Considering the spatiotemporal optimal scheduling strategy of electric vehicles entering the network

 Corresponding author: Xiu Wan Copyright © 2025 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0. Considering the spatiotemporal optimal scheduling strategy of electric vehicles entering the network Xiu Wan *, Yongqi Ren and Lingxiao Wu School of Electric Power Engineering, Nanjing Institute of Technology, Nanjing, Jiangsu, China. Global Journal of Engineering and Technology Advances, 2025, 22(03), 143-154 Publication history: Received on 14 February 2025; revised on 20 March 2025; accepted on 22 March 2025 Article DOI: https://doi.org/10.30574/gjeta.2025.22.3.0066 Abstract With the intensification of the contradiction between economic development, fossil fuel shortages, and severe environmental pollution, the development and widespread adoption of Electric Vehicles (EVs) have become an inevitable trend. The large-scale and disorderly charging of EVs connected to the grid will impose significant impacts on the power system, potentially leading to local overloads and threatening the security and economic operation of the grid. Therefore, this study investigates the coordinated optimization planning problem involving generators, EVs, and renewable energy sources (wind and solar). A spatiotemporal optimization strategy for EV charging scheduling is proposed. On the temporal scale, an optimal scheduling model based on unit commitment is established, aiming to minimize the operational costs of generators on the transmission grid side, PM2.5 emissions, total user charging costs, and the curtailment of wind and solar power. On the spatial scale, an optimal power flow-based scheduling model is developed to reduce distribution network losses, taking into account network security constraints and the spatial migration characteristics of EVs. The proposed EV charging scheduling strategy is simulated and analyzed on a power system model comprising a standard 10-machine transmission network and an IEEE 33-node distribution network. The results validate the effectiveness and superiority of the proposed spatiotemporal optimization scheduling strategy. Keywords: Electric Vehicles; Spatiotemporal Optimization Charging Strategy; Unit Commitment; Optimal Power Flow 1. Introduction With the continuous growth in the number of electric vehicles (EVs), their spatiotemporal distribution characteristics and the convergence of user behavior patterns may lead to large-scale disordered charging, posing significant load impacts on the power grid. At the same time, wind power, as a clean and renewable energy source, has experienced rapid development, but its grid integration may introduce stability risks to the power system [1]. Existing research has primarily focused on optimizing charging strategies in low-voltage distribution network scenarios, with limited consideration for the coordinated regulation of generation units on the transmission grid side [2-3]. In the field of transmission grid coordination optimization, some scholars have established objective functions that balance the operational costs of thermal power units and carbon emissions, achieving load curve smoothing through EV charging management [4-7]. Studies have confirmed that such coordination mechanisms can not only reduce the system's reliance on small-capacity peaking units but also effectively decrease overall operational costs and carbon emissions. Notably, bi-level optimization theory has recently demonstrated unique advantages in charging scheduling. Reference [8] proposed a bi-level optimization framework considering power grid security constraints: the upper-level model addresses the unit commitment problem to determine the optimal charging capacity for each time period, while the lower-level model allocates this capacity spatially under AC power flow constraints. Although this scheme is designed for the transmission grid, its practical scheduling flexibility remains limited due to the deterministic Global Journal of Engineering and Technology Advances, 2025, 22(03), 143-154 144 characteristics of EV distribution at nodes. The aforementioned EV charging strategies optimize scheduling separately in either the transmission or distribution network layers across temporal and spatial dimensions. However, as highlighted in reference [9], it is necessary to simultaneously optimize EV charging strategies in both the transmission and distribution network layers. In summary, this paper proposes a spatiotemporal optimization model-based EV charging scheduling strategy. This strategy optimizes the temporal coordination of EVs, generation units, and renewable energy sources on the transmission grid side, while considering the spatial mobility of EV charging loads on the distribution grid side. This paper assumes that EV charging behavior fully complies with grid scheduling. 2. Spatiotemporal optimization model of large-scale electric vehicles entering the network 2.1. Optimal scheduling modeling on time scale Considering the volatility and uncertainty of wind power, this paper adopts scenario-based method to describe the volatility and uncertainty of wind power. On the transmission side, in order to coordinate the charging load of electric vehicles with the output of generator set and the wind-view output in time to achieve the optimal effect, the upper level scheduling strategy based on the day-ahead unit combination model is adopted, and its optimization variables are the start and stop state of the unit and its output, the number of electric vehicles charged, wind abandon and light power in each period. The modeling process of optimal scheduling strategy on time scale is as follows. 2.1.1. Objective function On the time scale, the goal is to coordinate the charging load of electric vehicles on the transmission side with the output of the generator set and the scenery output, so as to improve the overall economy. Therefore, the optimization strategy on the transmission side should be able to reduce the operating cost of the generator set, reduce the emission of pollutants, increase the scenery absorption rate of new energy as much as possible, and reduce the charging cost of electric vehicle owners. Therefore, the objective function should include the fuel cost of unit operation, the cost of startup and shutdown, the penalty cost of pollutant emission, the charging cost of the owner, and the penalty cost of abandoning the scenery. Goal one: Fuel costs ( ) ,1 2 ,,,s s s i i t i i i t iot is t P a b c PC P= + + In the equation: ( ) , ,1 s ist itoPC represents the fuel cost of generating unit i at time period t under scenario s; i a , i b , and i c are the coefficients of the fuel cost characteristic curve for unit i, and , s it P is the active power output of generating unit i at time period t under scenario s. Goal 2: Penalty costs for pollutant emissions ( ) 2 , , ,2, (1 /100) ( )/10000][ s s s i i t i i ie tt iios t C P c Aar P P      =   −  + + In the equation: ( ) , ,2 s ist itoPC represents the PM2.5 emissions of generating unit i at time period t under scenario s; e c is the penalty price factor for PM2.5 emissions; Aar is the average ash content of coal on an as-received basis (%), with a default value of 20 in calculations; ω is the conversion coefficient from coal ash to PM2.5 (%), with a default value of 5.1 in calculations; η is the removal efficiency of control measures for PM2.5 (%), with a default value of 99 in calculations [7-8]; PM2.5 emissions are proportional to coal consumption, and , ii  and i  are the coal consumption characteristic curve coefficients of unit i. Target 3: start-stop costs off off off , ,off of 3, f , ,T , h i i i t i it c i i t i ost CS X H S X H   =   Global Journal of Engineering and Technology Advances, 2025, 22(03), 143-154 145 off 4, TT c ost t i i C=+ In the equation: 3 ,,itost C represents the startup cost of generating unit i at time period t; h i S is the hot startup cost of generating unit i; c i S is the cold startup cost of generating unit i; off ,it X is the continuous downtime of generating unit i before time period t; off i H is the transition time between hot startup and cold startup for unit i; 4, ,ost i t C is the shutdown cost of generating unit i at time period t; off i T is the minimum allowable downtime of generating unit i; and c i T is the cold startup time of generating unit i. In standard systems, the shutdown cost of thermal power units is typically a constant and is usually set to 0. Target 4: User charging cost , ,5 ss t t ev tost CcP= In the equation: 5,s ost t C represents the total charging cost of EV owners at time period t under scenario s; t c is the charging price for EVs at time period t, and , s ev t P is the EV charging load at time period t under scenario s. Goal six: The cost of abandoning scenery 1 1 , , ,, 1 61, Δ Δ s s s t w wind m t N M ost pv npv n t m C c P c P = =+=  In the equation: 6,s ost t C represents the penalty cost for wind and solar curtailment at time period t under scenario s; 1 M is the number of wind farms; w c is the penalty price for wind curtailment; ,, Δs wind m t P is the curtailed wind energy of wind farm m at time period t under scenario s; 1 N is the number of photovoltaic (PV) panels; pv c is the penalty price for solar curtailment; and ,, Δs pv n t P is the curtailed solar energy of PV panel n at time period t under scenario s. Equations (1) to (6) represent the fuel cost of generating units, the penalty cost for PM2.5 emissions, the startup cost, the shutdown cost, the user charging cost, and the cost of wind and solar curtailment, respectively. Among these, when determining the unit commitment sequence, the objective is to minimize the startup and shutdown costs of the units; when determining the operating base points of online units driven by wind power scenarios, the objective is to minimize the expected cost across all scenarios. The overall objective function can be expressed as: ( ) ( ) ( ) ( ) , 1 , , , , 6, 1 1 1 3, , 1 1,2 1, 5, min 1 [ ] s gg s ost i t s ost NN N TT s s s s i t i t i i t i i t i t t ost t t i s t ost ost iCu u E uCCPPCC  − = = = = =     − +    + + +       In the equation: T represents the total number of optimization time periods; g N is the total number of generating units; s N is the number of wind and solar scenarios; 3 ,,itost C is the startup cost function of thermal unit i at time period t; ,it u is the operating state of generating unit i at time period t, where 1 indicates operation and 0 indicates shutdown; {}E denotes the mathematical expectation over all scenarios; s  is the probability of occurrence of the combined wind and solar output scenario s; ( ) , ,1 s ist itoPC is the fuel cost function of thermal unit i; , s it P is the active power output of Global Journal of Engineering and Technology Advances, 2025, 22(03), 143-154 146 generating unit i at time period t under scenario s; ( ) , ,2 s ist itoPC is the PM2.5 emission penalty cost of thermal unit i; s t U is the total charging cost of EV owners at time period t under scenario s; and 6, s ost t C is the total penalty cost for wind and solar curtailment of wind farms at time period t under scenario s. (2) Constraint conditions The following constraints must be met at each time period t. Power balance constraints: 1 1 , , , , , , , , , , 1 1 1 , ( ) ( Δ(Δ)) g Ns s s s s s i t i t wind m t wind m t p N v n t p n M v t t ev nt m i u P P P P P D P = = = −++ = +−  In the equation: t D represents the total base load of the system at time period t; ,, s wind m t P is the predicted wind power output of wind unit mat time period t under scenario s; and ,, s pv n t P is the predicted photovoltaic output of PV panel n at time period t under scenario s. Rotation reserve constraints of the system: ( ) 1 1 max , , , , , , , , , , 11 1 (Δ(Δ)) g Ns s s s s i t i wind m t wind m t pv n t pv n t t ev t t m N M in u P P P P P D P R = ==  −+   ++ +−  In the equation: max i P represents the maximum output power of generating unit i; and t R is the system spinning reserve requirement at time period t. Unit output constraints: min max , , , s i i t i t i i t P u P P u In the equation: min i P is the minimum output power of generator set i. Climbing constraints: , , , 1 , ss d i i t i t u i R P P R − −  −  In the equation: ,ui R is the maximum up-regulation power of unit i in a single period; ,di R is the maximum power reduction of unit i in a single period. Unit minimum shutdown time constraints: max ,, s ev t ev t PP In the equation: max ,ev t P is the maximum power rechargeable during the t period; ,, 1 m Ts ev t e t ut s v PP = = In the equation: ,m ev t su P is the sum of all electric vehicles charged in a day; Abandon wind, abandon light restraint: Global Journal of Engineering and Technology Advances, 2025, 22(03), 143-154 147 , , , , , , , , 0Δ 0Δ ss wind m t wind m t ss pv n t pv n t PP PP   In the equation: ,, Δs wind m t P is the abandoned wind power; ,, s wind m t P is the predicted wind power; ,, Δs pv n t P is the power of abandoned light; ,, s pv n t P is the predicted photovoltaic output. 2.2. Optimal scheduling modeling at spatial scale The optimization strategy on the time scale determines the unit output, scenery output and the total charging load curve of electric vehicles in the transmission network layer, and the distribution network side needs to optimally distribute the total charging load of electric vehicles to each node in the distribution network according to the power supply situation of the transmission network and the spatial location distribution of electric vehicles in the distribution network. Therefore, this paper proposes a spatial optimization scheduling strategy based on the optimal power flow in the distribution network. By optimizing the power flow distribution, the total charging load of electric vehicles is optimally allocated to each node of the distribution network, and the optimization variable is the charging load of electric vehicles at each node in each period. 2.2.1. Objective function Generally, the distribution network operator hopes to distribute the charging load of electric vehicles on the most suitable nodes to improve the power flow distribution of the distribution network and reduce the total network loss of the distribution network. Therefore, the optimal scheduling model on the spatial scale aims to reduce the total network loss of the distribution network, and optimally distributes the EV charging load on the nodes of the distribution network. The objective function of optimal scheduling policy can be expressed as: Loss, 1 min Tst t fP = = In the equation: Loss, st P represents the total distribution network active power loss considered at time t (2) Constraint conditions Node power balance constraints: , , , , , 0 s s s G t D t ev t T t P P P P     − − − = , , , 0 ss G t D t T t Q Q Q    − − = In the equation: , s Gt P  is the active power emitted by the active power supply of node α under scene s at time period t; ,Dt P  is the active load of node α in time period t; ,, s ev t P  is the electric vehicle load charged at node α in time period t under scenario s; ,Tt s P  is the active power transmitted by node α at time period t under scene s; , s Gt Q  is the reactive power emitted by the reactive power supply of node α in scene s at time period t; ,Dt Q  is the reactive load of node α in time period t; , s Tt Q  is the reactive power transmitted by node α at time period t under scene s; K is the set of nodes except the equilibrium node in the distribution network. Node voltage amplitude constraints: ,min , ,max st V V V     In the equation: A and B are the maximum and minimum allowable voltage values of node α respectively. Global Journal of Engineering and Technology Advances, 2025, 22(03), 143-154 148 Node transmission power constraints: , ,max sj t j PP   In the equation: max ,ev P  is the maximum power that can be transmitted by the line between node α and node j; K 'is the set of all nodes in the distribution network. ,jt P  is the active power transmitted by the line between node α and node j at time period t in scenario s. Charging power constraints: max , , , 0s ev t ev PP   In the equation: max ,ev P  is the maximum rechargeable power of node α. Constraints on upper-layer scheduling results: , , , ss ev t ev t IPP    = In the equation: , s ev t P is the charging load at time t after time scale optimization; I represents a collection of nodes containing charging stations. 2.3. Solution method 2.3.1. Transmission side objective function solving method In this paper, in the simulation analysis of a large number of electric vehicles connected to the grid, the electric vehicle load is regarded as a dispatchable load, and the collaborative optimization of the power generation side and the load side is considered as a whole, so as to achieve the multi-objective optimization of the power generation and operation cost on the transmission side, improve the absorption rate of new energy landscape, and reduce the charging cost of the owner. The optimal scheduling time span takes 24 hours as a cycle, comprehensively analyzes the power output state of thermal power units, the absorption rate of new energy scenery and the EV charging situation, and reduces the cost expenditure and the fluctuation of the grid load on the basis of ensuring the changing needs of the owners. According to the above modeling and analysis, the piecewise linearization method is used to process the upper nonlinear model data, and then the Gurobi solver is used to solve the optimal solution of the above model. 2.3.2. Distribution side objective function solving method The quadratic flow constraint is considered in the spatial model constructed in this paper, because it is not easy to obtain the global optimal solution when solving the optimal value by the algorithm, and it often stops when solving the local optimal. In this paper, the second order cone relaxation method is used to convex relax the constructed constraints, and the second order cone programming method is used to solve the above targets, which can ensure the accuracy of the target solution and improve the efficiency of the solution. 3. Analysis of numerical examples In order to verify the feasibility and effectiveness of the proposed EV charging scheduling strategy considering the spatiotemporal optimization of new energy into the grid, this section constructs a power system simulation model including thermal power units, wind farms, photovoltaic arrays, transmission networks, distribution networks and charging stations, as shown in Figure 1. Global Journal of Engineering and Technology Advances, 2025, 22(03), 143-154 149 Figure 1 Simulation model of Power system 3.1. Analysis of optimization results on time scale In order to facilitate calculation, the model in this paper only considers the large-scale solar new energy access in the upper layer, and the small-scale solar new energy access in the lower distribution network layer is temporarily ignored. Considering the above situation, the following calculation example is set for analysis: Example 1: Electric vehicles are not included in the grid. Example 2: Including electric vehicles, unordered charging, the electricity price is the constant electricity price in Figure 2. Example 3: Including electric vehicles, optimal scheduling, constant electricity price. Example 4: Including electric vehicles, optimized scheduling, peak-valley electricity price, and charging electricity price as shown in Figure 2 Figure 2 Price of charging Global Journal of Engineering and Technology Advances, 2025, 22(03), 143-154 150 In the optimization model of the transmission network side, the cost pairs of each example are shown in Table 1. The comparison results of fuel cost of four examples show that when the disordered charging electric vehicle is added to example 2, the system operation cost reaches 527306.159 yuan, which is the highest among the four examples. By comparing the fuel cost of example 1 and example 2 in Table 1, we can see that, The fuel cost in example 2 is 93,367 yuan higher than that in example 1, because a large number of electric vehicles are connected to charge, which is equivalent to an electrical load, increasing the power demand on the load side, making the thermal power unit need to increase the power output, and thus the cost rises. By comparing the unit start-up cost in example 1 and example 2, it can be seen that the start-up cost in example 2 is 2,400 yuan higher than that in example 1, indicating that due to the disorderly access of electric vehicles, the start-up plan of the original unit has changed and the start-up cost of the thermal power unit has increased. The comparison of the results of example 2 and example 3 shows that the electric vehicle optimization scheduling method proposed in this paper can reduce the fuel cost of the system and the start-up cost of the thermal power unit, and optimize the operating cost of the system. This is because the model proposed in this paper improves the start-up plan of the thermal power unit and reduces the maximum output cost of the thermal power unit by optimizing the charging plan of the user. By comparing the results of example 3 and example 4, under the guidance of TOU price, example 4 can reduce the charging cost of EV users, while the fuel cost and start-up cost of the system hardly change. Further combined with Figure 3 and Figure 4, it can be seen that under TOU price, the dispatchable charging load of EV is transferred to the moment when the charging price is lower. Table 1 Results of different examples Example System operating cost（ yuan） Fuel cost (yuan) PM2.5 emission cost （yuan） Start-up cost （ yuan） Charging cost （yuan ） Abandonment cost（yuan） Example 1 425332.4853 409996.2344 12746.2509 2590 0 0 Example 2 527306.159 503363.3577 15547.202 4990 3405.6 0 Example 3 521555.3052 498206.9435 15472.7617 4470 3405.6 0 Example 4 521654.2765 498220.53 15489.794 4470 3473.95 0 Figure 3 Result of example 3 Global Journal of Engineering and Technology Advances, 2025, 22(03), 143-154 151 Figure 4 Result of example 4 3.2. Analysis of optimization results on spatial scale Distribution network side model solution is based on the model simulation calculation of IEEE33 nodes. In terms of electric vehicles, this paper mainly considers that three charging stations are connected to the distribution network, and studies the optimal spatial distribution of electric vehicles charging at the distribution network layer according to the optimal scheduling scheme of electric vehicles obtained at the transmission network side. The basic capacity of this distribution network is set to 100MVA, the reference voltage is set to 12.66kV, and the maximum output of electric vehicles in this distribution network model is set to about 450kW. The following three examples are set for comparative analysis • Example 5: Without electric vehicles. • Example 6: Including electric vehicles. • Example 7: Based on example 4, the charging load of different nodes is optimized. Figure 5 Load per node of increasing