1. Introduction
With the growing global environmental pressure and the implementation of my country’s “dual carbon” policy, electric vehicles and clean energy power generation have been widely promoted and adopted. This situation has brought intermittent fluctuation characteristics to the power supply side, while the large-scale integration of electric vehicles into the grid has further aggravated load instability and increased the peak-valley difference. In view of this, my research focuses on developing a microgrid scheduling method that simultaneously considers both economic efficiency and environmental protection during grid operation. I proposed an Improved Non-dominated Sorting Genetic Algorithm II (IMNSGA2) to optimize the scheduling scheme, aiming to enhance its scientific rationality and practical applicability.
High-efficiency microgrid scheduling can rationally configure the coordinated operation of various source-storage-load equipment, thereby improving the power supply stability of the microgrid and optimizing the operating states of power sources. Furthermore, microgrid optimal scheduling not only achieves efficient integration and consumption of clean energy but also provides power supply for electric vehicles, simultaneously ensuring the operational benefits of power enterprises while assisting the green and low-carbon transformation of the power industry. It provides reliable energy support for the popularization and promotion of electric vehicles.
From the perspective of power generation enterprises, this research not only improves the utilization rate of generated electricity and reduces unnecessary waste, but also increases their electricity sales volume and enhances operational income. From the perspective of grid enterprises, microgrid scheduling can rationally distribute power flow across the network, enabling coordinated operation among sources, storage, and loads, thus ensuring safe and stable power supply. From the user’s perspective, high-quality power supply can satisfy their electrical appliance usage requirements, ensuring orderly social production and enhancing user satisfaction with electricity services.
2. Microgrid System Structure and Electric Vehicle Load Modeling
Microgrids serve as carriers for distributed power sources and loads to achieve electricity supply and consumption. These power generation and consumption units are mutually independent and operate stably under the scheduling of the microgrid. The microgrid structure studied in my research includes renewable energy systems such as photovoltaic (PV) and wind turbines (WT), as well as controllable distributed generators like diesel engines, along with energy storage batteries and various loads including electric vehicle charging stations and conventional residential loads. The microgrid connects to the main grid through a public connection point (PCC). An Energy Management System (EMS) monitors the grid power flow in real time, evaluates the power supply-demand relationship promptly, and rapidly formulates scheduling schemes.
For the distributed generations in this microgrid, photovoltaic output power can be modeled as follow:
$$P_{pv} = P_r \frac{R}{R_s}[1 + \theta(T_c – T_r)]$$
where $P_r$ is the rated output power of PV system, $R$ and $R_s$ are the actual and ideal solar radiation intensity, $T_c$ and $T_r$ are actual and rated operating temperature of PV cells, respectively, and $\theta$ denotes the conversion efficiency coefficient.
Wind turbine output is given as a piecewise function of wind speed $v$:
$$P_{wt} = \begin{cases} 0, & v < v_{ci} \\ a v^3 + b v^2 + c v + d, & v_{ci} \leq v < v_r \\ P_r, & v_r \leq v < v_{co} \\ 0, & v \geq v_{co} \end{cases}$$
where $P_r$ is the rated power, $v_{ci}$, $v_r$ and $v_{co}$ are the cut-in, rated and cut-out wind speeds respectively, and $a$, $b$, $c$, $d$ are wind speed parameters.
The diesel engine operating cost includes the operation and maintenance expense, fuel cost, and the pollution penalty cost which can be expressed as:
$$C_{DE}(t) = K_{OM,DE}P_{DE}(t) + \alpha P_{DE}(t)^2 + \beta P_{DE}(t) + \gamma + \sum_{k=1}^{n} \lambda_{de,k}^e \cdot C_k$$
where $K_{OM,DE}$ denotes the operation and maintenance cost per unit of diesel engine, $\alpha$, $\beta$, $\gamma$ represent the fuel consumption coefficients, $\lambda_{de,k}^e$ is the emission volume of the $k$-th pollutant from diesel engine, and $C_k$ is the treatment price per unit of pollutant kind $k$.
For the energy storage battery, the state of charge (SOC) at scheduling time step $t$ is expressed as:
$$SOC(t) = \begin{cases} SOC(t-1) + P_{bess}(t)\eta^+ , & P_{bess}(t) > 0 \\ SOC(t-1) + P_{bess}(t)/\eta^- , & P_{bess}(t) \leq 0 \end{cases}$$
where $SOC(t)$ denotes battery state of charge at hour $t$, $P_{bess}(t)$ represents the charging or discharging power at hour t, and $\eta^+$, $\eta^-$ are the charging and discharging efficiencies, respectively.
Electric vehicle charging behavior is influenced by various factors including traffic habits, date types, temperature, and weather conditions. When performing Monte Carlo simulation for the EV charging load, the start time of charging follows a normal distribution model which expresses the probability density of charging start time at different hours:
$$f_{t}(t) = \begin{cases} \frac{1}{\sqrt{2\pi}\sigma_{t}}\exp\left[-\frac{(t-\mu_t)^2}{2\sigma_t^2}\right], & 0 \leq t < 12 \\ \frac{1}{\sqrt{2\pi}\sigma_t}\exp\left[-\frac{(t-24-\mu_t)^2}{2\sigma_t^2}\right], & 12 \leq t < 24 \end{cases}$$
where $\mu_t = 17.6$ represents the expected arrival time home and $\sigma_t = 3.41$ is the standard deviation. The daily driving mileage can be described by the logarithmic normal distribution shown as:
$$f_L(l) = \frac{1}{\sqrt{2\pi}\sigma_x l}\exp\left[-\frac{(\ln l – \mu_x)^2}{2\sigma_x^2}\right]$$
with $\mu_x = 3.2$ and $\sigma_x = 0.88$.
For different EV charging modes, I constructed both disorderly and orderly charging load models. If an electric vehicle owner chooses to participate in unified grid dispatch when orderly charging mode is implemented, their charging behavior could be classified as controllable state; otherwise it is uncontrollable. The total EV charging load at hour t is calculated as:
$$P_{EV}(t) = \sum_{i=1}^{N}[a(i,t) \cdot P_c + b(i,t) \cdot P_d]$$
where $a(i, t)$ and $b(i, t)$ are binary variables denoting whether vehicle i charges or discharges at hour t, and $N$ is total EV quantity. $P_c > 0$ denotes electric vehicle charging power, and $P_d < 0$ means discharging power.
In the orderly charging mode, the EVs are coordinated under the time-of-use pricing strategy and demand response signals to shift their charging periods away from the peak load intervals. The whole scheduling day is divided into peak, flat, and valley price periods. EV owners who respond to the grid’s dispatch signals are rewarded economically while the grid benefits from the valley-filling and peak-shaving effects.
3. NSGA2 Algorithm and Its Improvement
Multi-objective optimization problems require simultaneously optimizing several conflicting objective functions. The general mathematical formulation of multi-objective optimization is:
$$\min F(x) = [f_1(x), f_2(x), …, f_m(x)]^T$$
$$\text{s.t. } g_i(x) \leq 0, i = 1, 2, …, p$$
For two feasible solutions $x$ and $y$, solution $x$ Pareto dominates solution y (denoted as $x \prec y$) if and only if $f_i(x) \leq f_i(y)$ for all $i \in \{1,…,m\}$ and $f_j(x) < f_j(y)$ for at least one $j$. The Pareto optimal solution set contains all non-dominated solutions, and the corresponding objective vectors form the Pareto front in the objective space.
For the implementation of the NSGA2 algorithm, the process starts with initializing a parent population of size N. The algorithm applies fast non-dominated sorting to classify individuals, then calculates crowding distance to maintain diversity, and finally uses selection, crossover and mutation operators to generate offspring populations. An elitist strategy is applied by combining the parent and offspring populations, selecting the best N individuals via a non-dominated ranking mechanism. However, standard NSGA2 has some limitations: random initialization can lead to insufficient coverage of the decision space, which reduces the convergence accuracy, and the algorithm may easily fall into local optima when facing highly nonlinear complex problems such as microgrid scheduling.
To overcome these shortcomings, I introduced two important improvements into standard NSGA2 to produce an improved algorithm, denoted as IMNSGA2. The first improvement is the chaos initialization strategy. I used the Logistic map to generate the initial population, which ensures a more uniform coverage of the decision space and improves the population diversity:
$$x_{k+1} = \mu x_k(1 – x_k), \quad k = 0,1,2,…$$
where parameter $\mu$ is set to 3.7 in my research to ensure a fully chaotic sequence generating uniformly spread solutions within $[0, 1]$.
The second improvement introduces the genetic evolutionary elite selection strategy. In my IMNSGA2 algorithm, I implemented the following procedure:
Step 1: Obtain the non-dominated solution set $\mathcal{I}_1$ after the initial population is generated by the chaotic mapping.
Step 2: For each individual in set $\mathcal{I}_1$, calculate the best objective function value of every sub-objective, denoted by $Z_{best}^k$, and record the corresponding optimal solution vector as $g_{best}$.
Step 3: Calculate the difference index $\delta_i^k$ of every individual $g_i$ relative to $Z_{best}^k$ for all the sub-objectives:
$$\delta_i^k = \frac{|Z_i^k – Z_{best}^k|}{Z_{best}^k} \times 100\%$$
Step 4: Choose individual $g_{best}$ with the smallest value of $\delta_i^k$ as the current optimal solution, and generate the quasi-offspring individual:
$$g’_i = \alpha g_i + (1-\alpha)g_{best}$$
where the weighting coefficient $\alpha$ is set to 0.7.
Step 5: Compare the dominance relationship between $g_i$ and $g_i’$, and then retain the better individual for inheritance into the next generation.
Through these two improvements, the IMNSGA2 algorithm greatly improves the adaptability and optimization ability when facing complex engineering problems. To evaluate its performance, I selected the ZDT1, ZDT2, and IDTLZ2 standard benchmark functions. The IMNSGA2 algorithm parameters are set as population size of 187, maximum generation of 220, crossover probability 0.872, mutation probability 0.107, for both algorithms under test. The experimental results comparing NSGA2 and IMNSGA2 performance indexes are presented in table 1.
| Test function | Metric | GD | UNI | DIV | Time (s) |
|---|---|---|---|---|---|
| ZDT1 | NSGA2 | 0.00352 | 0.08347 | 0.74386 | 60.337 |
| IMNSGA2 | 0.00028 | 0.31872 | 0.15763 | 52.286 | |
| ZDT2 | NSGA2 | 0.00623 | 0.08864 | 0.79462 | 57.283 |
| IMNSGA2 | 0.00017 | 0.32968 | 0.17265 | 49.673 | |
| IDTLZ2 | NSGA2 | 0.00978 | 0.11811 | 0.70747 | 45.272 |
| IMNSGA2 | 0.00562 | 0.19522 | 0.46025 | 42.217 |
To quantitatively analyze the optimization performance, four evaluation metrics were calculated. The generation distance (GD) measures the average distance from the obtained Pareto front to the true Pareto front. The uniformity indicator (UNI) measures the deviation among the distances of successive solutions in the obtained non-dominated set. The diversity metric (DIV) describes the distribution width across the Pareto front. Lower GD and DIV values indicate better performance, while a higher UNI value indicates a more evenly distributed solution set.
From the results, my improved IMNSGA2 algorithm demonstrated superior convergence accuracy, solution distribution uniformity and diversity preservation across all three test functions compared with standard NSGA2. The GD values have decreased dramatically which proves my improved algorithm can approach the ideal Pareto front more closely. The UNI values of IMNSGA2 are all substantially higher than those of the original algorithm. Also, the computation time has been reduced, demonstrating the higher search efficiency of my improved algorithm in dealing with complex multi-objective optimization applications.
The multi-peak characteristics of those test functions simulate the volatility of distributed generation output in the microgrid scheduling problem. The excellent performance of IMNSGA2 in these tests proves that it has the capability to deal with the complex constraints introduced by the random fluctuation of photovoltaic and wind power.
4. Double-layer Optimal Scheduling Model for Microgrid with Electric Vehicle Charging
When electric vehicles integrate into the microgrid, the power grid and EV users have their own individual interests as the power supply and consumption sides. To satisfy the source-side and load-side demands simultaneously, I established a two-layer optimal scheduling model. In this architecture, the upper layer is the source-load collaborative model considering electric vehicle response. The lower layer is the microgrid layer whose objectives are focused on operating cost, environmental treatment cost, and the tie-line power fluctuation with the main grid. After the net load optimization result from the upper layer is transmitted to the lower layer, the two layers become closely related.
4.1 Upper Layer Optimization Model
In the upper layer, my objective functions include user comprehensive satisfaction and net load variance. The user satisfaction measures the subjective feeling of the electricity consumers for the power supply reliability and charging cost. Two sub-indicators were considered inside the satisfaction measurement. One is electricity comfort index which evaluates the comfort loss caused by EV charging time shifting. Its formula is:
$$C_{com} = \frac{\sum_{t=1}^{T}P_t}{\sum_{t=1}^{T}(P_t + \Delta P_t)}$$
The other one is the economic benefit index which evaluates how much money EV owners save from participating in the demand response at the electricity purchase side. Its formula is described as:
$$C_{eco} = \frac{\sum_{t=1}^{T}c(t)P(t)}{\sum_{t=1}^{T}[c(t)P(t) – c(t)P_a(t)]}$$
The overall user comprehensive satisfaction $f_1$ integrates these two indices:
$$f_1 = \theta_1 C_{com} + \theta_2 C_{eco}$$
where $\theta_1$ and $\theta_2$ are weight coefficients on comfort and economy objectives, both set at 0.5.
The second upper-layer objective function is to minimize the net load variance of the microgrid:
$$f_2 = \frac{1}{T}\sum_{t=1}^{T}(P_{net}(t) – P_{avr})^2$$
where $P_{net}(t)$ represents the net load at hour t after deducting the clean energy power from the total demand:
$$P_{net}(t) = P_{load}(t) + P_{ev}(t) – P_{wt}(t) – P_{pv}(t)$$
and $P_{avr} = \frac{1}{T}\sum_{t=1}^{T}P_{net}(t)$ is the average net load over the whole scheduling horizon of $T = 24$ hours.
The upper-layer model is subject to several constraints, such as electric vehicle battery SOC limitation, minimum comfort value, and minimum economic benefit value. The constraints are:
$$SOC_{ev}^{min} \leq S_{ev}(t) \leq SOC_{ev}^{max}$$
$$C_{com} \geq C_{com}^{min}$$
$$C_{eco} \geq C_{eco}^{min}$$
4.2 EV Charging Load Simulation and Demand Response Analysis
I set up a microgrid with 298 electric vehicles in a residential district of my country. Each EV has a battery capacity of 32 kWh and the charging mode is slow AC charging with rated power of 4.5 kW. The time-of-use electricity price scheme is listed in Table 2 below.
| Period Type | Time Window | Purchase Price (CNY/kWh) | Selling Price (CNY/kWh) |
|---|---|---|---|
| Peak | 10:00-15:00, 19:00-22:00 | 0.74 | 1.55 |
| Flat | 7:00-9:00, 16:00-18:00 | 0.42 | 0.60 |
| Valley | 23:00-24:00, 0:00-6:00 | 0.23 | 0.42 |
On weekdays, the EV charging behaviors were classified into three groups: 56 vehicles (19%) start charging after arriving at work in the morning with charging start time following normal distribution N(9, 0.5²); 186 vehicles (62%) charge at home after getting off work with charging start time following N(19, 1.5²); and 56 vehicles (19%) start charging randomly following uniform distribution U(0, 24). On rest days, the EV owners show greater mobility. In this scenario, 27 cars (9%) set out for traveling and start charging in early morning with starting time obeying U(0, 8); 95 vehicles (32%) charge during daytime with starting time obeying U(8, 18); 113 vehicles (38%) charge at night with starting time obeying U(18, 24); and the remaining 63 vehicles (21%) do not need to charge in this district microgrid. From these probability models, Monte Carlo simulation generates all EV charging loads.
According to the upper-layer model, the electric vehicle owners that charge orderly participate in the demand response signal and shift their charging loads from time windows of peak load (19:00-21:00) into the valley period (1:00-7:00) on working days. In the rest day scenario, smart charging schedules shift EV charging demand from the residential peak time (19:00-21:00) to the price valley periods (23:00-6:00). Table 3 lists the grid load conditions under different date types and scheduling modes.
| Date Type | Load Condition | Daily Max (kW) | Daily Min (kW) | Average (kW) | Peak-valley Diff. (kW) |
|---|---|---|---|---|---|
| Weekday | Original Load | 701.3 | 170.7 | 406.0 | 530.6 |
| Disorderly EV Charging | 1155.7 | 253.4 | 586.2 | 902.3 | |
| Orderly EV Charging | 786.5 | 457.2 | 575.6 | 329.3 | |
| Rest Day | Original Load | 701.3 | 170.7 | 406.0 | 530.6 |
| Disorderly EV Charging | 898.5 | 217.7 | 505.4 | 680.8 | |
| Orderly EV Charging | 792.5 | 330.3 | 502.1 | 462.2 |
From the load data, we can clearly discover that although the peak-valley difference of the electric vehicle charging load reaches a high value, the orderly charging mode greatly reduces the total load peak-valley gap, comparing with the disorderly charging scenario. The demand response has played a significant role in the valley filling. For weekdays the peak-valley difference is decreased by 573 kW, and for rest days it is reduced by 218.6 kW. This improvement is particularly beneficial to the microgrid operation stability. By flattening the load curve and reducing the peak-valley difference, the frequent ramping of power sources can be effectively alleviated.
After subtracting the wind and PV power output from the total demand curve, the net load curves are obtained. The objective function values of the upper-layer model before and after demand response on both date types are listed as follows in Table 4.
| Date Type | Demand Response | Charging Cost (CNY) | Economic Index | Comfort Index | Comprehensive Satisfaction | Net Load Variance (kW²) |
|---|---|---|---|---|---|---|
| Weekday | Before | 2191.75 | 1.0000 | 1.0000 | 1.0000 | 102029 |
| After | 1534.70 | 1.2987 | 0.8131 | 1.0559 | 20454 | |
| Rest Day | Before | 1264.08 | 1.0000 | 1.0000 | 1.0000 | 54131 |
| After | 850.29 | 1.3262 | 0.8723 | 1.0993 | 29758 |
On weekdays, after electric vehicles respond to the demand signal, the charging cost drops from 2191.75 to 1534.7 CNY, achieving a reduction ratio of 29.98%. Although the charging behavior change causes a decrease of the comfort level by 18.69%, the integrated satisfaction of every vehicle user rises from 1 to 1.0559 (5.59% improvement). In the meantime, the net load variance of the microgrid has dropped by 79.96%, dramatically improving the renewable energy consumption capacity and reducing the grid power fluctuation range. On rest days, the charging cost reduced by 32.73%, the integrated satisfaction increases to 1.0993, and the net load variance dropped by 45.03%, indicating consistent performance improvement of the proposed strategy across multiple types of days.
4.3 Lower Layer Microgrid Optimization Model
In the lower-layer model, I built three objective functions. The first objective is to minimize the microgrid operation and maintenance expense together with fuel and power transaction costs:
$$f_1^{lower} = \min \sum_{t=1}^{24}\left[C_{wt}(t)+C_{pv}(t)+C_{de}(t)+C_{es}(t)+C_{grid}(t)\right]$$
The operation and maintenance costs are calculated as linear functions of generating powers as follows:
$$C_{wt}(t) = \lambda_{wt}P_{wt}(t)$$
$$C_{pv}(t) = \lambda_{pv}P_{pv}(t)$$
$$C_{de}(t) = \lambda_{de}P_{de}(t) + k_{de}$$
$$C_{es}(t) = \sum_{t=1}^{T}c_{es,price}|P_{es}(t)|\Delta t$$
$$C_{grid}(t) = C_{buy}P_{buy}(t) – C_{sell}P_{sell}(t)$$
where $\lambda_{wt}$, $\lambda_{pv}$, $\lambda_{de}$ are the operation cost coefficients for wind, PV, and diesel generator, $k_{de}$ denotes diesel fuel consumption expense; $c_{es,price}$ is energy storage operation unit cost; $C_{buy}$ and $P_{buy}$ denote the price and quantity when purchasing electricity from the main grid, and $C_{sell}$ and $P_{sell}$ represent unit price and amount when selling electricity to the main grid.
The second lower-layer objective targets at minimizing the environmental pollution treatment cost resulting from the diesel engine and the purchased electricity from main grid. I considered three types of pollutants, i.e., SO2, NOx, and COx. Its mathematical form is:
$$f_2^{lower} = \min \sum_{t=1}^{T}\sum_{j=1}^{J}C_j\left[\sigma_{de,j}P_{de}(t) + \sigma_{grid,j}P_{buy}(t)\right]$$
where $C_j$ is the unit treatment cost of pollutant $j$; $\sigma_{de,j}$ and $\sigma_{grid,j}$ are the emission intensity of pollutant j from diesel generators and the main grid respectively.
The third lower-layer objective is to smooth the power exchanged through the tie-line between the microgrid and the upper main grid to guarantee reliability:
$$f_3^{lower} = \min \sum_{t=1}^{T-1}(P_{grid}(t+1) – P_{grid}(t))^2$$
The lower-layer model is subject to the following constraints: the power balance constraint:
$$P_{net}(t) = P_{de}(t) + P_{se}(t) + P_{grid}(t)$$
the diesel generator output constraints and ramp rate constraints, the energy storage system output constraints and state of charge constraints, as well as the tie-line capacity limit between the microgrid and the main grid. These are summarized below:
$$P_{de}^{min} \leq P_{de}(t) \leq P_{de}^{max}, \quad P_{de}^{down} \leq P_{de}(t)-P_{de}(t-1) \leq P_{de}^{up}$$
$$P_{se}^{min} \leq P_{se}(t) \leq P_{se}^{max}, \quad SOC_{se}^{min} \leq SOC_{se}(t) \leq SOC_{se}^{max}$$
$$P_{grid}^{min} \leq P_{grid}(t) \leq P_{grid}^{max}$$
In the actual scheduling operation, the microgrid adopts a strategy where the renewable output is consumed preferentially and the storage is used for valley filling. In my implementation, I follow the optimal scheduling strategy designed as:
The priority sequence for the demand response of electric vehicles is designed in my model as follows. When renewable power output from wind and PV is greater than the total load demand, the surplus power first charges the battery energy storage system; if the storage equipment has been fully charged, the excess energy is sold to the main grid. When the renewable generation is insufficient for the load, the storage battery discharges to supply the demand gap. If the combined generation from renewables and battery still cannot meet the required load, then we compare the diesel engine generation cost to the purchase price from the main grid, and choose the cheaper way to meet the power balance. This strategy can fully utilize the advantage of various flexible resources in a microgrid and further optimize the tie-line power and load curves.
| Pollutant Type | SO2 | NOx | COx |
|---|---|---|---|
| Emission factor of diesel engine (kg/kWh) | 0.00017 | 0.0112 | 0.543 |
| Emission factor of main grid (kg/kWh) | 0.00213 | 0.0017 | 0.877 |
| Treatment cost (CNY/kg) | 14.802 | 62.842 | 0.223 |
4.4 Simulation Results and Analysis
For the optimization of the lower-level model, the fundamental parameters are set as follows. The maximum output of diesel generator is 217 kW, its minimum output is 0, maximum ramp rate is 217 kW/h, and the operation coefficient and fuel cost are set to 0.0837 yuan/kW and 0.404 yuan/kWh. The energy storage battery has a maximum charge/discharge power of 218 kW, charging and discharging efficiencies of 0.903, and the bounds of SOC are 0.18 and 0.93. For the IMNSGA2 algorithm parameters chosen in this layer, the population size is 220, crossover probability 0.863, mutation probability 0.108, maximum evolution generation 478. The environmental emission coefficients and unit governance cost are specified in Table 5 above.
I implemented my double-layer scheduling model by using MATLAB R2018b on a computer equipped with a Ryzen 7 9700X CPU and 48 GB memory, running the Windows 10 operating system. The evolutionary algorithm was executed based on the real-coded chromosome representation of diesel output vector, battery power vector, and the exchange power with the main grid over the 24-hour dispatch horizon.
The microgrid source-storage-load coordination scheduling results under the weekday scenario before and after demand response are presented in Tables 6 and 7 respectively, comparing the objective values in both cases.
| Weekday Scenario | Operation Cost (CNY) | Pollution Treatment Cost (CNY) | Tie-line Power Variance (kW²) |
|---|---|---|---|
| Before Demand Response | 3634.19 | 3368.61 | 30720.74 |
| After Demand Response | 2902.31 | 2677.60 | 16443.26 |
| Reduction Ratio | 20.14% | 20.51% | 46.48% |
On weekdays, after the demand response shifts the electric vehicle charging load of the working day, the operation cost of the diesel generator drops by 20.14%, while the pollution treatment cost reduces by 20.51%. The improvement effect on the tie-line power fluctuation variance reaches 46.48%, showing a strong peak-shaving and valley-filling effect produced by advancing the electric vehicle orderly charging. The peak interconnected power decreases from 692.3 kW to 399.7 kW while the average transmission power is reduced by 60.67%.
Similarly, the results under the rest day scenario before and after the demand response are listed in Table 7.
| Rest Day Scenario | Operation Cost (CNY) | Pollution Treatment Cost (CNY) | Tie-line Power Variance (kW²) |
|---|---|---|---|
| Before Demand Response | 2737.02 | 2282.24 | 20985.87 |
| After Demand Response | 2443.80 | 1994.01 | 12934.24 |
| Reduction Ratio | 10.71% | 12.63% | 38.37% |
On the rest day, the cost reductions in operation, environmental treatment and tie-line power fluctuations are achieved by about 10.71%, 12.63%, and 38.37% after the implementation of the demand response mechanism, where the electric vehicle users are encouraged to move part of their daily high-price peak charging to low-price valley hours. The demand responsive charging strategy enables load flattening, reducing the burden of the generation units, and thus cuts both the operation cost and emissions produced by the diesel engine and main grid electricity generation.
To further verify the superiority of the improved IMNSGA2 algorithm in solving the complex microgrid scheduling problem, the Pareto fronts obtained by NSGA2 and IMNSGA2 are compared. The experiment shows that the final Pareto solution set obtained by IMNSGA2 dominates that produced by the standard NSGA2 over each scenario. The improved algorithm converges closer to the real Pareto optimal front, thus offering better decision-making alternatives for the microgrid operators.
Additionally, I compared the convergence curves of NSGA2 and IMNSGA2 on the weekday microgrid operation cost minimization. At the initial phase of generations 0-20, the IMNSGA2 begins with a lower initial cost due to the chaos initialization method, which finds well-distributed starting points covering low-cost and feasible regions of the search space. During the middle evolution stage from generation 20 to 100, IMNSGA2 maintains a greater descending slope due to the elite screening strategy that preserves the best operation patterns. After reaching generation 100, IMNSGA2 converges to the stable cost value of 2902.31 CNY, while standard NSGA2 still traps in a local optimum at about 150-th generation with a higher cost. These data strongly confirm the applicability of my improved algorithm on solving engineering problems with high non-linearity and strong coupling constraints.
The convergence performance observed in the microgrid scheduling model verifies that the double-layer architecture and algorithm improvement made in my research are both reasonable and effective. The IMNSGA2 algorithm exhibits stronger global search capability and higher accuracy convergence stability for the engineering practice than the standard NSGA2, since the improved initialization and evolutionary mechanisms are beneficial to prevent prematurity and overcome the weakness of getting stuck at local optima.
5. Conclusion and Future Works
In this research, I developed a double-layer optimal scheduling model for a microgrid with large-scale electric vehicle charging demand, and solved it by applying the improved NSGA2 algorithm. The principal conclusions obtained from my research are:
First, I constructed output models for photovoltaic panels, wind turbines, diesel generators and storage batteries based on the full investigation of the working principles and structural characteristics of a microgrid. For electric vehicles, I thoroughly examined random charging and orderly charging behaviors. By using the Monte Carlo method based on probability distributions of home arrival time and daily mileage, the EV charging load profiles under different date types and different charging modes are obtained for further study. This methodology can provide scientific foundations for making the optimal scheduling strategies.
Second, I deeply analyzed the theoretical principles and implementation details of the NSGA2 multi-objective evolutionary algorithm. To solve the issues like low convergence precision and easy fall into local optima in facing complex optimization applications, I brought in the chaos initialization strategy and the improved genetic evolutionary selection strategy. According to the calculation on several standard benchmark functions, the proposed IMNSGA2 algorithm has demonstrated superior performance in approximation, uniformity, and comprehensiveness relative to standard NSGA2. Consequently, this improved algorithm was selected as the solving means for the double-layer optimal scheduling of a microgrid with electric vehicle fleets.
Third, a comprehensive study was conducted on a resident community microgrid under working days and rest days respectively. The main conclusions drawn from the simulation results could be summarized. The peak-valley difference of power grid load has been effectively reduced by promoting the orderly charging mode of electric vehicles on both weekday and rest day. By transferring a proportion of the peak-time charging loads to the low-price valley periods with the demand response mechanism, the total load curve becomes much flatter, while the costumers’ integrated satisfaction has been increased from 1 to 1.0559 and 1.0993 on weekday and rest day, respectively, and at the same time the net load variance of the upper layer microgrid has been greatly decreased. Furthermore, the operation costs of the lower microgrid layer are considerably decreased by the coordinated source-grid-storage-load dispatch, along with the decreasing pollution treatment costs and the smoother tie-line power between microgrid and main grid. The optimized lower-level objective performance demonstrates better engineering values under IMNSGA2 than using the standard NSGA2, which successfully supports the main conclusions of this paper.
In summary, my research comprehensively analyzes every part of the microgrid system and has proposed an improved approach to optimize the interaction between electric vehicles and distributed generations, which offers a cost-effective and clean scheduling strategy to handle the severe challenge of increasing uptake of electric vehicles connected to the distribution grid.
In the future, there are some potentially interesting research areas to continue based on my work. For instance, the presented optimized model can be extended and verified on other regional microgrids with various distributed generation capacities and distinct electric vehicle charging demands. As more distributed generations of different types become mature and widely used in microgrids, my method will be updated to include those new power sources if needed. Moreover, further investigation that takes the uncertainty of electricity price signals and the electric vehicle users’ behavior decisions into account could help enhance more robust performance of the proposed scheduling architecture under severe stochastic situations.