As a researcher focusing on control engineering and the planning and operation of microgrids, I have devoted this study to addressing the pressing challenges of integrating electric vehicles (EVs) into multi-microgrid systems. The rapid growth of renewable energy and the global push toward low-carbon power systems require new modeling, pricing, and optimization tools. In this thesis, I present a systematic framework for microgrid operation that explicitly considers the stochastic mobility and charging behavior of electric vehicles, proposes a load-interval pricing strategy, and develops an improved wolf pack algorithm (IWPA) for economic dispatch. Throughout this article, I will emphasize how electric vehicles can be treated as dynamic energy assets rather than static loads, and how intelligent scheduling can improve both economic efficiency and system resilience.
The structure of this article is as follows. First, I introduce the background and related studies on microgrids, microgrid clusters, and vehicle-to-grid (V2G) technology. Second, I detail the mathematical models for wind, photovoltaic, hydro, battery, and diesel generation. Third, I describe the Monte Carlo simulation method for generating electric vehicle driving and charging behaviors, and I explain two pricing mechanisms: the traditional time-of-use (TOU) tariff and the proposed load-interval price strategy. Fourth, I elaborate on the development of the improved wolf pack algorithm, including spiral search, chaotic initialization with experience memory, and dynamic update inertia. Fifth, I present comparative results from benchmark functions and from microgrid cost optimization experiments. Finally, I analyze the coordinated operation of multiple microgrids with electric vehicles under both islanding and interconnected modes, including resilience tests with renewable fluctuations and diesel generator outages. The conclusions and future research directions are discussed at the end.
1. Background and Motivation
The tension between increasing global energy demand and the finite availability of fossil fuels has accelerated the transition toward decentralized power systems. Microgrids (MGs) represent an effective architecture for integrating distributed renewable generation, energy storage, and controllable loads. However, isolated MGs often struggle with reliability issues when renewable energy output is insufficient, particularly during adverse weather or equipment failures. To mitigate these challenges, multiple microgrids can be interconnected to form a microgrid cluster, allowing energy sharing and coordinated dispatch.
Electric vehicles add a new degree of flexibility because their onboard batteries may act as mobile storage units. When properly controlled, an electric vehicle can either draw power from the grid or inject power back into the grid through vehicle-to-grid (V2G) technology. I believe that electric vehicles can serve as spatial and temporal energy transfer resources, helping to flatten load profiles and increase renewable energy accommodation. Nevertheless, the random driving patterns of electric vehicle users and the limitations of conventional static pricing mechanisms often lead to adverse effects, such as new peak loads during low-price periods or insufficient coordination among different distributed generators.
The main goals of my research can be summarized as follows:
- To construct a realistic model of multi-microgrid systems containing wind turbines, photovoltaic panels, small hydro units, diesel generators, battery storage, and electric vehicles.
- To propose a load-interval price strategy that adjusts the electricity price based on the current load level rather than only on fixed clock intervals.
- To develop an improved wolf pack algorithm with stronger exploration capability and faster convergence, suitable for high-dimensional nonlinear economic dispatch problems.
- To analyze the resilience of a microgrid with electric vehicles under renewable energy fluctuations and generator failure scenarios.
- To compare isolated versus interconnected multi-microgrid operation and to quantify the benefits of sharing energy via electric vehicles.
2. System Architecture and Mathematical Models
2.1 Multi-Microgrid Configuration
The multi-microgrid system I studied consists of three geographically distributed microgrids. Microgrid 1 contains wind turbines (WT), photovoltaic panels (PV), a small hydro plant (HEP), a diesel engine (DE), battery storage (BAT), and a certain number of electric vehicles. Microgrid 2 includes WT, PV, DE, BAT, and electric vehicles. Microgrid 3 is primarily designed as a renewable-rich energy hub that can export electricity to the other two microgrids. All microgrids are connected to the main grid through a point of common coupling, which allows bidirectional power exchange. Figure 1 below illustrates a typical architecture of the system that I adopted; the figure is placed here to clarify the topological relationship between the distributed generators, storage units, electric vehicles, and the main grid.
2.2 Wind Power Model
The power output of a wind turbine is determined by the wind speed $v$. I utilized the standard piecewise function:
$$P_{WT}(v) = \begin{cases} 0, & v < v_{ci} \\ k_1 v^3 – k_2 v, & v_{ci} \le v < v_r \\ P_r, & v_r \le v \le v_{co} \\ 0, & v > v_{co} \end{cases} \tag{1}$$
where $v_{ci}$ is the cut-in speed, $v_r$ is the rated speed, $v_{co}$ is the cut-out speed, $P_r$ is the rated power, and $k_1$, $k_2$ are coefficients that approximate the power curve.
2.3 Photovoltaic Model
The output power of a photovoltaic array depends primarily on irradiance and cell temperature. I used the following simplified equation:
$$P_{PV}(t) = P_{STC} \frac{G(t)}{G_{STC}} \left[ 1 + \alpha_T \left( T_c(t) – T_{STC} \right) \right] \tag{2}$$
where $P_{STC}$ is the rated power under standard test conditions, $G(t)$ is the solar irradiance, $G_{STC}$ is the standard irradiance of 1000 W/m², $\alpha_T$ is the temperature coefficient (typically -0.0047 K$^{-1}$), $T_c(t)$ is the cell temperature, and $T_{STC}$ is the standard temperature of 25 °C.
2.4 Battery Storage Model
The battery energy content is modeled using discrete-time dynamics:
$$E_{BAT}(t) = \begin{cases} E_{BAT}(t-1) + \eta_{ch} P_{BAT}(t) \Delta t, & P_{BAT}(t) \ge 0 \\ E_{BAT}(t-1) + \frac{P_{BAT}(t)}{\eta_{dis}} \Delta t, & P_{BAT}(t) < 0 \end{cases} \tag{3}$$
where $P_{BAT}(t)>0$ means charging, $P_{BAT}(t)<0$ means discharging, $\eta_{ch}$ and $\eta_{dis}$ are charging and discharging efficiencies, and $\Delta t$ is the time step (usually one hour).
2.5 Hydro and Diesel Generator Models
For a small hydro unit, the output power is proportional to the water flow rate and head:
$$P_{HEP}(t) = \rho g \eta_{hydro} H(t) Q(t) = A H(t) Q(t) \tag{4}$$
where $\rho$ is the water density, $g$ is gravitational acceleration, $\eta_{hydro}$ is the efficiency, $H(t)$ is the effective head, $Q(t)$ is the water flow, and $A$ is a constant. In my models, small-scale hydro serves as a baseload power source with high predictability.
The diesel generator fuel cost function is approximated by a quadratic expression:
$$C_{DE}(P_{DE}) = k_1 + k_2 P_{DE} + k_3 P_{DE}^2 \tag{5}$$
where $k_1,k_2,k_3$ are fuel cost coefficients. Increasing diesel generator output causes significant emissions and fuel cost; therefore, an optimizer should minimize its usage unless necessary.
2.6 Electric Vehicle Modeling and Monte Carlo Simulation
Electric vehicle charging behavior is affected by the user’s daily travel distance and by the time when the vehicle arrives home after the last trip. The arrival time probability distribution can be expressed as
$$f_t(x) = \begin{cases} \frac{1}{\sigma_t \sqrt{2\pi}} \exp\left[-\frac{(x-\mu_t)^2}{2\sigma_t^2}\right], & \mu_t – 12 \le x < 24 \\ \frac{1}{\sigma_t \sqrt{2\pi}} \exp\left[-\frac{(x+24-\mu_t)^2}{2\sigma_t^2}\right], & 0 \le x < \mu_t – 12 \end{cases} \tag{6}$$
with $\mu_t = 17.5$ and $\sigma_t = 3.5$. The daily travel distance follows a lognormal distribution:
$$f_s(s) = \frac{1}{s \sigma_s \sqrt{2\pi}} \exp\left[-\frac{(\ln s – \mu_s)^2}{2\sigma_s^2}\right] \tag{7}$$
where $\mu_s = 3.16$ and $\sigma_s = 0.92$. I used the Monte Carlo method to generate random daily distances and arrival times for 20 electric vehicles in each microgrid. The state of charge (SOC) at arrival is given by
$$SOC_{EV} = \left(1 – \frac{s}{D}\right) \times 100\% \tag{8}$$
where $D$ is the vehicle’s rated driving range. The time required to fully charge is then
$$T_{ch} = \frac{W_h s}{100 \eta P_{EV}} \tag{9}$$
where $W_h$ is the energy consumption per 100 km, $P_{EV}$ is the rated charging power, and $\eta$ is the charging efficiency (assumed to be 0.9). To protect battery life, I restricted the SOC to stay between 10% and 90%.
Within a microgrid, I treat the fleet of electric vehicles as an aggregated storage resource. Let $P_{EV}(t)$ be the total power exchanged between the microgrid and the electric vehicle fleet. Positive values indicate that the microgrid charges the vehicles, while negative values indicate that electric vehicles discharge to the microgrid. The constraints are:
$$P_{EV,min} \le P_{EV}(t) \le P_{EV,max} \tag{10}$$
where $P_{EV,min}$ is the maximum discharging power (negative by convention) and $P_{EV,max}$ is the maximum charging power.
3. Pricing Strategies for Electric Vehicle Participation
3.1 Time-of-Use Pricing
Traditional time-of-use pricing divides a day into several fixed periods: valley, shoulder, and peak. In my simulations, the TOU prices are given in the following table:
| Time (h) | Price (CNY/kWh) |
|---|---|
| 0:00–7:00 | 0.300 |
| 8:00 | 0.712 |
| 9:00–11:00 | 1.120 |
| 12:00 | 1.210 |
| 13:00 | 1.120 |
| 14:00 | 1.210 |
| 15:00–18:00 | 0.712 |
| 19:00 | 1.120 |
| 20:00–21:00 | 1.210 |
| 22:00–23:00 | 1.120 |
Although TOU pricing is simple to implement and can be effective under typical daily patterns, it lacks the ability to respond to real-time load deviations. In my experiments, I observed that a large number of electric vehicles often begin charging immediately at 23:00, creating a secondary load peak. Similarly, many vehicle owners discharge at the same high-price hours, causing a sudden surplus of power that may not be aligned with local renewable generation.
3.2 Load-Interval Pricing
To address these shortcomings, I designed a load-interval pricing strategy. In this approach, the microgrid controller first measures the current total load $L(t)$. Then it selects a price based on the load interval to which $L(t)$ belongs. The following table lists the mapping between load intervals and electricity prices used in the case studies:
| Load interval (kW) | Price (CNY/kWh) |
|---|---|
| 0–80 | 0.300 |
| 80–100 | 0.712 |
| 100–120 | 1.120 |
| >120 | 1.210 |
The controller broadcast the current price to electric vehicle owners. The owners can respond by updating their charging or discharging plans. To prevent a thundering herd effect, each electric vehicle must submit a reservation for the amount of power it intends to buy or sell at that price level. The controller sorts these reservations according to their submission time and gives priority to earlier entries. This feedback mechanism smooths abrupt changes in the charging demand, thereby alleviating the formation of new load spikes.
I found that the load-interval pricing strategy is similar to a real-time pricing scheme but requires much less data processing because the price is not a continuous function of load; instead, it is a step function of the load interval. This makes the communication overhead lower and the method easier to integrate into conventional energy management systems.
4. Economic Dispatch Objective and Constraints
The total operating cost of a microgrid over a 24-hour horizon can be written as:
$$C_{total} = C_{EV} + C_{grid} + C_{env} + C_{fuel} + C_{OM} \tag{11}$$
where
- $C_{EV}$ is the net payment to electric vehicle owners, equal to the difference between the cost of electricity bought by vehicles and the benefit of electricity sold by vehicles. In many cases, this term is negative (the microgrid earns from selling energy to electric vehicle users).
- $C_{grid}$ is the net cost of power exchange with the main grid, defined as
$$C_{grid} = \sum_{t=1}^{24} P_{grid}(t) \cdot \pi_{grid}(t) \tag{12}$$
with $P_{grid}(t)>0$ representing import and $P_{grid}(t)<0$ representing export.
- $C_{env}$ is the environmental cost of emissions, primarily from diesel generators:
$$C_{env} = \sum_{t=1}^{24} \sum_{m} E_{m}(t) \cdot \gamma_m \tag{13}$$
where $E_m(t)$ is the emission amount of pollutant $m$ (CO2, SO2, NOx) and $\gamma_m$ is the corresponding treatment cost.
- $C_{fuel}$ is the fuel cost of diesel generators as described in Eq. (5).
- $C_{OM}$ is the operation and maintenance cost of all distributed energy resources and batteries.
The key system constraints are:
1. Power balance:
$$L(t) = P_{grid}(t) + P_{RES}(t) + P_{DE}(t) + P_{BAT}(t) + P_{EV}(t) \tag{14}$$
where $P_{RES}(t)$ is the total output from renewable sources (WT, PV, HEP). Positive values represent generation, while negative values for $P_{BAT}(t)$ and $P_{EV}(t)$ indicate charging. In some experiments, I also included power exchange between microgrids.
2. Generation limits: For every source $i$:
$$P_{i,min} \le P_i(t) \le P_{i,max} \tag{15}$$
3. Ramp limits: For diesel generators, the ramp constraint between consecutive hours is enforced as
$$|P_{DE}(t) – P_{DE}(t-1)| \le R_{DE} \tag{16}$$
with $R_{DE}$ being the maximum ramp rate.
4. Battery dynamics and SOC limits:
$$SOC_{BAT,min} \le SOC_{BAT}(t) \le SOC_{BAT,max} \tag{17}$$
$$P_{BAT,min} \le P_{BAT}(t) \le P_{BAT,max} \tag{18}$$
5. Electric vehicle fleet limits: As mentioned in Eq. (10). Additionally, the daily total energy exchanged with electric vehicles must be constrained to ensure that the aggregate SOC at the end of the day is not below the desired level, so that vehicle owners can still drive on the next day.
6. Main grid power exchange limit:
$$-P_{grid,max}^{export} \le P_{grid}(t) \le P_{grid,max}^{import} \tag{19}$$
5. The Improved Wolf Pack Algorithm
5.1 Original Wolf Pack Algorithm
The wolf pack algorithm simulates the predation behavior of gray wolves. In the standard version, there are three roles: the leading wolf (the individual with the best fitness), the scouting wolves, and the fierce wolves. Scouting wolves search the surrounding space; fierce wolves rush toward the leading wolf; if a scout or fierce wolf finds a better position, it becomes the new leader. At the end of each iteration, the worst wolves are eliminated and replaced by randomly generated new individuals.
In the original WPA, scout wolves update their positions according to
$$x_{i,d}^{k+1} = x_{i,d}^k + \sin(2\pi \phi) \cdot step_a \cdot H \tag{20}$$
where $H$ is a direction vector. Fierce wolves rush using
$$x_{i,d}^{k+1} = x_{i,d}^k + \frac{x_{lead,d}^k – x_{i,d}^k}{|x_{lead,d}^k – x_{i,d}^k|} \cdot step_b \tag{21}$$
Finally, wolves that are within the siege range attack the prey using
$$x_{i,d}^{k+1} = x_{i,d}^k + \lambda \cdot step_c \cdot |x_{lead,d}^k – x_{i,d}^k| \tag{22}$$
where $\lambda$ is a random number in $(-1,1)$.
5.2 Spiral Search Mechanism
The standard WPA often struggles with high-dimensional multimodal problems. To improve global exploration, I replaced the simple directional update of scout wolves with a spiral search. The inspiration comes from the spiral dynamics of whales and moths. Let the current individual be indicated by vector $X_i = [x_{i,1}, x_{i,2}, \ldots, x_{i,D}]$. I define an auxiliary two-dimensional coordinate system by projecting the current position with respect to the mean position of the pack. Then, the spiral update rule is given by
$$X_i^{new} = X_{avg} + R_1(\theta) \cdot (X_{best} – X_{avg}) + R_2(\theta) \cdot (X_{i} – X_{i+1}) \tag{23}$$
where $X_{avg}$ is the population average position, $X_{best}$ is the current leading wolf position, $X_{i+1}$ is a randomly selected neighbor, and $R_1$, $R_2$ are rotation matrices that depend on the polar angle $\theta$. In particular, the two-dimensional rotation is generated from the equations
$$u = \rho \cos(\theta), \quad v = \rho \sin(\theta), \quad \rho = a e^{b \theta} \tag{24}$$
with $a \in [0.5, 2]$ and $b \in [0.1, 0.5]$, and I decrement $\theta$ with iterations. This design permits each wolf to explore larger spiraling neighborhoods while gradually converging toward the leader.
5.3 Chaos and Experience-Based Initialization
One problem in the standard wolf pack algorithm is that new wolves are inserted randomly after each generation. This approach is too blind because it discards information from previous iterations. Therefore, I hybridized chaotic initialization with an experience term. The replacement formula for a new wolf is
$$X_{new} = \lambda_1 \cdot C(\mu) \cdot X_{rand} \cdot (1 – X_{rand}) + \lambda_2 \cdot (X_{best}^{(t-1)} – X_{avg}) \tag{25}$$
where $C(\mu)$ applies the logistic map parameter $\mu \in [3.57,4]$, $X_{rand}$ is a random vector with values in $(0,1)$, $X_{best}^{(t-1)}$ is the leading wolf position from the previous iteration, and $\lambda_1,\lambda_2$ are weights. I selected $\lambda_2 = 0.38$ based on preliminary experiments. The chaotic map provides diverse initial positions, while the experience term guides the new solutions toward promising regions found earlier.
5.4 Dynamic Update Ratio
In the original wolf pack algorithm, the number of eliminated wolves $R$ is constant or randomly selected from a fixed range:
$$R = \left[ \frac{n}{2\beta}, \frac{n}{\beta} \right] \tag{26}$$
where $\beta$ is a scaling factor and $n$ is the population size. To improve convergence, I used a decreasing inertia weight. The number of updated wolves at iteration $t$ is
$$R(t) = \left\lfloor R_{min} + (R_{max} – R_{min}) \cdot \left(1 – \frac{t}{T}\right)^2 \right\rfloor \tag{27}$$
where $T$ is the maximum iteration count. At the beginning, a larger proportion of individuals are replaced to maintain diversity; as iterations proceed, fewer wolves are removed so that the algorithm can focus on refining the local neighborhood.
5.5 Implementation Steps of IWPA
The pseudocode of the IWPA is summarized in the following table:
| Step | Action |
|---|---|
| 1 | Set population size, maximum iterations, step factors, max scout attempts, weights, etc. |
| 2 | Initialize the population using chaotic + experience-based initialization. Compute all fitness values and determine the leading wolf, scouting wolves, and fierce wolves. |
| 3 | While $t < T$: • Scouting wolves update positions by the spiral search formula (Eq. 23). • Fierce wolves rush toward the leader using Eq. (21). • If any wolf finds a better fitness, replace the leader. • When a fierce wolf enters the siege range, update its position with Eq. (22). • Correct any variables that violate boundary limits. • Update the leader if a better solution appears. • Replace $R(t)$ worst wolves using Eq. (25). |
| 4 | If the stopping criterion is met (maximum iterations or tolerance), output the leader position and its fitness. |
6. Benchmark Function Experiments
To validate the IWPA, I used ten benchmark functions from the CEC standard suite. Their dimensions, types, and theoretical minima are listed in the following table:
| Function | Dimension | Type | Theoretical min |
|---|---|---|---|
| F3 | 30 | Unimodal | 0 |
| F4 | 30 | Unimodal | 0 |
| F5 | 30 | Unimodal | 0 |
| F6 | 30 | Unimodal | 0 |
| F7 | 30 | Multimodal | 0 |
| F16 | 30 | Multimodal | 0 |
| F20 | 4 | Multimodal | 0 |
| F23 | 2 | Multimodal | 0 |
| F25 | 4 | Multimodal | 0 |
| F28 | 2 | Multimodal | 0 |
6.1 Effectiveness of Each Improvement
I compared the standard WPA with three variants: (a) only spiral search (LWPA); (b) only chaos-experience initialization (HWPA); (c) the complete IWPA. Each algorithm was run 10 times with population size 20 and maximum iterations 500. The statistical results, including best, worst, mean, and standard deviation, indicated that the spiral search improves the convergence speed, while the chaotic experience initialization dramatically increases accuracy. The IWPA achieved the best or second-best results in most functions. For example, on the unimodal function F3, the mean result of WPA was about 46.36, while the IWPA mean was as low as $9.70 \times 10^{-5}$. On the multimodal function F7, the mean of WPA was $5.38 \times 10^{-3}$, but the IWPA mean was $9.91 \times 10^{-5}$, which is two orders of magnitude better. The improvement ratio on F16 was even more significant, moving from $0.30$ to $1.65 \times 10^{-5}$.
These results confirm that all three improvement strategies work synergistically. The chaotic initialization increases diversity, the spiral search strengthens global exploration, and the dynamic update rule prevents premature convergence.
6.2 Comparison with Classical Metaheuristics
I selected particle swarm optimization (PSO) and whale optimization algorithm (WOA) as classical benchmarks. In many functions, IWPA outperformed both PSO and WOA by several orders of magnitude. For instance, on function F4, PSO had an average of 1.00, WOA had an average of $1.74 \times 10^{-4}$, and IWPA reached $4.39 \times 10^{-5}$. In F6, PSO and WOA yielded averages of 57.23 and $5.99 \times 10^{-3}$, while IWPA reached $6.28 \times 10^{-6}$. In F7, IWPA outperformed all other methods. In low-dimensional multimodal functions such as F20 and F23, all algorithms performed reasonably, but IWPA still produced highly consistent results with standard deviations close to zero. Statistical analysis of the convergence curves showed that IWPA converges faster than both WPA and the classical algorithms in most high-dimensional cases.
6.3 Comparison with Recent Metaheuristics
I also compared IWPA with four recently proposed optimizers: HPSOBOA (hybrid particle swarm and butterfly optimization with chaos), NPWOA (whale algorithm with nonlinear convergence and local perturbation), LHHO (leader Harris hawks optimization), and ISMTSA (information-sharing memory tunicate swarm algorithm). Table 3.6 in the main thesis reports the detailed numerical data. From those results, I observed that on the unimodal functions F3 and F4, some recent methods had very high precision in terms of mean values. However, IWPA was the only algorithm that was able to hit the true optimum (0.00) in some of the ten independent runs, even though its mean values were often less impressive due to occasional outliers. On the multimodal function F7, IWPA achieved a mean of $8.37 \times 10^{-5}$, which is at least one order of magnitude better than HPSOBOA, LHHO, and ISMTSA. In F23, only IWPA and two other recent algorithms consistently reached the global optimum. These findings suggest that IWPA provides a good balance between exploration and exploitation, making it suitable for complex real-world optimization tasks such as microgrid scheduling.
7. Economic Optimization for a Microgrid: Simulation Setup and Results
7.1 Simulation Parameters
The simulations were based on load and renewable generation data derived from the Australian Energy Market Operator (AEMO). I considered three microgrids with capacities described in the following table:
| Source type | Min power (kW) | Max power (kW) | O&M cost (CNY/kWh) |
|---|---|---|---|
| WT | 0 | 60 | 0.252 |
| PV | 0 | 70 | 0.084 |
| HEP | 0 | 60 | 0.090 |
| EV aggregate | -40 | 40 | 0.067 |
| DE | 6 | 90 | 1.435 |
| BAT | -40 | 40 | 0.035 |
| Grid | -120 | 120 | 0.007 |
The emission factors and treatment costs are listed below:
| Pollutant | Treatment cost (CNY/kg) |
|---|---|
| CO2 | 0.67 |
| SO2 | 8.99 |
| NOx | 15.49 |
For the diesel generator, the emission factors used were 460 kg/MWh for CO2, 0.003 kg/MWh for SO2, and 0.008 kg/MWh for NOx.
7.2 Results for a Single Microgrid
I first tested the IWPA versus PSO, WOA, LHHO, and ISMTSA on the day-ahead economic dispatch problem of Microgrid 1. Each algorithm ran 10 times independently. The best, worst, and mean objective values are reported in the table below.
| Algorithm | Best cost (CNY) | Worst cost (CNY) | Mean cost (CNY) |
|---|---|---|---|
| PSO | 3392.19 | 3435.65 | 3431.33 |
| WOA | 3386.09 | 3420.06 | 3403.07 |
| LHHO | 3234.25 | 3348.61 | 3248.91 |
| ISMTSA | 3339.62 | 3435.76 | 3424.09 |
| IWPA | 3151.61 | 3251.05 | 3231.20 |
The mean cost achieved by IWPA was about 6% lower than that of PSO, 5% lower than that of WOA, 1% lower than that of LHHO, and 6% lower than that of ISMTSA. In terms of the best solutions, IWPA improved the costs by 7%, 7%, 3%, and 6% relative to PSO, WOA, LHHO, and ISMTSA, respectively. The convergence curves exhibited that IWPA quickly descended to lower objective values within the first 100 iterations, confirming its strong search efficiency. The runtime overhead is slightly larger than that of WOA or PSO, but the reduction in operating cost compensates for the additional computation time in day-ahead scheduling.
7.3 Impact of the Load-Interval Pricing Strategy
In order to evaluate the proposed pricing strategy, I simulated Microgrid 1 and Microgrid 2 under two scenarios. The first scenario used the conventional TOU pricing; the second scenario used the load-interval pricing with price boundaries listed earlier. All other parameters remained identical. The results demonstrate remarkable differences.
When the load-interval pricing strategy was active, the net power import from the main grid fluctuated less. Specifically, the fluctuation amplitude of the power-exchange curve was reduced by approximately 40% in Microgrid 1 and by 28% in Microgrid 2. This is important because large swings in power exchange can cause frequency deviations and voltage issues in a wide-area network. By smoothing the import/export profile, the microgrid becomes more friendly to the main grid.
The diesel generator operation also changed significantly. Under TOU pricing, diesel generators often had to compensate for the simultaneous charging of many electric vehicles during evening hours. Under load-interval pricing, the aggregate generator output was more stable. The fluctuation range of diesel generator output decreased by about 28% for Microgrid 1 and 42% for Microgrid 2. The total diesel energy production decreased by 2% and 5%, respectively. Lower fuel consumption leads to a proportional reduction in polluting emissions. For microgrid 1, the total CO2 emissions decreased from approximately 478.97 kg to 441.54 kg under the load-interval pricing scenario. SO2 and NOx emissions similarly declined by small but meaningful amounts.
Economically, the load-interval pricing achieved a 3% to 4% reduction in total operating costs as compared with TOU pricing, depending on the test scenario and the selected optimizer. This confirms that a more responsive price signal can efficiently shift the charging behavior of electric vehicles and help the microgrid exploit cheap renewable energy when available.
7.4 Load Curve Smoothing
One of the most visible benefits appears in the net load curve. In the original scenario without any specialized electric vehicle coordination, the load profile contains a large peak in the evening. When TOU pricing is introduced and electric vehicles are allowed to charge during valleys, the original peak is partially reduced. However, a new smaller peak can appear immediately after the low-price period starts. In contrast, the load-interval pricing strategy almost completely avoids such secondary peaks. My calculations showed that the TOU strategy reduced the load fluctuation by about 30% compared with the uncontrolled case, whereas the load-interval pricing strategy reduced it by about 50%. The shape of the load curve under load-interval pricing was considerably flatter, indicating that the system can operate with lower spinning reserves and smaller capacity margins.
7.5 User Benefit and Charging Types
Electric vehicle owner profitability is crucial for the success of V2G programs. I compared the revenue of vehicle owners under the two pricing strategies. Surprisingly, the average total revenue for the fleet was slightly higher under TOU pricing, because owners could synchronize their discharge exactly with the fixed high-price periods. Under load-interval pricing, discharge decisions are based on load intervals, which are less predictable over the day. To make the load-interval pricing more attractive for electric vehicle owners, I suggest including a premium or compensation for battery degradation. The cost of battery degradation can be modeled as
$$C_{deg} = C_{battery} \cdot \frac{E_{discharge}}{N_{cycles} \cdot E_{capacity}} \tag{28}$$
where $C_{battery}$ is the replacement cost, $E_{discharge}$ is the total discharged energy during one cycle, $N_{cycles}$ is the determined cycle life, and $E_{capacity}$ is the rated battery capacity. Including such a term in the objective function could make the two pricing schemes more equitable for electric vehicle owners.
In terms of charging technologies, fast charging offers high power (often 40 kW or above) and can quickly absorb energy, but simultaneously creates step perturbations in the load profile. Slow charging (typically 3.5–7 kW) is much softer and can be more easily synchronized with fluctuating renewable energy. My simulations showed that the optimal strategy engages slow chargers during periods of high solar generation, while fast chargers are used only when the microgrid has a surplus of energy or when urgent load balancing is required. The presence of a mix of fast and slow charging electric vehicles improves dispatch flexibility and may reduce the need for stationary battery capacity.
8. Resilience Analysis of the Microgrid with Electric Vehicles
8.1 Response to Photovoltaic Power Fluctuation
To test robustness, I reduced the photovoltaic output to represent a sudden overcast condition. When the PV generation is unexpectedly low, the microgrid must immediately compensate for the missing power through other sources. Under the TOU pricing, the first response was to increase the diesel generator output, while the electric vehicles discharged only when the outage happened to coincide with a high-price period. Under the load-interval pricing strategy, the lower load after the outage triggered a higher price level, encouraging electric vehicles to discharge immediately. The scheduler was able to coordinate the discharge of electric vehicles and the diesel generator simultaneously, avoiding an abrupt rise in diesel fuel costs.
8.2 Response to Wind Power Fluctuation
I also simulated a scenario where the wind speed changed dramatically during the early morning. In a low-price period under TOU pricing, such a drop in wind power is dangerous because electric vehicle owners prefer to charge due to low electricity prices. This simultaneously increases demand while decreasing local generation. The diesel generator must drastically increase output, which increases emissions. Conversely, under load-interval pricing, when the load remains low but renewable generation falls, the actual net load (load minus renewable generation) rises, pushing the price into a higher interval. Consequently, some of the scheduled charging of electric vehicles is postponed, and a few electric vehicles offer discharging services, thereby reducing the need for diesel generation. This demonstrates that the load-interval price mechanism is more adaptable to real-time renewable output fluctuations.
8.3 Response to Diesel Generator Outage
The unforeseen outage of a diesel generator is a severe contingency for any islanded microgrid. In my experiment, the diesel generator is forced to shut down for several hours. Without additional support, the power balance may be violated or the load must be shed. With electric vehicles, the microgrid can still survive such an event if enough vehicles are connected and their battery capacities are sufficient. Under the TOU strategy, I observed a positive power imbalance during the peak-price hour because too many electric vehicles discharged simultaneously while the load was low. Under the load-interval strategy, the number of discharging vehicles was determined by the actual system load, yielding a smoother power balance.
However, it is worth noting that a single microgrid with only 20 electric vehicles may not have enough capacity to fully replace a diesel generator for many hours. Therefore, when the diesel generator outage persists for more than two hours, the load-interval strategy cannot guarantee that no load shedding occurs. To strengthen resilience in such extreme cases, I investigated the benefits of interconnecting multiple microgrids.
9. Multi-Microgrid Interconnected Operation
9.1 Motivation and Benefits
In a multi-microgrid cluster, different microgrids often experience opposite renewable generation patterns. For example, Microgrid 3 might have a large amount of wind power at night while Microgrid 2 faces a load peak. Instead of purchasing expensive electricity from the main grid, Microgrid 2 can import power from Microgrid 3 via a shared connection line. Electric vehicles can be used as spatial transfer agents because vehicles that are driven from one microgrid to another can physically move energy; in this thesis, I consider the aggregated effect of vehicles participating in V2G operations at different locations.
9.2 Comparison of Isolated and Interconnected Dispatch
I first calculated a day’s dispatch results for each microgrid as a fully isolated system. In this mode, Microgrid 2 had to import a significant amount of power from the main grid during the night, especially from 1:00 to 8:00. At that time, local wind generation was limited, and TOU tariffs were low. After interconnecting Microgrid 1 and Microgrid 3, the import from the main grid was almost entirely avoided during the daytime. Figure 4.17 of my original thesis demonstrates that the diesel generators in Microgrid 2 ran at lower power levels for the majority of hours, and the remaining negative gaps were filled by energy imported from neighboring microgrids.
The economic impacts are summarized in the following table, which shows the total cost of Microgrid 2 in interconnected mode. The lower and upper row ranges display variability across 10 independent simulation runs.
| Algorithm | Best cost (CNY) | Worst cost (CNY) | Mean cost (CNY) |
|---|---|---|---|
| PSO | 1472.71 | 1621.07 | 1568.25 |
| WOA | 1489.82 | 1593.27 | 1512.40 |
| LHHO | 1313.42 | 1583.64 | 1473.19 |
| ISMTSA | 1392.30 | 1582.85 | 1504.32 |
| IWPA | 1239.86 | 1506.67 | 1362.87 |
Comparing the mean cost from the isolated scenario (Table in Section 7.2) and the interconnected scenario for Microgrid 2, the cost reduction is substantial. More importantly, the interconnection also enhances the renewable energy penetration. Surplus energy in Microgrid 3 that would otherwise be curtailed can now be used to charge electric vehicles or satisfy load in Microgrid 2. This result supports my argument that multi-microgrid cooperation is beneficial for achieving high renewable energy accommodation.
9.3 Renewable Energy Accommodation
In isolated mode, when a microgrid encounters a local surplus of renewable energy, the excess power must be exported to the main grid at a low feed-in tariff or even curtailed. In interconnected mode, the surplus can be absorbed by a neighboring microgrid with a deficit, thereby reducing the total system emissions and the need for diesel generation. In my simulations, Microgrid 3, whose local load was small but whose wind generation was large, was able to export more than 40% of its daily renewable energy output to neighboring grids. This resulted in a near-zero curtailment rate, whereas in the isolated mode the curtailment rate reached about 15% for the same day.
The presence of electric vehicles in the receiving microgrids further improves the situation because they can accept power at a high rate when renewable energy is abundant, especially if the load-interval price mechanism lowers the price when the net load is small. Therefore, electric vehicles are an effective tool not only for time shifting but also for space shifting of energy in a multi-microgrid network.
10. Discussion and Future Work
10.1 Key Findings
From my research, I draw the following conclusions:
- The load-interval pricing strategy outperforms the traditional time-of-use pricing in terms of flattening the load curve, reducing the diesel generator output, and lowering pollutant emissions. The electric vehicle charging demand can be smoothly coordinated through a feedback price mechanism based on load level.
- The improved wolf pack algorithm (IWPA) is a reliable and efficient optimizer for microgrid economic dispatch. It enhances the search performance of the original wolf pack algorithm through spiral search, chaotic initialization, and dynamic population updates. The IWPA reduces the average optimal cost by 1% to 6% compared with the selected state-of-the-art algorithms.
- Electric vehicles provide essential flexibility during random renewable output variations and diesel generator failures, but only when a sufficiently large number of electric vehicles are connected and usable. The load-interval pricing method taps into this flexibility more effectively than a fixed tariff.
- Interconnected multi-microgrid operation together with electric vehicle integration can significantly reduce reliance on the central grid, boost renewable energy sharing, and achieve lower total operation costs.
10.2 Limitations
My study has several limitations that should be addressed in future research. First, the number of electric vehicles in each microgrid is relatively small (20). At such low penetration, the grid benefits are moderate. Larger fleets will require more complex forecasting and communication systems. Second, the electric vehicle battery model ignores degradation effects in the main optimization objective, which may distort the user compensation. Third, the microgrid-to-microgrid power transfer capacity and transmission losses were simplified. In a geographically distributed network, the inclusion of impedance and line losses would change the optimal dispatch. Fourth, the model assumes perfect forecasts of renewable output and load, which is never true in practice. Stochastic or robust optimization techniques should be combined with IWPA to make the solution more resilient. Fifth, IWPA’s computational time is still higher than some lightweight methods, although it remains acceptable for day-ahead scheduling.
10.3 Future Directions
I plan to extend this work in several directions. A more realistic electric vehicle aggregation model, including fast and slow chargers, random connection times, and driver response curves, would improve the evaluation of the load-interval pricing. I would also like to design a two-stage stochastic programming framework where the first stage decides unit commitments and the second stage adjusts the dispatch based on Monte Carlo scenarios. In that framework, IWPA could be used to solve the nonlinear second-stage subproblem. Another direction is to adopt a distributed optimization architecture that preserves privacy because different microgrids and electric vehicle owners may not want to share sensitive data. Algorithms such as the alternating direction method of multipliers (ADMM) can be integrated with IWPA to coordinate energy trading while maintaining data localism.
Finally, I would like to examine the interaction between multiple microgrids and the wholesale electricity market. The proposed load-interval pricing could be extended into a dynamic market mechanism where the microgrid places bids on behalf of the electric vehicle fleet. Such a scheme would allow real-time balancing and ancillary service provision while maintaining the comfort of vehicle owners. In that scenario, electric vehicles might become a primary operating resource rather than a passive load.
11. Conclusion
In this thesis, I presented a comprehensive study of multi-microgrid planning and operation with the participation of electric vehicles. I constructed mathematical models for renewable generators, battery storage, and electric vehicles, and I used Monte Carlo simulation to capture the stochastic charging behavior of electric vehicles. A load-interval pricing strategy was proposed as an improvement over fixed time-of-use pricing. Simulation experiments verified that this pricing strategy can effectively reduce peak-valley differences, decrease diesel generator fuel consumption, lower pollutant emissions, and improve the ability to respond to renewable fluctuations and generator outages.
I also developed an improved wolf pack algorithm that combines spiral search, chaotic initialization with experience memory, and dynamic population renewal. Ten benchmark functions confirmed that the IWPA is globally competitive with both classical and recent metaheuristic algorithms. When applied to microgrid economic dispatch, the IWPA achieved lower operating costs and better convergence performance than PSO, WOA, LHHO, and ISMTSA. Moreover, the interconnected multi-microgrid operation showed that sharing surplus renewable energy across microgrid boundaries and using electric vehicles as flexible resources can reduce the total cost by a large margin and improve clean energy utilization.
Overall, the combination of a responsive pricing method, a high-performance optimizer, and the integration of electric vehicles offers a practical path toward more economic, reliable, and low-carbon microgrid systems. I hope that the methods and findings of this research will be useful for future smart microgrid deployments and for enabling broader participation of electric vehicles in ancillary services and energy markets.