A Master–Slave Game Model of Electric Vehicle Participation in Electricity Markets under Multiple Incentives

Abstract

In order to achieve low carbon emissions in the power grid, the impact of new energy grid connections on the power grid should be reduced, as well as the peak-to-valley load difference caused by large-scale electric vehicle grid connections. This paper proposes a two-tier, low-carbon optimal dispatch master–slave game model involving virtual power plant operators as well as electric vehicle operators. Firstly, the carbon flow is tracked based on the proportional sharing principle, and the carbon emission factor during the charging and discharging process of electric vehicles is calculated. Secondly, the node carbon potential and time-sharing tariff are used to guide and change the charging behaviour of electric vehicles and to construct a master–slave game model for low-carbon optimal scheduling with the participation of multiple subjects, with economic scheduling at the upper level of the model and demand response scheduling at the lower level. Finally, the IEEE30 node system is used as an example to verify that the method adopted in this paper can effectively reduce the peak-to-valley difference of loads, reduce the carbon emissions of the grid, and reduce the cost of each participating entity.

1. Introduction

In recent years, climate change triggered by greenhouse gas (GHG) emissions has become a serious challenge globally as energy shortages and environmental problems caused by carbon emissions have become increasingly serious [1]. According to statistics, carbon emissions from China’s power sector account for about 40% of carbon emissions from energy activities in China [2,3]. In response to environmental degradation and the energy crisis, China proposed a “dual carbon target” in 2020, with carbon peaking by 2030 and carbon neutrality by 2060. The power industry is facing a huge test. Constructing a new type of power system with new energy as the main body is necessary for the development of the power industry [4].

Accelerating the construction of renewable energy sources such as wind power and photovoltaic is a requirement for power system transformation [5]. As renewable energy, represented here by wind power, becomes increasingly penetrated into the grid, the problems behind it are becoming more and more obvious. On the one hand, wind power has strong randomness, volatility [6], low prediction accuracy, and other characteristics that increase the system’s peaking burden, making the system’s peaking capacity, standby capacity, etc., constantly increase. On the other hand, wind power has a certain “anti-load” nature, which makes the wind abandonment phenomenon increasingly serious.

As a low-carbon and environmentally friendly means of transportation, electric vehicles (EVs) have been developing rapidly in the world, especially in China, which has become the world’s largest market for EVs for many years. However, due to the problem of significant randomness of EV owners themselves, large-scale electric vehicle access to the power grid will have certain impacts on the reliability and stability of the power grid, such as increasing the load peak-to-valley difference of the grid [7], causing the three-phase power imbalance of the grid [8], and increasing the maintenance cost of the grid, and other problems. Therefore, in order to reduce the load fluctuation and the phenomenon of wind and light abandonment, the development of effective charging and discharging strategies for electric vehicles is a hot issue in current research.

Most of the existing studies treat EVs as a flexible resource. As a flexible resource, electric vehicles can play an important role in the peaking of power grids, vehicle coordination, and the consumption of new energy sources such as wind power [9]. The authors of [10] established a robust two-layer optimal scheduling model for wind power, thermal power, and electric vehicles, which improves the consumption capacity of wind power and reduces the generation cost of thermal power. Another study [11] considered electric vehicles’ mobile energy storage characteristics and participation in grid interaction through Vehicle-to-Grid (V2G) technology in concert with renewable energy sources. The authors of [12] considered the volatility of wind power output and the stochastic nature of electric vehicle grid entry and established a two-layer inverse robust scheduling model containing virtual power plant (VPP) with the objective of maximising the profit of power generation from virtual power plants, which improves wind power consumption.

In the context of large-scale EV connectivity to the grid for charging, ref. [13] proposed a robust decentralised charging strategy that minimises the overall charging energy payment and the aggregated battery degradation cost of the EV while maintaining the robustness of the solution to the uncertainty of the grid power purchase price and inelastic load demand. An extended Jacobi-Proximal Alternating Direction Method of Multipliers algorithm was used to apply to the large-scale fleet scheduling problem. In terms of game pricing for EV participation in energy trading, ref. [14] proposed a game pricing mechanism for multi-microgrid energy trading that takes into account the uncertainty of EVs by building a Bayesian game model that takes into account the charging and discharging behavior of EVs, as well as the limitation of the battery capacity of EVs. Effective energy trading between multiple microgrids was achieved and can balance the interests of each participant in terms of time-of-use tariffs as well as real-time tariffs to guide electric vehicles to orderly charging and discharging.

The authors of [15] proposed a dynamic tariff mechanism to guide electric vehicles to carry out an orderly charging and discharging strategy, charging during load valleys and discharging during load peaks, which improves the consumption of wind power and reduces the user’s charging costs. The authors [16] described the relationship between time-of-use tariffs and EV charging using a dynamic game with the objective of reducing the peak-to-valley difference in the grid and minimising the cost of charging for EV gas vehicle users. The authors of [17] proposed an optimization method for dynamic tariffs to optimise the charging behaviour of electric vehicles in two phases, which reduces the peak-to-valley load difference and the charging cost for users. Another study [18] proposed a model to guide large-scale electric vehicles for charging and discharging based on regional peak-to-valley tariffs, but it tended to create new peak-to-valley differences.

Currently, the study of carbon emissions from power systems is gradually switching from the generation side to the load side. Most studies have been conducted in terms of carbon market transactions. The authors of [19] introduced the carbon emission rights trading mechanism to establish an optimal scheduling model by considering the low-carbon benefits and cost-effectiveness. The price changes in carbon emission equity trading will lead to the scheduling result, which reduces the carbon emission of the system to a certain extent. Another study [20] established a scheduling model for low-carbon-guided multivariate load impacts on the basis of obtaining the carbon emissions from the integrated energy system by using the carbon emission flow theory to calculate accurately. The authors of [21] introduced carbon trading into the optimal scheduling of electric vehicles, and the results show that the addition of electric vehicles with carbon trading to the scheduling not only reduces the carbon emissions of the system and the charging cost of the user, but also improves the capacity of wind power consumption.

In summary, most current studies guide electric vehicles to orderly charging and discharging through electricity price and carbon trading, and few utilise the combination of nodal carbon potential and electricity price. Therefore, this paper proposes a low-carbon scheduling method for aggregating virtual power plants and electric vehicles, which considers the interests of both the virtual power plant and the electric vehicle aggregator(EVA). Using the proportional sharing principle to calculate the strength of the nodal carbon potential of each node of the system, while the size of the nodal carbon potential is determined by the type of energy, such as the source measurement of thermal power accounted for a higher proportion of the node carbon potential of the EV side of the higher; new energy accounted for a higher proportion of the node carbon potential, then the node carbon potential is smaller. The node carbon potential is used to further calculate the precise carbon emissions during the electric vehicle discharge process. The node carbon potential and the electricity price are used to simultaneously guide the electric vehicles, encouraging them to discharge when the carbon emissions are high, reducing the carbon emissions from the power grid, realising the low carbon emissions of the system, and promoting the development of the power system.

2. Carbon Flow Theory

2.1. Theoretical Overview of Power System Carbon Flows

The main carbon emissions from power generation in the power system are to meet the demand for electricity from loads and are characterised as “off-site carbon emissions”. Therefore, the responsibility for carbon emissions cannot be borne solely by the power generation side; users consume electricity and need to bear a certain amount of carbon emission costs incurred in producing electricity. The power system carbon flow methodology is able to extrapolate carbon emissions from the generation side to the load side. Therefore, the carbon flow theory allows for the calculation of the carbon liability on the load side of the power system.

2.2. Theoretical Modeling of Carbon Emission Flows Based on the Proportional Sharing Principle

A certain system with N nodes with known network topology where there are K nodes with unit injection and M nodes with load.

2.2.1. Branch Power Flow Distribution Matrix

The branch power flow distribution matrix is an $N$-order square matrix, denoted by $\left[P_B\right]={\left(P_{Bij}\right)}_{N\times N}$. Constructed from the results of the tidal current distribution calculation. If two nodes $i$ and $j$ are connected by a branch and the active power flow from node $i$ to node $j$ between the two nodes is $p$, then $P_{Bij}=p$, $P_{Bji}=0$, and vice versa, $P_{Bij}=0$, $P_{Bji}=p$. In all other cases $P_{Bij}=P_{Bji}=0$, the value is 0 for all diagonal elements in the matrix.

2.2.2. Power Injection Distribution Matrix

The power injection distribution matrix is a $K\times N$ order matrix, denoted $\left[P_G\right]={(P_{\mathrm{G}kj})}_{K\times N}$. This matrix describes the active power injected into the power system by the generating unit, assuming that the kth generator is connected to node $i$ of the power system and the active power injected into the system is $p$, then $P_{Gkj}=p$, otherwise $P_{Gkj}=0$.

2.2.3. Load Distribution Matrix

The load distribution matrix is an $M\times N$ order matrix denoted as $\left[P_L\right]={(P_{Lmj})}_{M\times N}$. This matrix describes the amount of active load for the electrical loads of the power system. Assume that node $J$ is the mth node where load exists and the active load is $P$, then $P_{Lmj}=p$, otherwise $P_{Lmj}=0$.

2.2.4. Nodal Active Power Flux Matrix

The nodal active power flux matrix is an $N$-order square matrix, denoted $\left[P_N\right]={(P_{Nij})}_{N\times N}$. Based on Kirchhoff’s theorem, zero is the algebraic sum of the currents flowing into and out of a node at any moment. Therefore, the net power injection at any node is zero in the trend operation analysis. However, in the carbon flow calculation of the system, the nodal carbon potential of the system only considers the active power of the injected nodes, and the active power of the outgoing nodes does not affect the calculation of the nodal carbon potential. Assume that there exists node $i$, such that the set $I^{+}$ denotes the set of branches with tidal flow into node $i$. Then:

$$P_{Nii}={\displaystyle \sum }_{s\in I^{+}}{p}_{Bs}+p_{Gi}$$

(1)

where $p_{Gi}$ is the active power injected by the generator connected to node $i$.

2.2.5. Unit Carbon Emission Intensity Vector

Each generating unit has its own unique carbon emission characteristics, which are used as a known condition in the carbon emission flow calculation, assuming that the carbon emission intensity of the kth generator is $e_{GK}$, the vector representation of the unit carbon emission intensity of the generating units in the system is:

$$E_G={\left[\begin{array}{cccc}{e}_{G1}& e_{G2}& \cdots & e_{GK}\end{array}\right]}^T$$

(2)

2.2.6. Nodal Carbon Intensity Vector

The purpose of carbon emission flow calculation in a power system is to get the Nodal carbon intensity of each node of the system, assuming that the carbon intensity of the ith node in the system is $e_{Ni}$, the nodal carbon intensity vector of each node in the system can be expressed as:

$$E_N={\left[\begin{array}{cccc}{e}_{N1}& e_{N2}& \cdots & e_{NN}\end{array}\right]}^T$$

(3)

2.2.7. Branch Carbon Emission Flow Rate Distribution Matrix

The carbon flow rate for each branch can be derived after calculating the carbon potential at each node, denoted as $\left[R_B\right]={(R_{Bij})}_{N\times N}$, for an $N$ order square matrix. If node $i$ and node $j$ in the system have branch connections and the carbon flow rate from node $i$ to node $j$ via the branch is $r$, then $R_{Bij}=r$, $R_{Bij}=0$; If the carbon flow rate from node $j$ to node $i$ via the branch is $r$, then $R_{Bij}=0$ and $R_{Bij}=r$; if there is no branch connected between the two nodes, then $R_{Bij}=R_{Bij}=0$. The diagonal elements of the branch carbon emission flow rate distribution matrix are all zero.

2.2.8. Calculation of Carbon Potential of System Nodes

The carbon potential of node $i$ in the system is defined as

$$e_{Ni}={\displaystyle \frac{{{\displaystyle \sum }}_{s\in I^{+}}{p}_{Bs}{\rho }_s+p_{Gi}{e}_{Gi}}{{{\displaystyle \sum }}_{s\in I^{+}}{p}_{Bs}+p_{Gi}}}$$

(4)

The physical meaning is that the carbon potential of a system node $i$ is determined by the combined effect of the carbon emission streams generated by the generating units connected to the node and the carbon emission streams flowing into the node from other nodes.

Expressed in matrix form:

$$E_N={(P_N-P_B^{\mathrm{T}})}^{-1}{P}_G^{\mathrm{T}}{E}_G$$

(5)

3. Systemic Research Framework and Game Theory

3.1. Introduction to Game Theory

Game theory is also known as countermeasure theory. When there are interest relations or conflicts among multiple subjects participating in an activity, game theory can be used to utilise the decision maker’s own conditions and other information to make decisions that maximise the interests of oneself or the group.

In general, a complete game involves at least two or more players who compete for resources or benefits. This process involves a set of strategies of the players. The application of game theory usually has the following three assumptions.

• Decision-makers usually aim to maximise their personal interests or minimise losses, and they will not sacrifice their own interests to consider their overall interests. In other words, the decision-making subject is completely rational.
• All players in the game are assumed to be rational; that is, perfect rationality applies to everyone. In addition, all players understand that the others are also perfectly rational.
• It is assumed that participants have accurate beliefs and expectations about their environment and the behaviour of other participants.

There are many ways to classify game theory. The most common application is to divide it into cooperative games, non-cooperative games and evolutionary games based on whether the participants cooperate in pursuit of maximum benefits.

There is a binding agreement between the participants in a cooperative game. If the additional benefits obtained through cooperation in a cooperative game can be distributed, it is called a cooperative game with transferable payments, usually a coalition game; otherwise, it is called a cooperative game with non-transferable payments, which can be further divided into coalition games and negotiation problems.

Nash proved the existence of solutions to non-cooperative games under certain conditions, laying the foundation for modern non-cooperative game theory. In non-cooperative game theory, there is no binding agreement between the participants. It can be divided into static games and dynamic games. In static games, all participants take their actions at the same time but at different times, and the participants who take actions later do not know the strategies taken by the participants who take actions first. Dynamic games refer to the fact that there is a sequence of actions taken by the participants, and the participants can obtain historical information about the game and optimise their actions based on the information they have before taking action.

This paper selects a master–slave game model with virtual power plants as the main body of the game and electric vehicles as the slaves. As a dynamic, non-cooperative game, the participants have unequal status. In this paper, the decisions made by the virtual power plant are used as constraints for the decisions made by electric vehicles.

Evolutionary games were created by Smith. Unlike traditional games, which assume that players are completely rational, evolutionary games only require players to have limited rationality. The study of evolutionary games mainly includes two aspects: first, selecting a reasonable fitness function, which is similar to the payment function of traditional games; second, setting a reasonable selection and mutation mechanism. These two aspects of the research jointly determine the final evolutionary stable strategy.

3.2. Virtual Power Plant Vehicle-Grid Interaction Framework

The virtual power plant has the functions of “communication” and “aggregation”. It can integrate distributed power generation units, EVs, wind power, adjustable loads and other scattered parts in the power grid and participate in the regulation of the power grid as an intermediary.

The structure of the virtual power plant in this paper consists of wind turbines, photovoltaic units, gas turbine units, and conventional and electric vehicle loads. Considering the interesting relationship between electric vehicle owners and VPP operators, a two-layer optimization scheduling model of virtual power plants and electric vehicles is constructed: The upper layer considers the power generation cost of gas turbine units, photovoltaic units, wind power generation cost, and the cost of purchasing and selling electricity to establish an optimization model for the lowest operating cost of virtual power plant operators. At the same time, it relies on power flow calculation to calculate the carbon potential of each node. The lower layer controls the charging and discharging of electric vehicles according to the node carbon potential and electricity price, and builds an optimization model with the goal of minimising the charging cost of electric vehicles. The bilateral game is repeated to obtain the Nash equilibrium solution. The master–slave game framework diagram of the system is shown in Figure 1.

4. Double-Layer Low-Carbon Dispatch Master–Slave Game Model

4.1. Upper-Layer Virtual Power Plant Operator Optimization Model

4.1.1. Objective Function

The upper virtual power plant optimization dispatch model is a hub connecting the upper power grid and the lower electric vehicles. Its objective function is established with the lowest operating cost:

$$min{F}_{up}=f_{wind}+f_{pv}+f_{mt}+f_{c{o}_2}+f_{buy}-f_{sell}-f_{down}$$

(6)

Among them, $f_{wind}$ is the power generation cost of wind turbines; $f_{pv}$ is the power generation cost of photovoltaic units; $f_{mt}$ is the power generation cost of gas turbine units; $f_{c{o}_2}$ is the cost of virtual power plants participating in carbon market transactions; $f_{buy}$ is the cost of purchasing electricity from the main power grid; $f_{sell}$ is the cost of selling electricity to the main power grid; $f_{down}$ is the cost of selling electricity to electric vehicle aggregators.

4.1.2. Restrictions

(1)

Gas turbine output active power upper and lower limit constraints

$$P_{mtmin}\le P_{mt}\le P_{mtmax}$$

(7)

(2)

Gas turbine unit ramping constraints

$$-R_d<P_{mt}\left(t\right)-P_{mt}\left(t-1\right)<R_u$$

(8)

$R_u$ and $R_d$ are the up-slope and down-slope rates of the small gas turbine.

(3)

Distribution network and main grid tie-line constraints

$$P_{trans}\le P_{limit}$$

(9)

$P_{limit}$ is the upper limit of the power of the interconnection line between the distribution network and the main network.

(4)

Balance Node Constraints

$${\theta }_t^{\mathrm{ref}}=0$$

(10)

where ${\theta }_t^{\mathrm{ref}}$ is the voltage phase angle of the balanced node at time $t$.

(5)

Node power balance constraints

$${\displaystyle \sum }_{mt=1}^N{P}_{mt,t}+{\displaystyle \sum }_{w=1}^N{P}_{w,t}+{\displaystyle \sum }_{pv=1}^N{P}_{pv,t}-{\displaystyle \sum }_{l=1}^l\left(Plin{e}_{l,t}^{in}-Plin{e}_{l,t}^{out}\right)=D_{\exp ,t}$$

(11)

Among them, $P_{mt,t}$ is the gas turbine power injected into the node at time $t$, $P_{w,t}$ is the wind power injected into the node at time $t$, $P_{pv,t}$ is the photovoltaic power input into the node at time $t$, $Plin{e}_{l,t}^{in}$ is the power flowing into the node at time $t$, $Plin{e}_{l,t}^{out}$ is the power flowing out of the node at time $t$, and $D_{\exp ,t}$ is the predicted power of the node at time $t$.

4.2. Lower-Level Electric Vehicle Optimization Scheduling Model

4.2.1. Carbon Allowance Modeling for Electric Vehicles

Carbon trading mechanisms are effective measures to reduce carbon emissions from power systems. A party with excess carbon allowances can sell its excess carbon allowances in the market to increase its income; a party with carbon emissions higher than its carbon allowances needs to buy them in the carbon market to meet its carbon emissions.

Electric vehicles, as a new type of low-carbon transportation, have been developed on a large scale in recent years, providing a new development direction for energy saving and emission reduction in the transportation field. Consider the difference between the carbon emissions of a conventional fuel vehicle travelling the same distance and the carbon emissions generated during the charging process of an electric vehicle as a carbon allowance for the electric vehicle, which could be sold on the carbon trading market to increase the income of the electric vehicle owner. According to the current trading policy, the free issuance of carbon allowances for electric vehicles is more effective than new energy subsidies in utilising the emission reduction characteristics of electric vehicles. Since the baseline method promotes the energy saving and emission reduction of electric vehicles more significantly, the baseline method is adopted for the study.

Under the baseline method, electric vehicles receive carbon allowances:

$$Q_{ev,k}=\left(R_L\times {\alpha }_u-e_{m,t}^R\right)\times P_t^{EV}\times \mathsf{\Delta }t$$

(12)

where $Q_{ev,k}$ is the carbon quota obtained by the electric vehicle, $R_L$ is the mileage travelled by the electric vehicle per unit of electricity, ${\alpha }_u$ is the carbon emission coefficient per unit mile travelled by the conventional fuel vehicle, $e_{m,t}^R$ is the nodal carbon potential at node $m$ at time $t$, and $P_t^{EV}$ is the charging power of the electric vehicle at time $t$.

The benefits of EV participation in carbon market trading can be further obtained after obtaining EV carbon allowances as:

$$pric{e}_{carbon}=q_{ev}\times Q_{ev,k}$$

(13)

where, $q_{ev}$ is the selling price of carbon allowances for electric vehicles in units of RMB/$\mathrm{kg}$.

4.2.2. Objective Function

Low-carbon optimal scheduling of lower-tier EVs with minimum EV aggregator cost as an objective function:

$$min{F}_{donn}=f_{donn}-pric{e}_{ev}-pric{e}_{carbon}$$

(14)

Considering the satisfaction of EV owner-users as well as improving the enthusiasm of EV owners to participate in grid regulation, the charging cost of EV owners as well as the charging volume of EVs are optimised with the optimised objective function:

$$\min f_{e\nu }=\lambda \ast {\displaystyle \frac{\left(X\ast C_e-reward\ast P_c\ast pric{e}_{reward}\right)}{maxprice}}+\left(1-\lambda \right)\ast {\displaystyle \frac{-X\ast P_c}{C\ast 100}}$$

(15)

where $\left(X\ast C_e-reward\ast P_c\ast pric{e}_{reward}\right)/maxprice$ is the optimization of charging cost for EV users and $\left(-X\ast P_c\right)/\left(C\ast 100\right)$ is the optimization of EV charging volume.

4.2.3. Restrictions

(1)

Electric vehicle charging and discharging power constraints

$$\{\begin{array}{l}0\le P_{\mathrm{C},k,t}\le P_{\mathrm{C}max,t}\\ 0\le P_{\mathrm{DC},k,t}\le P_{\mathrm{DC}max,t}\end{array}$$

(16)

where $P_{\mathrm{C},k,t}$ and $P_{\mathrm{D},k,t}$ are the charging and discharging power of the EV vehicle at time $t$, and $P_{\mathrm{C}max,t}$ and $P_{\mathrm{DC}max,t}$ are the maximum values of the charging and discharging power of the EV vehicle, respectively.

(2)

Electric vehicle capacity constraints

$$S_{min}<SOC<S_{max}$$

(17)

In order to ensure the service life of electric vehicle batteries, the upper and lower limits of the usable capacity of electric vehicle batteries $S_{max}$ and $S_{min}$ are generally taken as 1 and 0.2, respectively.

(3)

User travel demand constraints

To ensure that the user’s travel needs are met, the electric vehicle’s charge $S_{f,k}$ At the end of charging, the value should be no less than the desired value set by the user and should not exceed the capacity of the battery.

$$S_{e,k}\le S_{f,k}\le 1$$

(18)

(4)

Electric vehicle dispatchable time constraints

Since the charging and discharging behaviour of an EV only takes place during the time it is connected to the grid, the EV dispatchable time constraint is:

$$t_{\mathrm{in},k}\le t_{V2G,k}\le t_{\mathrm{out},k}$$

(19)

5. Model Solution

5.1. Improved Particle Swarm Optimization Algorithm

The particle swarm optimization (PSO) algorithm is an evolutionary technique algorithm. It emerged from the study of the feeding behaviour of bird flocks. The basic idea of its algorithm is to find the optimal solution to the problem based on mutual cooperation and information sharing among individuals in the group.

The basic idea of the particle swarm algorithm is to initialise a set of populations; each particle has an initial velocity and position, calculate the fitness function, share information between particles to get the global optimal solution, and keep iterating to update the velocity and position of the particles so that the particles themselves can achieve the optimal adjustment. The vectors of the velocity and position of the particle in the $k$th iteration in the D-dimensional space are:

$${\nu }_{i,k}={[{\nu }_{i1,k}{\nu }_{i2,k}{\nu }_{i3,k}\cdots \cdots {\nu }_{iD,k}]}^{\mathrm{T}}$$

(20)

$$x_{i,k}={[x_{i1,k}{x}_{i2,k}{x}_{i3,k}\cdots \cdots x_{iD,k}]}^{\mathrm{T}}$$

(21)

The particle updates its velocity and position during each iteration by tracking its own local optimal and global optimal solutions:

$${\nu }_i^{k+l}=\omega {\nu }_i^k+c_1{r}_1\left(p_{\mathrm{besti}}^k-x_i^k\right)+c_2{r}_2\left(g_{\mathrm{besti}}^k-x_i^k\right)$$

(22)

$$x_i^{k+l}=x_i^k+{\nu }_i^{k+l}$$

(23)

where $k$ is the number of iterations, ${\nu }_i^k$ is the velocity of particle $i$ at the $k$th iteration; $c_1$, $c_2$ are the learning factors; $\omega$ is the inertia weight; $r_1$ and $r_2$ are the random numbers of [0, 1].

In the particle swarm algorithm, the inertia weights $\omega$ are closely related to the search ability of the algorithm. The larger the value of inertia weights, the stronger the global optimization ability and the weaker the local optimization ability; the smaller the value of inertia weights, the weaker the global optimization ability and the stronger the local optimization ability. Dynamic inertia weights can provide better optimization results than fixed values. The strategy of dynamic inertia weight optimization is:

$${\omega }_n=\{\begin{array}{cc}{\omega }_{p,min}+\left[{\displaystyle \frac{\left({\omega }_{p,max}-{\omega }_{p,min}\right)\times \left(f_n-f_{min}\right)}{f_{av}-f_{min}}}\right],\hfill & f_n\le f_{av}\hfill \\ {\omega }_{p,max},\hfill & f_n>f_{av}\hfill \end{array}$$

(24)

where ${\omega }_n$ is the inertia weight of population $n$; $f_n$ is the adaptation value of population n; ${\omega }_{p,min}$ and ${\omega }_{p,max}$ are the minimum and maximum values of the inertia weights, respectively; and $f_{av}$ and $f_{min}$ are the average and minimum adaptation of all current particles, respectively.

5.2. Solution Process

The solution flowchart of the two-tier optimal scheduling model developed in this paper is shown in Figure 2, and the specific steps are:

Step 1: Enter the raw data.

Step 2: Solve the optimal economic dispatch model of the upper-level virtual power plant operator, output the output of the units, and calculate the nodal carbon potential of each node using the carbon emission flow theory.

Step 3: Based on the electricity price as well as the nodal carbon potential guides the lower tier EVs to adjust their electricity demand, resulting in an adjusted EV charging demand.

Step 4: Substitute the EV charging demand data into the upper tier, re-solve the upper tier economic optimization scheduling, and output the updated node carbon potential to be passed to the lower tier EV aggregator.

Step 5: When the Nash equilibrium point is reached, output the cost as well as the carbon emissions, and if the Nash equilibrium point is not reached, repeat steps 2–step 4.

6. Case Analysis

6.1. Parameter Settings

The processor of the computing platform used in this paper is AMD Ryzen 7 6800H manufactured by Lenovo in Changchun, China, with Radeon Graphics 3.20 GHz and 16 GB of RAM.1.

This paper takes the IEEE30 node system as an example for analysis, and its network topology is shown in Figure 3. In the figure, node 1 is connected to the upper power grid, node 2, node 27, and node 22 are connected to small gas turbines, node 23 is connected to the wind turbine, and node 13 is connected to the photovoltaic generator.

The relevant parameters of the gas turbine unit are shown in

Table 1. Gas turbine unit parameters.

Number	$\mathbf{Maximum} \mathbf{Output} \mathbf{Power} ({\mathit{P}}_{\mathit{m}\mathit{t}\mathit{m}\mathit{a}\mathit{x}}$/MW)	$\mathbf{Minimum} \mathbf{Output} \mathbf{Power} ({\mathit{P}}_{\mathit{m}\mathit{t}\mathit{m}\mathit{a}\mathit{x}}$/MW)	$\mathbf{Maximum} \mathbf{Rising} \left(\mathbf{Falling}\right) \mathbf{Power} ({\mathit{P}}_{\mathit{u}}({\mathit{P}}_{\mathit{d}}$)/MW)	Natural Gas Price (CNY/kWh)	Power Generation Efficiency
1	2.5	0.50	1.00	0.175	0.196
2	2.0	0.35	0.75	0.175	0.196
3	1.5	0.20	0.60	0.175	1.196

. The electricity price that the virtual power plant operator purchases from the power grid at a time-of-use price is shown in

Table 2. Grid time-of-use electricity price lists.

Type of Periods	Periods Division	$\mathbf{Selling} \mathbf{Price} {\mathit{q}}_{\mathit{G}\mathit{s}}/$(CNY·(kWh)−1)	$\mathbf{Purchase} \mathbf{Price} {\mathit{q}}_{\mathit{G}\mathit{b}}/$(CNY·(kWh)−1)
Peak periods	08:00–11:00, 18:00–23:00	1.1295	0.9164
Flat periods	12:00–17:00	0.7263	0.5124
Valley periods	00:00–07:00, 23:00–24:00	0.3129	0.2017

. The electricity price that the virtual power plant operator sells to electric vehicle users is shown in

Table 3. Time-of-use electricity prices for virtual power plant operators.

Type of Periods	Periods Division	$\mathbf{Selling} \mathbf{Price} {\mathit{q}}_{\mathit{V}\mathit{s}}/$(CNY·(kWh)−1)
Peak periods	08:00–11:00, 18:00–23:00	1.322
Flat periods	12:00–17:00	0.832
Valley periods	00:00–07:00, 23:00–24:00	0.369

.

Latin hypercube sampling (LHS) was used to randomly generate 1000 wind power scenarios and photovoltaic scenarios, and the wind power and photovoltaic output curves of the four reduced scenarios are shown in Figure 4 and Figure 5. The probabilities of each scenario are 0.144, 0.277, 0.128, and 0.457. The cost of wind power generation is CNY 520/(MWh), and the cost of photovoltaic power generation is CNY 750/(MWh). The output limits of wind turbines and photovoltaic units are 6 MW and 4 MW, respectively. The benchmark price of carbon emission pollution control cost is CNY 0.21/kg. Assuming that there are 1000 EVs that can participate in the dispatch in the jurisdiction area, and the models are the same, the specific parameters of EV are shown in

Table 4. Electric vehicle parameters.

Model	Batteries Capacity (kWh)	Maximum Charging Power (kW)	Maximum Discharge Power (kW)	Charging Efficiency	Discharge Efficiency
EV	75	7.7	7.7	0.95	0.90

. Set the dispatch period to 24 h and the step length to 15 min.

6.2. Result Analysis

In order to verify the effectiveness of the method proposed in this paper, three scenarios are set for comparison:

Scenario 1: Considering a fixed electricity price, EVs do not participate in optimal scheduling, and carbon trading is not considered;

Scenario 2: Considering time-of-use electricity prices, electricity prices guide electric vehicles to participate in scheduling, and carbon trading is not considered;

Scenario 3: Considering time-of-use electricity prices, electricity prices and node carbon potential jointly guide EVs to participate in the system’s low-carbon optimization scheduling, and consider carbon trading.

To ensure the effectiveness of the comparison of various scenarios, this paper uses the same wind and solar output data with the highest Latin hypercube sampling probability as the scheduling data, as shown in Figure 6. Figure 7 shows the results of the EV equivalent load comparison under different scenarios obtained by optimising the master–slave game model. Figure 8, Figure 9 and Figure 10 show the EV charging and discharging power, gas turbine output, and VPP purchase and sales power in each time period when the EV adopts different charging and discharging strategies.

As shown in Figure 7, in the case of disordered charging, electric vehicles arrive at their destinations at the same time period and connect to the grid. The plug-and-play charging mode will lead to the “peak on peak” phenomenon, which will aggravate the peak-to-valley difference of load to a certain extent and cause certain harm to the grid. Under the orderly charging and discharging strategy, electric vehicles discharge at peak load and charge at low load, which reduces the peak-to-valley difference of the grid, reduces their own charging costs, and can meet the charging needs of users.

As shown in Figure 8a, when a fixed electricity price is used, electric car owners will access the grid for charging in the same time period. Combined with Figure 8b, it can be seen that at this time, the gas turbine output of the VPP cannot meet the user’s demand, and the VPP will purchase electricity from the main grid, which exacerbates the peak-to-valley difference of the grid and increases the carbon emissions of the power system; combined with Figure 9, it can be seen that time-of-use electricity prices can reduce the peak-to-valley difference phenomenon in the grid on a certain basis; as shown in Figure 10a, after adopting the two incentive measures proposed in this paper, electric car users discharge when the wind and solar output is insufficient; that is, when the carbon emissions in the system are high, reducing the carbon emissions of the system, and charge when the wind and solar output is high to prevent the phenomenon of wind and solar abandonment. Combined with Figure 10b, the amount of electricity purchased by VPP from the upper grid is reduced, effectively reducing carbon emissions.

It can be seen from

Table 5. Cost comparison of each scenario.

	Cost of Scenario 1 (CNY)	Cost of Scenario 2 (CNY)	Cost of Scenario 3 (CNY)
VPP Aggregator	112,684.27	97,690.16	88,063.14
EV Aggregator	—	18,507.16	16,302.19

that after adopting the strategy proposed in this article, the costs of virtual power plant operators and electric vehicle aggregators are reduced compared with using fixed electricity prices and only using time-of-use electricity prices; it can be seen from

Table 6. Carbon emissions by scenario.

	$\mathbf{Carbon} \mathbf{Emissions} \mathbf{in} \mathbf{Scenario} 1 (\mathbf{k}\mathbf{g}$)	$\mathbf{Carbon} \mathbf{Emissions} \mathbf{in} \mathbf{Scenario} 1 (\mathbf{k}\mathbf{g}$)	$\mathbf{Carbon} \mathbf{Emissions} \mathbf{in} \mathbf{Scenario} 1 (\mathit{k}\mathit{g}$)
EV	20,079.59	13,280.94	8194.51

that when electric vehicles adopt the strategy proposed in this article for orderly charging and discharging, the carbon emissions during the charging process of electric vehicles are greatly reduced. From

Table 7. Peak-to-valley load difference for each scenario.

	$\mathbf{Scene} 1 \mathbf{(}\mathbf{M}\mathbf{W}$)	$\mathbf{Scene} 2 \mathbf{(}\mathbf{M}\mathbf{W}$)	$\mathbf{Scene} 3 \mathbf{\left(}\mathbf{M}\mathbf{W}\right)$
Peak-to-valley variation in load	10.0584	4.9216	4.7952

, it can be seen that the peak-to-valley difference of the grid is reduced after adopting the strategy of this paper.

7. Conclusions

In view of the impact of large-scale access of renewable energy and electric vehicles to the power grid, this paper establishes a master–slave game model for double-layer optimization scheduling. The particle swarm algorithm is used to solve the Nash equilibrium point of the model. Through a simulation analysis of the example, the following conclusions are obtained.

(1)

The proposed method is able to accurately calculate the carbon emissions during the charging process of an electric vehicle, and through the calculation example, it can be obtained that by using the method proposed in this paper, the electric vehicle reduces the carbon emissions by 11,885.08 kg during the charging process.

(2)

The developed master–slave game model is able to reduce the cost of virtual power plant operator and electric vehicle operator by CNY 24,621.13 and 2204.97, respectively.

(3)

The guidance of node carbon potential and time-of-use electricity prices can enable electric vehicles to change their charging and discharging behaviours, reduce grid fluctuations, and maximise power consumption.

Currently, the study does not consider limiting factors, such as a larger increase in electricity prices after a grid failure. Subsequent studies will consider the trends in the costs of the various actors involved in dispatch after the occurrence of the limiting factors and whether they are able to meet the needs of EV owners.