real-time electricity price, predicted value of wind, photovoltaic and load power, the ETH-IES optimization layer takes minimizing the integrated operation cost as the objective function and takes the operation requirements of equipment as the constraint condition.

3. ETH-IES Equipment Model

3.1. Absorption Refrigerator Output Model

The refrigerator is generally chosen as a lithium bromide absorption refrigerator to cool the waste heat of a micro gas turbine. Its model is expressed as follows [26]:

$${\eta }_{MT}=0.0753{\left(\frac{P_{MT}}{P_{MT.\max }}\right)}^3-0.3095{\left(\frac{P_{MT}}{P_{MT.\max }}\right)}^2+0.4174\frac{P_{MT}}{P_{MT.\max }}+0.1068$$

(1)

$$Q_{MT}(t)=\frac{P_{MT}(t)(1-{\eta }_{MT}-{\eta }_L)}{{\eta }_{MT}}$$

(2)

$$Q_{AM}(t)={\eta }_{rec}{C}_{AM}{Q}_{MT}(t)$$

(3)

3.2. Mathematical Model of Ground Source Heat Pump

A ground source heat pump uses shallow geothermal resources for both heating and cooling, which is an energy-efficient air conditioning technology. It saves more than 40% of energy than conventional central air conditioning and has great potential in energy saving in large public buildings. Its model is as follows [27]:

$$Q_{HP}(t)=C_{OP}\cdot P_{HP}(t)$$

(4)

3.3. Mathematical Model of Energy Storage Device

Thermal storage devices and electric storage devices have similar operating characteristics, and their model can be expressed as follows [28]:

$$E_B(t)=\left\{\begin{array}{l}{E}_B(t-1)\cdot (1-\tau )+P_{B.ch}(t)\cdot {\eta }_{ch}\cdot \mathsf{\Delta }t\\ E_B(t-1)\cdot (1-\tau )-P_{B.dis}(t)/{\eta }_{dis}\cdot \mathsf{\Delta }t\end{array}\right.$$

(5)

3.4. Mathematical Model of Electrolyzer

The electrolyzer consumes electrical energy to produce hydrogen and heat, and the relationship between hydrogen production and electricity consumption can be expressed by the following equation, according to reference [29]:

$$P_t^{EL}={\lambda }_{H_2}{H}_2^{EL,t}$$

(6)

3.5. Mathematical Model of Hydrogen Storage Equipment

The hydrogen volume at the previous moment and the exchanging amount determine the current volume in the storage equipment [29]. Therefore, the mathematical model of hydrogen storage equipment can be expressed as:

$$H_2^{st,t}=H_2^{st,t-1}+H_{2,in}^{st,t-1}-H_{2,out}^{st,t-1}$$

(7)

$$P_{sto,t}^{H_2}=\frac{H_2^{st,t}{R}_{c}K}{V_{sto}-H_2^{st,t}b}-\frac{{\left(H_2^{st,t}\right)}^{2}a}{V_{sto}^2}$$

(8)

$$Soh{c}_t=\frac{P_{sto,t}^{H_2}}{P_{sto,rated}^{H_2}}$$

(9)

3.6. Mathematical Model of PEMFC

The actual output voltage of PEMFC can be considered as the difference between the Nernst voltage and the loss voltage, and the voltage loss leading to the drop in open circuit voltage can be divided into three categories: (1) active polarization; (2) ohmic polarization; and (3) concentration polarization [30].

Activation polarization is the overpotential generated to overcome the activation energy required for the electrochemical reaction on the catalytic surface. As mentioned earlier, this type of polarization plays a major role in voltage loss at low current densities and can be used to judge the effectiveness of catalysts at a given temperature. This type of voltage loss is complicated because it requires consideration of gaseous fuels, solid metal catalysts, and electrolytes. The catalyst can reduce the activation barrier height, but the voltage loss is inevitable. According to [30], The activation loss can be expressed by Tafel’s equation:

$$\mathsf{\Delta }{v}_{\mathrm{act}}=a+b\ln i$$

(10)

where $a=-\frac{RT}{nF}\ln \left(i_0\right)$, $b=-\frac{RT}{nF}$.

The formula for anode and cathode activation overpotential can be expressed as:

$$v_{\mathrm{act}}=\frac{RT}{nF\alpha }\ln {\left(\frac{i}{i_0}\right)}_{\mathrm{anode}}+\frac{RT}{nF\alpha }\ln {\left(\frac{i}{i_0}\right)}_{\mathrm{cath}}$$

(11)

Ohmic loss is calculated using Ohm’s law:

$$v_{\mathrm{ohmic}}=-ir$$

(12)

Mass transfer (or concentration loss) is calculated by the following formula:

$$v_{\mathrm{conc}}={\alpha }_1{i}_K\ln \left(1-\frac{i}{i_L}\right)$$

(13)

In order to calculate the Nernst voltage, it is necessary to use some pressure values of water, hydrogen and oxygen. By choosing a typical calculation condition in ref. [30], the saturation pressure of water, the local pressure of hydrogen, oxygen and the Nernst voltage are calculated as follows:

$$\log (P_{{\mathrm{H}}_2\mathrm{O}})=-2.1764+0.02953T_c+9.1837\times {10}^{-5}{T}_c{}^2+1.4454\times {10}^{-7}{T}_c{}^3$$

(14)

$$P_{{\mathrm{H}}_2}=0.5\times \frac{P_{{\mathrm{H}}_2,\mathrm{in}}}{\exp \left(\frac{1.653i}{T_{\mathrm{K}}{}^{1.334}}\right)}-P_{{\mathrm{H}}_2\mathrm{O}}$$

(15)

$$P_{{\mathrm{O}}_2}=\frac{P_{\mathrm{air}}}{\exp \left(\frac{4.192i}{T_{\mathrm{K}}{}^{1.334}}\right)}-P_{{\mathrm{H}}_2\mathrm{O}}$$

(16)

$$E_{\mathrm{Nernst}}=-\frac{G_{\mathrm{f},\mathrm{liq}}}{2F}+\frac{R{T}_{\mathrm{K}}}{2F}\ln \left(\frac{P_{{\mathrm{H}}_2\mathrm{O}}}{P_{{\mathrm{H}}_2}{P}_{{\mathrm{O}}_2}^{\frac{1}{2}}}\right)$$

(17)

The actual voltage is:

$$V=E_{\mathrm{Nernst}}+v_{\mathrm{act}}+v_{\mathrm{ohmic}}+v_{\mathrm{conc}}$$

(18)

4. Hierarchical Stochastic Optimization Model of ETH-IES with EVs

4.1. EV Charging and Discharging Management Layer

By formulating a reasonable energy management strategy, EVs can be charged and discharged in an orderly manner, so as to achieve peak shaving and valley filling of the load curve. However, at the same time, if the battery of an electric vehicle is frequently charged and discharged, the service life of the battery will be greatly reduced. Therefore, in the process of orderly charging and discharging, the degradation cost of EVs’ batteries must be considered. Based on this, this paper establishes a multi-objective optimal scheduling model with the goal of minimizing the variance of load curve and the dissatisfaction of EV owners participating in V2G.

4.1.1. The Degradation Cost of EV

The dissatisfaction of EV owners participating in V2G is mainly reflected in the large degradation cost caused by frequent charging and discharging of EV, and the degradation of the battery is mainly reflected in two aspects. On the one hand, the achievable cycles can be reduced; on the other hand, the actual full capacity of the battery can be reduced [31]. Frequent charge and discharge times, charge and discharge rate and other factors will affect the battery service life [32]. However, for the charge and discharge rate, when the battery operates within the rated current range, its impact on the battery service life can be ignored compared with other factors.

Figure 2 shows the relationship between discharge depth and recyclable times of a Ni-Cd battery [33].

The best fitting formula of battery life curve in Figure 2 is as follows:

$$L_B\left(DOD\right)=\mathrm{a}\times DO{D}^{-b}\times e^{-c\cdot DOD}$$

(19)

Referring to ref. [33], taking a discharge event as an example, the average output power of the battery during a time interval is $P_B(t)$, and then the depth of discharge (DOD) during this time interval can be expressed as follows:

$$DOD(\mathsf{\Delta }t)=\frac{P_B(t)\cdot \mathsf{\Delta }t}{E_{BA}(t)}$$

(20)

According to the definition of depth of discharge and the relationship between DOD and the recyclable times, the battery degradation cost can be obtained:

$$C_{Bde}\left(t,DOD\left(\mathsf{\Delta }t\right)\right)=\frac{C_{re}{P}_B\left(t\right)\mathsf{\Delta }t}{2L_B\left(DOD\left(\mathsf{\Delta }t\right)\right)E_{BA}\left(t\right)DOD\left(\mathsf{\Delta }t\right){\eta }_{Bc}{\eta }_{Bd}}$$

(21)

After a charging and discharging event, the actual full capacity of the battery will be reduced, and the actual full capacity of the battery at time $t+\mathsf{\Delta }t$ can be calculated by combining rated capacity $E_{B.rated}$ according to the following formula.

$$E_{BA}\left(t+\mathsf{\Delta }t\right)=E_{BA}\left(t\right)-\frac{E_{B.rated}}{L_B\left(DOD\left(\mathsf{\Delta }t\right)\right)}$$

(22)

Since the degradation cost of a battery at each time interval $\mathsf{\Delta }t$ can only be determined when a charging or discharging event is over, it is required to define the direction of the battery power flow. The definition of the direction indicator $g\left(t\right)$ is as follows:

$$g\left(t\right)=\left\{\begin{array}{l}1,P_B\left(t\right)\cdot P_B\left(t-1\right)\le 0\\ 0,P_B\left(t\right)\cdot P_B\left(t-1\right)>0\end{array}\right.$$

(23)

Combined with this variable, the cumulative power is defined as follows:

$$E_a\left(t\right)=\left(1-g(t)\right)E_a\left(t-1\right)+P_B\left(t\right)\mathsf{\Delta }t$$

(24)

Therefore, to sum up, the expression of operation cost considering the battery degradation effect is as follows:

$$C_B\left(t\right)=C_{Bde}\left(t,\frac{E_a\left(t\right)}{E_{BA}\left(t\right)}\right)-\left(1-g(t)\right)C_{Bde}\left(t,\frac{E_a\left(t-1\right)}{E_{BA}\left(t-1\right)}\right)$$

(25)

4.1.2. EV Charging and Discharging Optimization Model

(a)

Objective function 1

$$\min E\left(F_{{}_1}^{EV}\right)=\frac{{\displaystyle \sum _N{\displaystyle \sum _{t=1}^T\frac{1}{T}{\left(P_{load}\left(t\right)-Mean\left(P_{load}\right)\right)}^2}}}{N}$$

(26)

The first objective function is to reduce the expected value of load curve variance. It aims to achieve the effect of peak shaving and valley filling.

(b)

Objective function 2

$$\min E\left(F_{{}_2}^{EV}\right)=\frac{{\displaystyle \sum _N\frac{{\displaystyle \sum _{n=1}^{N_{ev}}{\displaystyle \sum _{t=2}^T{C}_B^n\left(t\right)}-C_B^{\min }}}{C_B^{\max }-C_B^{\min }}}}{N}$$

(27)

The second objective function is to reduce the dissatisfaction of EV owners participating in V2G. The value of this function ranges from 0 to 1, and changes linearly with the value of degradation cost. When the value is close to 1, it means that owners are dissatisfied with this mechanism.

(c)

Constraints

$$SO{C}_{\min }\le SO{C}_n\left(t\right)\le SO{C}_{\max }$$

(28)

$$-P_{cha}^{\max }\le P_{EV}^n\left(t\right)\le P_{dis}^{\max }$$

(29)

$$0\le I_n^{cha}\left(t\right)+I_n^{dis}\left(t\right)\le 1$$

(30)

The constraints mainly include the limitation of SOC and the charge-discharge power of EVs.

4.2. ETH-IES Optimization Layer

4.2.1. Objective Function

The main purpose of the ETH-IES optimization layer is to achieve economic optimization. The total cost mainly includes: switching the power cost of main network, the maintenance cost of each unit, the operation cost of micro gas turbines, and pollution gas treatment cost. The optimization objective function is:

$$\min E\left(F_{ETH-IES}\right)=\frac{{\displaystyle \sum _N\left(F_{utility}+F_{om}+F_{mt}+F_e\right)}}{N}$$

(31)

(a)

Switching power cost of main network:

$$F_{utility}={\displaystyle \sum _{t=1}^{N_t}\left[C_{buy}(t)\cdot P_{Grid\_buy}(t)\cdot \mathsf{\Delta }t+C_{sell}(t)\cdot P_{Grid\_sell}(t)\cdot \mathsf{\Delta }t\right]}$$

(32)

(b)

The maintenance cost of distributed energy resource:

$$F_{om}={\displaystyle \sum _{i=1}^{N_i}{\displaystyle \sum _{t=1}^{N_t}[\left|P_i(t)\right|}\cdot K_{om.i}\cdot \mathsf{\Delta }t]}$$

(33)

(c)

The micro gas turbines operation cost:

$$F_{mt}={\displaystyle \sum _{t=1}^{N_t}[C_{mt}\cdot f_{mt}\cdot P_{mt}(t)\cdot \mathsf{\Delta }t+\max \left\{0,S(t)-S(t-1)\right\}\cdot C_{mts}]}$$

(34)

(d)

The cost of pollution gas treatment:

$$F_e={\displaystyle \sum _{t=1}^{N_t}[Ce}S{O}_2\cdot E_{{\mathrm{SO}}_2}(t)+CeC{O}_2\cdot E_{{\mathrm{CO}}_2}(t)+CeN{O}_x\cdot E_{{\mathrm{NO}}_x}(t)]$$

(35)

4.2.2. Constraints

(a)

Power balance constraints:

$$P_{Batt}(t)+P_{MT}(t)+P_{PV}(t)+P_{WT}(t)+P_{Grid}(t)+P_{FC}(t)=P_E(t)+P_{Load}(t)$$

(36)

$$Q_{AM}(t)+Q_{HP}(t)+Q_{CS}(t)+Q_{FC}(t)+Q_E(t)=Q_{load}(t)$$

(37)

(b)

DG output power constraints:

$$P_{DG.\mathrm{i}.min}\le P_{DG.i}\le P_{DG.i.\max }$$

(38)

(c)

Climbing constraint of micro gas turbine:

$$\left\{\begin{array}{l}{P}_{MT}(t)-P_{MT}(t-1)\le R_{up}\cdot \mathsf{\Delta }t\\ P_{MT}(t-1)-P_{MT}(t)\le R_{down}\cdot \mathsf{\Delta }t\end{array}\right.$$

(39)

(d)

Exchange power of microgrid and main network constraints:

$$\left|P_{Grid}(t)\right|\le P_{Grid.\max }$$

(40)

(e)

Mutually exclusive constraints of power purchasing and selling:

$$U_{Buy}(t)+U_{Sell}(t)\le 1$$

(41)

(f)

Start and stop time constraints of micro gas turbine:

$$\left\{\begin{array}{l}{\displaystyle \sum _{k=1}^{T_{mup}}{U}_{t-k+1}}\ge T_{mup}\\ {\displaystyle \sum _{k=1}^{T_{mdown}}(1-U_{t-k+1})\ge T_{mdown}}\end{array}\right.$$

(42)

(g)

Battery operating constraints:

$$SO{C}_{\min }\le SOC(t)\le SO{C}_{\max }$$

(43)

$$-P_{ch.\max }\le P_{Batt}(t)\le P_{dis.\max }$$

(44)

$$\left|SOC(N_t)-SOC(1)\right|\le \epsilon$$

(45)

$$U_{Batt.ch}(t)+U_{Batt.dis}(t)\le 1$$

(46)

(h)

Thermal storage device constraints:

$${\lambda }_{\min }{S}_{ES}\le S_{ES}(t)\le {\lambda }_{\max }{S}_{ES}$$

(47)

$$-Q_{ch.\max }<Q_{CS}(t)<Q_{dis.\max }$$

(48)

(i)

Electrolyzer operating constraints:

$$P_{\min }^{EL}\le P_t^{EL}\le P_{\max }^{EL}$$

(49)

$$\mathsf{\Delta }{P}_{\min }^{EL}\le P_t^{EL}-P_{t-1}^{EL}\le \mathsf{\Delta }{P}_{\max }^{EL}$$

(50)

(j)

Hydrogen storage equipment operating constraints:

There are the following assumptions and constraints for the hydrogen storage equipment. Firstly, the storage equipment should have a certain amount of hydrogen at the beginning of the system to ensure that the storage equipment has the ability to regulate both charge and discharge. Secondly, the storage and discharge of hydrogen cannot occur at the same time and cannot be greater than the maximum storage and discharge power of the equipment. Finally, the stored hydrogen should be a positive value and cannot exceed the designed capacity of the equipment. Therefore, for hydrogen storage equipment, the constraints are as follows:

$$0\le H_{2,in}^{st,t}\le Y_{st,t}^{H_2}\cdot H_{2,in}^{st,\max }$$

(51)

$$0\le H_{2,out}^{st,t}\le \left(1-Y_{st,t}^{H_2}\right)\cdot H_{2,out}^{st,\max }$$

(52)

$$0\le H_2^{st,t}\le H_2^{st,rated}$$

(53)

4.2.3. Uncertainty Modeling

In the ETH-IES optimization layer, the impact of the uncertainty of wind power, photovoltaic power and load power is mainly considered. At present, many articles use normal distribution to describe the forecasting error of wind power and photovoltaic power, but the probability density curve is quite different from the frequency distribution histogram [34]. Other articles use Gaussian function to fit the wind power prediction error, but the variable value range of Gaussian function is positive infinity and negative infinity, and the actual wind power output has an interval range. Reference [35] uses beta distribution to fit the prediction error of photovoltaic and wind power, which can reasonably reflect the actual situation. This paper uses beta distribution to describe the probability density distribution of photovoltaic and wind power:

$$f(\frac{P}{P_{\max }})=\frac{\Gamma (\alpha +\beta )}{\Gamma (\alpha )\Gamma (\beta )}{(\frac{P}{P_{\max }})}^{\alpha -1}{(1-\frac{P}{P_{\max }})}^{\beta -1}$$

(54)

$$\alpha =\frac{{\mu }^2}{{\sigma }^2}(1-\mu )-\mu$$

(55)

$$\beta =\frac{1-\mu }{\mu }\alpha$$

(56)

where $P$ is the actual output power, and $P_{\max }$ is the maximum value of output power, which is used to normalize the actual output. $\Gamma (·)$ is gamma function, $\alpha$, $\beta$ is the shape parameter of beta function, and $\mu$ is the mathematical expectation of beta distribution, that is, the predicted average value of normalized output power. ${\sigma }^2$ is the variance of beta distribution, that is, the normalized power prediction variance.

5. Proposed Multi-Objective Sand Cat Swarm Optimization Algorithm

Based on sand cat swarm optimization (SCSO), this paper introduces a fast non-dominated sorting strategy, an elite strategy, and a crowding degree and crowding degree comparison operator, so that it has the ability of multi-objective optimization.

The SCSO algorithm is inspired by sand cat behavior in nature. Foraging and attacking prey are the two main behaviors of sand cats [25]. The proposed algorithm is inspired by the ability to detect low-frequency noise of sand cats.

1.

Initialize the population

In SCSO, the values of the variables are defined as sand cats, and the sand cat is a 1×d array representing the solution in a d-dimensional optimization problem.

The sand cat with the best value is selected as the best solution at the end of an iteration, and the other sand cats try to move toward this cat in the next iteration. In every iteration, the best solution can represent the cat that is closest to the prey.

2.

Search for prey

SCSO benefits from the sand cat’s low-frequency detection ability below 2 KHz. In mathematical modeling, with the iteration, this value $r_G$ will decrease linearly from 2 to 0 to approach the prey. Therefore, in order to find prey, it is assumed that the sensitivity range starts from 2 KHz to 0, as shown in Formula (57). The value $s_M$ is assumed to be 2.

$$r_G=s_M-\left(\frac{s_M\times ite{r}_c}{ite{r}_{\max }}\right)$$

(57)

where $ite{r}_c$ is the current iteration and $ite{r}_{\max }$ is the maximum iteration.

The major parameter that controls the transition between the exploration and exploitation phases is R, which is obtained by Formula (58). Due to this adaptive strategy, the transition of the two stages will be more balanced.

$$R=2\times r_G\times rand\left(0,1\right)-r_G$$

(58)

The search space is initialized randomly between defined boundaries. The sensitivity range of each sand cat is different, in order to avoid the local optimal trap, which is realized by Formula (59).

$$r=r_G\times rand\left(0,1\right)$$

(59)

Each cat updates its own location according to the best location ($\overrightarrow{Po{s}_{bc}}$), its current location ($\overrightarrow{Po{s}_c}$) and its sensitive range ($r$), as shown in Formula (60).

$$\overrightarrow{Pos}\left(t+1\right)=r\cdot \left(\overrightarrow{Po{s}_{bc}}\left(t\right)-rand\left(0,1\right)\cdot \overrightarrow{Po{s}_c}\left(t\right)\right)$$

(60)

3.

Attack prey

In order to model the attack phase of SCSO mathematically, the distance between the best position $\overrightarrow{Po{s}_b}$ and the current position $\overrightarrow{Po{s}_c}$ is calculated as shown in Formulas (61) and (62). Additionally, the sensitive range of the sand cat is considered as a circle, and SCSO uses the roulette selection algorithm to select a random angle for each sand cat.

$$\overrightarrow{Po{s}_{rnd}}=\left|rand\left(0,1\right)\cdot \overrightarrow{Po{s}_b}\left(t\right)-\overrightarrow{Po{s}_c}\left(t\right)\right|$$

(61)

$$\overrightarrow{Pos}\left(t+1\right)=\overrightarrow{Po{s}_b}\left(t\right)-r\cdot \overrightarrow{Po{s}_{rnd}}\cdot \cos \left(\theta \right)$$

(62)

4.

Exploration and exploitation

Adaptive values of $r_G$ and R parameters guarantee the phase of exploration and exploitation, which enables SCSO to seamlessly switch between the two stages. Formula (63) shows the location update of each sand cat during the exploration and exploitation. When $\left|R\right|\le 1$, sand cats are guided to attack their prey; otherwise, the task of sand cats is to find new possible solutions in the global region.

$$\overrightarrow{X}\left(t+1\right)=\left\{\begin{array}{l}\overrightarrow{Po{s}_b}\left(t\right)-\overrightarrow{Po{s}_{rnd}}\cdot \cos \left(\theta \right)\cdot r\begin{array}{ccc}& & \left|R\right|\le 1\end{array}\\ r\cdot \left(\overrightarrow{Po{s}_{bc}}\left(t\right)-rand\left(0,1\right)\cdot \overrightarrow{Po{s}_c}\left(t\right)\right)\begin{array}{ccc}& & \left|R\right|>1\end{array}\end{array}\right.$$

(63)

5.1. Algorithm Procedure

The flowchart of the proposed multi-objective sand cat swarm optimization algorithm is shown in Figure 3, and the specific steps are as follows:

1.

Initialize the sand cat population and generate the first-generation parent population;

2.

The roulette chooses the movement direction angle;

3.

Update the location of the sand cat swarm, and use the newly generated sand cat swarm as the offspring swarm;

4.

Combine the parent population with the child population and introduce elite strategy to expand the sampling space;

5.

Perform fast non-dominated sorting and retain excellent population individuals;

6.

Adopt the crowding degree and crowding degree comparison operator, and use it as the selection criterion of individuals in the population. Individuals in the quasi-Pareto domain can be evenly expanded to the entire Pareto domain, which ensures the population diversity;

7.

Select the excellent individuals in the population as the new parent population;

8.

Determine whether the maximum number of iterations is reached, otherwise turn to “2.”.

5.2. Algorithm Performance Verification

In order to verify the multi-objective optimization ability of the proposed MSCSO algorithm, this paper selects the ZDT1-ZDT6 benchmark function for verification. As shown in Figure 4, the obtained Pareto solution set is located at the lower left of the results of NSGA-Ⅱ algorithm, which indicates that it has better global search ability.

6. Simulation Analysis

6.1. Parameter Setting

In this paper, it is assumed that 50 EVs are connected to the ETH-IES. The Monte Carlo method can be used to obtain the basic information of EVs, such as the time of connecting to the system, the time of leaving, the initial state of charge, the expected state of charge and so on. In addition, EV loads are divided into four categories in this paper: ① EVs parked in parking lots for a long time and connected to charging piles; ② EVs that commute regularly according to the daily working hours; ③ EVs requiring emergency charging; ④ EVs that need to be driven out temporarily.

For various EV loads, the Monte Carlo scenario simulation is carried out according to

Table 1. Random parameters of various EV loads.

Random Parameter	Average	Variance
State of charge (SOC) of Category ② at the time of returning to the parking lot	0.2	0.1
Initial SOC of Category ③ during emergency charging	0.3	0.05
Expected SOC of Category ③ during emergency charging	0.8	0.05
The time when Category ② leave the parking lot	7:00	30 min
The time when Category ② return to the parking lot	18:00	30 min
Quantity of Category ④	4	9

:

Among them, the fourth type of EV load is randomly generated at any time throughout the day, and this type of EV does not account for more than 10% of the total number of EVs in the current parking lot.

Other parameters of EV are shown in

Table 2. Other related parameters of EV.

Parameter	Value	Parameter	Value
$E_{B.rated}/\mathrm{kWh}$	30	$SO{C}_{\min }/SO{C}_{\max }$	0.2/0.9
$C_{re}/\mathrm{RMB}$	15,000	$P_{\max }^{\mathrm{char}}/P_{\max }^{\mathrm{dis}}/\mathrm{kW}$	7/−7
${\eta }_{\mathrm{Bc}}$	0.9	${\eta }_{\mathrm{Bd}}$	0.9

[13]:

Real-time electricity price and the predicted value of wind power photovoltaic output is shown in Figure 5 and Figure 6 [33].

The pollutant emission coefficient and pollutant treatment cost of a gas turbine are shown in

Table 3. Pollutant treatment parameters.

Type of Gas	Cost (RMB/kg)	Pollution Emission Factors (g·(kWh)−1)
		Wind Turbine	Photovoltaic	Micro Gas Turbine	Energy Storage
CO	0.125	0	0	0.172000	0
CO2	0.210	0	0	184.082900	0
SO2	14.842	0	0	0.000928	0
NOx	62.964	0	0	0.618800	0

[25]:

MSCSO parameters are set as follows: maximum iteration times: ${\mathrm{iter}}_{\max }=1000$; population size: n = 100; maximum sensitivity range in MSCSO algorithm is 2.

6.2. Result Analysis

6.2.1. Scheduling Results of EV Charging and Discharging Management Layer

Figure 7 shows the SOC changes of ① and ② EVs that are always connected to the system. It can be seen that the EV charges at the low load period from 2:00 to 7:00, and feeds back electricity during the peak load period from 20:00 to 24:00. At other times, it is used as an energy storage device to reduce the variance of the load curve by bidirectional transmission of energy.

The Pareto solution set obtained by the EV charging and discharging management layer is shown in Figure 8. A compromising solution that comprehensively considers the dissatisfaction of EV owners and the variance of the load curve is selected: the dissatisfaction degree of EV owners is 0.3078, and the variance of load curve is 6636 $k{W}^2$. This compromising solution is compared with the disordered charging and discharging results when the dissatisfaction degree of EV owners is 0.1578, as shown in Figure 9. It can be clearly seen that under the strategy of this paper, the influence of the V2G participation dissatisfaction of EV owners and the variance of the load curve are comprehensively considered, so that EVs are charged and discharged in an orderly manner, which effectively produces the effect of peak shaving and valley filling.

In order to verify that MSCSO is more successful in solving the resulting optimization problems, a comparative test is carried out. As shown in Figure 10, the solution set obtained by MSCSO is at the lower left of NSGA-Ⅱ, which proves its superiority.

6.2.2. Scheduling Results of ETH-IES Optimization Layer

The stochastic optimization model can effectively solve the optimization scheduling problem with uncertain factors. In this paper, beta distribution is used to describe the probability density distribution of wind power and photovoltaic output. The typical output scenarios generated by the Monte Carlo simulation are shown in Figure 11 and Figure 12.

As shown in Figure 13, during the period from 2:00 to 8:00, the electricity price is at a low value, and part of the load gap in the microgrid can be filled by purchasing electricity from the main network. At 6:00, the electricity price reaches the lowest value. At this time, the microgrid stores low-cost electricity in batteries and hydrogen storage tanks while meeting the load demand. At 11:00 and during 15:00 to 17:00, the electricity price is at a high level. At this time, based on the consumption of wind power and photovoltaic power, the battery will release the electric energy stored in the low price period, and the micro gas turbine will also output the maximum power to sell electricity to the main network as much as possible. At the same time, PEMFC will convert hydrogen energy into electric energy to maximize economic benefits. During the period from 19:00 to 21:00, the load level of the microgrid is relatively high, and the electricity price is at the peak stage, so the battery is discharged first and the PEMFC converts hydrogen energy into electricity, and the remaining load power shortage will be purchased from the grid. In the whole dispatching cycle, the battery stores electric energy at the low power consumption and sells electric energy at the peak power consumption. The PEMFC, electrolyzer and hydrogen storage tank convert electric energy into hydrogen energy at the low load period and convert hydrogen energy back to electric energy at the peak load period, which greatly improves the operation economy and flexibility of the integrated energy system.

As shown in Figure 14, the thermal load in winter is low at noon and high in the morning and evening. Since the ground source heat pump belongs to the type of electric heat transfer equipment, and the thermal power of the absorption refrigerator depends on the waste heat emission of a micro gas turbine, the electrolyzer and PEMFC are electrothermal coupling units. The economy of ETH-IES can be optimized when the thermal storage device stores as much heat as possible at the low price period and releases as much heat as possible at the peak price period. Therefore, during the period from 3:00 to 8:00, the ground source heat pump unit will maintain a high output, and the excess heat energy will be stored in the thermal storage device. During the period from 10:00 to 17:00, as the electricity price is at the peak stage, the thermal storage device should be released as much as possible to reduce the output of the ground source heat pump unit.

As shown in Figure 15 and Figure 16, the cooling load in summer is characterized by high load demand at noon and low load demand in the morning and evening. There is no great difference in the supply of electric load compared with winter. During the period from 15:00 to 17:00, the demand for cooling load is high and the electricity price is at the peak stage. The absorption chiller outputs large cooling power, and the energy storage device and PEMFC also output large power. The ground source heat pump unit does not work, so ETH-IES has a higher economy.

Three strategies are considered for comparison. Strategy 1 is from the perspective of microgrid operators and only aims to reduce load variance; strategy 2 is from the perspective of EV owners, charging and discharging in a disorderly manner according to the owner’s wishes; while the strategy in this paper comprehensively considers EV owners participating in V2G dissatisfaction and total load curve variance. As shown in

Table 4. Comparison of indicators under different strategies.

Scheduling Strategy	Scheduling Cost (RMB)	EV Owner Dissatisfaction	$\mathbf{Load} \mathbf{Variance} \left(\mathit{k}{\mathit{W}}^2\right)$
1	634.26	1	5958
2	854.28	0.1578	9750
The proposed strategy	712.93	0.3078	6636

, compared with strategy 1, the scheduling cost of this strategy increased by 12.4%, the dissatisfaction of EV owners decreased by 0.69, and the load variance increased by 11.4%; Compared with strategy 2, the scheduling cost decreased by 16.55%, the dissatisfaction of EV owners increased by 0.15, and the load variance decreased by 31.94%. It can be seen that the strategy of this paper comprehensively considers the interests of both sides, and truly achieves a win-win situation.

6.2.3. Sensitivity Analysis

The volt-ampere characteristic curve of a single PEMFC and the relationship between the total output power of PEMFC group and current density are shown in Figure 17. It can be seen that the maximum output power is greatly affected by the current density during operation.

As shown in Figure 18, with the increase of the operating current density of the PEMFC, its maximum output power first increases and then decreases, corresponding to the comprehensive operation cost decreasing first and then increasing. It can be seen that, with the increase of the capacity of the proton exchange membrane fuel cell, the flexibility and economy of electrothermal load supply are improved, which also shows that the electro-hydrogen-heat coupled system has more advantages than the combined heat and power system.

7. Conclusions

This paper establishes a hierarchical stochastic optimal scheduling model of ETH-IES considering the EV V2G mechanism. The EV charging and discharging management layer aims to minimize the variance of the load curve and the dissatisfaction of EV owners participating in V2G. The V2G equivalent load is obtained by solving the proposed model using the MSCSO algorithm, and it is transmitted to the ETH-IES optimization layer. On this basis, the daily stochastic economic scheduling of ETH-IES including the PEMFC, electrolyzer and hydrogen storage tank is carried out with the goal of minimizing the operation cost. The following conclusions can be drawn:

1.

The degradation cost of EVs is modeled, and a multi-objective optimal scheduling model for EV charging and discharging is constructed to reduce the variance of the load curve and reduce the dissatisfaction of EV owners participating in V2G. Through simulation verification, this model can comprehensively consider the interests of EV owners and microgrid operators, which achieves a win-win situation.

2.

The electro-thermal-hydrogen coupling devices of the PEMFC, electrolyzer and hydrogen storage tank are modeled and introduced into the integrated energy system to improve its flexibility and economy. In addition, considering the uncertainty of EVs’ travel, renewable energy output and load power, a hierarchical stochastic optimization model is established. Compared with the results obtained by the deterministic optimization method, it is more responsive to the actual situation and has stronger robustness.

3.

Based on the SCSO algorithm, a fast non-dominated sorting strategy, elite strategy, crowding degree and crowding degree comparison operator are introduced, so that it has good convergence and is closer to the real Pareto front in solving high dimensional and nonlinear multi-objective optimization models. On this basis, combined with the Monte Carlo simulation method, the algorithm can efficiently solve multi-scenario multi-objective mixed integer nonlinear programming problems.

4.

The proposed strategy and algorithm are applied to typical ETH-IES, and it is verified that the strategy in this paper is the most win-win by comparing with the results of an EV disorderly charging and discharging strategy and only considering a load variance strategy. The operation cost of the proposed strategy is reduced by 16.55% compared with that under the disorderly charging and discharging strategy, which verifies the effectiveness of the proposed model and algorithm.