In recent years, as traditional energy sources face depletion and environmental pollution crises become increasingly severe, the integration of distributed renewable energy has accelerated. Electric vehicles, which rely on clean electrical energy, have been widely recognized as a low-carbon and environmentally friendly transportation solution, making them a promising future direction in the automotive industry. The number of electric vehicles in China has been growing year by year. However, the charging behavior of electric vehicle owners is highly concentrated in time and possesses strong randomness. When a large number of electric vehicles connect to the power grid during similar periods, it may lead to grid performance degradation, reduced stability, and increased charging costs for owners. To address these issues, this paper investigates orderly charging scheduling strategies for electric vehicles considering the integration of wind power resources into the grid. The main contributions of this work are summarized as follows.
1. Introduction
Since the reform and opening-up, China has transformed from an agricultural country into an industrial power. In 2023, the gross domestic product of China exceeded 126 trillion yuan, making it the second-largest economy in the world. The living standards of people have improved notably, and private cars have become increasingly common. According to the latest statistics from the Ministry of Public Security, by the end of 2023, the national motor vehicle count reached 435 million, including 336 million automobiles, an increase of 5.3% year-on-year. However, development is a double-edged sword. Traditional fuel vehicles, as the main force in the automotive field, consume petroleum and emit large amounts of exhaust gases, including carbon monoxide, nitrogen oxides, and particulate matter, which cause serious environmental pollution. Therefore, there is an urgent need to find new energy sources that can support long-term sustainable development and move toward a green and environmentally friendly society.
Compared with conventional fuel vehicles, electric vehicles, as a novel type of green, low-carbon, and low-pollution transportation tool, are gradually replacing traditional energy vehicles. This can effectively reduce the harm of vehicle exhaust to the environment and achieve the purpose of saving energy. With the strong promotion of the government in recent years, new energy vehicles led by electric vehicles have developed rapidly due to their low emission and low pollution advantages. In 2018, the government vigorously promoted policies such as exempting new energy vehicles from purchase tax and urged the construction of charging facilities in urban parking lots. In 2021, the State Council issued documents pointing out that by 2025, new energy vehicles will account for one fifth of total annual sales of new vehicles, and by 2035, pure electric vehicles will become the mainstream of the market. According to data released by the Ministry of Public Security, by the end of 2023, there were 20.41 million new energy vehicles in the country, among which 15.52 million were pure electric vehicles, an increase of 48.52% year-on-year. Moreover, with the rapid advancement of domestic electric vehicle enterprises, electric vehicles have achieved remarkable progress in endurance, power performance, and intelligent connectivity. Therefore, it is predicted that by 2030, the number of electric vehicles in China will reach 70 million, and the full electrification of automobiles has become an inevitable trend.
Although the electric vehicle industry is developing rapidly, the large-scale aggregation of electric vehicles will inevitably exert various impacts on the power grid supply side, user demand side, and charging infrastructure. Because the daily habits and driving behaviors of owners vary, the charging location, time, and mode of electric vehicles differ, forming a new type of electric load with aggregation and randomness. When the number of electric vehicles reaches a certain scale, these loads will affect the original power usage and endanger the stability of the power grid. On the one hand, during traditional peak load periods, a large number of electric vehicles will simultaneously connect to the grid, causing a “peak on peak” phenomenon that leads to transformer capacity violations, three-phase imbalance, and increased line losses. This reduces power supply quality and reliability. On the other hand, the charging facilities of electric vehicles are mostly nonlinear devices, and high-frequency AC/DC conversion will generate high-order harmonic pollution, affecting transformers, relay protectors, and other electrical equipment, thereby reducing power quality. At the same time, because electricity prices during peak periods are relatively high, the charging cost of electric vehicles increases, imposing economic pressure on owners and indirectly weakening the willingness of potential consumers to adopt electric vehicles.
In summary, with the growing popularity and development of electric vehicles, managing the large-scale integration of electric vehicles into the power grid is not only an opportunity but also a challenge. Therefore, it is essential to study how to formulate practical and feasible orderly charging strategies for electric vehicles.
2. Literature Review and Research Status
Currently, energy conservation, emission reduction, and clean production are key themes in the global effort to build a green ecology. In this context, electric vehicles have attracted significant attention from global automobile manufacturers and research institutions. Governments around the world have also introduced various policies to promote the sustainable development of electric vehicles.
The United States has placed the development of the new energy industry at the level of national energy security strategy since the late 20th century. In 2002 and 2009, the U.S. government and the Department of Energy successively formulated plans and invested funds in the research of power batteries and the construction of charging infrastructure. Japan, facing severe energy shortage, has long attached importance to the research and development of electric vehicles. In 1997, Toyota became the first company in the world to mass-produce hybrid electric vehicles. Since 2009, Japan has implemented a “green taxation” policy that exempts buyers of electric vehicles from 50% of the acquisition tax, promoting the popularization of electric vehicles.
In China, although the traditional automobile industry started relatively late, the emergence of electric vehicles provides a rare opportunity to achieve “corner overtaking” in the field of automobile autonomy. As early as 2001, China proposed the “three vertical and three horizontal” plan to carry out research and development of different types of electric vehicles and their core components. The continuous promotion of electric vehicles has led to increasing research on the impact of large-scale random charging loads on the power grid. Many scholars have studied the optimization scheduling of electric vehicles. For instance, some studies evaluated the impact of stochastic charging loads on the power grid under multiple scenarios and established orderly load models based on dynamic programming. Others used multi-objective genetic algorithms to optimize charging power and duration. Price elasticity matrices were employed to reflect the relationship between user demand and charging cost, effectively reducing the peak-valley difference of the distribution network. Some researchers divided users into categories according to their charging demands and optimized the charging time for each category, managing the number of vehicles per period. Additionally, several studies adopted sensitivity indices to prioritize charging nodes. Demand response theory has been used to study the correlation between user electricity consumption patterns and electricity prices. Real-time traffic information, such as road grade, congestion level, and vehicle speed, has been integrated into charging optimization strategies. Coordinated scheduling between electric vehicles and clean energy has been proposed to minimize marginal carbon emissions. Vehicle-to-grid technology has been studied in wind farms to mitigate the fluctuation caused by wind power. A fast-charging load guidance strategy based on adjustable stepped charging service fees was proposed to reduce charging costs and improve voltage quality. A comprehensive charging strategy considering random charging, mileage anxiety charging, and price-guided charging was developed and optimized by artificial bee colony algorithm. A bi-level optimization model for electric vehicle charging was established based on real-time regional grid load and electricity price. With the integration of electric vehicles into microgrids, the NSGA-II algorithm improved by Levy flight was used to optimize charging/discharging schedules. A spatiotemporal dual-scale electric vehicle optimization scheduling method based on regional decoupling was proposed for residential and office areas. Dynamic time-of-use electricity pricing models were formulated according to the number of electric vehicles being charged, effectively reducing network losses and improving voltage stability. The interaction network model between distribution network and electric vehicles was constructed, and optimization factors were assigned to charging stations, significantly reducing charging costs and load peak-valley differences.
Most current studies focus on balancing the comprehensive benefits between the supply side and the demand side through charging models. However, the integration of renewable energy is rarely considered. With the increasing construction of the energy internet in China, considering the scenario in which wind power is integrated into the grid, it is urgent to investigate orderly charging strategies for electric vehicles under the dispatch of renewable energy. Therefore, this paper studies orderly charging scheduling strategies for electric vehicles considering both wind power integration and user satisfaction, based on intelligent optimization algorithms.
3. Fundamentals of Electric Vehicles and Modeling of Uncoordinated Charging
3.1 Classification of Electric Vehicles
Modern electric vehicles have many advantages over fuel vehicles, such as energy saving, smooth driving, low noise, and high energy efficiency. The main types of electric vehicles include:
| Type | Energy source | Power source | Representative model |
|---|---|---|---|
| Battery Electric Vehicle (BEV) | Grid electricity | Electric motor | BYD Yuan PLUS |
| Hybrid Electric Vehicle (HEV) – non-plug-in | Fuel + electricity | Engine + motor | Nissan e-Power |
| Plug-in Hybrid Electric Vehicle – hybrid type | Fuel + grid electricity | Engine + motor | Lynk & Co 01 PHEV |
| Plug-in Hybrid Electric Vehicle – pure electric range extender type | Fuel + grid electricity | Electric motor (engine as generator) | AITO M7 |
| Fuel Cell Electric Vehicle (FCEV) | Hydrogen | Electric motor | Toyota Mirai |
3.2 Charging Modes
Electric vehicles can be charged through different modes. The main charging modes are summarized in table below.
| Charging mode | Advantages | Disadvantages | Applicable scenarios |
|---|---|---|---|
| Conventional (slow) charging | Simple facilities, low cost, less damage to battery, mild impact on grid | Long charging time | Residential areas, office parking lots |
| Fast charging | Short charging time, good user experience | Complex facilities, high cost, large impact on grid | Highway service areas, bus stations |
| Battery swapping | Very short time for battery replacement | Few swapping stations, non-standard battery sizes | Swapping stations |
| Wireless charging | Convenient, no range anxiety | High construction and maintenance cost, no unified international standard | Various scenarios |
For residential charging of private electric vehicles, the conventional slow charging mode is most common because owners usually park for several hours at home. Therefore, this study adopts the conventional charging mode.
3.3 Analysis of Lithium-Ion Battery Charging
Among various battery types, lithium-ion batteries have the best overall performance: high energy density, no memory effect, long cycle life, and high charging efficiency. Thus, they are the most promising battery type for electric vehicles. Charging methods mainly include constant current (CC), constant voltage (CV), and constant current-constant voltage (CC-CV). In practice, the CC-CV method is prevalent because it avoids excessive initial current and prevents overcharging. During the constant-current stage, the charging power can be approximated as constant because the voltage change is relatively small. Therefore, in the modeling of charging load, each electric vehicle is considered to charge at a fixed power level, typically around 7 kW for home slow charging.
3.4 Characteristics of Electric Vehicle Travel Behavior
The charging behavior of private electric vehicles is closely related to the daily routines of owners, which include the return time, departure time, and daily travel distance. Because there is currently no large-scale universal statistical survey specifically for electric vehicles in China, this paper refers to the National Household Travel Survey (NHTS) data of the United States to approximate typical household vehicle usage. The statistical distributions are used to generate daily travel behavior parameters for electric vehicle users.
For the return time, denoted as $T_r$, the probability density function can be fitted as a normal distribution:
$$
f(T_r) =
\begin{cases}
\dfrac{1}{\sqrt{2\pi}\sigma_r} \exp\left[-\dfrac{(T_r-\mu_r)^2}{2\sigma_r^2}\right], & 12 \le T_r \le 24 \\[6pt]
\dfrac{1}{\sqrt{2\pi}\sigma_r} \exp\left[-\dfrac{(T_r+24-\mu_r)^2}{2\sigma_r^2}\right], & 0 \le T_r < 12
\end{cases}
$$
where $\mu_r = 17.6$ and $\sigma_r = 3.4$. The departure time, denoted as $T_l$, also obeys a normal distribution with the following probability density:
$$
f(T_l) =
\begin{cases}
\dfrac{1}{\sqrt{2\pi}\sigma_l} \exp\left[-\dfrac{(T_l-\mu_l)^2}{2\sigma_l^2}\right], & 0 \le T_l < 12 \\[6pt]
\dfrac{1}{\sqrt{2\pi}\sigma_l} \exp\left[-\dfrac{(T_l-24-\mu_l)^2}{2\sigma_l^2}\right], & 12 \le T_l \le 24
\end{cases}
$$
where $\mu_l = 8.93$ and $\sigma_l = 3.25$. The daily driving distance $L$ follows a log-normal distribution:
$$
f(L) = \frac{1}{\sqrt{2\pi}\sigma L} \exp\left[-\frac{(\ln L-\mu)^2}{2\sigma^2}\right]
$$
with $\mu = 3.2$ and $\sigma = 0.88$. Based on these distributions, the initial state of charge (SOC) of an electric vehicle when the owner returns home can be calculated by:
$$
SOC_p = SOC_d – \frac{W_{100} L}{B_c}
$$
where $SOC_d$ is the desired state of charge before departure, $W_{100}$ is the energy consumption per 100 km, and $B_c$ is the battery capacity. The charging time $T_c$ can be expressed as:
$$
T_c = \frac{(SOC_d – SOC_p) B_c}{P_c \eta_c}
$$
where $P_c$ is the charging power and $\eta_c$ is the charging efficiency. In this study, the electric vehicle model is the BYD Yuan PLUS with battery capacity 49.92 kWh, energy consumption of 12.2 kWh per 100 km, pure electric range of 430 km, and charging power of 7 kW. The charging efficiency is 0.9.
3.5 Monte Carlo Simulation of Uncoordinated Charging
Monte Carlo simulation is a powerful tool for modeling the stochastic behavior of electric vehicle charging loads. Because the charging behavior of each electric vehicle contains randomness, but as the number of vehicles becomes large, the aggregated charging load becomes statistically describable. In this paper, the Monte Carlo method is used to simulate the uncoordinated charging behavior of electric vehicle owners. For a given number of electric vehicles $N$, each vehicle’s charging parameters (return time, departure time, driving distance) are randomly sampled from the probability models above. The charging period is determined from the return time and charging duration. The total charging load in each time interval t is computed as:
$$
P_{sum}(t) = \sum_{k=1}^N P_{ev,k}(t) \cdot \chi_k(t)
$$
where $\chi_k(t)$ equals 1 if the k-th electric vehicle is charging at time t, and 0 otherwise. The simulation is repeated many times and the average load is used.
In the simulation, a residential community with 2000 households is considered. The system base load is taken as a typical summer daily load curve of the region. The monthly electricity price is not considered in the uncoordinated charging, but the total load is obtained by adding the charging load to the base load. Electric vehicle penetration ratios of 10%, 20%, 30%, 40% and 50% are simulated. The obtained charging load curves and superimposed load curves show that the uncoordinated charging load is mainly concentrated in the period from 17:00 to 21:00, which coincides with the original peak hours of daily electricity consumption. This “peak on peak” phenomenon worsens with increasing penetration. The peak-valley difference of the total load increases significantly. This demonstrates that uncoordinated charging behavior without any guidance or scheduling has a negative influence on the security and stability of the power grid.
4. Orderly Charging Scheduling Strategy with Wind Power Integration
4.1 Influence of Load Fluctuation on Grid Losses
Power loss in the grid is closely related to load fluctuation. Suppose there are two transmission lines L1 and L2 delivering the same amount of energy over a period T. L1 carries a constant load $P_1$ while L2 carries a fluctuating load $P_2(t)$. If the line resistance is R, the power factor is $\cos\phi$, and the load voltage is U, then the energy losses are:
$$
\Delta W_1 = \left(\frac{P_1 R}{U \cos\phi}\right)^2 T
$$
$$
\Delta W_2 = \int_0^T \left(\frac{P_2(t) R}{U \cos\phi}\right)^2 dt
$$
Utilizing the Cauchy-Schwarz inequality, it can be shown that $\Delta W_2 \ge \Delta W_1$. In fact, the loss increment $\Delta W = \Delta W_2 – \Delta W_1$ is proportional to the variance of $P_2(t)$:
$$
\Delta W = \frac{R}{2 (U\cos\phi)^2} S
$$
where $S$ is the variance of the load curve. Therefore, a larger fluctuation in load leads to higher transmission losses. Reducing the peak-valley difference is beneficial for the economic and safe operation of a power grid.
4.2 Wind Power Integration and its “Anti-Peak-Shaving” Effect
Wind power generation is characterized by its stochastic nature and its output is highly variable. Generally, wind speed is stronger at night and weak in the daytime, which often makes wind power output inversely correlated with the original load profile. If wind power is treated as negative load, the equivalent load curve can be obtained by subtracting the wind power output from the base load. In this paper, a typical daily wind power output curve is used. The original distribution network load peak-valley rate is 73.6%, while after wind power integration the peak-valley rate increases to 98.7%. Consequently, wind power integration exacerbates the peak-valley difference and increases the peak-shaving pressure. Thus, it is necessary to adopt demand-side management, such as time-of-use (TOU) electricity pricing, to guide electric vehicle owners to charge during periods with abundant wind power and low base load, thereby reducing the curtailment of wind power and stabilizing the grid.
4.3 Peak-Valley Period Partition Based on Fuzzy Clustering
Fuzzy clustering is an effective tool for classifying time periods into peak, flat, and valley periods, because the boundary between these periods is inherently vague. A fuzzy equivalence clustering algorithm based on the transitive closure method is adopted. First, for each hourly time point $i$, the membership degrees of peak and valley are computed via semi-trapezoidal membership functions:
$$
\mu_{fi} = \frac{P_{L}(T_i) – P_{L,\min}}{P_{L,\max} – P_{L,\min}}
$$
$$
\mu_{gi} = \frac{P_{L,\max} – P_{L}(T_i)}{P_{L,\max} – P_{L,\min}}
$$
where $P_L(T_i)$ is the equivalent load at time $T_i$, and $P_{L,\max}$ and $P_{L,\min}$ are the maximum and minimum equivalent load during the day. A matrix of time point attributes is constructed:
$$
\mathbf{T} =
\begin{bmatrix}
\mu_{f1} & \mu_{g1} \\
\mu_{f2} & \mu_{g2} \\
\vdots & \vdots \\
\mu_{f24} & \mu_{g24}
\end{bmatrix}
$$
The data are standardized by translation-standard deviation transformation:
$$
\mu_{ki}’ = \frac{\mu_{ki} – \bar{\mu}_k}{S_k}, \quad k = f,g
$$
Then, the fuzzy similarity relation is established using the weighted absolute value subtraction method. The fuzzy similarity matrix $\mathbf{R}$ is then transformed into a fuzzy equivalence matrix through the transitive closure method. By varying the threshold value $\lambda$, dynamic clustering is carried out. The final partition with three clusters is obtained. According to the principle that each period duration should be no less than 6 hours, reasonable periods are selected. In this study, the resulting peak, flat, and valley periods are given in Table below. The corresponding time-of-use electricity price is designed based on a flat price of 0.8 yuan/kWh with a 30% premium or discount for peak and valley prices.
| Price type | Time periods | Price (yuan/kWh) |
|---|---|---|
| Peak | 9:00-14:00, 18:00-21:00 | 1.04 |
| Flat | 7:00-9:00, 14:00-18:00, 21:00-23:00 | 0.80 |
| Valley | 1:00-7:00, 23:00-24:00 | 0.56 |
4.4 Particle Swarm Optimization with Adaptive Chaos
The classic particle swarm optimization algorithm (PSO) is inspired by the social behavior of bird flocks. In PSO, a set of particles moves in a D-dimensional solution space. The velocity and position of each particle are updated as follows:
$$
v_{id}^{k+1} = w v_{id}^{k} + c_1 r_1 (pbest_{id}^{k} – x_{id}^{k}) + c_2 r_2 (gbest_{d}^{k} – x_{id}^{k})
$$
$$
x_{i}^{k+1} = x_{i}^{k} + v_{i}^{k+1}
$$
where w is the inertia weight, $c_1$ and $c_2$ are learning factors, $r_1$ and $r_2$ are random numbers in [0,1], pbest is the personal best position, and gbest is the global best position. PSO suffers from premature convergence and can easily fall into local optima. Thus, we enhance PSO from three aspects:
(1) Adaptive inertia weight. The inertia weight w is linearly decreased from $w_{\max}$ to $w_{\min}$ with the iterative process:
$$
w = w_{\max} – \frac{w_{\max} – w_{\min}}{iter_{\max}} \cdot iter
$$
(2) Adaptive learning factors. The cognitive component $c_1$ and social component $c_2$ are adjusted dynamically. In the early stage, larger $c_1$ and smaller $c_2$ encourage global exploration; in the later stage, smaller $c_1$ and larger $c_2$ enhance convergence:
$$
c_1 = 0.5 + 1.5 \cos\left(\frac{\pi \cdot iter}{2\cdot iter_{\max}}\right)
$$
$$
c_2 = 0.5 + 1.5 \cos\left(\frac{\pi \cdot iter}{2\cdot iter_{\max}} – 1\right)
$$
(3) Chaotic initialization using Tent map. The initial population is generated by Tent map to improve population diversity and uniform distribution:
$$
f(x) =
\begin{cases}
2x, & 0 \le x < 0.5 \\
2(1-x), & 0.5 \le x \le 1
\end{cases}
$$
This improved algorithm is referred to as adaptive chaotic particle swarm optimization (CPSO). Its flow chart is straightforward: initial population via chaotic map, calculation of fitness, updating of velocity and position, and iteration until the stopping criterion is met.
4.5 Orderly Charging Optimization Model
This paper establishes a multi-objective optimization model for orderly charging of electric vehicles considering wind power integration. The objectives are:
Objective 1: Minimize the load variance of the grid representing the equivalent load fluctuations:
$$
\min F_1 = \frac{1}{T}\sum_{t=1}^{T} \left( P_{b,t} + P_{e,t} – P_{w,t} – P_{av}\right)^2
$$
where $P_{b,t}$ is the base load at time t, $P_{e,t}$ is the electric vehicle charging load at time t, $P_{w,t}$ is the wind power output at time t, $P_{av}$ is the average load over the day, and T is the number of time periods (24).
Objective 2: Minimize the total charging cost for electric vehicle owners:
$$
\min F_2 = \sum_{t=1}^{T} \sum_{k=1}^{N} P_{sum,k}(t) \cdot C(t)
$$
where $P_{sum,k}(t)$ is the charging power of the k-th vehicle at time t and $C(t)$ is the electricity price at time t.
The two objectives are normalized and combined into a single objective function:
$$
\min F = \lambda_1 \frac{F_1}{F_1^N} + \lambda_2 \frac{F_2}{F_2^N}
$$
where $F_1^N$ and $F_2^N$ are the values of $F_1$ and $F_2$ before optimization (i.e., uncoordinated charging), and $\lambda_1 = \lambda_2 = 0.5$ are weighting factors taking the interests of both the grid and users into account.
The following constraints are considered:
(1) Charging time constraints: Charging cannot start before the owner returns home and should finish before departure:
$$
T_{r,k} \le T_{s,k}, \quad T_{s,k} + T_{c,k} \le T_{l,k}
$$
where $T_{r,k}$ is the return time, $T_{s,k}$ is the charging start time, $T_{c,k}$ is the required charging time, and $T_{l,k}$ is the departure time of the k-th vehicle.
(2) Charging demand constraints: The SOC after charging must reach the desired value but not exceed the maximum battery capacity:
$$
SOC_{d,k} \le SOC_{s,k} + \sum_{t=1}^{24} \chi_k(t) \le SOC_{\max}
$$
(3) Load capacity constraint: The total load must be lower than the transformer’s maximum available active power:
$$
\sum_{k=1}^N P_{ev,k}(t) + P_{b,t} \le \lambda_T B_T \eta_T
$$
where $B_T$ is the transformer capacity, $\lambda_T$ is the power factor, and $\eta_T$ is the efficiency.
4.6 Simulation Results of CPSO-based Scheduling
The simulation environment is MATLAB R2018b. The base scenario assumes a residential community with 2000 households and an electric vehicle penetration rate of 50%, i.e., 1000 electric vehicles participating in charging scheduling. The transformer capacity is 1600 kVA with power factor 0.85 and efficiency 0.9. The algorithm parameters are $w_{\max}=0.9$, $w_{\min}=0.4$, population size 100, and maximum iterations 100. The optimization results from PSO and CPSO are compared with the uncoordinated case.
Figure (convergence curves) showed that PSO converges prematurely early, while CPSO maintains a slower but steadier convergence. The final load curves after orderly charging are flatter than those of uncoordinated charging. The numerical results are summarized in Table.
| Charging strategy | Load variance (kW²) | Charging cost (yuan) | Wind power utilization (kW) | Peak-valley rate (%) |
|---|---|---|---|---|
| Uncoordinated | 2,946,205.83 | 7,235.42 | 7,358.4 | 96.83 |
| Coordinated PSO | 1,562,978.12 | 5,251.68 | 7,795.9 | 76.81 |
| Coordinated CPSO | 1,503,580.79 | 5,100.27 | 8,055.6 | 73.31 |
Compared with uncoordinated charging, CPSO reduces the load variance by 48.97%, reduces the total charging cost by 29.51%, and increases wind power utilization by 697.2 kW. The CPSO also outperforms the standard PSO, showing that the proposed adaptive chaotic initialization and parameter adjustment improve the solution quality.
5. Further Improvement through Adaptive Chaotic Simulated Annealing Particle Swarm Optimization
5.1 Principle of Simulated Annealing
The simulated annealing (SA) algorithm originates from the physical annealing process of solids. It accepts a worse solution with a certain probability according to the Metropolis criterion, which enables the algorithm to escape local optima. The Metropolis criterion is:
$$
P = \begin{cases}
1, & E_j \le E_i \\
\exp\left(-\frac{E_j – E_i}{T}\right), & E_j > E_i
\end{cases}
$$
where $E_i$ and $E_j$ are the energies of the current and candidate solutions, and T is the current temperature. By slowly decreasing T, the algorithm gradually converges to a global optimum while allowing controlled jumps out of local optima.
5.2 Design of the Integrated Algorithm SACPSO
To further improve the performance of CPSO, we incorporate the Metropolis acceptance mechanism into the particle swarm optimization. The proposed algorithm is called adaptive chaotic simulated annealing particle swarm optimization (SACPSO). The key idea is to apply the simulated annealing selection in the global best update process. At each iteration, each particle’s fitness is converted to an acceptance probability at the current temperature T as follows:
$$
F_i = \exp\left(-\frac{f_i – f_{gbest}}{T}\right)
$$
$$
C_i = \frac{\sum_{j=1}^i F_j}{\sum_{j=1}^n F_j}
$$
Then, a new global best is selected by a roulette wheel strategy based on the cumulative probabilities $C_i$:
$$
C_{i-1} < random(0,1) \le C_i
$$
This mechanism allows particles to move towards a suboptimal but promising region, enhancing the ability to escape from local optima. After each iteration, the temperature is decreased according to the cooling schedule $T = \alpha T$, where $\alpha$ is the cooling factor. In this study, $\alpha = 0.8$. The initial temperature is chosen based on the initial global best fitness:
$$
T_0 = \frac{f(gbest)}{\ln 5}
$$
The rest of the algorithm follows the same adaptive chaotic scheme of CPSO. The flowchart can be summarized as: chaotic initialization, adaptive parameter updates, particle movement, Metropolis-based gbest selection, and cooling operation until the stopping criterion.
5.3 Benchmark Function Test
To verify the effectiveness of the proposed SACPSO algorithm, benchmark tests are conducted on the Sphere function:
$$
f_1(x_1,x_2) = x_1^2 + x_2^2
$$
and the Rastrigin function:
$$
f_2(x_1,x_2) = x_1^2 + x_2^2 – 10\cos(2\pi x_1) – 10\cos(2\pi x_2) + 20
$$
The first function is unimodal, and the second is a multimodal function with numerous local minima. Each algorithm is independently run 10 times with 100 particles and 100 iterations. The statistical results are presented below.
| Function | Algorithm | Minimum | Maximum | Average | Standard deviation |
|---|---|---|---|---|---|
| Sphere | PSO | 1.74e-05 | 1.65e+00 | 2.22e-01 | 7.03e-01 |
| CPSO | 9.65e-08 | 3.97e-03 | 5.578e-04 | 1.26e-03 | |
| SACPSO | 0 | 1.843e-04 | 6.312e-05 | 8.22e-05 | |
| Rastrigin | PSO | 2.19e-04 | 5.44e-01 | 6.19e-02 | 1.71e-01 |
| CPSO | 2.93e-05 | 2.51e-03 | 8.37e-04 | 8.26e-04 | |
| SACPSO | 1.55e-08 | 1.76e-06 | 6.36e-07 | 5.71e-07 |
From the benchmark results, SACPSO achieves significantly better solution accuracy and stability than both PSO and CPSO, especially on the multimodal Rastrigin function. The Metropolis mechanism enables the algorithm to jump out of local traps and continuously find better solutions. The convergence curves demonstrate that SACPSO converges faster and reaches a much lower fitness value than the other algorithms.
5.4 Simulation Results of SACPSO-based Orderly Charging
The SACPSO algorithm is applied to the orderly charging scheduling model under the same simulation scenario as before. The results are compared with PSO and CPSO in the following table.
| Charging strategy | Load variance (kW²) | Charging cost (yuan) | Wind power utilization (kW) | Peak-valley rate (%) |
|---|---|---|---|---|
| Uncoordinated | 2,935,443.28 | 7,235.42 | 7,246.8 | 96.30 |
| Coordinated PSO | 1,491,911.85 | 5,288.15 | 7,644.7 | 76.02 |
| Coordinated CPSO | 1,406,082.25 | 5,118.62 | 7,978.6 | 71.91 |
| Coordinated SACPSO | 1,362,508.21 | 4,798.08 | 8,155.6 | 68.77 |
Compared with uncoordinated charging, SACPSO reduces the load variance by 53.58%, reduces the total charging cost by 33.69%, and increases wind power utilization by 908.8 kW. Compared with CPSO, SACPSO further improves the load variance by approximately 3.1%, charging cost reduction by 6.3% and wind power utilization by 2.2%. Therefore, SACPSO offers the best scheduling performance and contributes to a more stable and economical grid.
5.5 Impact of Electric Vehicle Penetration Rate
To analyze the effect of different penetration rates on the optimization results, three penetration levels (40%, 50%, and 60%) are simulated using the SACPSO algorithm. The corresponding numbers of electric vehicles are 800, 1000, and 1200.
| Penetration rate | Load variance (kW²) | Total charging cost (yuan) | Wind power utilization (kW) | Average cost per vehicle (yuan/(day·vehicle)) |
|---|---|---|---|---|
| 40% | 1,563,542.08 | 3,856.17 | 6,261.9 | 4.82 |
| 50% | 1,409,857.68 | 4,731.55 | 7,619.5 | 4.73 |
| 60% | 1,190,859.19 | 5,615.90 | 8,833.1 | 4.68 |
As the penetration rate grows, the total charging cost increases because more vehicles are charged, but the per-vehicle daily charging cost actually decreases slightly. Meanwhile, the load variance is effectively reduced, indicating that the scheduling algorithm can better coordinate a larger number of electric vehicles to smooth the load curve. Wind power utilization also significantly improves. Hence, encouraging more electric vehicles to participate in orderly charging is beneficial to the grid as long as the charging infrastructure and transformer capacity are sufficient.
5.6 Impact of Electricity Price Variation Amplitude
The sensitivity of the optimal scheduling results to the peak-valley price difference is investigated. The flat price is set at 0.8 yuan/kWh, and the peak and valley prices are obtained by marking up and discounting the flat price by 20%, 30%, and 40%. The penetration rate is fixed at 50%.
| Price variation | Load variance (kW²) | Total charging cost (yuan) | Wind power utilization (kW) |
|---|---|---|---|
| 20% | 1,371,740.03 | 5,194.73 | 7,834.6 |
| 30% | 1,368,881.59 | 4,603.54 | 7,982.5 |
| 40% | 1,365,738.91 | 3,984.12 | 8,059.7 |
A larger price difference makes electric vehicle owners more willing to shift their charging demand to the valley period, thus reducing the total charging cost. Although the improvement in load variance is modest, the utilization of wind power is enhanced. However, the price difference should not be excessively high; otherwise, it might create an unreasonable load concentration in valley hours or impose additional burden on other stakeholders. Therefore, electricity pricing strategies should be designed carefully to balance the interests of supply side, users, and grid stability.
6. Conclusion and Future Work
This paper systematically studies the orderly charging scheduling technology of electric vehicles based on intelligent optimization. The main conclusions are as follows:
(1) The simulation based on the Monte Carlo method shows that uncoordinated charging of electric vehicles will enlarge the peak-valley difference of the grid. The higher the penetration rate, the more serious the impact.
(2) Integrating wind power into the grid exhibits an anti-peak-shaving characteristic that further intensifies load fluctuations. By applying fuzzy clustering to the equivalent load curve, reasonable peak, flat and valley periods can be obtained. A comprehensive orderly charging model considering both grid load variance and user charging cost is established. The adaptive chaotic particle swarm optimization algorithm (CPSO) effectively solves this model, leading to lower load variance, reduced charging costs, and increased wind power utilization.
(3) To further improve the optimization performance, the adaptive chaotic simulated annealing particle swarm optimization algorithm (SACPSO) is proposed. Benchmark test functions verified its superior global search capability and convergence accuracy. When applied to the orderly charging model, SACPSO provides even better scheduling results. The analysis of different penetration rates and price fluctuation ranges indicates that reasonable price signals and the participation of more electric vehicles can improve the performance of the orderly charging strategy.
Future work can be carried out from the following aspects. First, more accurate travel behavior data of electric vehicle users in China should be collected, including geographic, weather, and sociodemographic factors. Second, with the development of V2G technology, bidirectional charging and discharging can provide more flexibility for grid peak shaving. Third, renewable sources such as solar energy can be incorporated into the coordinated scheduling. Fourth, more recent meta-heuristic optimization algorithms may be applied to solve the scheduling model, potentially offering even better solutions.