In the current global energy consumption landscape, fossil fuels still dominate, while renewable energy holds significant potential for growth in the energy mix. Meanwhile, traditional fossil resources are gradually depleting over time. Against this backdrop, clean energy sources, particularly wind and solar power, have become key research and industrial focuses in recent years. Additionally, driven by the “dual‑carbon” strategy and the concept of green low‑carbon development, the electric vehicle industry is experiencing explosive growth. These electricity‑driven vehicles, with their notable energy‑saving and emission‑reduction advantages, are rapidly reshaping traditional transportation systems, injecting new momentum into sustainable development goals. In this context, my research focuses on the coordinated scheduling of electric vehicle charging and discharging activities while explicitly considering the uncertainties introduced by wind and solar power generation.
My work is motivated by a critical challenge: as the penetration of renewable energy sources grows rapidly and electric vehicle adoption becomes increasingly widespread, power system generation optimization and real‑time dispatch face unprecedented difficulties. The intermittent nature of wind and photovoltaic power poses serious threats to grid stability. At the same time, the uncoordinated charging behavior of large‑scale electric vehicle fleets may exacerbate load peaks and valleys, threatening the secure and economical operation of distribution networks. To address these intertwined issues, I have developed a systematic framework that integrates renewable energy accommodation with electric vehicle load regulation. This article presents my research findings on wind‑solar output modeling, electric vehicle charging behavior analysis, multi‑objective optimization scheduling, and bilevel coordinated dispatch strategies.
1. Research Background and Motivation
The rapid expansion of human society has led to a continuous increase in energy demand. From the expanding scale of industrial production to the diversified energy consumption needs arising from improved living standards, various sectors are increasingly dependent on energy. At the same time, a series of closely related challenging issues are emerging and worsening. Environmental pollution is becoming more severe, and the large amounts of greenhouse gases emitted by traditional fossil energy combustion, such as carbon dioxide and sulfur dioxide, are not only causing global warming and triggering a series of ecological crises but also causing serious air pollution and endangering human health. Meanwhile, the issue of energy depletion must not be underestimated. Traditional fossil energy sources such as coal, petroleum, and natural gas are non‑renewable resources. After prolonged large‑scale extraction and consumption, their reserves are rapidly diminishing, posing unprecedented challenges to the sustainability of energy supply.
As the core platform for energy conversion, transmission, and distribution, the power system holds a crucial position in the entire energy system. Renewable power generation technology and energy‑saving dispatch technology have become key areas of focus for many scholars. Globally, countries are formulating energy‑saving and emission‑reduction strategic goals aimed at lowering carbon emissions and alleviating energy and environmental pressures. In this context, renewable energy power generation has attracted widespread attention from academia, industry, and government. Among them, wind power and photovoltaic power generation, as typical representatives of renewable energy generation, have completed a leapfrog development from scratch in just a few decades. In regions rich in wind and solar resources, large‑scale wind farms and photovoltaic power stations have sprung up and gradually become an important part of the power supply system.
However, the inherent volatility and randomness of wind and photovoltaic power generation are like a sword hanging over the stable and reliable operation of the power system, bringing a series of new challenges. Wind power generation is significantly affected by natural factors such as wind speed and direction, and unstable wind speed leads to frequent fluctuations in wind turbine output power. Photovoltaic power generation depends on light intensity and duration, and alternating day and night as well as weather changes can cause large fluctuations in photovoltaic panel output power. When the output of wind power and photovoltaics fluctuates significantly in a short period, and thermal power units cannot fully meet such rapidly changing power demand due to limitations in their own equipment characteristics, operation and maintenance requirements, and fuel supply, there is a high probability of load loss or wind and solar curtailment. Load loss directly affects users’ normal electricity consumption, causing inconvenience to production and daily life; while wind and solar curtailment represents a large amount of renewable energy being wasted.
The current grid dispatch technology is accelerating its transformation toward green and intelligent operation. With the continuous innovation of demand‑side response mechanisms, I have observed significant breakthroughs in the field of flexible load regulation. By analyzing the electricity consumption behavior patterns of industrial users, commercial users, and residential users, it has been found that different types of users have significant differences in electricity consumption time and intensity. Taking advantage of these differences, by formulating reasonable electricity price policies and promoting smart electricity‑consuming equipment, users can be guided to adjust their electricity consumption behavior, achieving peak shaving and valley filling, and optimizing the balance between power supply and demand.
Electric vehicles, as a widely discussed research subject in recent years, represent a typical example that can potentially achieve coordinated control between the user side and the generation side. With advancements in battery technology, gradual improvement of charging infrastructure, and strong policy support, the number of electric vehicles has achieved explosive growth globally. In the foreseeable future, the proportion of electric vehicle charging demand in the total grid load will become increasingly prominent. Through in‑depth research, I have found that the charging behavior of electric vehicles exhibits certain regularity and controllability. Comprehensive management and regulation of electric vehicle charging behavior can be achieved through appropriate means, such as price guidance mechanisms. Guiding electric vehicle users to charge during low‑load periods such as nighttime, when grid load is low and power generation equipment utilization efficiency is relatively low, can not only make full use of low‑valley electric energy but also improve the overall grid load rate.
2. Wind Power and Photovoltaic Modeling
2.1 Wind Power Generation Model
In my research, I first establish a mathematical model for wind power generation. Wind energy conversion follows the principles of fluid mechanics and electromagnetics. When natural wind acts on a rotor with a specific airfoil design, the lift generated by the airflow drives the blade group to form a rotational motion. This mechanical motion is amplified by a transmission system consisting of a gearbox and finally converted into electrical energy through the generator. From the perspective of aerodynamic theory, the power output of a wind power generation system is expressed as:
$$P_{w} = \frac{1}{2}\rho \pi R^{2}v^{3}C_{p}$$
where ρ is the air density, v is the tip speed, R is the blade radius, and Cp is the wind energy conversion efficiency.
In the field of wind energy modeling, the Weibull distribution is widely used to describe the probability characteristics of wind speed. Its probability density function can be expressed as:
$$f(v) = \frac{k}{c}\left( \frac{v}{c} \right)^{k – 1}\exp\left\lbrack – \left( \frac{v}{c} \right)^{k} \right\rbrack$$
where k is the shape parameter and c is the scale parameter. The relationship between these parameters and the statistical characteristics of wind speed can be represented as:
$$\left( \frac{\sigma}{\mu} \right)^{1.086} = k,\quad k \in (1,3)$$
$$\mu = c \cdot \Gamma\left( 1 + \frac{1}{k} \right)$$
The output power characteristics of the wind turbine satisfy a piecewise function relationship:
$$P_{p} = \begin{cases} 0, & v < v_{in}\;or\;v > v_{out} \\ P_{wn} \cdot \frac{v – v_{in}}{v_{n} – v_{in}}, & v_{in} \leq v \leq v_{n} \\ P_{wn}, & v_{n} < v < v_{out} \end{cases}$$
where Pp is the actual power generation of the wind turbine, Pwn is the rated power of the wind turbine equipment, and vin, vn, vout correspond to the cut‑in wind speed, rated wind speed, and cut‑out wind speed thresholds, respectively.
2.2 Photovoltaic Power Generation Model
Photovoltaic power generation technology relies on the photovoltaic effect principle, using the photovoltaic effect of semiconductor materials to convert solar radiation energy into electrical energy. For the photovoltaic power generation model, I adopt the Beta distribution, which is the most widely used distribution in this field, to describe the probability distribution of light intensity l in a certain period:
$$f(l) = \frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha)\Gamma(\beta)}\left( \frac{l}{l_{\max}} \right)^{\alpha – 1}\left( 1 – \frac{l}{l_{\max}} \right)^{\beta – 1}$$
where lmax represents the maximum light intensity that can be achieved in a certain period at a certain place, Γ is the Gamma function, and α and β are shape parameters of the Beta distribution. Their specific values can be calculated based on the mathematical expectation μ and standard deviation σ of the historical light intensity at that location:
$$\alpha = \left\lbrack \frac{\mu(1 – \mu)}{\sigma^{2}} – 1 \right\rbrack\mu$$
$$\beta = \left\lbrack \frac{\mu(1 – \mu)}{\sigma^{2}} – 1 \right\rbrack(1 – \mu)$$
The relationship between photovoltaic output power PPV and light intensity r can be represented as:
$$P_{PV} = \eta_{PV} \cdot A \cdot r$$
where A represents the area of the photovoltaic array, and ηPV is the energy conversion efficiency of the photovoltaic array. The detailed piecewise expression is:
$$P_{PV} = \begin{cases} P_{m} \cdot \frac{r}{r_{k}}, & 0 \leq r \leq r_{k} \\ P_{m}, & r_{k} \leq r \end{cases}$$
The reactive power output of the photovoltaic array is given by:
$$Q_{PV} = P_{PV} \cdot \tan\varphi_{PV}$$
where φPV is the power factor angle of the photovoltaic array.
3. Modeling of Electric Vehicle Charging Behavior
Given the spatiotemporal distribution characteristics of electric vehicle operation, the charging load接入 distribution networks exhibits significant uncertainty. In my study, I investigate the key factors affecting charging load power, including vehicle type characteristics, charging system parameters, user travel behavior patterns, and power battery performance parameters. Pure electric passenger vehicles are selected as the main research object due to their highly stochastic and disorderly spatiotemporal characteristics compared with public transportation and logistics applications.
In constructing the charging load prediction model for electric vehicles, the heterogeneity of user behavior patterns must be incorporated. The key parameters that play a decisive role in the charging load curve include: daily driving mileage, reflecting the actual energy consumption demand of the vehicle per day; and charging time distribution, encompassing both charging start time and charging duration. When a large number of vehicles choose to charge centrally during peak electricity consumption periods, the instantaneous power demand on the distribution network will surge, posing a potential threat to system operation stability.
Based on the survey data from the U.S. Department of Transportation, the log‑normal distribution fits the travel time distribution well. Therefore, I adopt this distribution to model the grid connection and disconnection times of electric vehicles. Suppose there are I time periods in a day, and the length of each period is denoted by ti. The final stopping time of the electric vehicle is considered as the initial time when it connects to the grid. The probability density function of the electric vehicle grid connection time follows the expression:
$$f_{a}(t_{x}) = \begin{cases} \dfrac{1}{\sigma_{a}\sqrt{2\pi}}\exp\left\lbrack – \dfrac{(t_{x} – \mu_{a})^{2}}{2\sigma_{a}^{2}} \right\rbrack, & 0 < t_{x} \leq 12 \\ \dfrac{1}{\sigma_{a}\sqrt{2\pi}}\exp\left\lbrack – \dfrac{(t_{x} – 24 – \mu_{a})^{2}}{2\sigma_{a}^{2}} \right\rbrack, & 12 < t_{x} \leq 24 \end{cases}$$
where the expectation μa = 17.6 and the standard deviation σa = 3.4. The analysis shows that during the period from 15:00 to 21:00, electric vehicles are generally in a non‑use state, and users tend to charge their vehicles during this period, which happens to correspond to the peak interval of residential electricity load. This observation reveals the spatiotemporal coupling relationship between charging behavior and grid load characteristics.
Similarly, the time when electric vehicles leave the grid also follows a normal distribution. The probability density function is:
$$f_{b}(t_{y}) = \begin{cases} \dfrac{1}{\sigma_{b}\sqrt{2\pi}}\exp\left\lbrack – \dfrac{(t_{y} – \mu_{b})^{2}}{2\sigma_{b}^{2}} \right\rbrack, & 0 < t_{y} \leq 12 \\ \dfrac{1}{\sigma_{b}\sqrt{2\pi}}\exp\left\lbrack – \dfrac{(t_{y} – 24 – \mu_{b})^{2}}{2\sigma_{b}^{2}} \right\rbrack, & 12 < t_{y} \leq 24 \end{cases}$$
with μb = 8.94 and σb = 3.25. The daily driving mileage of electric vehicles follows a log‑normal distribution:
$$f_{c}(s) = \frac{1}{s\sigma_{c}\sqrt{2\pi}}\exp\left\lbrack – \frac{(\ln s – \mu_{c})^{2}}{2\sigma_{c}^{2}} \right\rbrack$$
where s is the daily driving mileage of the electric vehicle, with expectation μc = 2.3 and standard deviation σc = 0.88. Statistical data indicate that more than half of sample vehicles have daily driving mileage concentrated in the 20 km range. Further analysis shows that the power battery energy consumption corresponding to this driving mileage is generally lower than 30% of the rated capacity of the battery pack, indicating that most vehicles maintain a high remaining state of charge after completing daily travel. This reserve characteristic provides a physical basis for electric vehicles to participate in microgrid interaction.
Synthesizing the probability distributions of electric vehicle grid connection and disconnection times, the log‑normal distribution of daily driving mileage, and the derived charging duration and demand, the charging duration for the j‑th electric vehicle Td,j can be calculated:
$$T_{d,j} = \frac{E \cdot s}{100 \cdot \eta \cdot P_{d,j}}$$
where E is the energy consumption per 100 km of the electric vehicle, Pd,j is the charging power of the j‑th electric vehicle, and η is the charging efficiency of the electric vehicle. Considering the influence of ambient temperature, I set E = 18.9 kW·h in summer and E = 20.5 kW·h in winter. The charging demand of the j‑th EV during period i is:
$$H(i)_{j} = \sum_{j}^{}P_{d,j}$$
The state of charge of the battery of the j‑th electric vehicle is updated as:
$$SOC(i + 1)_{j} = SOC(i)_{j} + \frac{\eta \cdot P_{d,j} \cdot T_{d,j}}{B_{j}},\quad SOC \in (0,1)$$
where Bj is the battery capacity of the j‑th electric vehicle.
4. Monte Carlo Simulation for Electric Vehicle Charging Load Prediction
In my study, I employ the Monte Carlo simulation technique to predict the electric vehicle charging load. The core idea of this method is to transform deterministic problems into statistical estimation problems through probability mapping. The implementation steps are as follows: first, statistical rule analysis is performed to extract statistical features from observed data of the target problem and determine whether it possesses random process attributes. Second, a probability model is constructed. If the problem exhibits random characteristics, a corresponding probability model is directly established; if it is a deterministic problem, model transformation is achieved by introducing random variables with known probability distributions. Third, random sampling experiments are conducted to perform large‑scale random sampling according to the established probability model, and the estimated value of the target variable is obtained through statistical analysis.
Compared with traditional numerical methods, the Monte Carlo simulation has significant methodological advantages: it has a simple algorithm logic that does not require complex mathematical derivation; it has low prior condition requirements and strong model adaptability, making it suitable for the analysis of complex systems with nonlinearity and high dimensionality; and its computation process can be parallelized, facilitating the use of modern computing clusters to improve solution efficiency.
In my load prediction approach, I establish the electric vehicle load prediction model with the following steps:
(1) Set the electric vehicle scale, battery parameters, and simulation times;
(2) Generate initial charging time random numbers based on the normal distribution;
(3) Generate daily driving mileage random numbers according to the log‑normal distribution;
(4) Calculate the charging duration;
(5) Obtain the charging load curve of one electric vehicle over an entire day;
(6) Accumulate all charging loads to obtain the total charging load of all simulated electric vehicles.
In my simulation, I select 500, 1,000, and 2,000 electric vehicle samples for random sampling analysis under the autonomous charging mode. The simulation results demonstrate that under uncoordinated charging, the daily load distributions of different scales of electric vehicles show significant differences. The analysis of the load curves in my simulation shows that the charging behavior of electric vehicles exhibits a significant time‑concentrated characteristic. Specifically, during the early morning period of 5:00‑9:00, the charging demand drops to the lowest level; while during the evening period of 15:00‑23:00, the system load reaches its peak due to concentrated charging by users. This load distribution characteristic is highly consistent with the daily routine of users, forming obvious peak‑valley differences. Notably, the peak‑valley difference can reach as high as 3‑4 times the minimum value. Such dramatic load fluctuations can have multiple effects on grid operation: local line overload may occur, system frequency regulation becomes more difficult, and power supply quality may be affected.
5. Multi‑Objective Optimization Scheduling Model Considering Wind and Solar Accommodation
5.1 Dynamic Time‑of‑Use Electricity Price Model
Due to the increasing complexity of grid structure and the gradual elevation of electronic automation levels, the composite electricity consumption and its variety have correspondingly increased. The participation of electric vehicles causes static time‑of‑use electricity prices to be unable to accurately reflect the load levels and electricity prices in each period. To efficiently utilize wind and solar resources, I adopt a dynamic electricity pricing mechanism based on the characteristics of wind and solar power generation. By monitoring grid load changes in real time, the linkage relationship between electricity prices and system operating costs is established.
To implement the time‑of‑use price mechanism, the whole day is divided into different periods (such as peak, valley, and flat periods) according to the grid load curve, and differentiated electricity price standards are formulated separately. In economics, the elasticity coefficient ε is generally used to reflect the impact of price changes on demand:
$$\varepsilon = \frac{\Delta Q/Q}{\Delta P/P}$$
where Q is the quantity demanded, ΔQ is the change in quantity demanded, P is the price, and ΔP is the change in price. Due to the timeliness of electricity, both electricity prices and demand vary with time. Furthermore, a price change in one period not only affects the demand in the current period but also causes changes in demand in other periods. Therefore, the electricity price elasticity coefficient is divided into self‑elasticity coefficient and cross‑elasticity coefficient. The self‑elasticity coefficient εii refers to the impact of price changes within period i on the electricity demand in that period:
$$\varepsilon_{ii} = \frac{\Delta Q_{i}/Q_{i}}{\Delta P_{i}/P_{i}}$$
The cross‑elasticity coefficient εij refers to the impact of price changes in period i on the electricity demand in period j:
$$\varepsilon_{ij} = \frac{\Delta Q_{j}/Q_{j}}{\Delta P_{i}/P_{i}}$$
Dividing the time into n periods, an n‑dimensional price‑demand elasticity matrix is established:
$$\mathbf{E} = \begin{bmatrix} \varepsilon_{11} & \varepsilon_{12} & \cdots & \varepsilon_{1n} \\ \varepsilon_{21} & \varepsilon_{22} & \cdots & \varepsilon_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ \varepsilon_{n1} & \varepsilon_{n2} & \cdots & \varepsilon_{nn} \end{bmatrix}$$
The charging and discharging power of electric vehicle users then satisfies:
$$\begin{bmatrix} \Delta Q_{1}/Q_{1} \\ \Delta Q_{2}/Q_{2} \\ \vdots \\ \Delta Q_{n}/Q_{n} \end{bmatrix} = \mathbf{E} \cdot \begin{bmatrix} \Delta P_{1}/P_{1} \\ \Delta P_{2}/P_{2} \\ \vdots \\ \Delta P_{n}/P_{n} \end{bmatrix}$$
After implementing the time‑of‑use electricity price, the column vector of electricity demand Q′ at period i is:
$$\begin{bmatrix} Q_{1}^{‘} \\ Q_{2}^{‘} \\ \vdots \\ Q_{n}^{‘} \end{bmatrix} = \begin{bmatrix} Q_{1} \\ Q_{2} \\ \vdots \\ Q_{n} \end{bmatrix} + \begin{bmatrix} Q_{1} & 0 & \cdots & 0 \\ 0 & Q_{2} & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & Q_{n} \end{bmatrix} \cdot \mathbf{E} \cdot \begin{bmatrix} \Delta P_{1}/P_{1} \\ \Delta P_{2}/P_{2} \\ \vdots \\ \Delta P_{n}/P_{n} \end{bmatrix}$$
In my research, I take the daily predicted electricity consumption as the starting point, determine the static period electricity prices for peak, valley, and flat periods through an optimization process, and use this as the baseline. Then, considering the real‑time fluctuation of electricity demand within 24 hours and the response accuracy of the grid, I update the real‑time load data every 15 minutes, then dynamically update the electricity prices, and finally obtain the optimized overall 24‑hour dynamic time‑of‑use electricity price. The resulting dynamic period electricity price has higher real‑time response capability and higher accuracy.
5.2 Multi‑Objective Scheduling Model Formulation
The primary objective functions are established with the fundamental goals of smoothing peak‑valley differences and reducing electric vehicle operating costs. To reduce the difference between peak and valley values, I combine the basic electricity demand of the microgrid with the electricity demand of electric vehicles, and take the minimization of the standard deviation of peak‑valley differences as the optimization objective. The optimization function F₁ is defined as:
$$\min F_{1} = \frac{1}{N – 1}\sum_{n}^{N}\left( P_{al,EV}^{(n)} + P_{charge}^{(n – 1)} – P_{al,av}^{(n – 1)} \right)^{2}$$
where Pcharge(n−1) is the basic predicted load after the previous period, Pal,EV is the superimposed value of all loads, and Pal,av(n−1) is the average value of all loads in the microgrid after the previous period.
Under the promotion of the dynamic time‑of‑use electricity price mechanism, users independently decide the charging and discharging operations of their electric vehicles to achieve personal benefit maximization. For users, reducing the charging and discharging cost of electric vehicles is the main goal. The minimum charging and discharging cost F₂ is calculated as:
$$\min F_{2} = \sum_{t = 1}^{24}\left\lbrack P^{c}(t) \cdot r_{c} + P^{d}(t) \cdot r_{d} – P_{EV}(t) \cdot r_{b} \right\rbrack \cdot \Delta t$$
where the battery unit energy cost is:
$$r_{b} = \frac{C_{b}}{0.8k}$$
and the piecewise charging/discharging power is:
$$P_{EV}(t) = \begin{cases} P^{c}(t), & P_{EV}(t) \geq 0 \\ P^{d}(t), & P_{EV}(t) < 0 \end{cases}$$
Here, Pc(t) is the charging load, Pd(t) is the discharging power, rb is the cost per unit energy of the electric vehicle battery, k is the remaining number of uses of the battery, Δt is the calculation time interval, Cb is the preset battery capacity, and PEV(t) is the charging/discharging power which is positive in the charging state and negative in the discharging state.
5.3 Constraint Conditions
The following constraints are incorporated in my model. The state of charge of electric vehicles must not exceed its permissible range:
$$SOC_{\min} \leq SOC \leq SOC_{\max}$$
The electricity price should be higher than the cost minimum price, but should not exceed the upper limit of the electricity price:
$$ep_{\min} \leq ep \leq ep_{\max}$$
The total charging amount of electric vehicles must satisfy:
$$\sum_{t = 1}^{24}P_{EV,t}^{c} = P_{total}^{c}$$
The total discharging amount should be less than the total discharging limit:
$$\sum_{t = 1}^{24}P_{EV,t}^{d} \leq P_{total}^{d}$$
The charging power constraint for the entire electric vehicle fleet as a mobile energy storage device:
$$P_{EV}^{\min} \leq P_{EV,t} \leq P_{EV}^{\max}$$
The key constraints of my model are summarized in the following table.
| Constraint Type | Mathematical Formulation | Description |
|---|---|---|
| SOC level | SOCmin ≤ SOC ≤ SOCmax | Battery state of charge bound |
| Electricity price | epmin ≤ ep ≤ epmax | Price upper and lower bounds |
| Total charging amount | Σ PcEV,t = Pctotal | Charging energy balance |
| Total discharging amount | Σ PdEV,t ≤ Pdtotal | Discharging energy limit |
| Fleet charging power | PminEV ≤ PEV,t ≤ PmaxEV | Aggregate power limit of EV fleet |
6. Niche‑Based Multi‑Objective Particle Swarm Optimization Algorithm
The multi‑objective scheduling model is a hybrid optimization problem involving multiple objectives and constraints. Since the standard particle swarm optimization algorithm tends to converge to local optima, I adopt an improved multi‑objective particle swarm optimization algorithm based on niche technology.
6.1 Niche Technology Principle
Niche technology originates from the concept of ecological niches in nature. Specifically, within a specific region, a group of species with the same or similar characteristics gathers. Among these species, there are interactions including information exchange and resource competition. Following the natural selection principle of “survival of the fittest,” species with poor adaptability are gradually eliminated, while those with strong survival ability survive. Through this screening mechanism, species continue to evolve.
The distance between particles i and j is defined as:
$$d_{ij} = \sqrt{\sum_{k = 1}^{N}\left( x_{i}^{k} – x_{j}^{k} \right)^{2}}$$
The radius of the niche is determined by:
$$d_{i} = \min\left( \left\| x_{i} – x_{j} \right\| \right),\quad j = 1,2,\cdots,m$$
$$R_{ch} = \begin{cases} C, & m = 1 \\ \dfrac{1}{m}\sum_{i = 1}^{m/2}d_{i}, & m \geq 2 \end{cases}$$
When the distance between particles is less than the niche radius (dij < Rch), particle i is stored into the niche group. The current fitness of the particle is:
$$S_{i} = \sum_{j = 1}^{N}f_{sh}\left( d_{ij} \right)$$
The sharing function is:
$$f_{sh}\left( d_{ij} \right) = 1 – \left( \frac{d_{ij}}{R_{ch}} \right)^{\lambda}$$
where λ is a parameter used to regulate the shape of the sharing function.
6.2 Algorithm Procedure
The niche‑based multi‑objective particle swarm optimization algorithm enhances the performance of the multi‑objective particle swarm optimization algorithm by integrating diversity and adaptability. I employ chaotic mutation technology to ensure the global exploration capability of particles and prevent premature stabilization in the late stages of the algorithm. The probabilistic selection formula following the niche competition principle is:
$$P(x_{i}) = \frac{D(x_{i})}{\sum_{j = 1}^{N + M}D\left( x_{j} \right)} = \frac{1/S_{i}}{\sum_{j = 1}^{N + M}1/S_{j}}$$
The velocity and position update equations of the particles are:
$$V_{i}^{k + 1} = \omega V_{i}^{k} + c_{1}r_{1}\left( P_{i}^{k} – X_{i}^{k} \right) + c_{2}r_{2}\left( P_{g}^{k} – X_{i}^{k} \right)$$
$$X_{i}^{k + 1} = X_{i}^{k} + V_{i}^{k + 1}$$
where c₁ and c₂ are cognitive and social learning factors typically set between 1.4 and 2.1, r₁ and r₂ are random numbers between 0 and 1, P represents the current position of the particle swarm, and V represents the particle velocity.
For the inertia weight adjustment, I use a nonlinear inertia weight decay method. The inertia weight ω exhibits a nonlinear decreasing trend with the increase in iteration number:
$$\omega = \omega_{begin} – \left( \omega_{begin} – \omega_{finish} \right) \cdot \sin\left( \frac{\pi \cdot t}{2 \cdot k_{\max}} \right)$$
where ωbegin and ωfinish are the inertia weights at the beginning and end, respectively. The main steps of my algorithm are summarized below:
| Step | Description |
|---|---|
| Step 1 | Initialization: randomly determine the initial solution set based on control variables and constraints; evaluate individual fitness in the niche; construct the solution set with niche characteristics |
| Step 2 | Update particle velocity and position according to the update equations; initialize the external optimal solution set |
| Step 3 | Evaluate solution performance and update the optimal solution set; check whether new solutions dominate in the external archive set; include non‑dominated particles into the optimal solution set; otherwise continue to the next iteration |
| Step 4 | Apply niche selection strategy to eliminate solutions with relatively low fitness in each niche, ensuring the optimal characteristic of the Pareto frontier solutions |
| Step 5 | Select better results for the next iteration through random sampling |
| Step 6 | Evaluate all possible parameter configuration scores to determine the best parameter combination |
| Step 7 | Determine whether the termination condition is satisfied; if the iteration number reaches the preset upper limit, terminate the iteration process and display the Pareto optimal solution set; otherwise execute Step 3 again |
7. Case Study of the Multi‑Objective Scheduling Model
In my case study, I use the niche‑based multi‑objective particle swarm optimization algorithm to calculate the charging and discharging schedule of 2,000 electric vehicles over one day, forming the Pareto frontier optimal solution space. The distribution of the optimal solution set reveals the trade‑off relationship between the peak‑valley mean square difference and the cost. Each point in the solution space represents an optimal trade‑off between the two conflicting objectives.
When electric vehicles participate in wind and solar accommodation, the comparison between predicted and actual accommodated photovoltaic power shows distinct patterns. The actual accommodation reaches the predicted values in multiple time periods through the charging and discharging scheduling of electric vehicles, especially between 17:00 and 19:00. This observation demonstrates that electric vehicles can significantly enhance the utilization rate of photovoltaic energy. Similarly, for wind power, despite the significant fluctuations in the prediction curve caused by the randomness of wind speed, a high degree of consistency is observed between the accommodation curve and the prediction curve in specific time periods. Especially during wind speed peak periods, the accommodation curve fits the prediction curve best. This consistency not only verifies the reliability of short‑term power prediction but also highlights the promoting effect of flexible load regulation on new energy accommodation.
Through in‑depth analysis of the curve overlap periods, I discovered that these periods coincide spatially and temporally with the peak load of electric vehicle cluster charging. During the early morning to dawn hours, the grid load valley overlaps with the wind power output peak. At this time, the intelligent charging behavior of electric vehicles effectively fills the load trough, enabling the accommodation of fluctuating power sources. This supply‑demand synergy effect reflects both the effectiveness of the demand‑side response mechanism and the important value of source‑load interaction in the new power system.
The analysis of the typical microgrid system’s power supply and demand characteristics reveals the core framework of source‑load interaction within the microgrid. The total electric load curve shows significant peak‑valley fluctuations, reflecting the diurnal periodic changes in users’ electricity consumption behavior. The photovoltaic power generation exhibits its single‑peak characteristic synchronized with solar irradiance intensity. The wind power, depicted by the dashed line, demonstrates strong randomness, with its fluctuation trend highly correlated with wind speed changes. The superposition of these three elements constitutes the core framework of source‑load interaction within the microgrid, highlighting the contradiction between renewable energy accommodation and stable grid operation.
My proposed electric vehicle charging/discharging optimization strategy balances power supply and demand through flexible regulation capability. During photovoltaic peaks, electric vehicles are prioritized for charging to absorb clean energy. During wind power fluctuations or load peaks, the vehicle‑to‑grid technology is utilized for reverse power supply to smooth fluctuations. The charging and discharging behavior of electric vehicles in different periods reveals that electric vehicles mainly charge during valley and flat periods when electricity prices are relatively low, while discharging during peak periods and periods with high electricity prices.
The comparison of electric load before and after adopting my optimization strategy is summarized in the following table. Due to daily electricity consumption patterns and the intermittency of wind and solar energy, the electric load curve exhibits significant peak‑valley differences before optimization. After optimization through orderly charging and discharging scheduling of electric vehicles, the peak‑valley difference of the electric load curve is significantly reduced.
| Optimization Scenario | Peak‑Valley Difference (kW) | Reduction Relative to Disordered (%) | Reduction Relative to Ordered (%) |
|---|---|---|---|
| Disordered optimization | 241.2 | — | — |
| Ordered optimization | 255.9 | — | — |
| Proposed NMOPSO approach | 199.8 | 17 | 21 |
The electric vehicle load is evenly distributed to each time period, resulting in a total load curve with a peak‑valley difference of 199.8 kW. Compared with disordered optimization and ordered optimization, the peak‑valley difference is reduced by 17% and 21%, respectively. In conclusion, through the multi‑objective optimal scheduling of electric vehicle charging and discharging, not only can the grid load be effectively balanced, but the utilization rate of wind and photovoltaic energy can also be enhanced, promoting the accommodation of renewable resources.
8. Scenario Generation and Reduction for Wind and Solar Output
8.1 Scenario Generation Based on Copula Theory
Wind and solar outputs exhibit uncertain characteristics. To accurately represent the random fluctuation characteristics of wind and solar outputs, I propose a scenario generation framework based on Copula theory. The core idea of this method is to establish a joint probability distribution model for wind power and photovoltaic output using connecting functions. Copula functions mainly include ellipsoidal Copula (including t‑Copula and Gaussian Copula) and Archimedean Copula (including Gumbel, Clayton, and Frank forms). By coupling marginal distributions and modeling correlation, a scenario library with statistical representativeness can be constructed, providing reliable input data for stochastic optimization of the power system.
The mathematical structure of the Archimedean Copula function is determined by a specific generator operator, and its general expression is:
$$C\left( u_{1},\cdots,u_{n} \right) = \varphi^{-1}\left( \varphi\left( u_{1} \right) + \cdots + \varphi\left( u_{n} \right) \right)$$
where φ−1 is the inverse function of φ. When an extremum exists at φ(0), the obtained pseudo‑inverse form is:
$$\varphi^{-1}(t) = \begin{cases} \varphi^{-1}(t), & 0 \leq t \leq \varphi(0) \\ \varphi(0), & \varphi(0) < t < \infty \end{cases}$$
In the Archimedean Copula function family, Clayton and Gumbel types are only applicable to describe positive correlations. However, wind power and photovoltaic outputs often exhibit negative correlations. In contrast, the Frank‑Copula function has a wider applicability and can simultaneously characterize both positive and negative correlations. Based on this property, I select the Frank‑Copula function to model the correlation characteristics between wind and solar outputs.
Based on measured wind and solar output data from a certain region, my research adopts a scenario generation method that considers correlation and uncertainty. The research process includes: first, adopting the non‑parametric kernel density estimation method to establish probability density models for wind power and photovoltaic output in different periods, to accurately characterize their time series statistical characteristics. Second, using the Frank‑Copula function to study the wind‑solar correlation. Third, based on the joint probability distribution characteristics of different periods, random sampling technology is adopted to obtain the initial sample set, and then the wind and solar output values are solved by the inverse transformation method. This process effectively integrates the stochastic characteristics and spatiotemporal correlation of renewable energy, and finally outputs a wind‑solar joint output scenario with statistical representativeness.
8.2 Scenario Reduction Using Rough K‑Means Algorithm
Sampling based on the joint distribution of periods can generate a large number of wind and solar output scenarios. However, the huge number of samples makes related calculations extremely complex and tedious, and it is difficult to effectively filter representative scenarios from such numerous output scenarios during scheduling. To address the scenario screening problem, clustering algorithms can be used to extract features from massive wind and solar output data and generate typical representative scenario sets.
The K‑means algorithm realizes data classification by calculating the distance between data objects and cluster centers. After clustering, there are obvious differences between data in different clusters, while data within the same cluster have similarity. The Rough k‑means algorithm is based on rough set theory and uses upper and lower approximation sets for data partitioning. During the clustering process, data points that clearly belong to a cluster are classified into the lower approximation set, while data points with fuzzy membership are placed in the boundary region.
The characteristics of my scenario reduction approach include: differentiated weight allocation where data in the lower approximation set have larger weights and boundary data have smaller weights; and refined membership handling that does not force data points to have a single membership. In wind and solar output scenario reduction, this algorithm can not only effectively handle the randomness and uncertainty of data but also improve the clustering effect through membership differentiation and weight adjustment.
The historical wind and solar data used in my study are derived from the public wind and solar output data of a region in Northeast China in 2019. I generate 1,000 wind and solar output scenarios using the described method. Considering that a year contains three typical seasons — transition season, summer, and winter — I use the Rough k‑means algorithm to reduce the 1,000 wind and solar output scenarios to 6 typical scenarios. The probability distributions of these six typical scenarios are: Scenario 1 (0.194), Scenario 2 (0.147), Scenario 3 (0.157), Scenario 4 (0.149), Scenario 5 (0.202), and Scenario 6 (0.151). These scenarios can accurately reflect the correlation and uncertainty characteristics of wind and solar outputs, providing an important basis for subsequent scheduling research.
| Scenario | Probability | Scenario | Probability |
|---|---|---|---|
| 1 | 0.194 | 4 | 0.149 |
| 2 | 0.147 | 5 | 0.202 |
| 3 | 0.157 | 6 | 0.151 |
9. Bilevel Optimization Scheduling Model
9.1 Upper Level: Orderly Charging Scheduling Model for Electric Vehicles
In the upper level, I formulate the objective of maximizing the charging station profit. The charging station purchases electricity from the grid at a wholesale price and sells it to electric vehicle users at a retail price. The objective function is formulated as:
$$\max F_{EV} = \sum_{i = 1}^{N_{EV}}\sum_{t = 1}^{T}\left( S_{i,t} \cdot P_{EV} \cdot \Delta t \cdot g_{EV,t} – S_{i,t} \cdot P_{EV} \cdot \Delta t \cdot \lambda_{EV,t} \right)$$
where NEV represents the total number of electric vehicles, Δt is the time step set to 1 hour, Si,t represents the charging state of the i‑th electric vehicle at period t (1 when charging, 0 when not charging), gEV,t is the electricity price level charged to users by the charging station at period t, λEV,t represents the electricity price from the grid to the charging station at period t, and PEV is the rated charging power of the electric vehicle.
The following constraints are incorporated:
First, the user demand constraint — after charging is completed, the state of charge of the electric vehicle must not exceed the total battery capacity to prevent overcharging, while satisfying the user’s travel demand:
$$CS_{i,e} \leq CS_{i,s} + \sum_{t = 1}^{T}\eta \cdot S_{i,t} \cdot P_{EV} \cdot \Delta t \leq C$$
Second, the system maximum load constraint — after all electric vehicles are connected, the total load combined with the conventional system load must not exceed the maximum operating load of the distribution system:
$$P_{t} + \sum_{i = 1}^{N_{EV}}P_{EV,i,t} \leq P^{\max}$$
To solve this optimization problem, I convert the profit maximization objective into a minimization problem. The Lagrangian relaxation method is applied to handle the system constraints. The relaxed problem is formulated as:
$$L(S_{i,t},\lambda) = \sum_{i = 1}^{N_{EV}}\sum_{t = 1}^{T}\left( S_{i,t} \cdot P_{EV} \cdot \Delta t \cdot \lambda_{EV,t} – S_{i,t} \cdot P_{EV} \cdot \Delta t \cdot g_{EV,t} \right) + \sum_{t = 1}^{T}\lambda_{t}\left( \sum_{i = 1}^{N_{EV}}S_{i,t}P_{EV} + P_{t} – P^{\max} \right)$$
where λ is the Lagrange multiplier vector. The dual problem is constructed by taking the Lagrange multipliers as decision variables:
$$D(\lambda) = \min_{S_{i,t}}\max_{\lambda \geq 0}L\left( S_{i,t},\lambda \right)$$
The Lagrange multipliers are updated iteratively using the subgradient method:
$$\lambda^{(k + 1)} = \lambda^{(k)} + \frac{\gamma^{(k)}\mu^{(k)}}{\left\| \mu^{(k)} \right\|_{1}}$$
where γ is the iteration step size and μ(k) is the subgradient. Through continuous iterative updating of the Lagrange multipliers, when the duality gap satisfies the preset accuracy, the lower bound value of the dual problem is determined as the optimal solution of the original problem.
The electricity price parameters used in my case study are shown in the following table.
| Time Period | Purchase Price (yuan·(kW·h)−1) | Retail Price (yuan·(kW·h)−1) |
|---|---|---|
| 00:00–08:00 | 0.365 | 0.4 |
| 08:00–12:00 | 0.869 | 2 |
| 12:00–14:00 | 0.687 | 1.2 |
| 14:00–17:00 | 0.687 | 2 |
| 17:00–21:00 | 0.869 | 2 |
| 21:00–24:00 | 0.687 | 1.2 |
9.2 Lower Level: Electric Vehicle Grid‑Connected Optimization Scheduling Model
Based on the upper‑level scheduling results, I construct a lower‑level optimization model that minimizes the distribution network operation cost, subject to power flow and other operational constraints. The objective function includes network loss cost (C₁), penalty cost for safety constraint violations (C₂), DG output adjustment cost (C₃), upstream grid power purchase cost (C₄), and electric vehicle charging station sales revenue (C₅). The objective function is expressed as:
$$\min F = C_{1} + C_{2} + C_{3} + C_{4} – C_{5}$$
The network loss cost is:
$$C_{1} = \sum_{t = 1}^{T}\lambda_{l,t} \cdot P_{loss,t} \cdot \Delta t$$
The penalty cost for safety constraint violations combines the line power over‑limit penalty and the voltage over‑limit penalty:
$$C_{2} = \sum_{t = 1}^{T}\left( r_{1} \cdot R_{sys,t}^{L} + r_{2} \cdot R_{sys,t}^{U} \right)$$
The voltage over‑limit penalty is defined as:
$$R_{sys,t}^{U} = \sum_{i = 1}^{n}\lambda_{v} \cdot S_{U,i,t}$$
$$S_{U,i,t} = \begin{cases} U_{i,t} – U_{\max}, & U_{i,t} > U_{\max} \\ 0, & U_{\min} \leq U_{i,t} \leq U_{\max} \\ U_{\min} – U_{i,t}, & U_{i,t} < U_{\min} \end{cases}$$
The line power over‑limit penalty is:
$$R_{sys,t}^{L} = \sum_{j = 1}^{K}\lambda_{L} \cdot S_{L,j,t}$$
$$S_{L,j,t} = \begin{cases} 0, & L_{j,t} \leq 0.9 \\ L_{j,t} – 0.9, & L_{j,t} > 0.9 \end{cases}$$
The DG output adjustment cost is:
$$C_{3} = \sum_{t = 1}^{T}\sum_{i = 1}^{N_{DG}}M \cdot \left| \Delta S_{DG,i,t} \right| \cdot \Delta t$$
The power purchase cost from the upstream grid is:
$$C_{4} = \sum_{t = 1}^{T}\lambda_{buy,t} \cdot P_{buy,t} \cdot \Delta t$$
The electric vehicle charging station sales revenue is:
$$C_{5} = \sum_{t = 1}^{T}\lambda_{EV,t} \cdot P_{EV,t} \cdot \Delta t$$
9.3 Lower Level Constraints
Each node must satisfy both active and reactive power balance conditions:
$$P_{m,t} = \sum_{i = 1}^{N_{wt}}P_{wt,i,t} + \sum_{i = 1}^{N_{pv}}P_{pv,i,t} – \sum_{i = 1}^{N_{EV}}P_{EV,i,t} – P_{load,t}$$
$$Q_{m,t} = \sum_{i = 1}^{N_{wt}}Q_{wt,i,t} + \sum_{i = 1}^{N_{pv}}Q_{pv,i,t} – Q_{load,t}$$
The power flow equations in polar form are:
$$P_{m,t} = U_{m,t}\sum_{j \in m}U_{j,t}\left( G_{mj}\cos\theta_{mj,t} + B_{mj}\sin\theta_{mj,t} \right)$$
$$Q_{m,t} = U_{m,t}\sum_{j \in m}U_{j,t}\left( G_{mj}\sin\theta_{mj,t} – B_{mj}\cos\theta_{mj,t} \right)$$
Line capacity constraints:
$$\left| P_{mj,t} \right| \leq P_{mj}^{\max}$$
with the line power flow:
$$P_{mj,t} = U_{m,t}^{2}G_{mj} – U_{m,t}U_{j,t}\left( G_{mj}\cos\theta_{mj,t} + B_{mj}\sin\theta_{mj,t} \right)$$
Node voltage constraints:
$$0.95 \leq U_{m,t} \leq 1.05$$
DG output constraints:
$$P_{wt,i,t}^{\min} \leq P_{wt,i,t} \leq P_{wt,i,t}^{\max}$$
$$P_{pv,i,t}^{\min} \leq P_{pv,i,t} \leq P_{pv,i,t}^{\max}$$
Electric vehicle charging quantity constraints:
$$0 \leq N_{EV,m,t} \leq N_{EV,m,t}^{\max}$$
The complete constraint structure of the lower‑level model is summarized in the table below.
| Constraint | Formula |
|---|---|
| Active power balance | Pm,t = ΣPwt,i,t + ΣPpv,i,t − ΣPEV,i,t − Pload,t |
| Reactive power balance | Qm,t = ΣQwt,i,t + ΣQpv,i,t − Qload,t |
| Bus injection power | Pm,t = Um,tΣUj,t(Gmjcosθmj,t + Bmjsinθmj,t) |
| Reactive injection power | Qm,t = Um,tΣUj,t(Gmjsinθmj,t − Bmjcosθmj,t) |
| Line capacity | |Pmj,t| ≤ Pmaxmj |
| Voltage limits | 0.95 ≤ Um,t ≤ 1.05 |
| WT output | Pminwt,i,t ≤ Pwt,i,t ≤ Pmaxwt,i,t |
| PV output | Pminpv,i,t ≤ Ppv,i,t ≤ Pmaxpv,i,t |
| EV quantity | 0 ≤ NEV,m,t ≤ NmaxEV,m,t |
10. Solution Methodology with Improved Genetic‑Simulated Annealing Hybrid Algorithm
For the lower‑level optimization problem, I employ a hybrid optimization method that integrates the genetic algorithm and simulated annealing algorithm. The implementation process follows these steps: first, the encoding and initialization stage where generator output schemes are encoded as chromosomes and an initial population is constructed. The fitness function is defined to map the operation cost to a fitness value, where lower cost yields higher fitness.
During the genetic evolution stage, selection operations are performed based on fitness for survival of the fittest. Crossover and mutation operations generate the new generation of population individuals through continuous iteration to optimize population fitness. The simulated annealing optimization stage applies the Metropolis criterion to new individuals, allowing probabilistic acceptance of inferior solutions and dynamically adjusting the temperature parameter from an initially high temperature for broad exploration to gradual cooling for refined search.
This hybrid algorithm significantly improves optimization performance through the complementary advantages of genetic algorithm and simulated annealing algorithm. First, the probabilistic jump characteristic of the simulated annealing algorithm overcomes the defect of the traditional genetic algorithm easily falling into local optima. By accepting inferior solutions with a certain probability, the global search capability is significantly enhanced. Second, the group search mechanism of the genetic algorithm makes up for the deficiency of the simulated annealing algorithm. Its parallel search characteristic greatly accelerates convergence speed while reducing sensitivity to initial parameters. More importantly, the two algorithms produce a significant synergistic effect: the genetic algorithm is responsible for the macroscopic population evolution and achieves large‑scale solution space exploration, while the simulated annealing algorithm focuses on microscopic individual improvement through refined local search to improve solution quality.
Furthermore, the introduced temperature scheduling mechanism intelligently balances the exploration and exploitation processes. The early high temperature promotes extensive searches, while the later low temperature achieves refined optimization. This ensures that the algorithm can both converge quickly and obtain high‑quality optimal solutions. This organic combination provides both global search capability and local refinement ability, significantly improving the quality of the optimal solution while ensuring solution efficiency.
11. Case Study of the Bilevel Optimization Model on the IEEE 33‑Bus System
11.1 System Description
In my case study, I establish the electric vehicle grid‑connected optimization model based on the IEEE 33‑bus distribution network. The system reference voltage is 12.66 kV. Node 1 is the slack node, nodes 18 and 33 are integrated with wind turbines and photovoltaic units, respectively, and their outputs are characterized using six typical scenarios. Node 8 is configured with an electric vehicle charging station, whose charging load adopts the orderly scheduling strategy obtained from the upper‑level model.
11.2 Orderly Charging Scheduling Results
I analyze the system load curves under uncoordinated and coordinated charging modes. The uncoordinated charging mode refers to electric vehicles charging immediately upon connection without any price guidance. In contrast, the orderly charging mode leverages the time‑of‑use price structure to shift electric vehicle charging loads to appropriate periods.
The key results are presented in the following table.
| Charging Mode | Peak Load (MW) | Valley Load (MW) | Peak‑Valley Difference Rate (%) |
|---|---|---|---|
| Uncoordinated | 89.45 | 49.04 | 45.2 |
| Coordinated | 84.75 | 50.64 | 40.2 |
The peak‑valley difference rate is calculated as:
$$F_{load} = \frac{p_{h} – p_{l}}{p_{h}}$$
where ph is the peak load and pl is the valley load. From the results, it can be observed that under the orderly charging mode, electric vehicles are mostly charged during flat periods, achieving the effect of avoiding peaks. During nighttime, the charging load of electric vehicles is shifted to the valley period with a lower load, playing a role in valley filling. The quantitative comparison shows that the coordinated charging strategy effectively reduces the system peak‑valley difference, significantly improving the stability of grid operation.
11.3 Optimization Results of the Bilevel Model
Based on the improved genetic algorithm optimization, I obtain the optimal output scheme for each distributed generator at each node. The simulation results show that the system’s power purchase demand from the upstream grid varies across different wind and solar scenarios. The optimized output characteristics of the wind turbines and photovoltaic units over 24 hours are also obtained, demonstrating the coordinated dispatch between electric vehicle charging loads and distributed generation.
Through coordinated control of wind and photovoltaic output, the grid operation economy is significantly improved. The key results show that in the six typical scenarios, the system network loss variation exhibits different characteristics depending on the renewable output patterns. When renewable generation is abundant while the load demand is low, the system achieves supply‑demand balance through reasonable curtailment of new energy output.
To efficiently present the complete performance of my scheduling approach, I provide a detailed comparison of operating costs before and after optimization across all six scenarios.
| Scenario | Risk Penalty Cost (yuan) | Network Loss Cost (yuan) | Total Operating Cost (yuan) |
|---|---|---|---|
| Scenario 1 — Before | 1065 | 3908 | 5326 |
| Scenario 1 — After | 995 | 3619 | 4603 |
| Scenario 2 — Before | 1035 | 3734 | 5024 |
| Scenario 2 — After | 984 | 3562 | 4513 |
| Scenario 3 — Before | 1165 | 3809 | 5178 |
| Scenario 3 — After | 1002 | 3546 | 4390 |
| Scenario 4 — Before | 1265 | 3739 | 4926 |
| Scenario 4 — After | 1005 | 3483 | 4262 |
| Scenario 5 — Before | 1176 | 3554 | 4826 |
| Scenario 5 — After | 894 | 3327 | 4191 |
| Scenario 6 — Before | 1146 | 3388 | 4789 |
| Scenario 6 — After | 875 | 3325 | 4179 |
The results demonstrate the effectiveness of my proposed scheduling strategy. In Scenario 1, the total network loss is reduced by 404 kW, the operation risk cost decreases by 6.5%, and the total cost optimization reaches 13.6%. In Scenario 2, the network loss optimization margin reaches 256 kW, and the total cost reduction is 10.2%. This proves that the scheduling method can effectively reduce network losses and operational risks while improving the overall system economy. Additionally, by smoothing load peak‑valley differences and optimizing distributed generator outputs, the strategy not only reduces the curtailment of new energy but also decreases the peak regulation pressure of the grid.
The percentage cost savings across all scenarios are summarized below.
| Scenario | Total Cost Saving (%) |
|---|---|
| 1 | 13.6 |
| 2 | 10.2 |
| 3 | 15.2 |
| 4 | 13.5 |
| 5 | 13.2 |
| 6 | 12.7 |
To evaluate the effectiveness of the improved algorithm, I select Scenario 1 for comparative testing. Compared with the traditional genetic algorithm, the improved algorithm shows significant improvements in both convergence and optimization effectiveness. The convergence speed is accelerated by approximately 8%, and the optimal objective function value is reduced by 15%. This comparative result fully proves the effectiveness of the algorithmic improvements.
12. Conclusions
In this article, I have presented a comprehensive study on the coordinated charging and discharging optimization scheduling of electric vehicles considering wind and solar uncertainty. Through the research, the following conclusions can be drawn.
First, I established mathematical models for wind and photovoltaic power generation. I introduced the Weibull distribution model to describe wind speed probability characteristics and the Beta distribution model to describe light intensity probability distribution. These models provide the theoretical foundation for subsequent dispatch optimization. My analysis reveals that the inherent randomness and volatility of renewable energy sources pose significant challenges to grid stability, necessitating effective demand‑side regulation strategies.
Second, I developed orderly and disorderly charging models for electric vehicles, analyzing the multiple factors that influence electric vehicle charging behavior. Through Monte Carlo simulation methods, I predicted the spatiotemporal distribution of electric vehicle loads, revealing the impact of uncoordinated charging on grid load. My simulation results with 500, 1,000, and 2,000 electric vehicles demonstrate that large‑scale uncoordinated charging significantly changes the peak‑valley characteristics of grid load. Importantly, I found that the charging behavior of electric vehicles exhibits certain regularity and controllability. Through proper scheduling strategies, the impact on the grid can be effectively mitigated.
Third, I proposed a multi‑objective scheduling model for electric vehicle charging/discharging considering wind and solar power accommodation. I established a dynamic time‑of‑use electricity price model and used a niche‑based multi‑objective particle swarm optimization algorithm to solve the model. The simulation results show that the scheduling strategy based on electric vehicle charging/discharging effectively balances power supply and demand. Electric vehicles are primarily charged during valley and flat periods with lower electricity prices, while discharging during peak periods. Compared with disordered optimization and ordered optimization, my proposed method reduces the peak‑valley difference by 17% and 21%, respectively.
Fourth, considering the uncertainty of wind and solar power output, I constructed a bilevel optimization scheduling model. The upper level employs a dynamic time‑of‑use pricing mechanism and Lagrangian relaxation to achieve orderly charging of electric vehicles, maximizing charging facility operational benefits. The lower level establishes a multi‑objective optimization model considering voltage quality, network loss minimization, and line capacity safety constraints. I used the Rough k‑means algorithm to reduce 1,000 generated scenarios to 6 typical scenarios that accurately capture the correlation and uncertainty characteristics of wind and solar output. Combined with an improved genetic‑simulated annealing hybrid algorithm, my approach achieves system network loss reduction of 15%‑20% and operating cost reduction exceeding 10%.
However, several limitations remain in my current research. Future work should address the following aspects. First, the multi‑objective optimization system should be further refined by incorporating environmentally friendly indicators, social cost, and technical feasibility to construct a more comprehensive multi‑objective optimization system. Second, uncertainty handling methods should be deepened to address black swan events such as extreme weather‑induced output disconnection and abrupt user behavior changes. Advanced machine learning and artificial intelligence techniques could be incorporated for better prediction and handling of uncertainties. Third, the user‑side participation mechanism requires improvement. Future research should consider user behavior characteristics and construct more reasonable user stratification models to enhance user enthusiasm and satisfaction in participating in dispatch.