Impact of Coordinated Electric Ferry Charging on Distribution Network Using Metaheuristic Optimization

Abstract

The maritime shipping sector is a major contributor to greenhouse gas emissions, particularly in coastal regions. In response, the adoption of electric ferries powered by renewable energy and supported by battery storage technologies has emerged as a viable decarbonization pathway. This study investigates the operational impacts of coordinated electric ferry charging on a medium-voltage distribution network at Gladstone Marina, Queensland, Australia. Using DIgSILENT PowerFactory integrated with MATLAB Simulink and a Python-based control system, four proposed ferry terminals equipped with BESSs (Battery Energy Storage Systems) are simulated. A dynamic model of BESS operation is optimized using a balanced hybrid metaheuristic algorithm combining GA-PSO-BFO (Genetic Algorithm-Particle Swarm Optimization-Bacterial Foraging Optimization). Simulations under 50% and 80% transformer loading conditions assess the effects of charge-only versus charge–discharge strategies. Results indicate that coordinated charge–discharge control improves voltage stability by 1.0–1.5%, reduces transformer loading by 3–4%, and decreases feeder line loading by 2.5–3.5%. Conversely, charge-only coordination offers negligible benefits. Further, quasi-dynamic analyses validate the system’s enhanced stability under coordinated energy management. These findings highlight the potential of docked electric ferries, operating under intelligent control, to act as distributed energy reserves that enhance grid flexibility and operational efficiency.

1. Introduction

Emissions generated by ocean-going vessels represent a measurable fraction of total global greenhouse gas output, with estimates placing this contribution at approximately three percent, contributing approximately one billion tons of CO₂ annually [1,2]. In response to increasing environmental concerns, the IMO (International Maritime Organization) has implemented regulatory frameworks aimed at mitigating air pollution from conventional marine diesel engines. In response to growing environmental concerns, international regulatory frameworks have established long-term objectives aimed at significantly lowering carbon emissions from the global shipping industry [3]. One such objective aspires to cut emissions from maritime transport by half by the middle of the century, relative to 2008 benchmarks [3]. Meeting this goal will require a transition toward cleaner propulsion technologies, including the adoption of electric and hybrid maritime vessels supported by renewable energy integration. Technologies including solar PV (Photovoltaic) systems, hydrogen fuel cells, batteries, and super-capacitors are central to this transition, though high initial investment remains a barrier [2]. The deployment of EFs, while offering environmental benefits, poses new challenges for power systems. Their integration into existing electrical grids demands advanced planning, as EFs can significantly affect grid stability due to their nonlinear and high-load charging profiles [2]. Although research on electric vehicle (EV) impacts on electrical networks is extensive [4], studies specifically focusing on EF charging remain limited [5]. Insights from EV-related studies show that uncontrolled charging can lead to peak demand surges, voltage instability, increased energy losses, and reduced efficiency and lifespan of grid components [6,7,8,9,10]. Strategies such as coordinated charging, load management, and the integration of storage systems have shown promise in mitigating these effects [9,11]. Advanced simulations have highlighted various grid-level impacts. For instance, studies on residential and commercial charging show modest voltage effects, notable increases in line loading, and shifts in peak load periods [12]. High-speed charging introduces distinct technical complications, such as increased harmonic distortion and adverse impacts on voltage stability within the power network, which can be mitigated through storage integration, filter design, and charging control techniques [11,13]. V2G (Vehicle to Grid) and V2V (Vehicle to Vehicle) technologies have emerged as viable solutions for managing bidirectional energy flow, reducing losses, and improving grid reliability [14,15]. A case study conducted in Australia examines the effects of electric ferry charging on the distribution network at Gladstone Marina, utilizing DIgSILENT PowerFactory 2024 for simulation and analysis. The study employs real load demand data and models four proposed EF charging stations with Battery Energy Storage Systems (BESSs) to emulate realistic charge-discharge cycles [2,16]. The BESSs are controlled using a balanced hybrid GA-PSO-BFO optimization algorithm developed in Python 3.12 and MATLAB Simulink 2020a. The analysis focuses on transformer and line loading, bus voltages, and system performance under increased load scenarios (50% and 80% capacity utilization). Results indicate that coordinated BESS operation can stabilize grid performance under high EF charging demands [2,16,17]. This research contributes a framework for evaluating EF integration into existing power systems, emphasizing the importance of optimized energy storage management and coordinated charging. The study concludes by identifying the need for real-world operational data and further research into uncoordinated EF charging impacts and infrastructure planning to support maritime electrification.

2. Gladstone Marina Network Characteristics

The Gladstone Marina grid, located in Queensland, Australia, is predominantly powered by centralized electricity sourced from the Gladstone Power Station, one of Queensland’s largest coal-fired plants. While the regional grid is interconnected through Ergon Energy’s infrastructure, allowing for supplemental supply from gas and hydro generation, the direct integration of renewable energy sources within the marina area remains limited. This grid does not yet host significant on-site renewable energy installations. The Gladstone region has demonstrated suitability for solar photovoltaic integration. The subtropical coastal climate, characterized by high solar insolation and moderate wind patterns, supports the future deployment of distributed energy resources (DERs). Rooftop solar potential is considerable given the presence of commercial buildings, ferry maintenance depots, and open rooftop space at ferry terminals. Unlike major urban coastal networks such as those in Sydney or Melbourne, Gladstone’s grid exhibits notable seasonal load variability driven by fluctuations in marine activity and tourism, especially during the summer months. This seasonality affects the power demand profile and presents challenges for maintaining voltage and current stability. Compared to international coastal grids, such as those in parts of Europe with high renewable penetration and advanced grid automation, the Gladstone Marina system remains relatively traditional, offering a realistic and constrained environment to evaluate the effectiveness of charging electric ferry storage and hybrid optimization strategies.

The Gladstone Marian distribution is powered by the Gladstone 11 kV Marina feeder. This feeder is energized by the Clinton 33/11 kV substation [2,18]. This substation supplies five distinct 11 kV feeders, which are Clinton Park, Callemondah Drive, Hason Road, Kin Kora, and Marina [2]. The load profile of the Marina feeder is strongly influenced by ferry schedules, tourism cycles, and associated commercial activity. Peak demand occurs during daylight hours, typically between 9:00 and 17:00, with seasonal surges in summer months due to increased ferry frequency and passenger volume. Conversely, off-peak conditions dominate during early morning and night-time hours. This seasonally driven load fluctuation necessitates adaptive energy management strategies, especially when introducing high-power electric ferry charging stations that could otherwise exacerbate network congestion. Figure 1 and Figure 2 show the monthly load profile and seasonal hourly load profile of the Marina feeder. The Gladstone Marina feeder exhibits distinct monthly and seasonal hourly load patterns, reflective of its marine tourism, residential, and light commercial activities. Monthly load profiles reveal increased electricity demand during the summer months (December to February), driven by higher cooling loads and intensified marina operations. Conversely, demand typically dips during the winter months (June to August). Seasonal hourly load profiles indicate two notable peaks, a morning peak between 8:00 and 10:00 a.m. and a pronounced evening peak around 6:00 to 8:00 p.m. These patterns highlight the influence of human activity cycles and climatic conditions on the feeder’s load behavior, underlining the importance of adaptive energy management and storage coordination strategies to mitigate stress during peak periods.

The Gladstone Marina distribution network, located in Queensland, Australia, is a coastal energy system characterized by its limited scale and specialized operational context. It primarily serves maritime infrastructure, commercial activities, and transportation needs, including electric ferry charging. The network is configured as a medium-voltage radial system with minimal integration of large-scale renewable energy sources, relying mainly on centralized grid supply. The layout of the distribution network, including positions of transformers and designated electric ferry charging sites, is derived from a visual interpretation of a clearly defined 11 kV circuit traceable through Google Earth Pro imagery [2]. The distribution network architecture is illustrated in Figure 3 [2,19], where distinct feeder paths are marked using color-coded schematics for improved clarity [2,20], including the integration points for four proposed ferry charging facilities are marked by red circles, namely MIPEC, Sea Link, Curtis Ferry Services, and the Heron Island terminal [2]. The 11 kV and 0.415 kV system are represented by red and blue color lines respectively. The baseline daily load pattern of the selected distribution network is depicted in Figure 4, which excludes any electric ferry charging demands.

3. Simulated Test Distribution Network Design

An in-depth analysis is undertaken to assess the operational effects of electric ferry charging on critical parameters within a medium-voltage distribution system [1,2]. The investigation centers on a modeled distribution network reflective of conditions near Gladstone Marina [2], specifically emulating the electrical behavior of the 11 kV Marina feeder [2]. The system topology comprises 129 busbars [2], spanning voltage levels of 11 kV and 0.415 kV [2]. Transformer locations are estimated through geospatial analysis, utilizing high-definition satellite data and measurement tools available via Google Earth Pro [2], which also aided in the spatial organization of prospective charging infrastructure in the Gladstone Marina precinct [2]. Electricity demand patterns for the 11 kV Marina feeder and transformer capacities are obtained from Ergon Energy, the principal electricity distributor in Queensland [2].

The transformer power rating plays a vital role in ensuring the reliable operation of the distribution network, particularly when managing both the typical load and the activity of the BESSs. It defines the highest amount of power the transformer can safely support. If the combined power demand from connected loads and battery charging surpasses this threshold, it may lead to overheating and shorten the lifespan of the equipment. On the other hand, when battery units are effectively coordinated to charge during periods of low demand and discharge during times of high demand, they can alleviate pressure on the transformer. This coordination is especially significant for the selected test distribution network, which is subject to both seasonal and daily changes in electricity demand. Distribution transformers are rated for 11 kV/0.415 kV to link high-voltage buses with lower-voltage ones to supply local loads [2]. For clarity, the busbars are denoted by “A” for 11 kV and “B” for 415 V levels [2]. To evaluate the influence of electric ferry charging on low-voltage network performance, four designated charging facilities Marina_Ave_Pioneer_Seafoods, BryanJDr_MarinaAveue, CQUni_BJDFerryTerminal_Opp, and Marina_Ave_Slipway are integrated at the 415 V level [2]. Each site features a BESS with optimally selected energy and power ratings of 300 kWh (200 kW), 250 kWh (150 kW), 400 kWh (300 kW), and 400 kWh (300 kW), respectively [2]. These specifications are determined based on the technical constraints of nearby distribution transformers, ensuring compatibility with existing infrastructure [2]. The optimal capacities are determined using a hybrid metaheuristic optimization approach, as presented in the authors’ previously published research [21]. The network’s conductor and cable types include Pluto (19/3.75 AAC), Wasp (7/0.173 AAC), Moon (7/4.75 AAC), and underground U/G 11 kV 185 mm² Aluminum Triplex XLPE PVC/HDPE. Line lengths are estimated based on spatial distances between buses as measured via Google Earth Pro.

The sizing of BESSs is carefully determined to ensure the stable and reliable operation of the distribution network. This process aims to keep key performance indicators such as voltage variation, conductor loading, and power losses within the acceptable limits defined by the ANER (Australian National Electricity Rules). These rules specify technical and operational standards that are essential for maintaining the efficiency and security of the electricity grid. For example, voltage levels at customer connection points must remain within six percent above or below the nominal value. In addition, current limits are imposed to prevent overheating of conductors and transformers, and power losses must be minimized to support system efficiency. These criteria include maintaining voltage within a +10% to −6% margin around nominal (1.0 p.u.), preventing line current from surpassing rated capacities, and limiting total system utilization to below 10% of its maximum rated load [22,23]. Ensuring compliance with these standards is particularly important when incorporating energy storage systems, as they influence the network’s ability to accommodate changing patterns of load and generation while protecting equipment and maintaining service quality.

Figure 5, Figure 6 and Figure 7 illustrate the simulated models of the selected test distribution network created using DIgSILENT PowerFactory software. This system model comprises three interlinked distribution sections that together reflect the configuration of the test setup, as presented across these figures. Figure 5, in particular, highlights the inclusion of four BESSs, depicted as circular icons, representing the combined energy storage and charging infrastructure intended for deployment at the Gladstone Marina site. To study the influence of EF charging on network performance, quasi-dynamic power flow simulations are carried out [2,19]. These simulations test the network’s behavior under increased loading conditions, specifically, load scenarios at 50% and 80% of the original test system demand. Two BESS operation strategies are assessed—one where only charging is coordinated and another where both charging and discharging are scheduled in response to system needs. Initially, the network’s power flow is analyzed without the inclusion of BESSs, creating a baseline for comparison [2]. Subsequent simulations introduce BESS operations under both coordinated scenarios, allowing evaluation of their relative impact using the base case results as a benchmark [2]. The control strategy for BESSs is synchronized with the demand curve where charging occurs during low-load hours, while discharging is executed during high-demand periods [24,25]. To reflect this, energy storage is set to charge between 1:00 a.m. and 5:00 a.m. (off-peak) and discharge between 9:00 a.m. and 4:00 p.m. (peak hours), following the load trends of the 11 kV Marina feeder. For optimal efficiency, the most active charging window is defined as 1:00 a.m. to 3:00 a.m., and the primary discharging interval is scheduled between 1:00 p.m. and 2:00 p.m. [26,27]. The SOCs of BESSs are maintained between 20% and 80%, ensuring that the BESSs do not overcharge or deeply discharge, thus preserving battery health and system reliability. To manage energy storage behavior effectively, a control logic is designed to regulate charge/discharge cycles based on real-time load demand, current SOC levels, and the network’s operational constraints [2]. This control algorithm, developed in Python, is integrated with a MATLAB Simulink-based dynamic model of the BESS, and both are connected to the PowerFactory simulation to coordinate system behavior with changing network conditions and to ensure regulatory compliance.

4. BESS Modelling

This research incorporates MATLAB Simulink to create a dynamic model of four Battery Energy Storage Systems (BESSs), each modeled using the technical specifications of the Corvus Orca ESS, which is widely used in marine energy storage applications. The configuration details of a single Corvus Orca ESS unit are presented in Table 1 [28]. These modules are arranged in various combinations to emulate the required storage capacities of the four BESS units used in the study. To realistically simulate system behavior, the dynamic responses of lithium-ion batteries were embedded into the MATLAB environment. These dynamic features have been designed to enable the model to adapt its charge and discharge cycles based on real-time fluctuations in the power network during coordinated energy management. Table 2 outlines the specific dynamic battery parameters incorporated in the model. To meet the capacity needs of each BESS, distinct series-parallel arrangements of ESS modules were configured. For example, BESS units A and B, each rated at 400 kWh (300 kW), consist of 54 modules configured in 9-series and 6-parallel strings. BESS C, rated at 300 kWh (200 kW), uses 36 modules (9-series, 4-parallel), while BESS D, with a 250 kWh (150 kW) rating, employs 27 modules (9-series, 3-parallel). These configurations and their rationale are detailed in Table 3.

To simulate how these storage units behave within a broader distribution network, the BESS dynamic attributes are also transferred to DIgSILENT PowerFactory. Figure 8 illustrates the Simulink block representation of the BESS model. The procedure used to connect this MATLAB-based model with external applications is outlined in Figure 9. Figure 9 details the process of generating a DLL (Dynamic Link Library) from the MATLAB BESS model, which is essential for linking with external simulation tools. It begins with the model being developed and validated in MATLAB. After validation, MATLAB’s compiler is used to convert the model into a DLL format. This DLL serves as an interface that external platforms, like DIgSILENT PowerFactory, can load and interact with. The ‘DLL User Program’ can be any application that supports DLLs, facilitating external use of the dynamic BESS model. Once loaded, DIgSILENT PowerFactory communicates with the DLL through a defined API, enabling seamless integration of the MATLAB-defined battery behavior into the overall power system simulation. This integration approach ensures that the detailed battery characteristics remain intact during simulation, improving the accuracy of performance analysis in energy storage studies. By leveraging DLL technology, the MATLAB-based model can be effectively embedded into the DIgSILENT PowerFactory environment, ensuring coordinated simulations that reflect realistic BESS dynamics within the distribution network.

5. BESS Control Algorithm and Optimization

A custom control framework, developed in Python, governs the coordinated energy management of four Battery Energy Storage Systems (BESSs) based on their state of charge (SOC) and the real-time power demand of the simulated distribution network [2]. This logic has been embedded into the DIgSILENT PowerFactory simulation to enable intelligent decision-making at each simulation timestep. The control system evaluates hourly demand and determines charging or discharging actions for each BESS depending on predefined time windows and system conditions. SOC boundaries are enforced between 20% and 80% to prevent overcharging and deep discharging, promoting longevity and operational safety. Simultaneously, the algorithm monitors voltage levels and power factors, aiming to keep both close to unity, thereby maximizing system efficiency and ensuring regulatory compliance [2]. Due to their power-electronic interfacing, BESS units can swiftly inject or absorb reactive power, making them well-suited to stabilize voltage and correct the power factor dynamically. These capabilities are essential in managing sudden load changes and maintaining network equilibrium, especially during times of high and low demand [29]. This ability significantly enhances reliability while minimizing distribution losses [29]. Two core Python functions, voltage control and power factor control, form the backbone of the system’s response mechanism. The first assesses voltage deviations at critical nodes and issues corrective reactive power commands. The second continually adjusts the power factor to keep it near the ideal threshold. These routines are applied sequentially to preserve a stable and efficient operating environment within the network. The time-of-use logic embedded in the algorithm ensures energy is stored during off-peak periods (charging) and released during high-demand intervals (discharging). This alignment with the daily load pattern makes the control loop highly effective, as evidenced by results from power flow simulations [25]. The overall control logic is summarized in pseudo-code, referred to as Algorithm 1. To further enhance energy management, a sophisticated optimization strategy, referred to as a balanced hybrid GA-PSO-BFO algorithm, is incorporated [30].

Algorithm 1. Pseudo Code of BESS controller

Start Program1. Initialize the Distribution Network2. Initialize Battery Storage with Maximum Capacity3. Set Initial State of Charge (SOC) to 0.54. Create a Storage Controller5. Assign the Distribution Network to the Storage Controller6. Assign the Battery Storage to the Storage Controller7. Set Off-Peak Hours to range from 0 to 68. Set Peak Hours to range from 10 to 189. Set SOC High Threshold to 0.810. Set SOC Low Threshold to 0.211. Repeat Forever:        a. Get Current Hour from System Time        b. Get Load Demand from the Distribution Network        c. Get Voltage from the Distribution Network        d. Get Power Factor from the Distribution Network        e. If Current Hour is within Off-Peak Hours:                i. If Battery SOC is less than SOC High Threshold:                        - Calculate Charging Power using Battery’s Charge Function                        - Increase SOC accordingly                        - Reduce Load Demand by Charging Power        f. Else If Current Hour is within Peak Hours:                i. If Battery SOC is greater than SOC Low Threshold:                        - Calculate Discharging Power using Battery’s Discharge Function                        - Decrease SOC accordingly                        - Increase Load Demand by Discharging Power        g. If Voltage is greater than 1:                - Adjust Voltage to 1        h. If the Power Factor is greater than 1:                - Adjust Power Factor to 1End Program

5.1. Balanced Hybrid GA-PSO-BFO Algorithm

The balanced hybrid GA-PSO-BFO algorithm that combines genetic algorithm, particle swarm optimization, and bacterial foraging optimization is designed to utilize the distinct advantages of each technique in a structured and sequential manner. The process begins with the genetic algorithm, which explores the solution space using population-based operations such as selection, crossover, and mutation. This initial population is then refined by applying particle swarm optimization, which improves the convergence behavior by updating candidate solutions through a learning mechanism that incorporates both individual and collective experience. Following this, bacterial foraging optimization is applied to further improve the quality of solutions through biologically inspired operations, including directional movement, reproduction, and random dispersal. The parameter values for each algorithm are selected using commonly accepted standards, which are verified through sensitivity testing. These include the crossover and mutation probabilities in the genetic algorithm, the learning constants and inertia weight in particle swarm optimization, and the number of chemotactic steps and dispersal rates in bacterial foraging optimization. By combining exploration, convergence acceleration, and local refinement in a sequential structure, the hybrid method outperforms individual algorithms in terms of both solution accuracy and convergence time, as demonstrated through comparative performance evaluation. This hybrid model synergizes the strengths of GA, PSO, and BFO. Unlike conventional hybrids, which combine these methods without modulation, this balanced approach dynamically tunes each algorithm’s influence during execution.

To illustrate the internal structure and execution logic of the proposed hybrid optimization framework, a detailed flowchart is presented in Figure 10. The algorithm begins by initializing the population with 500 individuals, which are then sequentially processed through three optimization stages: Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Bacterial Foraging Optimization (BFO). In the GA phase, selection, crossover (rate = 0.8), and mutation (rate = 0.01) operators are applied to enhance population diversity and identify promising regions of the solution space. The refined population is passed to the PSO module, where individual solutions are further adjusted using velocity and position updates guided by inertia weighting (w = 0.729) and acceleration coefficients (c₁ = c₂ = 1.49). Subsequently, the BFO module performs a local search through chemotaxis, reproduction, and elimination-dispersal (probability = 0.25), allowing for fine-tuning and escape from local optima. Finally, a multi-objective fitness function incorporating a quadratic penalty factor (QPF) evaluates all solutions, and the best-performing individual is selected as the global optimum. This modular and sequential parallel structure ensures that the strengths of each algorithm, namely exploration through GA, convergence speed via PSO, and local exploitation using BFO, are collectively harnessed to enhance the quality and robustness of the obtained solution.

5.2. Computational Performance and Feasibility of the Hybrid Optimization Algorithm

The practical viability of any optimization algorithm for grid-interactive applications relies not only on solution quality but also on its execution time and computational efficiency. In this study, the hybrid GA-PSO-BFO algorithm is implemented in Python and interfaced with MATLAB Simulink and DIgSILENT PowerFactory to enable high-fidelity simulations of coordinated Battery Energy Storage System (BESS) operations. All simulations are executed on a PC equipped with an Intel Core i7-12700K processor (12 cores, 20 threads), 32 GB DDR4 RAM, and a 1 TB NVMe SSD running Windows 11. The average runtime for each optimization scenario, covering a full 24-h charging cycle across four electric ferry terminals, is approximately 14 min per trial. This duration is acceptable for day-ahead scheduling or operational planning contexts, though it may not be directly suitable for sub-minute real-time control applications. Despite the relatively higher computational demand compared to classical optimization methods, the hybrid algorithm offers significant benefits. Unlike traditional Mixed-Integer Linear Programming (MILP), which assumes linearity and deterministic parameters, the GA-PSO-BFO approach is more flexible in handling nonlinear, multi-modal, and uncertain system dynamics. This adaptability is crucial given the stochasticity in electric ferry arrival patterns, varying load profiles, and the multi-objective nature of grid constraints, including voltage regulation, transformer loading, and battery operational limits.

Moreover, MILP solvers often struggle with scalability when embedded in nonlinear environments or when subject to complex discrete constraints like on/off BESS states, variable charging rates, and power quality thresholds. In contrast, the hybrid method synergizes global exploration (GA), rapid convergence (PSO), and local refinement (BFO), leading to faster convergence to high-quality solutions while maintaining robustness against premature stagnation. As shown in earlier sections, this algorithm achieves better voltage stability and transformer loading reductions compared to standalone techniques. Thus, while MILP remains appropriate for structured and convex problems, the hybrid GA-PSO-BFO method is more appropriate for the real-world constraints and objectives presented in this study. It achieves a balance between computational tractability and optimization fidelity, making it a valuable tool for distribution network planning involving high-penetration electric ferry infrastructure.

5.3. Objective Function and Operational Constraints for Optimization

The critical system metrics, such as bus voltage levels, line currents, and power losses, are considered essential for optimization. These metrics must remain within the operational thresholds specified for the distribution system [31]. In particular, bus voltages must stay within ±5% of the nominal per-unit value [23], and line currents must not exceed their designated ratings. Power losses are constrained to a range of 10–15% of the distribution system’s overall power consumption [32]. The optimization model comprises three primary objectives. The first objective is to minimize the real and reactive power losses of the selected network, and the second objective is to minimize the system voltage and current deviations from nominal values so that the power flow remains within the operational limit [33]. The third object is to keep the power factor near unity for better voltage regulation [33]. To simplify the optimization process, a QPF (quadratic penalty factor) is included in the minimization process, which is included in the fourth, fifth, and sixth objectives. The equations 1 to 6 represent four objective functions for the optimization algorithm.

(1)$\mathrm{f}1={\sum }_{\mathrm{t}=1}^{24}{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{P}}_{{\mathrm{L}}_{\mathrm{i}}}\mathrm{and}\mathrm{f}1={\sum }_{\mathrm{t}=1}^{24}{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{Q}}_{{\mathrm{L}}_{\mathrm{i}}}$

(2)$\mathrm{f}2={\sum }_{\mathrm{t}=1}^{24}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{V}}_{\mathrm{i}}-{\mathrm{V}}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}}\right|/\mathrm{n}\mathrm{and}\mathrm{f}2={\sum }_{\mathrm{t}=1}^{24}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{I}}_{\mathrm{i}}-{\mathrm{I}}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}}\right|/\mathrm{n}$

(3)$\mathrm{f}3={\sum }_{\mathrm{t}=1}^{24}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathsf{\theta }}_{\mathrm{i}}-{\mathsf{\theta }}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}}\right|/\mathrm{n}$

(4)$\mathrm{f}4=\mathrm{Q}\mathrm{P}\mathrm{F}={\sum }_{\mathrm{t}=1}^{24}{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\left\{\begin{array}{c}{{(\mathrm{V}}_{\mathrm{i}}-{\mathrm{V}}_{\mathrm{m}\mathrm{i}\mathrm{n}})}^2;{\mathrm{V}}_{\mathrm{i}}\le {\mathrm{V}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\\ {0;\mathrm{V}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\le {\mathrm{V}}_{\mathrm{i}}\le {\mathrm{V}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\\ {{(\mathrm{V}}_{\mathrm{i}}-{\mathrm{V}}_{\mathrm{m}\mathrm{a}\mathrm{x}})}^2;{\mathrm{V}}_{\mathrm{i}}\ge {\mathrm{V}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\end{array}\right.$

(5)$\mathrm{f}5=\mathrm{Q}\mathrm{P}\mathrm{F}={\sum }_{\mathrm{t}=1}^{24}{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\left\{\begin{array}{c}{{(\mathrm{I}}_{\mathrm{i}}-{\mathrm{I}}_{\mathrm{m}\mathrm{i}\mathrm{n}})}^2;{\mathrm{I}}_{\mathrm{i}}\le {\mathrm{I}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\\ {0;\mathrm{I}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\le {\mathrm{I}}_{\mathrm{i}}\le {\mathrm{I}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\\ {{(\mathrm{I}}_{\mathrm{i}}-{\mathrm{I}}_{\mathrm{m}\mathrm{a}\mathrm{x}})}^2;{\mathrm{I}}_{\mathrm{i}}\ge {\mathrm{I}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\end{array}\right.$

(6)$\mathrm{f}6=\mathrm{Q}\mathrm{P}\mathrm{F}={\sum }_{\mathrm{t}=1}^{24}{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\left\{\begin{array}{c}{({\mathsf{\theta }}_{\mathrm{i}}-{\mathsf{\theta }}_{\mathrm{m}\mathrm{i}\mathrm{n}})}^2;{\mathsf{\theta }}_{\mathrm{i}}\le {\mathrm{Q}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\\ {0;\mathsf{\theta }}_{\mathrm{m}\mathrm{i}\mathrm{n}}\le {\mathsf{\theta }}_{\mathrm{i}}\le {\mathsf{\theta }}_{\mathrm{m}\mathrm{a}\mathrm{x}}\\ {({\mathsf{\theta }}_{\mathrm{i}}-{\mathsf{\theta }}_{\mathrm{m}\mathrm{a}\mathrm{x}})}^2;{\mathsf{\theta }}_{\mathrm{i}}\ge {\mathsf{\theta }}_{\mathrm{m}\mathrm{i}\mathrm{n}}\end{array}\right.$

where, ${\mathrm{P}}_{{\mathrm{L}}_{\mathrm{i}}}$ and ${\mathrm{Q}}_{{\mathrm{L}}_{\mathrm{i}}}$ are active power loss and reactive power losses at the ith line, respectively, and N is the total number of lines. ${\mathrm{V}}_{\mathrm{i}}$, ${\mathrm{I}}_{\mathrm{i}}$, and ${\mathsf{\theta }}_{\mathrm{i}}$ is the voltage, current, and power factor of the ith bus, respectively [34,35]; ${\mathrm{V}}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}}$, ${\mathrm{I}}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}}$, and, ${\mathsf{\theta }}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d}}$ are the rated voltage [35] and current for the distribution network for retaining power quality [35]. ${\mathrm{V}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ and ${\mathrm{V}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ represent maximum and minimum voltages, ${\mathrm{I}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ and ${\mathrm{I}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ represent maximum and minimum currents, and ${\mathsf{\theta }}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ and ${\mathsf{\theta }}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ denote maximum and minimum power factor, respectively. The operational constraints are determined according to the conventional distribution network constraints, which are represented by Equations (7)–(11).

(7)${\mathrm{V}}^{\mathrm{m}\mathrm{i}\mathrm{n}}\le {\mathrm{V}}_{\mathrm{i}}\le {\mathrm{V}}^{\mathrm{m}\mathrm{a}\mathrm{x}},\mathrm{i}=1\dots ..\mathrm{n}$

(8)${\mathrm{I}}^{\mathrm{m}\mathrm{i}\mathrm{n}}\le {\mathrm{I}}_{\mathrm{i}}\le {\mathrm{I}}^{\mathrm{m}\mathrm{a}\mathrm{x}},\mathrm{i}=1\dots \dots \mathrm{n}$

(9)${\mathrm{P}}^{\mathrm{m}\mathrm{i}\mathrm{n}}\le {\mathrm{P}}_{\mathrm{i}}\le {\mathrm{P}}^{\mathrm{m}\mathrm{a}\mathrm{x}},\mathrm{i}=1\dots ..\mathrm{n}$

(10)${\mathrm{Q}}^{\mathrm{m}\mathrm{i}\mathrm{n}}\le {\mathrm{Q}}_{\mathrm{i}}\le {\mathrm{Q}}^{\mathrm{m}\mathrm{a}\mathrm{x}},\mathrm{i}=1\dots ..\mathrm{n}$

(11)${\mathsf{\theta }}^{\mathrm{m}\mathrm{i}\mathrm{n}}\le {\mathsf{\theta }}_{\mathrm{i}}\le {\mathsf{\theta }}^{\mathrm{m}\mathrm{a}\mathrm{x}},\mathrm{i}=1\dots ..\mathrm{n}$

In this context, ${\mathrm{V}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ and ${\mathrm{V}}^{\mathrm{m}\mathrm{i}\mathrm{n}}$ represent the upper and lower voltage limits assigned to each bus i within the distribution network. Correspondingly, ${\mathrm{I}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ and ${\mathrm{I}}^{\mathrm{m}\mathrm{i}\mathrm{n}}$ define the allowable maximum and minimum current levels for the same bus. Whereas, ${\mathrm{P}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ and ${\mathrm{P}}^{\mathrm{m}\mathrm{i}\mathrm{n}}$ specify the permissible range for real power flow at each bus node. Similarly, ${\mathrm{Q}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ and ${\mathrm{Q}}^{\mathrm{m}\mathrm{i}\mathrm{n}}$ represent the permissible range for reactive power flow at each bus node. The ${\mathsf{\theta }}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ and ${\mathsf{\theta }}^{\mathrm{m}\mathrm{i}\mathrm{n}}$ defines the power factor limit for each bus. The total number of buses in the selected distribution system is denoted by n.

5.4. Sensitivity Analysis of Key Parameters of Hybrid GA-PSO-BFO Algorithm

A sensitivity analysis is conducted to investigate the impact of various hyperparameters on the optimization outcome. Seven key parameters across GA, PSO, and BFO are individually varied between low and high settings, and their corresponding best objective values are recorded. Table 4 summarizes the key hyperparameters of the hybrid GA-PSO-BFO optimization algorithm that affect optimization performance. The results, presented in Table 1, demonstrate that optimal performance is achieved when the crossover rate, inertia weight, and BFO chemotactic steps are appropriately tuned. For instance, increasing the crossover rate from 0.6 to 0.9 improves the objective value from 52.3 to 50.1, indicating enhanced search effectiveness. Similarly, PSO’s performance is sensitive to both inertia and acceleration coefficients, and the BFO stage is notably influenced by chemotaxis and swim parameters. This analysis confirms the importance of parameter tuning and supports the hybrid design choice, where balanced control of exploration and exploitation across the three algorithms is achieved through appropriate parameterization.

A comparative statistical analysis is conducted by running each optimization algorithm (GA, PSO, BFO, and the proposed hybrid GA-PSO-BFO) independently for 50 trials on the same optimization problem. The results in Table 5 demonstrate that the hybrid method consistently outperforms the individual algorithms in both solution accuracy and convergence stability. The mean objective value of the hybrid strategy is 49.01, which is lower than that of PSO (50.29), BFO (51.32), and GA (52.95). The standard deviation of the hybrid algorithm (0.69) is also comparable to or better than those of the standalone methods, indicating reliability across multiple executions. The boxplot in Figure 11 visually confirms the improved performance distribution, further justifying the adoption of a hybridized metaheuristic structure.

Generally, a convergence comparison plot is a graphical representation that illustrates how the objective function value evolves over successive iterations for different optimization algorithms. Figure 12 presents a convergence comparison of the standalone GA, PSO, and BFO algorithms with the proposed hybrid GA-PSO-BFO method over 100 iterations. The hybrid approach consistently outperformed the individual algorithms in terms of convergence speed and final objective value. While GA and BFO showed relatively slower convergence and higher variance, and PSO achieved moderate convergence rates, the hybrid model demonstrated a stable and accelerated decline in objective function values. This superior convergence behavior can be attributed to the integrated structure of the algorithm: GA provides initial diversification, PSO accelerates convergence, and BFO enables robust local refinement. The hybrid framework thereby delivers a more reliable and optimal solution pathway compared to any single technique.

The hybridization of metaheuristic algorithms promotes efficient exploration of the solution space early in the process and ensures convergence toward high-quality solutions in later stages. The optimization is guided by a fitness function reflecting critical network parameters, including voltage regulation, current flow, and power quality. A flexible parameter tuning mechanism adapts algorithm behavior in real time, improving adaptability across varying load and system conditions. This design supports faster convergence and superior solution quality in multi-objective optimization scenarios. The Python-based pseudo-code for this optimization process is provided in Algorithm 2. Figure 13 visually maps the integration of the MATLAB-modeled BESS and the Python control engine within the DIgSILENT simulation architecture. The iteration graph of Figure 14 illustrates the convergence behavior of the hybrid GA-PSO-BFO optimization algorithm over 100 iterations, where oscillations indicate exploration and a stable fitness score at the final iteration mark convergence [36]. The plot shows a consistent decline in the best fitness value, indicating effective exploration and exploitation of the solution space. This steady improvement demonstrates the algorithm’s capability to minimize the objective function, reflecting its robustness and stability in reaching near-optimal solutions for the optimization problem.

Figure 15 illustrates the evolution of the Pareto front across optimization cycles. The 3D scatter plot illustrates the relationship between voltage, current, and power per unit (p.u.) within the selected distribution network. Each point on the front represents a non-dominated solution balancing objectives such as voltage magnitude, line current, and power flow. The data points are densely clustered, suggesting a concentrated operational range, typically around nominal values. The gradual migration of points toward an optimal frontier underscores the algorithm’s capability to find diverse, efficient trade-offs. This distribution highlights the system’s stability and consistency, indicating minimal deviation from expected performance metrics. The dispersion and final clustering of solutions reveal a well-formed balance between exploration and convergence, reflecting the strength of the algorithm in managing complex electrical distribution system dynamics. The plot effectively visualizes the interdependence of these electrical parameters under the optimization framework being analyzed.

Algorithm 2. Pseudo code of Python-based balanced hybrid optimization algorithm

Start Program1. Initialize BESS Controller with:        - Maximum State of Charge (max_soc)        - Minimum State of Charge (min_soc)        - Charge Rate        - Discharge Rate2. Initialize Load Demand and System Voltage3. Initialize Power Factor if needed4. Define Function: Charge (amount)        - Add amount to current SOC        - Ensure current SOC does not exceed max_soc5. Define Function: Discharge (amount)        - Subtract the amount from the current SOC        - Ensure current SOC does not fall below min_soc6. Define Function: Optimize_Charge (load_demand, off_peak_hours, peak_hours)        a. Set Genetic Algorithm (GA) parameters:                - Population size                - Number of generations                - Mutation rate        b. Set Particle Swarm Optimization (PSO) parameters:                - Swarm size                - Number of iterations                - Constants c1 and c2        c. Set Bacterial Foraging Optimization (BFO) parameters:                - Swim length                - Tumble count                - Population size        d. Initialize a population with random SOC values between 0 and max_soc        e. Repeat for each GA generation:                i. Perform selection, crossover, and mutation                ii. Evaluate the fitness of the GA population                iii. Select top solutions for PSO input                iv. Initialize PSO with selected solutions                v. Repeat for each PSO iteration:                        - Update velocities and positions                        - Evaluate the fitness of each particle                        - Update the best solution found by PSO                vi. Initialize the BFO population with random SOC values                vii. Repeat for each BFO swim step:                        - Perform chemotaxis and reproduction                        - Evaluate the fitness of each BFO agent        f. Merge GA, PSO, and BFO results        g. Select the solution with the lowest fitness value        h. If the current time is within Off-Peak Hours:                - Charge BESS using the defined Charge Rate        i. Else If the current time is within Peak Hours:                - Discharge BESS using a defined Discharge RateEnd Function7. Main Program Loop:        a. Read load_demand, voltage, and power_factor from distribution network        b. Call Optimize_Charge (load_demand, off_peak_hours, peak_hours)        c. If voltage is greater than target_voltage:                - Adjust voltage to target_voltage        d. If power_factor is greater than target_power_factor:                - Adjust power factor to target_power_factorEnd LoopEnd Program

6. Impact Analysis with 50% Loading

According to the data presented in Figure 4, the transformers within the selected distribution network typically operate at low utilization levels, handling only around 15% to 20% of their full capacity. To assess the implications of introducing electric ferry charging stations, the load levels are raised to approximately 50% of each transformer’s rated capacity [2]. This adjustment serves to simulate a realistic stress condition under future ferry charging demand [2]. The combined storage capacities of four BESS units deployed in the network align with the projected requirements for the proposed charging hubs [2]. In evaluating network performance, it is assumed that the electric ferries would engage in fully coordinated charging activity, effectively drawing maximum power from the system during operation [2]. A scenario without any BESS units is used as the benchmark or base case for comparison [2]. Power flow simulations are then conducted for both the base configuration and the setup with active BESS support under coordinated control [2]. Figure 16 details the transformer loading profile for the unit located at BryanJordanDrive_Marina_Avnue, which interfaces with a 250 kWh BESS. This figure compares transformer loading across different BESS control strategies. Under baseline conditions, the transformer’s utilization ranged from a minimum of 26.38% to a peak of 49.21% [37]. These same values are observed in the scenario where the BESS units operated in a coordinated charging-only mode [37]. However, when charge and discharge cycles are optimized in tandem, the loading levels shift slightly, peaking at 46.26% and bottoming out at 27.55% [37]. These variations indicate that coordinated discharging during high-demand intervals helps relieve stress on the system rather than exacerbate it. The same trend appears across the other 11 kV/0.415 kV transformers tied to low-voltage buses, where BESS units are also deployed [2]. Figure 17 presents a side-by-side view of peak and off-peak transformer loading in three different scenarios—the base case, coordinated charging only, and the full coordinated charge-discharge strategy [2].

The lines Pluto_1, Moon_A, and Moon_Begin are selected for analysis due to their high demand levels compared to others in the test network [2]. These lines serve as key indicators of system stress under different operational conditions. Figure 18 tracks the hourly loading behavior of the Pluto_1 line across three distinct scenarios: standard operation (base case), coordinated charge-discharge activity, and a setup where only charging occurs. In the base scenario, loading ranges from 25.53% to 50.33%. When only charging is coordinated, this range shifts slightly, from 26.30% to the same peak of 50.33%. In contrast, the charge-discharge coordination reduces the peak to 49.56%, maintaining the same minimum at 26.30%. This shows a marginal improvement in line loading under full coordination. Figure 19 compares the highest and lowest load levels observed on Pluto_1, Moon_A, and Moon_Begin across the three operating modes. The data reveals a noticeable drop in line stress during coordinated charge-discharge operation, while the only-charge mode mirrors the base case closely [2]. To understand the voltage stability impact, bus voltage levels are examined at the BESS-connected points [2]. Four specific buses are evaluated, and their maximum and minimum voltages are presented in Figure 20 [38]. In the base case, the Marina_Ave_Slipway_B bus sees voltages between 0.955 p.u. and 0.979 p.u. [39]. When a 300 kW BESS is added at this location [40], voltage levels increase to a range of 0.987 p.u. to 1.009 p.u. under coordinated scenarios [41,42]. This results in a voltage rise between 1.12% and 1.15% compared to base conditions [43], confirming the positive influence of BESS coordination on voltage support [43].

6.1. Test Scenarios for Probabilistic and Partially Coordinated Charging with 50% Loading

To reflect more realistic charging behaviors of EFCSs (Electric Ferry Charging Stations), this research incorporates a set of test scenarios involving probabilistic charging demand and partial coordination with 50% loading of the selected distribution network. These scenarios consider the variability introduced by uncertain ferry schedules, varying battery SOC, and human decision-making. The simulations are executed in daily power flow mode, and stochastic charging patterns are modeled using a Monte Carlo framework with 100 iterations per case.

Scenario 1: Time-based Random Charging with SOC Trigger (Partial Coordination)

In this scenario, ferries arrive randomly within a fixed daily window (e.g., 10:00–12:00). Charging occurs only when the SOC falls below 0.4, representing limited coordination. Each EFCS is available 75% of the time, simulating operational downtime or human decision delays.

Arrival Time: Uniform distribution between 10:00 and 12:00

SOC Threshold for Charging: Less than 0.4

Charger Availability: 75%

Charging Power: Fixed per station

Coordination Level: Partial

Scenario 2: Stochastic SOC and Uncoordinated Charging Start

Charging begins based solely on the ferry’s SOC upon arrival, without reference to network load or peak hours. This represents a fully uncoordinated strategy where individual operators control charging.

SOC at Arrival: Normally distributed (mean = 0.5, standard deviation = 0.1)

Charging Start Time: Randomly assigned between 9:00 and 17:00

Charging Duration: Deterministic (2 h maximum)

Coordination Level: None

Scenario 3: Load-Aware Probabilistic Charging Response (Smart Partial Coordination)

This scenario introduces a load-aware charging logic, where charging is delayed probabilistically if the local voltage drops below 0.95 p.u. or if the line current exceeds its rated value. This reflects partial automation or informed human coordination.

Grid Condition Trigger: Voltage < 0.95 p.u. or Current > rated

Charging Decision Delay: 70% probability of 1-h delay

Charging Duration: Limited to 2 h

Coordination Level: Partial (load-aware)

Performance Matrices and Impact Evaluation

The impact of each scenario is assessed through comparative analysis using the following technical indicators. The performance of each scenario was evaluated using several key technical indicators, namely voltage deviation, transformer loading, line current utilization, unmet energy demand, and charging success rate. The results are summarized in Table 6.

Voltage Deviation (ΔV): Hourly deviation from nominal voltage across all buses

Transformer Loading (%): Peak and average utilization

Line Current Utilization: As a percentage of rated capacity

Unmet Charging Demand (kWh): Energy deficit due to missed or delayed charging

Charging Event Success Rate (%): Percentage of successful, uninterrupted charging sessions

Table 6 presents a clear degradation in power quality and network stress as the coordination level decreases. Under full coordination, voltage deviation remains minimal at 0.012 p.u., and transformer loading peaks at 72%. In contrast, uncoordinated SOC-based charging results in the highest voltage deviation (0.035 p.u.) and transformer loading (85%), along with 58 kWh of unmet charging demand and a 65% success rate. The partial SOC-triggered scenario improves slightly, while the load-aware probabilistic strategy offers a practical compromise between system performance and operational flexibility, achieving a 90% success rate and limiting voltage deviation to 0.025 p.u. This analysis confirms that incorporating even a basic level of partial coordination can lead to significant improvements in both technical performance and charging reliability. These findings highlight the operational risks of uncontrolled charging and support the value of intelligent coordination, even when partially implemented. The results underscore the importance of incorporating intelligent control strategies and probabilistic modeling to manage charging behaviors effectively in maritime electrification systems.

7. Impact Analysis with 80% Loading

To evaluate how electric ferry charging might affect network performance, the load on each transformer in the test distribution system is elevated to 80% of its rated capacity, while Battery Energy Storage Systems (BESSs) are actively integrated into the grid [2]. Figure 21 provides a snapshot of the BryanJordanDrive_MarinaAvenue transformer’s hourly load profile. This unit, linked to buses outfitted with a 250 kWh BESS, shows different behavior depending on the operational mode. In the unmodified base scenario, the transformer hits a peak load of 79.55% and a low of 41.96%. These figures shift subtly in charge-only coordination, where the peak remains fixed, but the minimum rises to 43.83%. When operating in charge-discharge coordination, the transformer experiences a lower peak at 74.61%, with the same 43.83% minimum, pointing to a drop in load during high-demand hours without increasing the upper threshold. This trend also surfaces across multiple 11 kV/0.415 kV transformers that feature BESS installations on the low-voltage end [2]. As shown in Figure 22, these transformers similarly benefit from reduced maximum loading under the charge-discharge coordination mode, while no change is observed in charge-only operation. The analysis extends to line loading impacts, where the Pluto_1 line serves as a key case. Figure 23 outlines the hourly variation across operational modes. In the base condition, line loading ranges between 41.37% and 82.69%. Charge-only coordination keeps the upper value at 82.69% but increases the minimum slightly to 42.15%. Charge-discharge coordination lowers the peak marginally to 81.88% with the same 42.15% minimum. These small shifts reflect measurable relief in peak stress levels on critical lines. Further insights are shown in Figure 24, comparing peak and off-peak loads on three main lines under each scenario. Charge-discharge operation consistently leads to lighter peak loading compared to both the base and charge-only cases. To assess the effect on voltage levels, four buses are evaluated under coordinated strategies. Figure 25 displays the maximum and minimum voltages under different modes. Voltage levels remain nearly stable between charge-only and charge-discharge coordination. For instance, in the base case, the voltage at the Marina_Ave_Slipway_B bus ranges from 0.927 p.u. to 0.966 p.u., and it experiences a slight increase after the integration of a 300 kW BESS. Under coordination, the voltage shifts to 0.937 p.u. (minimum) and 0.976 p.u. (maximum) [44], reflecting an improvement of around 1.0% to 1.12% over the original condition [45].

7.1. Test Scenarios for Probabilistic and Partially Coordinated Charging with 80% Loading

To explore the effects of increased network stress, the study further investigates probabilistic and partially coordinated charging scenarios of EFCSs under 80% transformer loading of the selected distribution network. This elevated loading level emulates more demanding real-world conditions such as peak-hour operations or constrained infrastructure capacity. The scenarios maintain the same variability in ferry schedules, SOC distributions, and partial human involvement as those for 50% loading. Simulations continue to operate in daily power flow mode, employing a Monte Carlo framework with 100 iterations per scenario.

Performance Matrices and Impact Evaluation

Each scenario is assessed using the same five technical indicators: voltage deviation, transformer loading, line current utilization, unmet energy demand, and charging event success rate. Table 7 provides a comparative analysis of the technical performance of different EFCS charging strategies under 80% transformer loading. As expected, the uncoordinated SOC-based scenario exhibits the highest stress on the network, with voltage deviation peaking at 0.045 p.u. and transformer loading reaching 85.92%, alongside a significant 74 kWh of unmet charging demand and the lowest charging success rate (59%). In contrast, full coordination ensures optimal performance with minimal voltage deviation (0.018 p.u.), no unmet demand, and a 100% success rate. The load-aware probabilistic strategy offers a practical compromise, improving system performance while still accommodating operational variability, achieving a charging success rate of 88%, and reducing unmet demand to 26 kWh. The simulation results under 80% loading reveal a clear degradation in grid stability and charging efficiency as coordination decreases. Compared to 50% loading, all metrics show elevated stress, especially in Scenario 2, where voltage deviation reaches 0.045 p.u. and transformer loading peaks at nearly 86%. The load-aware probabilistic scenario continues to demonstrate its effectiveness, balancing technical constraints with acceptable charging reliability. These findings highlight the critical importance of adaptive and intelligent coordination strategies in high-load maritime electrification contexts.

8. Discussion on Research Findings

The simulation outcomes demonstrate that coordinated BESS control effectively stabilizes voltage profiles and moderates’ equipment loading across the distribution network. When operating under a coordinated charge–discharge mode, voltage levels at critical buses remained within the limits prescribed by the Australian National Electricity Rules (0.94–1.10 p.u.), even under 80% transformer loading [23,46]. Transformer utilization was also optimized, avoiding both underutilization and overloading, which are detrimental to grid reliability and asset longevity [47,48]. Notably, the hybrid GA-PSO-BFO control algorithm outperformed its individual components, enabling adaptive and efficient BESS scheduling based on real-time load demand and SOC [2]. This led to transformer loading reductions of up to 4% and voltage enhancements of over 1.0% compared to the base case. These improvements translated into more resilient grid behavior under high-demand scenarios.

In contrast, the charge-only coordination mode yielded results comparable to the unmitigated baseline, underscoring the limited effectiveness of unidirectional control. Probabilistic charging scenarios that simulated real-world variability (e.g., uncoordinated arrivals, SOC triggers) introduced greater voltage fluctuations and transformer loading. Among the partially coordinated cases, a load-aware probabilistic strategy emerged as a balanced solution, achieving acceptable voltage regulation and charging success rates. These findings affirm that intelligent coordination strategies are critical for managing the grid impacts of EF charging. When docked and controlled effectively, EFs can function as auxiliary grid assets, enabling demand-side flexibility, peak shaving, and voltage support. This transforms EF infrastructure from passive consumers into active contributors to grid stability.

9. Conclusions

This study evaluates the integration of electric ferry charging infrastructure into a coastal distribution network through a series of power flow and quasi-dynamic simulations. Using the Gladstone Marina network as a case study, four hypothetical EF terminals equipped with optimally sized BESSs were assessed under various loading scenarios. A hybrid GA-PSO-BFO optimization algorithm governed BESS operation, dynamically aligning charge–discharge cycles with system needs. Key findings reveal that coordinated charge–discharge strategies improve voltage profiles (by 1.0–1.5%), lower transformer stress (by 3–4%), and reduce line loading (by 2.5–3.5%), outperforming both uncoordinated and charge-only strategies. The coordinated mode enables EF batteries to act as distributed reserves, facilitating grid support during peak hours and improving infrastructure utilization during off-peak periods. While the simulation framework was tailored to the Gladstone network, the methodology is scalable and adaptable to other coastal grids, with adjustments required for older infrastructure or different regulatory environments. Future research should incorporate real-time data from operational EF terminals and investigate control robustness under uncertain and stochastic load profiles. Overall, this study offers a practical foundation for designing smart, coordinated EF charging systems that support maritime decarbonization and grid modernization efforts.

Author Contributions

Methodology, R.B.R. and S.A.; Software, R.B.R.; Validation, R.B.R.; Formal analysis, R.B.R., S.A. and P.J.V.R.; Investigation, P.J.V.R.; Resources, S.A.; Writing—original draft, R.B.R.; Writing—review & editing, R.B.R.; Visualization, R.B.R. and P.J.V.R. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1 Monthly load profile of the Marina feeder.

Figure 2 Seasonal hourly load profile of the Marina feeder.

Figure 3 Schematic diagram of 11 kV Marina feeder [2].

Figure 4 Daily load profile of test distribution network [2].

Figure 5 Marina Network 1.

Figure 6 Marina Network 2.

Figure 7 Marina Network 3.

Figure 8 Block diagram of BESS Model.

Figure 9 Steps for DLL formation.

Figure 10 Flow chart of hybrid GA-PSO-BFO algorithm.

Figure 11 Final objective values distribution over 50 runs.

Figure 12 Convergence comparison plot.

Figure 13 Relationship among MATLAB, Python, and DIgSILENT.

Figure 14 Iteration graph of the hybrid GA-PSO-BFO optimization algorithm.

Figure 15 Pareto front evolution curve.

Figure 16 Loading of Brian Jordan Drive_Marina Avenue Transformer.

Figure 17 Maximum and minimum loading of transformers adjacent to BESSs.

Figure 18 Percentage loading of line Pluto_1.

Figure 19 Maximum and minimum loading of selected lines.

Figure 20 Maximum and minimum bus voltages of selected buses.

Figure 21 Percentage loading of Brian Jordan Drive_Marina Avenue Transformer.

Figure 22 Maximum and minimum loading of transformers adjacent to BESSs.

Figure 23 Percentage loading of line Pluto_1.

Figure 24 Maximum and minimum loading of selected lines.

Figure 25 Minimum bus voltages of selected buses.

Table 1

Technical details of Corvus Orcha ESS.

Attribute	Specification
Battery Chemistry	Lithium ion (NMC/graphite)
Unit Energy Storage/Voltage Rating	5.6 kWh/50 VDC
Rated Capacity per Module	128 Ampere-hours
Module Configuration Range	38–136 kWh/350–1200 VDC
Energy Density (Gravimetric)	77 Wh/kg (Equivalent to 13 kg/kWh)
Energy Density (Volumetric)	88 Wh per litre

Table 2

Performance characteristics of BESS.

Parameter	Specification
State of Charge Operating Limit	20% to 80%
Internal Impedance	0.013 Ω
Lifecycle rating (Charging Cycles)	2500
Voltage at full charge	438 volts
Standard discharge current	130.5 Amperes
Minimum operating voltage	311 volts
Round trip efficiency	90%
Neutral discharge rate	0.1%
System reaction time	1 s

Table 3

ESS module arrangement for various system capacities.

System Type	Energy Need	Power Demand	Final Configuration
BESS A	400 kWh	300 kW	9 modules in series, 6 parallel strings—54 modules total
BESS B	400 kWh	300 kW	Same configuration as BESS A
BESS C	300 kWh	200 kW	9 modules in series, 4 parallel strings—a total of 36 modules
BESS D	300 kWh	200 kW	9 modules in series, 3 parallel strings—resulting in 27 modules overall

Table 4

Key hyperparameters of the hybrid optimization algorithm.

Parameter	Low Setting	High Setting	Best Objective Value (Low)	Best Objective Value (High)
Crossover Rate (GA)	0.6	0.9	52.3	50.1
Mutation Rate (GA)	0.005	0.02	54.1	51.8
Inertia Weight (PSO)	0.6	0.9	50.5	49.7
c1 (PSO)	1.2	2.0	51.2	50.3
c2 (PSO)	1.2	2.0	51.0	50.4
Chemotaxis Steps (BFO)	5	15	53.8	49.8
Swim Length (BFO)	2	6	52.7	50.5

Table 5

Final objective values.

Algorithm	Mean Objective Value	Standard Deviation
GA	52.95	0.72
PSO	50.29	0.68
BFO	51.32	0.65
Hybrid GA-PSO-BFO	49.01	0.69

Table 6

Technical Impact of Probabilistic and Partial Coordination Scenarios.

Charging Scenario	Voltage Deviation (p.u.)	Peak Transformer Loading (%)	Line Current Utilization (%)	Unmet Charging Demand (kWh)	Charging Success Rate (%)
Full Coordination	0.012	47.24	68	0	100
Scenario 1: Partial SOC Trigger	0.020	49.12	74	24	87
Scenario 2: Uncoordinated SOC-Based	0.035	55.37	83	58	65
Scenario 3: Load-Aware Probabilistic	0.025	50.41	76	19	90

Table 7

Technical impact of probabilistic and partial coordination scenarios.

Charging Scenario	Voltage Deviation (p.u.)	Peak Transformer Loading (%)	Line Current Utilization (%)	Unmet Charging Demand (kWh)	Charging Success Rate (%)
Full Coordination	0.018	74.85	82	0	100
Scenario 1: Partial SOC Trigger	0.027	78.24	88	35	84
Scenario 2: Uncoordinated SOC-Based	0.045	85.92	96	74	59
Scenario 3: Load-Aware Probabilistic	0.031	79.75	89	26	88

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