Research on Optimal Scheduling Strategy of Microgrid Considering Electric Vehicle Access

Abstract

The random output of renewable energy and the disorderly grid connection of electric vehicles (EV) will pose challenges to the safe and stable operation of the power system. In order to ensure the reliability and symmetry of the microgrid operation, this paper proposes a microgrid optimization scheduling strategy considering the access of EVs. Firstly, in order to reduce the impact of random access to EVs on power system operation, a schedulable model of an EV cluster is constructed based on the Minkowski sum. Then, based on the wavelet neural network (WNN), the renewable energy output is predicted to reduce the influence of its output fluctuation on the operation of the power system. Considering the operation constraints of each unit in the microgrid, the network active power loss and node voltage deviation are taken as the optimization objectives, and the established microgrid model is equivalently transformed via second-order cone relaxation to improve its solution efficiency. Based on network reconfiguration and flexible load participation in demand response, the economy and reliability of system operation are improved. Finally, the feasibility and effectiveness of the proposed method are verified based on the simulation examples.

1. Introduction

In order to realize the low-carbon operation of the power system, renewable energy power generation has developed rapidly [1,2]. The increasing demand for electric energy and severe environmental pollution problems have promoted the development of microgrid technology, which is conducive to improving the penetration rate of renewable energy and realizing the on-site production and consumption of energy [3,4,5]. EVs have great advantages and potential for reducing carbon emissions in the transportation field and alleviating the energy crisis. And EVs are expected to become the main mode of road transportation. The uncertainty of renewable energy output and the disorderly grid connection of EVs have brought great challenges to the safe and stable operation of power systems. To ensure the feasibility and symmetry of the microgrid, it is of great significance to carry out research on the optimal operation of the microgrid considering the access of EVs [6,7,8].

Due to the volatility and intermittence of renewable energy output, this will aggravate the imbalance between the supply side and the demand side of the power system. Many methods have been applied to reduce the uncertainty of renewable energy output and ensure the safe and stable operation of power systems. In [9], by establishing an energy trading model based on the prediction interval of renewable energy power generation, demand-side flexible resources are used to improve the uncertainty of renewable energy output. By establishing a scenario-based stochastic optimization model, a scenario set considering the error of renewable energy output prediction is generated by sampling in [10,11]. The accuracy of the stochastic optimization method is related to the quantity and quality of the generated scene set. In order to ensure the accuracy and feasibility of the established model, a large number of scenes need to be generated. But this also brings a large computational burden to the solution of the problem. In this paper, the output of renewable energy is predicted with WNN, and the uncertainty of renewable energy output on power systems is alleviated using demand-side flexible resources such as flexible loads and EVs.

As a flexible demand-side resource, microgrid operators can participate in the optimal operation of power systems and improve their operating status by signing charging agreements with EV aggregators. At present, the relevant literature has carried out corresponding research on the problem of EVs participating in microgrid optimal scheduling. In [12], a hierarchical scheduling system was established according to the interest relationship between EV charging and discharging stations and microgrid operators. The time-of-use electricity price was formulated based on different working conditions to guide EVs to charge and discharge orderly, and the mixed integer linear programming algorithm was used to calculate and solve the proposed model. In [13], the minimum operating cost of microgrids was considered the objective function, and the influence of EV charging load uncertainty on the optimal scheduling of microgrids was also considered. The disordered and ordered charging models were established to solve the optimal scheduling scheme in the worst scenario. In [14], considering the uncertainty of EV users’ default, the first and second stage scheduling models were established with the minimum operating cost of microgrid and the minimum difference of EV users’ income, respectively. The proposed models can effectively reduce the operating cost of the system and deal with EV users’ default. Most of the existing research focuses on the uncertainty of microgrid operation scheduling caused by EV users’ disorderly charging and does not fully consider the high-dimensional computational burden caused by the direct participation of large-scale EVs in the optimal scheduling of power systems [15]. In this paper, by establishing an EV cluster schedulable model, the computational pressure of problem solving is reduced while ensuring an accurate description of the charging behavior of EVs.

In order to reduce the impact of distributed power output fluctuation on the operation stability of microgrid systems, this paper proposes a microgrid optimal scheduling strategy considering the schedulability of EV clusters. In order to characterize the travel habits of EVs and explore the load–storage capacity of EV clusters, the load–storage schedulable capacity domain of EV clusters is constructed based on the Minkowski sum. Then, based on the WNN, the output of the wind turbine is predicted to reduce the influence of its volatility and intermittence on the day-ahead optimal scheduling scheme of the microgrid. Considering the operation constraints of each unit in the power system, a microgrid optimization model with the minimum active network loss and node voltage deviation as the optimization objective is established, and the model is equivalently transformed based on second-order cone relaxation. Through network reconfiguration and flexible load participation in demand response, the power flow distribution and operation of microgrid systems are optimized, and the operation reliability and economy of microgrid systems are improved. Finally, the feasibility and effectiveness of the proposed method are verified based on simulation examples. The main contributions are as follows:

(1)

In order to reduce the challenge and influence of the disorderly grid connection of EVs on the safe and stable operation of the power system, a dispatchable capacity model of EV set load storage is established based on Minkowski sum. In order to reduce the influence of renewable energy output uncertainty on the safe and stable operation of power systems, the renewable energy output is predicted based on WNN;

(2)

To improve the overall voltage quality and economic benefits of the system, taking into account the reduction of active network loss and the reduction of voltage deviation as the optimization objectives, the load fluctuation of the microgrid system operation can be effectively suppressed, and the operation cost of the system can be significantly reduced by means of network reconfiguration and flexible load participation in demand response.

The rest of this paper is organized as follows: Section 2 presents the schedulable model of the EV cluster, the day-ahead optimal scheduling model of the microgrid, and the transformation and deformation of the model. Section 3 introduces the established simulation test system parameters. In Section 4, the effectiveness and feasibility of the proposed method are verified using a comparative analysis of simulation examples. Finally, Section 5 concludes this work.

2. Theoretical Analysis

The research object of this paper is the superior power grid and microgrid managed using different operators. It relies on the information interaction between the two to make decisions on the optimal scheduling scheme of the microgrid and optimize the operation status of the microgrid system. As shown in Figure 1, the microgrid system structure diagram considering EV access is established in this paper.

The upper power grid and the microgrid realize power interaction through the tie line. The microgrid dispatching center formulates an optimized dispatching plan by collecting relevant data on the equipment and lines. It maximizes the overall efficiency of operation under the premise of ensuring the safety and stability of the microgrid systems. The model established in this paper is multi-period day-ahead optimization scheduling. It can be written in the following compact form as follows:

$$\{\begin{array}{ll}\min F\hfill & =\min {\displaystyle \sum _{i=1}^n{F}_i\left(x_t\right)},t\in \mathrm{T}\hfill \\ s.t.\hfill & h\left(x_t\right)=0\hfill \\ & g\left(x_t\right)\le 0\hfill \end{array}$$

(1)

where F is the objective function of the optimization model; $x_t$ is the decision variable of the optimization model; $F_i(x_t)$ is the objective function of the ith optimization model; and $h(x_t)$ and $g(x_t)$ are the equality constraints and inequality constraints of the optimization model.

Figure 2 shows the optimal microgrid scheduling framework considering the schedulability of the EV cluster. Firstly, the influence of the direct grid connection of individual EVs on the safe and stable operation of the power grid is reduced by establishing a schedulable model of EV clusters. Secondly, based on the WNN, the renewable energy output is predicted, and the system operation state is improved by the flexible load participating in the demand response on the demand side. Based on the network reconfiguration, the reliability of the power grid is improved by improving the power flow distribution of the system. Finally, by setting different operating scenarios for comparative analysis, the feasibility and effectiveness of the proposed method are verified.

2.1. Schedulable Charging and Discharging Model of EV Cluster

In view of the challenges brought by the large-scale disorderly grid-connection of EVs to the safe and stable operation of the power system, this paper is based on Minkowski sum equivalents of the individual EVs with large prediction randomness to obtain the charging and discharging model of the EV cluster so that it can flexibly and controllably participate in the optimal scheduling of the power system.

In order to establish an accurate and feasible schedulable charging and discharging model of the EV cluster based on a large number of historical data of the charging and discharging behaviors of EV users, this paper uses the Gaussian mixture model to model the arrival/departure times of EV users:

$$\{\begin{array}{c}{f}_k^{\mathrm{a}}(t_{\mathrm{a}})={\displaystyle \sum _{l=1}^L{\rho }_l\frac{1}{\sqrt{2\pi }{\sigma }_{\mathrm{a},l}}\exp (-\frac{t_{\mathrm{a},l}-{\mu }_{\mathrm{a},l}}{2{\sigma }_{\mathrm{a},l}^2}),t_{\mathrm{a}}\in T}\\ f_k^{\mathrm{d}}(t_{\mathrm{d}})={\displaystyle \sum _{l=1}^L{\rho }_l\frac{1}{\sqrt{2\pi }{\sigma }_{\mathrm{d},l}}\exp (-\frac{t_{\mathrm{d},l}-{\mu }_{\mathrm{d},l}}{2{\sigma }_{\mathrm{d},l}^2}),t_{\mathrm{d}}\in T}\end{array}$$

(2)

where $t_{\mathrm{a}}$ and $t_{\mathrm{d}}$ are the times for EV users to arrive and leave the charging and discharging station; ${\rho }_l$ is the corresponding distribution proportion coefficient of the Gaussian mixture model; ${\mu }_{\mathrm{a},l}$ and ${\sigma }_{\mathrm{a},l}$ are the expectation and variance of arrival time; and ${\mu }_{\mathrm{d},l}$ and ${\sigma }_{\mathrm{d},l}$ are the expectation and variance of departure time.

Figure 3 shows the Gaussian mixture model of EV arrival time and departure time.

Due to the randomness of the charging and discharging behavior of individual EV users, it is not guaranteed to accurately predict the travel time distribution of each EV. Therefore, the EV cluster is considered a research object to reduce the randomness of individual EVs and improve the applicability of the established model. The grid-connected scale of EVs at each charging and discharging station can be expressed as follows:

$$\{\begin{array}{l}{N}_{k,t}^{\mathrm{CS}}=N_{k,t-1}^{\mathrm{CS}}+N_{k,t}^{\mathrm{A}}-N_{k,t}^{\mathrm{D}}\hfill \\ N_{k,t}^{\mathrm{A}}=(F_k^{\mathrm{a}}(t+1)-F_k^{\mathrm{a}}(t))\cdot N_k^{\mathrm{EV}}\hfill \\ N_{k,t}^{\mathrm{D}}=(F_k^{\mathrm{d}}(t+1)-F_k^{\mathrm{d}}(t))\cdot N_k^{\mathrm{EV}}\hfill \end{array}$$

(3)

where $N_{k,t}^{\mathrm{CS}}$ is the number of EVs in the charging and discharging station of unit k at hour t; $N_{k,t}^{\mathrm{A}}$ and $N_{k,t}^{\mathrm{D}}$ are the number of EVs arriving and departing at the charging and discharging station of unit k at hour t; $F_k^{\mathrm{a}}(t)$ and $F_k^{\mathrm{d}}(t)$ are the cumulative density functions of Equation (2); and $N_k^{\mathrm{EV}}$ is the total number of EVs that reach the charging and discharging station in one day of unit k.

By introducing Boolean variables to define the grid-connected and off-grid states of EV users, the EV individuals in the same scheduling period can use Minkowski sum to characterize the schedulability of EV clusters, and the multi-dimensional decision variables of the original EV individuals are equivalently transformed into the single-dimensional decision variables of the EV cluster, alleviating the pressure of the model calculation to solve the dimension:

$$\{\begin{array}{l}{P}_{k,t}^{\mathrm{CS},\mathrm{c}}={\displaystyle \sum _{n\in I_k^{\mathrm{EV}}}{u}_{n,t}{P}_{n,t}^{\mathrm{ev},\mathrm{c}}};P_{k,t}^{\mathrm{CS},\mathrm{d}}={\displaystyle \sum _{n\in I_k^{\mathrm{EV}}}{u}_{n,t}{P}_{n,t}^{\mathrm{ev},\mathrm{d}}}\hfill \\ E_{k,t}^{\mathrm{CS},\max }={\displaystyle \sum _{n\in I_k^{\mathrm{EV}}}{u}_{n,t}{E}_n^{\max }};E_{k,t}^{\mathrm{CS},\min }={\displaystyle \sum _{n\in I_k^{\mathrm{EV}}}{u}_{n,t}{E}_n^{\min }}\hfill \end{array}$$

(4)

where $P_{k,t}^{\mathrm{CS},\mathrm{c}}$ and $P_{k,t}^{\mathrm{CS},\mathrm{d}}$ are the charging and discharging power of the charging and discharging station of unit k at hour t; $u_{n,t}$ is the on-grid and off-grid state of EV of unit n at hour t; $I_k^{\mathrm{EV}}$ is the number of EV clusters at the charging and discharging station of unit k; $P_{n,t}^{\mathrm{EV},\mathrm{c}}$ and $P_{n,t}^{\mathrm{EV},\mathrm{d}}$ are the charging and discharging power of the EV of unit n at hour t; $E_{k,t}^{\mathrm{CS},\max }$ and $E_{k,t}^{\mathrm{CS},\min }$ are the upper and lower limits of the amount of electricity of the charging and discharging station of unit k at hour t; and $E_n^{\max }$ and $E_n^{\min }$ are the upper and lower limits of the power of the EV of unit n.

2.2. Day-Ahead Optimal Scheduling Model of Microgrid

The output of distributed generation has the characteristics of intermittence and fluctuation. In order to reduce the impact on the operation and scheduling of microgrids, it is necessary to predict the output of distributed generation. WNN is based on a BP neural network, and the transfer function of hidden layer nodes is a wavelet basis function. WNN takes into account the forward propagation of signals and the back propagation of errors. The program flow chart of the WNN algorithm is shown in Figure 4. The overall structure of WNN is shown in Figure 5.

The hidden layer output $h(j)$ and predictive output $y(k)$ of the model are expressed as follows:

$$h\left(j\right)=h_j\left(\frac{{\displaystyle \sum _{i=1}^k{w}_{ij}{x}_i-b_j}}{a_j}\right),j=1,2,\mathrm{\dots },l$$

(5)

$$y(k)={\displaystyle \sum _{i=1}^l{w}_{ik}h(i),k=1,2,\mathrm{\dots }m}$$

(6)

where $w_{ij}$ is the connection weight of unit ij; $w_{ik}$ is the connection weight of unit ik.

The connection weight and network parameters of WNN are modified using the gradient correction method so that the predicted output of the model gradually approaches the ideal target value. In this paper, the Morlet wavelet basis function is selected as follows:

$$y=\cos (1.75x)e^{-\frac{x^2}{2}}$$

(7)

In order to reduce the influence of distributed power access on the operation state of microgrids, this paper selects two indexes of network active power loss $F_{\mathrm{loss}}$ and node voltage deviation $F_{\mathrm{u}}$ to quantitatively analyze the effectiveness and feasibility of a microgrid optimal scheduling strategy, which can be shown as follows:

$$\{\begin{array}{l}{F}_{\mathrm{loss}}={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{ij=1}^M{I}_{ij,t}^2{r}_{ij}}}\hfill \\ F_{\mathrm{u}}={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{i=1}^N\frac{\left|U_{i,t}-U_{\mathrm{e}}\right|}{U_{\mathrm{e}}}}}\hfill \end{array}$$

(8)

where $I_{ij,t}$ is the line current of unit ij at hour t; $r_{ij}$ is the line resistance of unit ij; $U_{i,t}$ is the node voltage of unit i at hour t; and $U_{\mathrm{e}}$ is the node-rated voltage.

Due to the different quantization units of the objective function in the established multi-objective optimization problem, it is difficult to directly and objectively judge which kind of power grid operation state is better. It needs to be normalized to comprehensively evaluate the operating state of the power system. $F_{\mathrm{loss}}$ and $F_{\mathrm{u}}$ are used as the objective functions to solve the problem, respectively. The two sets of values correspond to the operating boundary values of the two objective functions. Then, $F_{\mathrm{loss}}$ and $F_{\mathrm{u}}$ are normalized according to the operating boundary values. The auxiliary variable $\xi$ represents the minimum value of each objective function after normalization. The auxiliary variable $\xi$ is used to comprehensively evaluate the operating state of the power system: the larger the $\xi$ is, the better the operation state of the power grid is. The original multi-objective optimization problem is transformed into a single-objective problem for solving the maximum value of $\xi$:

$$f_i^{*}=\frac{F_i^{\max }-F_i}{F_i^{\max }-F_i^{\min }},i=1,2$$

(9)

$$\xi =\min (f_1^{*},f_2^{*})$$

(10)

where $f_i^{*}$ is the normalized value of the ith objective function $F_i$; $F_i^{\max }$ and $F_i^{\min }$ are the maximum and minimum values of $F_i$ calculated when another objective function is used as the solution object; and $\xi$ is the minimum value of the normalization results of each objective function.

In order to ensure the feasibility and effectiveness of the established microgrid optimal scheduling model considering the access of EVs, the system unit operation constraints considered in this paper are as follows:

(1)

Power flow balance constraints:

$$\{\begin{array}{l}{p}_{j,t}=P_{ij,t}-r_{ij}{I}_{ij,t}^2-{\displaystyle \sum _{k:j\to k}{P}_{jk,t}},\left|p_{j,t}\right|\ge \delta \hfill \\ q_{j,t}=Q_{ij,t}-x_{ij}{I}_{ij,t}^2-{\displaystyle \sum _{k:j\to k}{Q}_{jk,t}},\left|q_{j,t}\right|\ge \delta \hfill \\ I_{ij,t}^2=\frac{P_{ij,t}^2+Q_{ij,t}^2}{U_{i,t}^2}\hfill \end{array}$$

(11)

where $p_{j,t}$ and $q_{j,t}$ are the node active power and reactive power of unit j at hour t; $P_{ij,t}$ and $Q_{ij,t}$ are the branch active power and reactive power of unit ij at hour t; $x_{ij}$ is the line reactance of unit ij; and $\delta$ is a very small positive number;

(2)

Safe operation constraints:

$$\{\begin{array}{c}{U}_{i,\min }\le U_{i,t}\le U_{i,\max }\\ I_{ij,\min }\le I_{ij,t}\le I_{ij,\max }\end{array}$$

(12)

where $U_{i,\max }$ and $U_{i,\min }$ are the upper and lower limits of voltage amplitude of unit i; $I_{ij,\max }$ and $I_{ij,\min }$ are the upper and lower limits of branch current of unit ij;

(3)

EV cluster operation constraints [16]:

$$\{\begin{array}{l}0\le P_{k,t}^{\mathrm{CS},\mathrm{c}}\le u_{k,t}^{\mathrm{CS}}{P}_{k,\max }^{\mathrm{CS},\mathrm{c}}\hfill \\ 0\le P_{k,t}^{\mathrm{CS},\mathrm{d}}\le (1-u_{k,t}^{\mathrm{CS}})P_{k,\max }^{\mathrm{CS},\mathrm{d}}\hfill \\ E_k^{\mathrm{CS},\min }\le E_{k,t}^{\mathrm{CS}}\le E_k^{\mathrm{CS},\max }\hfill \\ E_{k,t}^{\mathrm{CS}}=E_{k,t-1}^{\mathrm{CS}}+{\eta }_{\mathrm{c}}{P}_{k,t}^{\mathrm{CS},\mathrm{c}}-P_{k,t}^{\mathrm{CS},\mathrm{d}}/{\eta }_{\mathrm{d}}\hfill \end{array}$$

(13)

where $u_{k,t}^{\mathrm{CS}}$ is the Boolean variable of the equivalent charging and discharging state of EV cluster of unit k at hour t; $P_{k,\max }^{\mathrm{CS},\mathrm{c}}$ and $P_{k,\max }^{\mathrm{CS},\mathrm{d}}$ are the upper limits of equivalent charging and discharging power of EV cluster of unit k; $P_{k,t}^{\mathrm{CS}}$ is the equivalent grid-connected power of EV cluster in charging station of unit k at hour t; $E_{k,t}^{\mathrm{CS}}$ is the equivalent battery capacity of unit k at hour t; $E_k^{\mathrm{CS},\max }$ and $E_k^{\mathrm{CS},\min }$ are the upper and lower limits of battery capacity of EV cluster in charging station; and ${\eta }_{\mathrm{c}}$ and ${\eta }_{\mathrm{d}}$ are the charging and discharging coefficient of EV;

(4)

Flexible load operation constraints [17]:

$$\{\begin{array}{l}{P}_{i,t}^{\mathrm{load}}=P_{i,t}^{\mathrm{load}0}+P_{i,t}^{\mathrm{fle}}=P_{i,t}^{\mathrm{load}0}+P_{i,t}^{\mathrm{stop}}+P_{i,t}^{\mathrm{tran}}\hfill \\ P_{i,t}^{\mathrm{stop}}=P_{i,t}^{\mathrm{stop}0}-\Delta P_{i,t}^{\mathrm{stop}},\Delta P_{i,t}^{\mathrm{stop}}\ge 0\hfill \\ P_{i,t}^{\mathrm{tran}}=P_{i,t}^{\mathrm{tran}0}+P_{i,t}^{\mathrm{add}}-P_{i,t}^{\mathrm{sub}},P_{i,t}^{\mathrm{add}}\ge 0,P_{i,t}^{\mathrm{sub}}\ge 0\hfill \\ {\displaystyle \sum _{t=1}^T{P}_{i,t}^{\mathrm{tran}}}={\displaystyle \sum _{t=1}^T{P}_{i,t}^{\mathrm{tran}0}}\hfill \\ P_{i,t}^{\mathrm{tran},\min }\le P_{i,t}^{\mathrm{tran}}\le P_{i,t}^{\mathrm{tran},\max }\hfill \end{array}$$

(14)

where $P_{i,t}^{\mathrm{load}}$ is the total load power of unit i at hour t; $P_{i,t}^{\mathrm{load}0}$ and $P_{i,t}^{\mathrm{fle}}$ are the fixed load power and flexible load power of unit i at hour t; $P_{i,t}^{\mathrm{stop}}$ is the interruptible load power of unit i at hour t; $P_{i,t}^{\mathrm{stop}0}$ and $\Delta P_{i,t}^{\mathrm{stop}}$ are the initial interruptible load power and load interruption involved in demand response of unit i at hour t; $P_{i,t}^{\mathrm{tran}}$ and $P_{i,t}^{\mathrm{tran}0}$ are the transferable load power and initial transferable load power of unit i at hour t; $P_{i,t}^{\mathrm{add}}$ and $P_{i,t}^{\mathrm{sub}}$ are the increment and reduction of transferable load power of unit i at hour t; and $P_{i,t}^{\mathrm{tran},\max }$ and $P_{i,t}^{\mathrm{tran},\min }$ are the upper and lower limits of a transferable load participating in demand response;

(5)

Interaction power constraints between main network and microgrid:

$$-P_{\mathrm{change},\max }\le P_{\mathrm{change},t}\le P_{\mathrm{change},\max }$$

(15)

where $P_{\mathrm{change},t}$ and $P_{\mathrm{change},\max }$ are the interaction powers between the main network and microgrid at hour t and maximum interaction power;

(6)

Network reconfiguration constraints:

$$\{\begin{array}{l}{\displaystyle \sum _{(ij)\in B}{z}_{ij}=n_{\mathrm{b}}-n_{\mathrm{s}}}\hfill \\ m_{ij}=(1-z_{ij})\cdot \mathrm{M}\hfill \\ U_{j,t}^2\ge U_{i,t}^2-m_{ij}-2(r_{ij}{P}_{ij}+x_{ij}{Q}_{ij})+(r_{ij}^2+x_{ij}^2)I_{ij,t}^2\hfill \\ U_{j,t}^2\le U_{i,t}^2+m_{ij}-2(r_{ij}{P}_{ij}+x_{ij}{Q}_{ij})+(r_{ij}^2+x_{ij}^2)I_{ij,t}^2\hfill \end{array}$$

(16)

where $z_{ij}$ is the Boolean variable of line breaking state; $n_{\mathrm{b}}$ and $n_{\mathrm{s}}$ are the total network node number and network root node number; and $\mathrm{M}$ is a sufficiently large positive number.

2.3. Transformation and Deformation of the Model

The constraints of the microgrid day-ahead optimal scheduling model established above include quadratic terms and integer terms. It belongs to a mixed-integer nonlinear non-convex mathematical problem, which is a polynomial complexity non-deterministic (NP-hard) problem. Figure 6 shows the schematic figure of second-order cone relaxation. Based on the second-order cone relaxation method, this paper transforms the original non-convex and nonlinear problem into a second-order cone optimization problem that can be solved more efficiently by relaxing the quadratic equality constraint into a second-order cone constraint.

Let ${\tilde{I}}_{ij,t}=I_{ij,t}^2$ and ${\tilde{U}}_{i,t}=U_{i,t}^2$, then the safe operation constraints can be written as follows:

$$\{\begin{array}{c}{I}_{ij,\min }^2\le {\tilde{I}}_{ij,t}\le I_{ij,\max }^2\\ U_{i,\min }^2\le {\tilde{U}}_{i,t}\le U_{i,\max }^2\end{array}$$

(17)

The power flow balance constraints can be written as follows:

$$\{\begin{array}{l}{p}_{j,t}=P_{ij,t}-r_{ij}{\tilde{I}}_{ij,t}-{\displaystyle \sum _{k:j\to k}{P}_{jk,t}},\left|p_{j,t}\right|\ge \delta \hfill \\ q_{j,t}=Q_{ij,t}-x_{ij}{\tilde{I}}_{ij,t}-{\displaystyle \sum _{k:j\to k}{Q}_{jk,t}},\left|q_{j,t}\right|\ge \delta \hfill \\ {\tilde{I}}_{ij,t}=\frac{P_{ij,t}^2+Q_{ij,t}^2}{{\tilde{U}}_{i,t}}\hfill \end{array}$$

(18)

After equivalent transformation and relaxation, the standard second-order cone form can be obtained as follows:

$${\Vert \begin{array}{c}2P_{ij,t}\\ 2Q_{ij,t}\\ {\tilde{I}}_{ij,t}-{\tilde{U}}_{i,t}\end{array}\Vert }_2\le {\tilde{I}}_{ij,t}+{\tilde{U}}_{i,t},\forall ij\in B$$

(19)

3. Model Building

In order to further verify the feasibility and effectiveness of the microgrid optimal scheduling model considering the access of EVs, based on the Matlab 2021b platform, the model is modeled and the CPLEX solver is called to solve the problem. This paper conducts research and analysis based on the improved IEEE33 node system, and the node location distribution is shown in Figure 7. The basic parameters of the IEEE33 node network are detailed in [18].

The rated voltage level of the test network system is 12.66 kV, and the voltage amplitude is $\pm$1.05 pu. The maximum branch current is 500 A. The interactive power between the main network and the microgrid is 750 kW. It is assumed that the connected EVs are the same type, the capacity of each EV is 24 kWh, and the access power range is −3~3 kW. The charging and discharging coefficients of EVs are 0.95. The operating costs of the established microgrid system are shown in

Table A1. Operation cost of microgrid system.

Parameter	Value(USD/kWh)	Parameter	Value(USD/kWh)
The unit cost of active power loss	0.1158	The unit compensation cost of transferable load	0.0073
The unit cost of interactive power	0.093	The unit compensation cost of interruptible load	0.0577
The unit output cost of wind turbine	0.0435	The unit compensation cost of EV users	0.0791

. The time-of-use electricity price is shown in

Table A2. Time-of-use electricity price.

Time	Electricity Sales Price (USD/kWh)	Electricity Purchase Price (USD/kWh)
1:00–7:00(Valley time)	0.0724	0.0556
8:00–10:00, 19:00–24:00 (Peak time)	0.1951	0.1503
11:00–18:00(Usual time)	0.1302	0.1003

. The load curve of the microgrid is shown in Figure 8.

4. Result Analysis

In order to reduce the influence of fluctuation and intermittence in distributed power output on microgrid operation, this paper predicts the output of distributed power based on WNN. Taking photovoltaic power generation as an example, the output prediction results are shown in Figure 9. It can be seen from the results in the figure that the photovoltaic output prediction based on WNN has high prediction accuracy. It can provide original data support for the formulation of a day-ahead optimal scheduling scheme for microgrids.

Considering the access of EVs, the microgrid is randomly optimized. Multiple sets of examples are set to compare and analyze the effectiveness and feasibility of the scheduling results. In order to verify the superiority of the proposed microgrid optimal scheduling scheme considering the access to EVs, the following four cases are set up for analysis in

Table A3. Operating condition of cases.

Scene Mode	The Operation Considered
Case 1	None
Case 2	The impact of EV access
Case 3	The impact of EV access and network reconfiguration
Case 4	The impact of EV access, network reconfiguration, and demand response

.

Table A4. Microgrid operation results under different scenarios.

Scene Mode	floss(MW)	fu(pu)	F (Normalization)	Microgrid Operation Cost(USD)
Case 1	8.2672	58.3628	0.7972	2807.91
Case 2	7.0688	57.4321	0.8205	2621.39
Case 3	2.9829	18.1345	0.8516	1983.57
Case 4	2.4405	17.7196	0.9665	2177.79

shows the microgrid operation results under different scenarios. The results show that the optimal scheduling of microgrids with EV access, considering network reconfiguration and demand response, can significantly reduce the network loss and node voltage deviation of microgrids and improve the economic benefits of microgrid operation.

Figure 10 shows the microgrid voltage levels under different operating scenarios. The voltage amplitudes of Case 1 and Case 2 are higher than the rated voltage amplitude due to the lack of network reconfiguration and demand response, as shown in Figure 10a and Figure 10b, respectively. The extended IEEE33 node test systems after network reconfiguration are shown in Figure 11a,b. Network reconfiguration can effectively improve the power flow distribution of the microgrid system. Figure 10c shows that the voltage distribution of Case 3 has been significantly improved. As shown in Figure 10d, Case 4 considers the influence of demand response on the basis of Case 3, which further improves the voltage quality of the system.

Figure 12 shows the comparison of flexible loads before and after participating in demand response. Without considering the participation of flexible load in demand response, the load peak-valley difference of the microgrid system is 396.26 kW. Considering the flexible load participating in the demand response, the load peak-valley difference of the microgrid system is 308.12 kW, which is 88.14 kW lower than before. The simulation results show that the participation of flexible load in demand response can effectively suppress the load fluctuation of system operation and improve the operation reliability of microgrid systems.

In order to improve the calculation speed of the established model and ensure the accuracy of the solution, this paper equivalently transforms the established model based on second-order cone relaxation and sets the model accuracy analysis index ${\Delta }_{ij,t}$ to verify that the model after second-order cone relaxation is accurate and feasible:

$${\Delta }_{ij,t}=\left|{\tilde{U}}_{j,t}{\tilde{I}}_{ij,t}-(P_{ij,t}^2+Q_{ij,t}^2)\right|$$

(20)

Figure 13 shows the error analysis histogram of the equivalent model. The different colors represent different sizes of error values. Taking Case 4 as an example for verification analysis, it can be seen from Figure 13 that the order of magnitude of the solution error of the model after the second-order cone relaxation equivalent transformation is 10⁻⁵. The solution error of the model established in this paper is within the allowable range. The second-order cone relaxation can improve the calculation speed of the problem while ensuring the accuracy of the solution, and the optimal scheduling model for microgrids considering EV access after second-order cone transformation is effective.

5. Conclusions

In this paper, considering the random output of distributed generation and the operation constraints of microgrid units, a microgrid optimization scheduling model considering the access of EVs is established to ensure the feasibility and symmetry of the microgrid. The construction of an EV cluster schedulable model based on Minkowski sum can effectively improve the flexibility and accuracy of large-scale EV cluster pre-scheduling. The prediction of renewable energy output based on WNN can effectively reduce the influence of its output uncertainty and volatility on the safe and stable operation of power systems. Considering the operation constraints of each unit in the microgrid system and taking into account the objective function of the network active power loss and node voltage deviation as the optimization objects, the operation state of the microgrid system is optimized based on network reconfiguration and flexible load participation demand response. This method can significantly improve the operation reliability and economy of the microgrid system. Within the allowable calculation error range, the established model is equivalently transformed based on the second-order cone relaxation, which improves the solution speed of the model while ensuring its accuracy.

The microgrid optimal scheduling model considering EV access established in this paper is a day-ahead optimal scheduling model. By predicting the output of renewable energy and establishing the scheduling model of the EV cluster, the influence of these uncertain factors on the safe and stable operation of the power system is reduced, and the operation state of power grid is improved through demand-side flexible resources, but the influence of prediction errors on the formulation of the optimal scheduling strategy is not fully considered. In the future research process, the influence of prediction error on power system operation will be fully considered to make it more in line with the actual operation of the power grid.