The rapid proliferation of battery electric vehicles (EVs) represents a significant shift in the transportation sector, driven by advancements in smart cabin technologies and a growing global emphasis on environmental sustainability. This surge necessitates the parallel development of a robust and extensive network of Electric Vehicle Charging Stations (EVCS). However, the widespread integration of these stations into existing power distribution networks introduces substantial technical and economic challenges. The inherent randomness and high-power demand of EV charging loads can severely impact grid stability, leading to increased network losses, voltage fluctuations, and heightened peak demand.
To mitigate these adverse effects and facilitate a smoother energy transition, this research proposes a novel, comprehensive planning framework. The core idea is the joint optimal planning of EVCS and Battery Energy Storage Systems (BESS). By strategically co-locating and sizing these components, the system can buffer the grid from volatile charging demands. This study formulates a multi-objective optimization model that holistically considers the often-conflicting interests of three key stakeholders: the EVCS investor, the power grid operator, and the EV users. To solve this complex problem efficiently, we employ an advanced Multi-Objective Mayfly Algorithm (MOMA) coupled with an Improved Grey Target Decision-Making (IGTDM) method for selecting the best compromise solution.
1. Modeling Framework for EV Charging Demand and BESS
Accurate forecasting of EV charging demand is the cornerstone of effective planning. The charging behavior of a battery EV car is highly stochastic, depending on user driving patterns. We model this randomness using probability density functions (PDFs) for key variables.
1.1 Probabilistic Modeling of EV User Behavior
The daily driving distance of a battery EV car is assumed to follow a lognormal distribution:
$$f_d(d) = \frac{1}{d \sigma_d \sqrt{2\pi}} \exp\left(-\frac{(\ln d – \mu_d)^2}{2\sigma_d^2}\right)$$
where $d$ is the daily travel distance, and $\mu_d$ and $\sigma_d$ are its mean and standard deviation, respectively.
The start time of a daily trip for a battery EV car is modeled as a mixture of two normal distributions, reflecting morning and evening commute peaks:
$$f_t(t_{ev}) = \frac{\gamma}{\sigma_{t,1}\sqrt{2\pi}} \exp\left(-\frac{(t_{ev} – \mu_{t,1})^2}{2\sigma_{t,1}^2}\right) + \frac{1-\gamma}{\sigma_{t,2}\sqrt{2\pi}} \exp\left(-\frac{(t_{ev} – \mu_{t,2})^2}{2\sigma_{t,2}^2}\right)$$
where $t_{ev}$ is the trip start time, $\mu_{t,1}, \sigma_{t,1}$ and $\mu_{t,2}, \sigma_{t,2}$ are parameters for the two peaks, and $\gamma$ is a weighting factor.
The initial State of Charge (SOC) of a battery EV car at the start of the day is also modeled with a normal distribution:
$$f_s(S_{ev}) = \frac{1}{\sigma_s \sqrt{2\pi}} \exp\left(-\frac{(S_{ev} – \mu_s)^2}{2\sigma_s^2}\right)$$
where $S_{ev}$ is the initial SOC.
Using these PDFs, a Monte Carlo simulation is performed to generate a large ensemble of daily driving profiles for a fleet of battery EV cars. The required charging energy $P_{ev}^{cha}$ for a vehicle is then determined based on its post-trip SOC ($S_{tr}$):
$$
P_{ev}^{cha} =
\begin{cases}
(S_{max} – S_{ev}) \cdot E_{ev}, & \text{if charging immediately (no trip)} \\
(S_{max} – S_{tr}) \cdot E_{ev}, & \text{if charging after a trip} \\
0, & \text{if no charging needed}
\end{cases}
$$
where $S_{max}$ is the maximum SOC, $E_{ev}$ is the battery capacity of the EV, and $S_{tr} = S_{ev} – \frac{D \cdot E_{loss}}{E_{ev}}$, with $D$ being the distance traveled and $E_{loss}$ the energy consumption per kilometer.
1.2 Battery Energy Storage System (BESS) Model
To address the short-term, high-power nature of EV charging loads, Lithium-ion battery-based BESS is selected for its fast response and efficiency. The state of the BESS is updated as follows:
$$
E_{bess}(t+1) =
\begin{cases}
E_{bess}(t) + P_{bess}^{cha}(t) \cdot \eta_{cha} \Delta t, & \text{Charging} \\
E_{bess}(t) – \frac{P_{bess}^{dis}(t)}{\eta_{dis}} \Delta t, & \text{Discharging}
\end{cases}
$$
where $E_{bess}(t)$ is the energy stored at time $t$, $P_{bess}^{cha/dis}(t)$ is the charge/discharge power, and $\eta_{cha/dis}$ are the efficiency coefficients.
2. Multi-Objective Optimization Model
The planning problem is formulated with three primary objectives to balance economic and technical performance.
2.1 Objective Functions
Objective 1: Minimize Total Annualized Cost. This cost encompasses the investment and operational expenses for both EVCS and BESS.
$$ \min F_1 = C_{an}^{evcs} + C_{lcc}^{bess} $$
The EVCS cost includes land purchase, equipment, and operation & maintenance (O&M):
$$
\begin{aligned}
C_{an}^{evcs} &= \mu_{crf}^{evcs} \sum_{n=1}^{N_{evcs}} (C_{land,n} + C_{eq,n} + C_{om,n}^{evcs}) \\
C_{land,n} &= C_{land} \cdot [N_{cs} \cdot A_p \cdot (1+\alpha) + A_{ep}] \\
C_{eq,n} &= C_{fix} + C_{cs} \cdot N_{cs} + \beta \cdot E_{evcs} \\
C_{om,n}^{evcs} &= \gamma_{om}^{evcs} \cdot E_{evcs}
\end{aligned}
$$
The BESS cost includes total capital cost, O&M, replacement, and recycling costs:
$$
\begin{aligned}
C_{lcc}^{bess} &= \mu_{crf}^{bess} \sum_{n=1}^{N_{bess}} (C_{tc,n} + C_{om,n}^{bess} + C_{rmc,n} – C_{rc,n}) \\
C_{tc,n} &= C_{bat} E_{bess,r} + C_{inv} P_{bess,r} \\
C_{om,n}^{bess} &= \gamma_{om}^{bess} \cdot C_{tc,n} \\
C_{rmc,n} &= C_{tc,n} \sum_{h=1}^{N_{rm}} \frac{1-\theta}{(1+p)^{h T_{rm}}} \\
C_{rc,n} &= C_{tc,n} \sum_{h=1}^{N_{rm}} \frac{\delta}{(1+p)^{h T_{rm}}}
\end{aligned}
$$
Objective 2: Minimize Active Power Losses in the Distribution Network. High and fluctuating loads from battery EV car charging can increase network losses significantly.
$$ \min F_2 = \sum_{t=1}^{T} \sum_{c=1}^{N_{line}} R_c |I_c(t)|^2 $$
where $R_c$ is the resistance of branch $c$, and $I_c(t)$ is the current flowing through it at time $t$.
Objective 3: Minimize Load Fluctuation. A smooth load profile reduces stress on grid infrastructure and generation resources.
$$ \min F_3 = \sum_{t=1}^{T-1} \sum_{q=1}^{N_{node}} |P_q(t+1) – P_q(t)|^2 $$
where $P_q(t)$ is the net load at node $q$ at time $t$.
2.2 Constraints
The optimization is subject to various technical and operational constraints:
EVCS Constraints:
$$ D_{evcs}^{r,min} \le D_{evcs}^d \le D_{evcs}^{r,max}, \quad E_{evcs}^{min} \le E_{evcs} \le E_{evcs}^{max} $$
These ensure reasonable spacing between stations and limit their installed capacity.
Power Grid Constraints:
$$ U_q^{min} \le U_q \le U_q^{max}, \quad P_{dn} = P_{loss} + P_{ev,load} + P_{bess} $$
These maintain nodal voltages within limits and enforce power balance.
BESS Constraints:
$$
S_{bess}^{min} \le S_{bess}(t) \le S_{bess}^{max}, \quad P_{bess}^{cha,min} \le P_{bess}^{cha}(t) \le P_{bess}^{cha,max}, \quad P_{bess}^{dis,min} \le P_{bess}^{dis}(t) \le P_{bess}^{dis,max}
$$
These manage the storage’s state of charge and charge/discharge power rates.
3. Solution Methodology: MOMA-IGTDM
To solve this complex, non-linear, multi-objective optimization problem, we employ the Multi-Objective Mayfly Algorithm (MOMA). MOMA is a metaheuristic inspired by the swarming behavior of mayflies, featuring distinct male and female populations that interact through attraction and mating to explore the Pareto front effectively.
3.1 Multi-Objective Mayfly Algorithm (MOMA)
The position update for a mayfly (a potential solution) is given by:
$$ x_p(k+1) = x_p(k) + v_p(k+1) $$
The velocity update differs for male and female mayflies and depends on their personal best ($pbest$), the global best ($gbest$), and mutual attraction. For a male mayfly that is not the current best:
$$ v_p^{m}(k+1) = v_p^{m}(k) + \alpha_1 e^{-\beta r_p^2}(pbest_p – x_p^m(k)) + \alpha_2 e^{-\beta r_g^2}(gbest – x_p^m(k)) $$
For the best male, a dancing component is added: $v_p^{m}(k+1) = v_p^{m}(k) + d \cdot r$, where $d$ is a dance coefficient and $r$ is a random vector. Female mayflies are attracted to males based on a comparison of their fitness values $f(x)$:
$$ v_p^{f}(k+1) = \begin{cases} v_p^{f}(k) + \alpha_2 e^{-\beta r_{fm}^2}(x_p^m(k) – x_p^f(k)), & \text{if } f(x_p^f) > f(x_p^m) \\ v_p^{f}(k) + fl \cdot r, & \text{if } f(x_p^f) \le f(x_p^m) \end{cases} $$
Mating between top males and females produces offspring, enriching the population’s diversity:
$$ offspring_1 = L \cdot x_p^{m} + (1-L) \cdot x_p^{f}, \quad offspring_2 = L \cdot x_p^{f} + (1-L) \cdot x_p^{m} $$
where $L$ is a random number in [0,1].
3.2 Improved Grey Target Decision-Making (IGTDM)
MOMA produces a set of non-dominated solutions (Pareto front). To select a single, best-compromise solution without subjective bias, we use an IGTDM method weighted by the Entropy Weight Method (EWM).
First, a decision matrix $X$ is constructed using normalized objective values ($F_j^i$) along with two distance metrics for each solution $i$:
$$ X = [F_j^i, E_d^i, M_d^i] $$
where the Euclidean Distance $E_d^i = \sqrt{\sum_{j=1}^{m} (F_j^i – Y_j)^2}$ and the Mahalanobis Distance $M_d^i = \sqrt{(F^i – u)^T \Sigma^{-1} (F^i – u)}$ measure proximity to the ideal point and account for correlations, respectively.
The EWM calculates objective weights $\omega_j$ based on the information entropy $e_j$ of each criterion:
$$ e_j = -\frac{1}{\ln n} \sum_{i=1}^{n} p_j^i \ln(p_j^i), \quad \omega_j = \frac{1 – e_j}{\sum_{j=1}^{m} (1 – e_j)}, \quad \text{where } p_j^i = \frac{x_j^i}{\sum_{i=1}^{n} x_j^i} $$
The “bull’s-eye” (ideal solution) $b^{best}$ in the normalized, weighted decision space is identified. Finally, the weighted Mahalanobis distance $M_{d,a}^i$ of each solution to the bull’s-eye is calculated. The solution with the smallest $M_{d,a}^i$ is selected as the optimal compromise plan.
4. Case Study and Results Analysis
The proposed model and algorithm are tested on a modified IEEE 33-bus radial distribution system. A fleet of 2000 battery EV cars is simulated. The algorithm parameters are set as: maximum iterations = 250, population size = 50, archive size = 100. Results are compared with a standard Multi-Objective Particle Swarm Optimization (MOPSO) algorithm.
4.1 Optimization Results
The table below summarizes the key performance indicators for different planning scenarios.
| Algorithm / Scenario | Power Loss (MWh) | Load Fluctuation (MW) | Total Cost (Million $) |
|---|---|---|---|
| Base Case (No EVCS) | 0.9145 | 7.726 | — |
| MOMA (EVCS only) | 2.3293 | 16.7615 | — |
| MOMA (EVCS + BESS) | 2.3462 | 9.957 | 4.8849 |
| MOPSO (EVCS only) | 3.6337 | 22.109 | — |
| MOPSO (EVCS + BESS) | 3.6749 | 20.107 | 4.5778 |
The detailed configuration obtained by MOMA for the joint EVCS-BESS system is as follows:
| Bus Location | EVCS Capacity (kW) | BESS Capacity (kW) |
|---|---|---|
| 3 | 442.93 | 1464.73 |
| 19 | 401.25 | 2505.24 |
| 21 | 410.61 | 579.25 |
| 25 | 402.69 | 1542.07 |
| 5 | 401.29 | 1402.33 |
| 22 | 417.80 | 1229.59 |
4.2 Performance Analysis
The results clearly demonstrate the efficacy of the proposed joint planning approach. Integrating BESS with EVCS leads to a dramatic improvement in grid stability. Compared to the “EVCS only” scenario, the MOMA-based plan with BESS reduces the load fluctuation metric by 40.6% (from 16.76 MW to 9.96 MW), while incurring only a marginal 0.72% increase in power losses. This trade-off is highly favorable for grid operation. The BESS effectively performs peak shaving and valley filling, smoothing the net load curve seen by the distribution network.
While the MOPSO solution yields a slightly lower investment cost, it results in significantly higher power losses (56.6% higher than MOMA) and worse load fluctuation. This highlights MOMA’s superior ability to navigate the complex search space and find solutions that better balance all three objectives. The Pareto front obtained by MOMA showed good diversity and convergence.
The operational strategy of the configured BESS units further validates the model. The charge/discharge power profiles show active engagement, charging during low-load periods (often coinciding with low electricity prices or high renewable output) and discharging during EV charging peaks, thereby flattening the aggregate demand.
5. Conclusion
This research presents a comprehensive framework for the optimal co-planning of Electric Vehicle Charging Stations and Battery Energy Storage Systems. By modeling the stochastic demand of battery EV cars and formulating a tri-objective optimization problem, the study successfully addresses the economic concerns of investors, the service quality for users (implied via load satisfaction), and the technical challenges faced by the grid, notably stability and efficiency.
The integration of BESS is proven to be a critical enabler, transforming EVCS from a passive load burden into a flexible grid asset capable of mitigating load fluctuations. The advanced Multi-Objective Mayfly Algorithm, combined with the Improved Grey Target Decision-Making method, proved effective in solving this complex problem, yielding a planning solution superior to a conventional MOPSO approach. The proposed methodology offers a practical tool for planners and utilities to develop a cost-effective and grid-friendly EV charging infrastructure, facilitating the sustainable integration of electric mobility. Future work will incorporate more granular traffic network constraints, such as queuing at charging stations and road congestion effects, to further enhance the realism and applicability of the model.