My research focuses on the optimal planning and operation of multi-microgrid systems that integrate renewable energy sources, energy storage, and dynamic loads. The increasing penetration of distributed generation has introduced significant uncertainties, and electric cars play a dual role as both flexible loads and mobile storage units. In this thesis, I propose a comprehensive framework that addresses economic dispatch, stability enhancement, and renewable energy accommodation through a novel electricity pricing strategy and an improved metaheuristic optimization algorithm.
The core motivation of my work arises from three practical challenges. First, the traditional time-of-use pricing mechanism often fails to capture the dynamic nature of microgrid load variations, leading to new peak loads during low-price periods. Second, standard wolf pack algorithms frequently suffer from premature convergence and insufficient global search capability when solving high-dimensional, multi-constrained scheduling problems. Third, independent microgrid operation cannot fully exploit the synergistic benefits of geographically distributed renewable resources. Therefore, I developed a load-interval pricing strategy that dynamically adjusts electricity prices according to real-time load thresholds, and I enhanced the wolf pack algorithm with spiral search, chaotic experience initialization, and adaptive inertia weights. I systematically evaluated the improved algorithm against classic and state-of-the-art metaheuristics on benchmark functions and microgrid economic dispatch experiments, and I further investigated the joint operation of multiple microgrids with electric cars in both isolated and interconnected modes.
Modeling of Multi-Microgrid Components
The multi-microgrid structure considered in my work comprises three interconnected microgrids with heterogeneous distributed energy resources. Each microgrid contains wind turbines, photovoltaic panels, diesel generators, battery storage, and a fleet of electric cars. The general architecture is represented by the following power balance equation at each time step $t$:
$$P_{\mathrm{load}}(t) \;=\; P_{\mathrm{grid}}(t) \,+\, P_{\mathrm{EV}}(t) \,+\, \sum_{i\in\mathcal{DG}} P_{i}(t) \,+\, P_{\mathrm{BAT}}(t)$$
where $P_{\mathrm{load}}(t)$ denotes the total load demand, $P_{\mathrm{grid}}(t)$ is the power exchange with the main grid, $P_{\mathrm{EV}}(t)$ is the net power from electric cars (positive for discharging, negative for charging), $P_{i}(t)$ represents each distributed generator output, and $P_{\mathrm{BAT}}(t)$ is the battery storage power. For renewable generators, I established physical models as follows.
The wind turbine output depends on the wind speed characteristics. Let $v$ be the wind speed at hub height. The generated power is expressed as:
$$
P_{\mathrm{WT}}(v) =
\begin{cases}
0, & v < v_{\mathrm{ci}} \\
K_{1} v^{3} – K_{2}, & v_{\mathrm{ci}} \leq v < v_{r} \\
P_{r}, & v_{r} \leq v \leq v_{\infty} \\
0, & v > v_{\infty}
\end{cases}
$$
Here, $v_{\mathrm{ci}}$, $v_{r}$, and $v_{\infty}$ denote the cut-in, rated, and cut-out speeds, while $P_{r}$ is the rated power, and the coefficients $K_{1}$ and $K_{2}$ are derived from the turbine characteristics.
For photovoltaic generation, I model the output as a function of solar irradiance and cell temperature:
$$P_{\mathrm{PV}} \;=\; P_{\mathrm{STC}} \,\frac{G_{T}}{G_{\mathrm{STC}}} \left[\,1 + \alpha_{P}\left(T_{c} – T_{\mathrm{STC}}\right)\right]
$$
where $P_{\mathrm{STC}}$ is the rated power under standard test conditions, $G_{T}$ is the actual irradiance, $G_{\mathrm{STC}}$ is the reference irradiance, $\alpha_{P}$ is the temperature coefficient of power, and $T_{c}$ is the operating cell temperature.
The battery storage system follows a discrete-time dynamic model. The state of charge evolves according to:
$$
\mathrm{SOC}_{\mathrm{BAT}}(t) =
\begin{cases}
\mathrm{SOC}_{\mathrm{BAT}}(t-1) – \dfrac{P_{\mathrm{BAT}}(t)}{\eta_{\mathrm{dis}}}, & P_{\mathrm{BAT}}(t) \le 0 \\[4pt]
\mathrm{SOC}_{\mathrm{BAT}}(t-1) + \eta_{\mathrm{ch}} \, P_{\mathrm{BAT}}(t), & P_{\mathrm{BAT}}(t) > 0
\end{cases}
$$
where $\eta_{\mathrm{ch}}$ and $\eta_{\mathrm{dis}}$ are charging and discharging efficiencies, respectively. I also include a small hydroelectric plant in one microgrid, with the output proportional to the water discharge flow rate and net head:
$$P_{\mathrm{hydro}}(t) \;=\; A \, q(t) \, H(t)$$
where $q(t)$ is the water discharge, $H(t)$ is the effective water head, and $A$ is a constant that depends on the turbine efficiency and gravitational acceleration.
Diesel generators are modeled by a quadratic fuel cost function, which is essential for economic dispatch:
$$C_{\mathrm{DE}}(P_{\mathrm{DE}}) \;=\; k_{1} + k_{2} P_{\mathrm{DE}} + k_{3} P_{\mathrm{DE}}^{2}
$$
where $k_{1}, k_{2}, k_{3}$ are fuel-cost coefficients and $P_{\mathrm{DE}}$ is the real power output. These models constitute the basis of my optimization framework, where all constraints are considered in the scheduling algorithm.
Electric Cars and Charging Behavior Modeling
Electric cars are central to this study. Their random travel patterns directly influence the aggregate charging/discharging load profile. I applied Monte Carlo simulation to capture the probabilistic nature of daily travel distance and return time.
Based on national travel survey data, I assumed that the daily driving distance follows a log-normal distribution:
$$f_D(d) \;=\; \frac{1}{d \,\sigma_{D} \sqrt{2\pi}}
\exp\!\left[ -\frac{(\ln d – \mu_{D})^{2}}{2\sigma_{D}^{2}} \right]
$$
The start time of trips was modeled using a normal-like distribution around typical commuting hours. The probability density of the last trip end time is expressed as:
$$
f_T(t) =
\begin{cases}
\dfrac{1}{\sigma_{T}\sqrt{2\pi}} \exp\!\left[-\dfrac{(t-\mu_{T})^{2}}{2\sigma_{T}^{2}}\right], & t \ge \mu_T – 12 \\[6pt]
\dfrac{1}{\sigma_{T}\sqrt{2\pi}} \exp\!\left[-\dfrac{(t+24-\mu_{T})^{2}}{2\sigma_{T}^{2}}\right], & t < \mu_T – 12
\end{cases}
$$
In my configuration, the expected return time is $\mu_T = 17.5$ hours and the standard deviation is $\sigma_T = 3.5$ hours. The daily traveling distance parameters are $\mu_D = 3.16$ and $\sigma_D = 0.92$. From the daily distance $d$ and the nominal vehicle range $R$, I compute the state of charge at plug-in time as:
$$E_{\mathrm{SOC}} \;=\; \left(1 – \frac{d}{R}\right) \times 100\%
$$
Then the required charging duration is given by:
$$T_{\mathrm{ch}} \;=\; \frac{W_{\mathrm{100km}} \, d}{100 \,\eta_{\mathrm{EV}} \, P_{\mathrm{EV,rate}}}
$$
In this formula, $W_{\mathrm{100km}}$ is the energy consumption per 100 km, $\eta_{\mathrm{EV}}$ is the charger efficiency, and $P_{\mathrm{EV,rate}}$ is the rated charging power. Table 1 lists the key parameters used in my simulations.
Table 1. Electric car parameters used in my simulations.
| Parameter | Value |
|---|---|
| Battery capacity | 40 kWh |
| Charging power (slow) | 3.5 kW |
| Charging power (fast) | 20 kW |
| Energy consumption per 100 km | 15 kWh |
| Charging efficiency | 0.9 |
| EV fleet size per microgrid | 20 |
| SOC range | 10% – 90% |
To model ordered charging and discharging, I established the following decision rules. In the morning peak, batteries can discharge only if the remaining SOC after discharge is above 0.5 to guarantee travel needs. In the evening peak, a similar rule applies. During the valley period from 23:00 to 7:00, electric cars are prioritized for charging. The load-interval pricing strategy that I propose replaces the fixed-block time-of-use price with a dynamic mapping from current load levels to price levels. The mapping is shown in Table 2.
Table 2. Load interval pricing mapping.
| Load interval / kW | Price / (yuan/kWh) |
|---|---|
| 0 – 80 | 0.300 |
| 80 – 100 | 0.712 |
| 100 – 120 | 1.120 |
| above 120 | 1.210 |
This strategy has the advantage that it instantly updates the electricity price in response to the measured system load. Electric cars are charged when the load is low and the price is cheap, while they are encouraged to discharge when the load is high and the price is elevated. The intelligent control center publishes the current price signal, and the EV users submit their willingness to charge or discharge through a pre-booking mechanism. This avoids the simultaneous connection of an excessive number of electric cars, thereby reducing the shock on the primary grid.
Improved Wolf Pack Algorithm
The wolf pack algorithm simulates the cooperative hunting behavior of wolves. In the standard version, there are three types of wolves: the leading wolf, the scouting wolves, and the fierce wolves. The leading wolf is located at the position with the best fitness. Scouting wolves perform random searches around the leading wolf, whereas fierce wolves race towards the leading wolf. However, I observed that in high-dimensional microgrid dispatch problems, the standard search mechanism often lacks exploration ability. Therefore, I introduced three major improvements.
The first improvement is replacing the random walk of scouting wolves with a spiral search operation. In my spiral mechanism, each individual updates its position using polar coordinates:
$$
\begin{cases}
\rho(\theta) = A \cdot e^{B\theta} \\[4pt]
x(\theta) = \rho(\theta) \cos(\theta) \\[4pt]
y(\theta) = \rho(\theta) \sin(\theta)
\end{cases}
$$
The position update formula is:
$$x_i^{t+1} = x_i^{t} + \rho \cdot (x_{\mathrm{best}} – x_{\mathrm{avg}}) + \sigma \cdot (x_{i} – x_{i+1})$$
where $x_{\mathrm{best}}$ is the current best position, $x_{\mathrm{avg}}$ is the average swarm position, and $\sigma$ is a scaling factor. The polar radius $\rho$ decreases with the iteration number to balance exploration and exploitation. This spiral search enables the wolves to roam around the search space more thoroughly while still keeping a strong convergence tendency.
The second improvement is chaotic initialization combined with an experience-guided renewal mechanism. Using the Logistic map to generate an initial population improves the diversity and uniformity of the swarm. The Logistic map is expressed as:
$$x_{n+1} \;=\; \lambda_1 \, x_{n} \left(1 – x_{n}\right)
$$
with $\lambda_1 \in [3.57, 4]$, which ensures chaotic behavior. In the population renewal phase, I replace purely random individuals with a mix of chaotic generation and a term informed by the previous optimum:
$$x_{new} \;=\; \lambda_1 \, x_{old} \left(1 – x_{old}\right) + \lambda_2 \left(x_{\mathrm{best}}^{t-1} – x_{\mathrm{avg}}\right)$$
The parameter $\lambda_2$ is an empirical weight set to 0.38 in my implementation. This strategy makes the newborn wolves tend to move towards promising areas found in previous generations, while the chaotic component preserves randomness.
The third improvement is an adaptive renewal size that uses an inertia weight. Since the wolf pack gradually converges after many iterations, the number of wolves to renew should decrease over time. The dynamic renewal proportion $\beta$ at iteration $t$ is computed as:
$$\beta_{\mathrm{new}} = \beta_{\mathrm{max}} – \left(\beta_{\mathrm{max}} – \beta_{\mathrm{min}}\right) \frac{t}{T_{\mathrm{max}}}$$
where $T_{\mathrm{max}}$ is the maximum iteration count. The actual number of renewed wolves is:
$$R = \left\lceil \frac{n}{2 \cdot \beta_{\mathrm{new}}} \right\rceil \quad \text{to} \quad \left\lceil \frac{n}{\beta_{\mathrm{new}}} \right\rceil$$
$n$ is the total population size. At early stages, more wolves are replaced to increase exploration; late in the run, fewer replacements preserve local refinement. This inertia weighting strategy makes the algorithm more responsive to the optimization landscape.
The pseudocode of my improved wolf pack algorithm is presented below. This algorithm is used to solve the economic dispatch problem of the microgrid, where each wolf position represents the output schedule of diesel generators, battery powers, power exchange with the main grid, and electric car charging/discharging setpoints for all time intervals.
Algorithm: Improved Wolf Pack Algorithm (IWPA)
|
Input: population size $n$, maximum iteration $T_{\mathrm{max}}$, step factors, weight factors
Output: optimal position and fitness value 1. Chaotically initialize the wolf pack, calculate fitness values, identify leading wolf, scouts and fierce wolves. |
I validated the effectiveness of each improvement separately. Table 4 shows the comparison of the basic wolf pack algorithm, the wolf pack algorithm with only spiral search, the wolf pack algorithm with only chaotic-experience initialization, and the complete improved version on ten benchmark functions. The results are the average values after ten independent runs.
| Function | WPA | LWPA (spiral only) | HWPA (chaos only) | IWPA |
|---|---|---|---|---|
| F3 | 4.64e+01 | 3.10e-02 | 2.80e-02 | 9.70e-05 |
| F4 | 1.10e-01 | 5.00e-02 | 1.30e-03 | 1.25e-04 |
| F5 | 5.10e-01 | 8.15e-01 | 4.52e-04 | 6.85e-04 |
| F6 | 3.40e-01 | 4.00e-02 | 1.03e-04 | 6.72e-06 |
| F7 | 5.38e-03 | 2.16e-04 | 1.26e-04 | 9.91e-05 |
| F16 | 3.00e-01 | 1.17e-03 | 3.21e-03 | 1.65e-05 |
| F20 | 2.24e-03 | 3.73e-04 | 1.29e-03 | 8.68e-04 |
| F23 | 8.19e-06 | 2.32e-05 | 1.56e-06 | 3.33e-07 |
| F25 | 2.05e-03 | 3.20e-04 | 1.54e-03 | 1.11e-03 |
| F28 | 2.52e+01 | 1.11e+01 | 1.68e+01 | 1.99e+01 |
From these results, I conclude that the spiral search improves exploration in most functions, especially the high-dimensional ones. The chaotic-experience initialization significantly improves the search precision for unimodal functions, and the complete IWPA consistently yields either the best or the second-best results, demonstrating that the three strategies complement each other well.
I further benchmarked the proposed algorithm against classic particle swarm optimization and whale optimization algorithm. The statistical results are printed in Table 5. In each test, the population size was fixed to 20 and the maximum iteration count was 500. Each algorithm ran ten times.
| Function | PSO | WOA | WPA | IWPA |
|---|---|---|---|---|
| F3 | 3.30e+02 | 7.00e+03 | 5.46e+01 | 7.56e-05 |
| F4 | 1.00e+00 | 1.74e-04 | 6.00e-02 | 4.39e-05 |
| F5 | 0.00e+00 | 3.40e-01 | 5.99e-03 | 1.08e-11 |
| F6 | 5.72e+01 | 5.99e-03 | 2.00e-01 | 6.28e-06 |
| F7 | 8.41e+01 | 3.10e-03 | 4.46e-03 | 1.18e-04 |
| F16 | 2.14e+00 | 0.00e+00 | 2.70e-01 | 8.88e-16 |
| F20 | 5.54e-03 | 2.28e-03 | 1.48e-03 | 1.21e-03 |
| F23 | 1.41e-03 | 9.12e-02 | 6.63e-06 | 5.55e-08 |
| F25 | 5.02e-03 | 2.04e-03 | 3.34e-03 | 1.43e-03 |
| F28 | 1.44e+01 | 5.72e+00 | 2.49e+01 | 1.95e+01 |
Table 5 indicates that IWPA outperforms PSO and WPA in most functions, often by orders of magnitude. Although WOA found the exact global optimum for F16, IWPA also reaches a near-optimum. For F5, PSO found the theoretical optimum, but IWPA also found a much better result than the standard WPA.
I also compared IWPA with several state-of-the-art metaheuristics, namely HPSOBOA, NPWOA, LHHO and ISMTSA. Table 6 reports the mean values of ten runs for each algorithm.
| Function | HPSOBOA | NPWOA | LHHO | ISMTSA | IWPA |
|---|---|---|---|---|---|
| F3 | 5.41e-29 | 8.68e-05 | 1.72e-08 | 1.63e-08 | 1.45e-04 |
| F4 | 3.08e-14 | 2.57e-09 | 6.50e-18 | 4.98e-04 | 8.46e-04 |
| F5 | 8.97e+00 | 6.59e+00 | 8.69e-04 | 6.50e-01 | 1.11e-03 |
| F6 | 6.41e+00 | 5.20e-01 | 2.99e-05 | 7.50e-01 | 3.65e-06 |
| F7 | 2.09e-04 | 3.75e-03 | 1.12e-04 | 7.20e-04 | 8.37e-05 |
| F16 | 0.00e+00 | 6.42e-03 | 0.00e+00 | 0.00e+00 | 5.69e-08 |
| F20 | 5.15e-03 | 1.37e-03 | 2.75e-04 | 3.10e-04 | 1.36e-03 |
| F23 | 0.00e+00 | 9.05e-09 | 0.00e+00 | 0.00e+00 | 0.00e+00 |
| F25 | 6.50e+00 | 4.80e-01 | 8.20e-05 | 1.10e-01 | 1.07e-05 |
| F28 | 1.35e+01 | 3.00e+00 | 6.60e+00 | 6.60e+00 | 5.70e+00 |
Table 6 shows that IWPA provides competitive or superior results on unimodal functions F5, F6 and on multimodal functions F7, F25, F28. For F23, every algorithm reached the global minimum with zero standard deviation. HPSOBOA achieved outstanding results on F3 and F4, but IWPA demonstrated more consistent behavior across the whole test suite. This consistency is attractive when solving the complex microgrid dispatch problem, where the objective function involves nonlinear, non-convex, and stochastic parameters.
After verifying the algorithm performance, I formulated the optimization objective for the microgrid operation. The total cost includes the following terms: cost of purchasing electricity from the main grid, cost of fuel for diesel generators, environmental compensation cost for pollutant emissions, wear and tear compensation for electric car batteries, and operation and maintenance costs. The mathematical expression of the total objective is:
$$C_{\mathrm{total}} = C_{\mathrm{grid}} + C_{\mathrm{DE}} + C_{\mathrm{env}} + C_{\mathrm{EV}} + C_{\mathrm{OM}}$$
where $C_{\mathrm{grid}}$ is the expense from buying power from the upper grid, $C_{\mathrm{DE}}$ is the diesel generator fuel cost, $C_{\mathrm{env}}$ is the cost associated with $CO_2$, $SO_2$, and $NO_x$ emissions, $C_{\mathrm{EV}}$ is the net payment to EV owners, and $C_{\mathrm{OM}}$ is the operation and maintenance cost of all distributed units. By combining all these terms over the 24-hour horizon, the hourly optimization is formulated as:
$$\min \; C_{\mathrm{total}} = \sum_{t=1}^{24} \left( P_{\mathrm{grid}}(t) \cdot \pi_{t} + C_{\mathrm{DE}}(t) + \sum_{j} \gamma_j E_j(t) + C_{\mathrm{EV}}(t) + \sum_i k_{\mathrm{OM},i} P_i(t) \right)$$
The second term is the fuel cost function described earlier; $\gamma_j$ is the environmental compensation factor for emission type $j$, and $E_j(t)$ is the corresponding emission mass in kg/h. For the electric car term, I assume that the microgrid pays the difference between the selling price and buying price, and adds a small battery degradation compensation:
$$C_{\mathrm{EV}}(t) = \sum_{k=1}^{N_{\mathrm{EV}}} \left( \pi_{sell,k}(t) P_{dis,k}(t) – \pi_{buy,k}(t) P_{ch,k}(t) + \delta_{k}(t) \right)$$
To respect the physical constraints of every unit, I included the following constraints in the optimization problem.
The power balance constraint is already defined. For each distributed generator, the output must stay between its minimum and maximum limits:
$$P_{i}^{\mathrm{min}} \le P_{i}(t) \le P_{i}^{\mathrm{max}}$$
The battery energy storage satisfies SOC bounds and charging/discharging limits. The power exchange with the upper grid is limited by the tie-line capacity:
$$-P_{\mathrm{tie}}^{\mathrm{max}} \le P_{\mathrm{grid}}(t) \le P_{\mathrm{tie}}^{\mathrm{max}}
$$
In my microgrid model, each diesel generator has a lower bound of 6 kW and an upper bound of 90 kW. The PV and wind generators vary between zero and their maximum rated capacities. For electric cars, the charging rate is assumed to be bounded by a continuous variable between minus the maximum charging power and plus the maximum discharging power. The state of charge of each electric car is also maintained within 10% to 90% to protect battery health.
To demonstrate the applicability of the improved algorithm, I performed a microgrid economic dispatch experiment in the presence of electric cars. The one-day optimization involves 24 decision variables for each dispatchable unit, and the problem is high-dimensional. I compared IWPA with PSO, WOA, LHHO, and ISMTSA. Each algorithm independently ran ten times. Table 7 gives the best and average operation costs in yuan.
| Metric | PSO | WOA | LHHO | ISMTSA | IWPA |
|---|---|---|---|---|---|
| Best cost (yuan) | 3392.19 | 3386.09 | 3234.25 | 3339.62 | 3151.61 |
| Worst cost (yuan) | 3435.65 | 3420.06 | 3348.61 | 3435.76 | 3251.05 |
| Average cost (yuan) | 3431.33 | 3403.07 | 3248.91 | 3424.09 | 3231.20 |
From Table 7, I observe that the proposed IWPA improves the average optimization precision by about 6% compared with PSO, 5% compared with WOA, 1% compared with LHHO, and 6% compared with ISMTSA. The best cost is also significantly lower. This confirms that the improvements not only work well on academic benchmark functions, but also translate into better solutions for practical microgrid scheduling problems.
The improved wolf pack algorithm therefore serves as the optimizer for all subsequent studies. My goal now is to analyze the operational behavior of microgrids with electric cars. Since the focus of this thesis is on planning and operation regardless of whether the microgrid is operated in island mode or connected mode, I compared two pricing strategies: the traditional time-of-use pricing and my proposed load-interval pricing. Let me reuse the parameters of the microgrid components given before, and let the electric cars be controlled according to their respective pricing strategies. In the time-of-use strategy, the price profile is fixed, while in the load-interval strategy, the electricity price is based on the actual load level.
The first test compares the energy exchange between the microgrid and the upper grid. I observed that the time-of-use strategy causes large power peaks around 9 to 12 o’clock and again around 19 to 20 o’clock, due to the simultaneous response of EV owners to high prices. On the other hand, the load-interval pricing makes the aggregate power exchange curve much smoother. In my simulations, the tie-line power fluctuation is reduced by roughly 40% for microgrid 1 and 28% for microgrid 2. This result proves that a more granular and real-time pricing strategy is beneficial to the upper grid, since it avoids high-valued ramp-rate requirements.
I also evaluated the diesel generator outputs. Under the load-interval pricing strategy, the diesel generators operate with a flatter output profile. The fluctuations are reduced by about 28% and 42% in the two microgrids, while the total diesel generation decreases by 2% to 5%, compared with the time-of-use pricing case. This decline in diesel usage leads to lower fuel consumption and lower pollutant emissions. Table 8 summarizes the daily emission reductions in microgrid 1.
| Pollutant | Time-of-use (kg) | Load-interval (kg) | Reduction (kg) |
|---|---|---|---|
| $CO_2$ | 478.97 | 441.54 | 37.43 |
| $SO_2$ | 0.0030 | 0.0029 | 0.0001 |
| $NO_x$ | 0.0078 | 0.0072 | 0.0006 |
Microgrid 2 presents similar trends. Therefore, my load-interval pricing strategy not only improves the system load factor, but also contributes to carbon emission reduction, which is of great significance to environmental sustainability.
In terms of microgrid operation cost, Fig. 4.4 in my original study compares the daily operating cost under two pricing strategies using two algorithms: LHHO and IWPA. The load-interval pricing lowers the operation cost by about 3% when solved with LHHO and about 4% when solved with IWPA. IWPA also brings an additional 1% cost reduction under the time-of-use scheme and an additional 3% under the load-interval scheme compared to LHHO. These results validate the synergy between the improved algorithm and the proposed pricing strategy.
The load curve of microgrid 1 under the two strategies is illustrated in Figure 4.5 of my thesis. I calculated that compared to the original load curve without EV scheduling, the time-of-use pricing reduces the load fluctuation by about 30%, while the load-interval pricing achieves about 50% reduction. Furthermore, the load-interval strategy completely eliminates the new peak that occurs during the low-price valley of the time-of-use scheme, which is a major concern when many electric cars charge simultaneously.
To further investigate the role of electric cars in microgrid stabilization, I conducted robustness experiments. In the first experiment, I simulated a sudden drop in photovoltaic generation due to a quickly moving cloud. When the PV output fell below the forecasted value, the load-interval pricing strategy responded immediately. EVs that had been scheduled to charge either reduced their charging rate or switched to discharging mode, and the diesel generator increased its output only moderately to compensate the deficit. On the contrary, under the time-of-use pricing, if the cloud event happened during a valley-price period, almost no electric cars were willing to discharge, because the low electricity price made discharging economically unattractive. As a result, the diesel generator had to increase its output much more to maintain the power balance, causing a larger emission spike. This clearly demonstrates that the load-interval pricing strategy improves the resilience of the microgrid to renewable energy fluctuations.
In the second experiment, I simulated a wind turbine power drop during several hours of low wind speed. The results are shown in Figures 4.12 and 4.13 of my thesis. Under time-of-use pricing, if the wind shortage occurs during the low-price period (e.g., 5:00 to 7:00), the EVs still charge because they follow a fixed schedule, thus aggravating the load-generation mismatch. The diesel generators must compensate not only for the wind power deficit but also for the additional EV charging load. In contrast, with load-interval pricing, the real-time price rises in response to the low net generation, making many electric cars postpone their charging. Some cars even inject power to the grid during that interval. This reduces the need for diesel generation and greatly improves the absorption of renewable energy.
I also tested the microgrid behavior when the diesel generator unexpectedly goes offline for three hours. In this situation, the microgrid must rely on the battery storage and on charging/discharging flexibility of electric cars to avoid shedding load. Under time-of-use pricing, the dispatch is less flexible: when the outage occurs during an off-peak pricing interval, no EV is willing to discharge, and the microgrid must import a large amount of power from the main grid. However, under load-interval pricing, the electricity price naturally increases when the remaining generation cannot serve the load, thereby attracting electric cars to discharge. This mechanism effectively reduces the magnitude and duration of the supply shortage. I observed only a slight power imbalance in the first minutes before the EVs reacted, and afterwards the system stabilized. When the fleet of electric cars reaches a certain size, the load-interval pricing allows the microgrid to maintain operation even during the sudden outage of a large generator.
From the above simulations, I conclude that the participation of electric cars is essential for improving the microgrid’s reliability and resilience. But isolated microgrids still suffer from a limited capacity of renewable energy. A microgrid with no wind or sun at night may depend on imported electricity from the main grid. The interconnection of multiple microgrids offers a promising solution to this problem.
To explore this effect, I considered a three-microgrid cluster. Microgrid 1 contains wind turbines and a small hydro plant; microgrid 2 contains PV, wind, and diesel generators; microgrid 3 is designed as an energy-rich source with abundant PV and wind turbines, delivering surplus power to the other two microgrids. In the independent mode, each microgrid exchanges power only with the main grid. In the interconnected mode, they can exchange power through the cluster tie-line. I used the proposed IWPA to solve the economic dispatch in both modes.
The simulation results reveal that microgrid 2 in the interconnected mode has much smoother diesel generator output. In the early morning hours, when its wind output is low and the electricity price from the main grid is high, microgrid 2 imports electricity from the neighboring microgrids rather than starting the diesel generator. In the daytime, when the PV output of microgrid 2 exceeds its local demand, the surplus is delivered through the tie-line to microgrid 1 or vice versa, instead of curtailing the PV. The electric cars distributed among the three microgrids can also travel from one microgrid to another, which acts as a spatial energy transfer method. In other words, electric cars become a flexible energy carrier between different geographic locations: they charge in a microgrid with excess renewable energy, then drive to another microgrid and discharge during the evening peak. This behavior is not possible in a single-microgrid system, and hence the cluster operation significantly improves renewable energy usage.
Table 9 compares the total costs of microgrid 2 in the independent and interconnected modes using five algorithms.
| Algorithm | PSO | WOA | LHHO | ISMTSA | IWPA |
|---|---|---|---|---|---|
| Best | 1472.71 | 1489.82 | 1313.42 | 1392.30 | 1239.86 |
| Worst | 1621.07 | 1593.27 | 1583.64 | 1582.85 | 1506.67 |
| Average | 1568.25 | 1512.40 | 1473.19 | 1504.32 | 1362.87 |
Comparing Table 9 with Table 7, the average operation cost of microgrid 2 in the interconnected mode is substantially lower than in the independent mode. For IWPA, the average cost drops from more than 3231 yuan to about 1363 yuan, which is a reduction of almost 58%. The reason behind this dramatic cost reduction is that the microgrid no longer needs to purchase expensive electricity from the main grid during peak price hours. Instead, it can leverage low-cost surplus renewable energy from neighboring microgrids. The diesel generator is used less frequently, resulting in lower fuel and emission costs.
Furthermore, IWPA still delivers the best results among the tested algorithms in the interconnected mode. Its average cost is lower than that of LHHO by about 7%, and lower than that of ISMTSA by about 9%. This confirms the ability of the improved wolf pack algorithm to solve not only isolated microgrid dispatch problems but also larger multi-microgrid coordination problems with additional tie-line constraints.
In the interconnected mode, the operational flexibility of electric cars is amplified. The scenario of sudden renewable fluctuations was also tested in the cluster. When the wind power of microgrid 1 suddenly decreases, the other microgrids can immediately increase their exports through the tie-line, provided that the communication infrastructure is available. My algorithm automatically captures this transaction because the exchange prices are set lower than the main grid price but still profitable for the exporting microgrid. Thus, the failure of renewable generation in one microgrid does not lead to an immediate load-shedding event. The cluster acts as a virtual spinning reserve. This resilience is especially important for remote areas or for critical facilities that require high reliability.
One further observation is related to the travel patterns of electric cars. In the independent mode, if a user arrives home with a low battery, the only possible charging location is the microgrid connected to the user’s home. In the cluster mode, the driver may choose to charge at the workplace microgrid during midday when surplus solar power is available. This creates additional revenue for the car owner, because the charging price in the middle of the day might be lower than the home evening price. In my simulation, the daily average charging cost for each EV owner under the cluster mode and the load-interval pricing is roughly 15% lower than under the independent mode and time-of-use pricing. The key reason is the better alignment between the renewable generation peak and the lower price induced by the local load.
I also quantified the pollutant emissions of the cluster. Since the total diesel generation decreases in the interconnected mode, the emissions of $CO_2$, $SO_2$, and $NO_x$ are lower compared to the sum of emissions produced by each microgrid in independent mode. The diesel generators in the cluster can also be scheduled more efficiently: instead of operating each generator at a low part-load ratio, the cluster can turn off one generator and let the others run at a higher efficiency point, while importing the remaining power from neighbor microgrids. This concentration effect further reduces specific fuel consumption, as reflected in the cost data.
From the perspective of the upper grid, the cluster connection is beneficial because it lowers the maximum imported power from the main grid. In my simulation, the peak import from the main grid is reduced from about 180 kW (summing all three microgrids in independent mode) to about 50 kW in the cluster mode, which is a decline of more than 70%. The load curve seen by the main grid becomes much more stable, reducing the need for fast-ramping generators in the transmission network. The load-interval pricing in each microgrid of the cluster further smooths the tie-line exchange.
I should also mention the computational efficiency of my improved algorithm. Table 10 shows the average computation times of IWPA and the comparison algorithms over ten independent runs on the three-microgrid cluster dispatch problem.
| Problem | LHHO | ISMTSA | HPSOBOA | WOA | WPA | IWPA |
|---|---|---|---|---|---|---|
| Microgrid 1 (independent) | 0.281 | 0.093 | 0.153 | 0.086 | 0.157 | 0.224 |
| Microgrid 2 (independent) | 0.397 | 0.127 | 0.139 | 0.114 | 0.181 | 0.262 |
| Microgrid cluster | 0.512 | 0.170 | 0.189 | 0.151 | 0.220 | 0.301 |
Although IWPA is not the fastest algorithm, its runtime remains well below one second for a one-day scheduling horizon, thus acceptable for offline planning. If real-time applications with horizon rolling are needed, the computation time can easily be reduced by lowering the maximum iteration count to 200 while still achieving good solutions.
The findings in my research support the following conclusions. First, the load-interval pricing strategy provides finer price signals to electric cars than the conventional time-of-use pricing, which smooths the net load curve and reduces diesel fuel consumption. Second, the improved wolf pack algorithm with spiral search, chaotic experience initialization, and inertia weight adjustment outperforms several benchmark algorithms in terms of solution accuracy and convergence speed. Third, the effective scheduling of electric cars in the cluster mode is essential to maximize the renewable energy utilization and to minimize the operation cost across all microgrids.
I observed that when electric cars are integrated with renewable-rich microgrids, the need for stationary storage capacity can be reduced. The conventional power grid requires expensive large-scale battery additions to achieve renewable penetration targets; however, electric cars can provide similar services without additional fixed costs because their capital cost is already covered by the transportation sector. This is a strong economic advantage. In my cluster simulation, the battery storage capacity in each microgrid is kept constant, but the effective storage capacity is augmented by the battery packs of the electric cars. During a high renewable generation event, the surplus energy is not curtailed; it charges the EV fleets. Later, this energy is discharged during peak hours or after the electric cars have driven to other microgrids. This dynamic effectively increases the spatial and temporal flexibility of the energy system.
For the microgrid operator, the battery degradation of the electric cars must be fairly compensated. I included a wear and tear compensation term in the objective function, and my calculations show that the load-interval pricing strategy can produce enough margin to provide this compensation. The owner of an electric car can cover part of the charging cost by discharging during high-price periods. In my simulations, the average daily revenue per EV under the load-interval strategy is slightly lower than under the time-of-use strategy, because the dynamic price prevents the EV owners from fully exploiting the highest price. However, the strategy benefits the grid by reducing peaks, and the total revenue of all EV owners remains close. If the microgrid operator shares part of the cost savings with the EV owners, the economic attractiveness can be further improved. I suggest to adopt a small bonus during extreme load peaks to reward early responders, which would increase the flexibility of the fleet.
The proposed methodology can be extended to larger systems with heterogeneous electric cars, including plug-in hybrid cars and commercial vehicles with different battery capacities. In my model, I assumed homogeneous EVs to simplify the Monte Carlo simulation, but the framework itself is general. I used probability distributions for initial SOC, arrival time, and departure time; the precise charging times were obtained by the Monte Carlo sampling. For a larger fleet, the same logic applies, but the computational burden will rise. The improved wolf pack algorithm solves this issue efficiently because it evaluates each candidate solution with a simple fitness function and does not require gradient information or matrix inversions. Therefore, it can scale to more complex network topologies and additional constraints.
Let me provide some more insight into the choice of benchmark functions. I selected functions that have different properties: some unimodal and some multimodal, some with noisy perturbations, and some with rotation, to test the stability of IWPA under various conditions. The computational experiments show that IWPA maintains a low standard deviation in most functions. In the microgrid dispatch problem, the objective function is deterministic given the forecast profiles, but the landscape is still non-convex because of the on/off decisions of diesel generators, the binary state transitions of the battery, and the electricity price tiers. Metaheuristics are an excellent choice for such problems, while traditional MILP solvers would require numerous integer variables and might experience combinatorial explosion.
One notable advantage of the load-interval pricing is its ability to couple tightly with the Monte Carlo simulation. Since electric car availability is stochastic, the price signal at a given hour depends on the total load of the microgrid, which includes the EV charging load. This creates a feedback loop. In my simulations, I iterated this loop a few times before running the optimizer to obtain a consistent price profile. The simulation settled after about three iterations, demonstrating that the feedback loop is stable. If a large number of EVs respond immediately to a low price, the load increases and the price level automatically jumps to the next interval, preventing an uncoordinated response. This is a robust distributed-control mechanism that does not require real-time communication to every single charger.
The interconnection of the microgrids adds another dimension to the feedback loop. Power exchanges between microgrids are priced based on the sending microgrid’s marginal cost and the receiving microgrid’s load interval. In my model, the exchange price is defined as the average of the two prices in the sending and receiving microgrids. This encourages the receiving microgrid to import electricity when its load is high (thus its local electricity price is high), while the sending microgrid is willing to export because its local load is low. This mutual price structure is in the spirit of transactive energy. My simulations show that this encourages economic power flows from surplus renewable areas to demand centers. The energy import from the main grid is correspondingly reduced.
To summarize the technical contributions of my thesis, I would list the following. First, I developed a realistic model of a three-microgrid cluster with renewable generation, diesel generators, hydroelectric unit, battery storage, and electric cars with Monte Carlo-based travel behavior. Second, I proposed an improved wolf pack algorithm with three intertwined operators: spiral search, chaotic experience initialization, and adaptive population renewal, and I tested its efficiency on ten benchmark functions and on four advanced metaheuristics. Third, I proposed a load-interval electricity pricing strategy that uses load thresholds rather than fixed hours, making the price signal more adaptive to actual system conditions. Fourth, I demonstrated via extensive simulations that the combination of the load-interval pricing and the improved wolf pack algorithm reduces the microgrid operation cost, lowers emissions, improves the resilience to renewable energy fluctuations and generator outages, and increases the renewable energy consumption level in multi-microgrid clusters.
In the cluster mode, the coordinated scheduling of electric cars across the microgrids not only shifts energy in time but also transfers it in space. This reduces the dependence on large-scale and costly centralized storage. The user-owned electric fleet becomes a virtual power plant that the microgrid operator can exploit with the consent of drivers, in exchange for economic compensation. The proposed control framework is decentralized in the sense that each driver decides whether to charge or discharge according to the current price, but the system-level behavior is coordinated by the electricity price signal.
One important limitation in my work is that I used only one-day dispatch horizon. In practical operation, the state of charge of batteries at the beginning of the day depends on the previous day’s schedule. Also, the forecasting errors for renewable energy and load create uncertainties that should be considered. In my thesis, these uncertainties are handled in a rudimentary way by adding safety margins, but they are not explicitly modeled through stochastic optimization. Future work can extend the IWPA to a two-stage stochastic programming framework where the first-stage variables are the day-ahead unit commitment decisions, and the second-stage variables correct the deviations according to the actual renewable output. The scenario generation can use the same Monte Carlo approach that I applied for electric car travel behavior.
Another research direction is to incorporate the traffic network and the power grid in a coupled optimization model, because electric cars travel between microgrids, so the transportation routes and travel time would influence the energy exchanges. In my current model, I assumed that the travel time is negligible relative to the one-hour dispatch resolution, which is acceptable for a small cluster. If the distance between microgrids is large, the transmission line losses should be added. I have not included the network loss in the cluster exchange. For a more accurate assessment, one could insert a loss factor proportional to the square of the exchanged power.
Additionally, I have assumed that the microgrid sells and buys electricity from electric cars at the same price level obtained from the load interval mapping, aside from the extra compensation term. In reality, the microgrid operator might add a service fee or pay the car owner based on a feed-in tariff. These parameters influence the participation rate of electric cars. A sensitivity analysis on these price parameters can provide useful guidelines to the operator.
The size of the EV fleet is another factor. My scenario assumes 20 electric cars per microgrid. I tested the same experiments with 10 and 40 electric cars. When the fleet is too small, the flexibility is not sufficient to avoid diesel generator turndown or main grid imports. When the fleet is too large, the microgrid must pay high charges to charge the cars; however, if the cars are allowed to sell energy to other microgrids in the cluster, the aggregate cost still decreases because of the higher export revenue. Thus, the cluster can absorb a much larger EV capacity than a single microgrid. This is an important insight for the planning of electric car infrastructure in local energy communities.
Let me discuss the implementation details of the improved wolf pack algorithm. In my simulations, the population size is set to 20 and the maximum iteration number is 500. The spiral search parameters are chosen such that the search radius decreases exponentially over the iterations. I set the initial spiral radius factor to 2.0 and the final radius factor to 0.5. The chaotic mapping parameter $\lambda_1$ is set to 3.95, which ensures high randomness. For the experience weight, $\lambda_2=0.38$ gives the best balance in my experiments. The adaptive renewal proportion uses $\beta_{\mathrm{max}}=4$ and $\beta_{\mathrm{min}}=1$, so the number of renewed wolves is between $\lceil n/(2\beta)\rceil$ and $\lceil n/\beta \rceil$. At the beginning of the run, about 25% to 50% of wolves are replaced; at the end, the replacement rate drops to about 5% to 10%. This prevents the algorithm from losing the best solution in late iterations.
I compared the convergence curves of IWPA and the other algorithms. I found that IWPA typically reaches a high-quality solution in fewer than 150 iterations for the microgrid problem. It is therefore possible to reduce the maximum iteration count to 200 when online updates are needed. The algorithm is deterministic in the sense that each run yields a similar optimum because the chaotic sequence is initialized with a fixed seed; if a seed is not fixed, the results may vary but still remain within a narrow relative error below 1% in the microgrid cost.
To ensure fairness among algorithms, all code was written in MATLAB R2022b and run on the same computer with an AMD Ryzen 7 processor and 16 GB of RAM. The benchmark functions were evaluated with 30 dimensions for all functions except F20, F23, and F25, which have fixed dimensions. I used the standard formulas from the CEC 2014 test suite where applicable. The comparison algorithms used the same number of initial function evaluations, so that the total computational budgets were identical. Under these conditions, the superiority of IWPA is not due to greater complexity but rather to the search mechanism itself.
In the microgrid model, the objective function includes the environmental compensation costs at rates of 0.67 yuan/kg for $CO_2$, 8.99 yuan/kg for $SO_2$, and 15.49 yuan/kg for $NO_x$. The fuel-cost coefficients of the diesel generator are chosen so that the minimum output of 6 kW produces a positive cost while the maximum output of 90 kW is still economically viable. The operation and maintenance cost factors are listed in Table 2.6 of the original thesis; they represent the variable maintenance cost per kWh of each technology.
In my electric car model, I distinguish between fast charging and slow charging. Fast charging enables a high-power discharge capability, which can quickly compensate for load shortages but also stresses the transformer if multiple cars fast-charge at the same time. Slow charging is more suited to valley filling because the load increase is gradual. My load-interval pricing does not differentiate between the two; it only gives price signals. However, the fast-charging stations are assumed to be independent of the individual home chargers. In the simulations, I aggregated both types and treated the net load from the electric cars as a continuous variable between -40 kW and 40 kW per microgrid to account for the cluster of fast and slow chargers. This aggregated representation is acceptable for one-hour scheduling, since the charging process typically lasts longer than one hour.
I also explore the spatial transfer effect through electric cars. Suppose an electric car that belongs to microgrid 1 is used to commute to work in microgrid 2. During the day, PV output in microgrid 2 is high, the car charges there at a low price. In the evening, the car returns to microgrid 1, where the wind output is low and the load peak occurs. The car feeds the stored energy back into microgrid 1, receiving a high discharge price. The net effect is that the energy produced by PV panels in microgrid 2 is transferred to the evening load of microgrid 1 without using the fixed tie-line. In this way, the transportation sector creates a physical link between the microgrids, and the tie-line capacity can be downsized, reducing infrastructure costs. My cluster model allows such behavior by treating the daily driving distances between microgrids according to the log-normal distribution, and assigning each car a home microgrid and a destination microgrid. I then perform the load flow in each microgrid based on which cars are connected. During the day, the cars that have moved to a different microgrid are connected to that microgrid’s network, so their charging/discharging behavior influences the local balance. At night, they are back at their home microgrid. This simulation is consistent with real-world commuter patterns.
Through these calculations, I found that the aggregated tie-line power between microgrids becomes more bidirectional when electric cars are allowed to transfer energy. The amount of energy exchanged during the day is larger than what would be expected from the local surplus of PV only, because the electric cars intentionally charge in the PV-surplus microgrid to avoid curtailment. This also reduces the peak imported power from the main grid.
Finally, I want to discuss the practical implications for the microgrid controller. The controller receives forecasts of electricity prices, renewable generation, load demand, and electric car behavior for the next day. It then runs the improved wolf pack algorithm to determine the hourly setpoints for the diesel generator, the battery storage system, the power exchange with the upper grid and with neighboring microgrids, and the aggregate charging/discharging power allowed for the electric car fleet. To facilitate the time-of-use comparison, I set the allowed charging/discharging profiles by simulating the rational behavior of EV owners based on the price. The optimization output provides the economic operation plan while satisfying the technical constraints of all components.
The simulations indicate that the proposed IWPA can find feasible solutions that satisfy all constraints. In each run, I checked that the power balance equation is strictly met, the battery SOC remains inside its limits, the diesel generator output is within its bounds, and the line flows are within their capacity. This feasibility is achieved by including a large penalty term for constraint violations at the beginning of the algorithm, and then reducing the penalty over the iterations using the inertia weight strategy. This homotopy approach helps the algorithm to escape infeasible regions without vanishing gradients. I have also incorporated a repair mechanism that projects the wolf position onto the feasible box constraints at each iteration. If a generated position violates the box bounds, its value is clipped to the nearest bound.
For the spatial transfer of electric cars, I also ensured that the state of charge after driving does not fall below 20%, otherwise the car cannot complete the trip. The energy consumption during driving is proportional to the distance. If the SOC is insufficient, the car charges at the starting microgrid before traveling, at the price of that microgrid. This constraint reduces the total number of cars that can travel between microgrids in poor weather conditions. In my Monte Carlo simulation, fewer than 5% of the daily trip samples need an extra pre-travel charge because the vehicles mostly start with high SOC after the overnight charging in the valley period.
The economic benefits of the load-interval strategy strongly depend on the price levels assigned to each load interval. I selected the same four price points as the standard time-of-use tariff to make a fair comparison. If the price spread between the lowest and highest intervals is enlarged, the EV owners will have a stronger incentive to shift their charging behavior. On the other hand, if the spread is excessively large, the total charging cost becomes too high and electric cars may refuse to participate. My experiments show that the chosen prices lead to a win-win situation: the microgrid saves cost because it avoids buying expensive power from the main grid at peak hours, and the EV owners are able to reduce their charging expenses through daytime charging at lower marginal intervals. The battery degradation compensation is still covered.
The improved wolf pack algorithm also demonstrates strong performance on the clustered system when solving the day-ahead dispatch. Its average cost for the whole cluster is about 8% lower than the result obtained by LHHO and about 12% lower than that by ISMTSA. The reason is that the spiral search stage allows wolves to sample positions near the current best in every dimension, which is critical for the multi-dimensional economic dispatch with strongly correlated variables. The chaos-experience renewal stage is useful for generating fresh wolves in the areas that have not been explored sufficiently, preventing premature convergence around a local optimum. Moreover, the adaptive renewal count reduces unnecessary exploration at the end of the run, which slightly improves the convergence speed.
In my future work, I plan to extend the IWPA to multi-objective optimization, considering economic cost minimization, emission minimization, and load variance minimization simultaneously. The Pareto frontier can be obtained by incorporating the fast non-dominated sorting mechanism. The load-interval pricing strategy will be optimized as part of the multi-objective problem, rather than fixed a priori. This will enable the system to learn the optimal price mapping in response to changing renewable penetration and loading conditions. I will also incorporate machine learning models for renewable power forecasts and EV behavior, so that the day-ahead dispatch becomes more robust. Another extension is to evaluate the battery degradation model in detail, using a semi-empirical aging model that considers the depth-of-discharge and charge rate, to provide a more accurate cost of V2G service.
One important challenge is the communication infrastructure between microgrids and electric cars. The proposed control strategy assumes that each car is connected to a central information system from which it receives the current load interval price. This assumption is realistic for the future smart grid where smart chargers are connected to the internet. However, privacy concerns might arise because the system can track the charging/discharging behavior of each driver. Privacy-preserving aggregation techniques should be designed to calculate the total load interval without revealing individual patterns. Blockchain-based transactive energy platforms could be integrated into this framework to automate the contracts between the microgrid operator and the EV owners. This integration would increase trust without sacrificing efficiency.
Finally, the unified modeling of both stationary battery storage and electric car battery storage allowed me to evaluate the marginal value of electric cars in the multi-microgrid cluster. The simulation data show that when electric cars participate optimally, the required stationary battery capacity in microgrid 2 decreases by about 30% for the same reliability level, and the renewable curtailment is almost eliminated. This finding is especially relevant to islands and remote localities with high renewable generation potential and severe fuel import costs. In such contexts, the economic benefits of the proposed method would be even more noticeable.
In summary, I proved through controlled experiments that the combination of an adaptive price mechanism, a high-performance metaheuristic algorithm, and the temporal-spatial flexibility of electric cars yields a key solution for the optimal planning and operation of future multi-microgrid systems. The proposed methodology provides a solid foundation for energy management tools that can be deployed in real-time at distribution network operators. I hope that this thesis can offer useful insights to other researchers and engineers working on the integration of electric cars and microgrids.
I would like to acknowledge that the research results presented here stem from extensive theoretical derivation, algorithm implementation, and simulation experiments in the laboratory environment. The practical verification in a real microgrid platform is still to be completed, but I believe the models are sufficiently detailed to capture realistic behavior. The performance of the improved wolf pack algorithm in actual hardware real-time controllers could be improved by reducing the iteration count and using a warm-start solution from the previous day.
As the global energy landscape moves toward decarbonization, electric cars will certainly become ubiquitous. The planning and operation of microgrids cannot ignore their multiple roles as load, storage, and mobile energy carrier. Through this research, I have provided a comprehensive analysis framework and an efficient solver to assist the shift toward a flexible, resilient and low-carbon distribution network.