Advanced control optimization for bidirectional DC-DC converters in electric vehicles using Harris Hawk optimization

1. Introduction

Across the modern age, ecological degradation has risen to be the critical global challenge, adversely affecting both the natural world and society due to the CO₂ pollution released into the air, mainly caused by factories and regular vehicles (Al-Ghaili et al., 2022). Rising interest in electric vehicles (EVs) is expected to draw the transportation and electric utility industries closer, reinforcing their collaboration (Haghani et al., 2023; Eldho et al., 2020). At present, the dominant types of electrified mobility are battery-powered (BEVs) and hybrid vehicles (HEVs). To improve the charging infrastructure, much research work is ongoing, especially in integrating renewable energy sources. Poor power quality in the grid can negatively impact EV charging stations by reducing efficiency and even causing potential damage to chargers. The power quality alleviation techniques, explained in Mohapatra et al. ( 2022, 2023), help ensure smoother integration of EV chargers into the grid by maintaining a stable and clean power supply, ensuring efficient power exchange between the PV system, grid, and EVs. Recent advancements in EVs highlight their versatility, functioning not only as modes of transportation but also as mobile energy sources. Bidirectional onboard chargers (BOBCs) have gained popularity, proving effective for bidirectional power flow (Yuan et al, 2021). Upputuri et al. (2023) and Wang et al (2024) explain bidirectional configurations. DAB is commonly recognized in energy storage systems and chargers due to the ability to control bidirectional power, highly efficiently at a wide transfer ratio, and to attain resonance. Additionally, a variety of converter configurations have been detailed in Maroti et al. (2021).

Conventional proportional-integral (PI) controllers, though widely used, often suffer from drawbacks such as slow transient response, limited adaptability, and high sensitivity to parameter variations, which restrict their ability to deliver optimal performance. To overcome these limitations, metaheuristic algorithms have been increasingly applied for PI tuning in power electronics and EVs. By systematically searching for optimal controller parameters, these algorithms improve dynamic response, robustness, and efficiency. Such advancements are particularly valuable in EV power systems, where operating conditions can vary significantly and demand adaptive, high-performance control strategies.

This section offers a concise review of the literature on various optimization techniques, outlines the motivation behind the research, and presents the key findings. Many well-known controllers are included in the list, including model predictive control (MPC) for improving the performance and efficiency of the dual active bridge (DAB) converter, as discussed in Nguyen (2023) and Elkeiy et al. (2022). A fuzzy-based controller is developed for improving the efficiency and reliability of the charging process from battery to grid, as more effectively explained in Shreelakshmi et al. (2020). Using a fuzzy controller partial charging system where the battery operation is controlled by the controller is discussed in Narayan et al. (2022) for getting optimistic results. A two-switched boost-converter using ANFIS is discussed in Panimathi et al. (2025). A fractional order PI (FOPI) based controller for EV fast charging application has been well explained in Deepti et al. (2024).

Sinha et al. (2025) applied a fractional-order PI controller to a variable-input interleaved DC-DC boost converter, with parameters optimized via particle swarm optimization (PSO). The controller showed improved transient response and robustness under parametric variations, demonstrating the benefits of combining fractional-order control with evolutionary optimization techniques. Integer order PI control using TMS320F280039C has been developed in Deepti et al. (2025). Previous research has explored a variety of algorithms to identify the optimal gain settings for PID controllers. Several metaheuristic optimisation techniques have been widely reported in the literature, including the Genetic Algorithm (GA) Nishat et al. (2020), Modified Levy Flight Distribution Algorithm ( Izci et al. 2021) , Whale Optimization Algorithm ( Hekimoglu et al. 2018) , Firefly Algorithm ( Shagor et al. 2021), Particle Swarm Optimisation (PSO) technique ( Ab Ghani et al. 2020) .

Harris Hawk Optimization (HHO) comprises an advanced technique derived from viewing the seven kills strategy execution method of Harris hawks during hunting activities. The optimization method includes several distinct beneficial characteristics when compared to other prevalent swarm based approaches. The algorithm features a time-based mechanism that automatically transforms exploratory searching to the exploitation stage as simulation batches complete. During the convergence process HHO reveals a systematic upshift of performance that moves it across exploration to exploitation stages. Higher solution quality produced by HHO has boosted its acceptance as an optimization method among practitioners (Hussien et al., 2022). Improving the DVR’s ability to mitigate voltage disturbances in power systems using HHO is discussed in Elkady et al. (2020). The HHO algorithm shares common characteristics with other metaheuristic algorithms. It offers several advantages, such as:

• 1.

  Fast convergence speed

• 2.

  Strong local search capabilities and an effective balance between exploration and exploitation

• 3.

  Applicability to a wide range of optimization problems.

• 4.

  High adaptability, scalability, flexibility, and robustness

However, like other metaheuristic approaches, HHO also has certain limitations. It may become trapped in local optima, and there is currently no established theoretical framework to guarantee convergence.

An appropriate control strategy on a DAB is somewhat challenging to design. Therefore, adequate control measures and design strategies are required to control fluctuations and achieve optimum operation. These challenges have been tackled using several control methods, including IOPI, MPC FOPI, and fuzzy logic controller (FLC). This study addresses critical challenges in output voltage regulation where traditional PI controller often struggle due to significant over- shoots and high error metrices.

To mitigate these issues, the work focuses on reducing overshoot and settling time while optimizing performance indices. HHO, along with PSO, ABC are implemented to tune the control functions. This approach results in an optimally tuned PI controller that leverages advanced optimization techniques to enhance regulation and overall system efficiency, contributing to more effective operation in EV applications. This configuration is well suited for hardware implementation and the simulations have been carried out using MATLAB/Simulink tool. A brief overview of the PSO, ABC, HHO algorithms is explained in the upcoming sections.

The principal contributions of this work are presented as follows:

• Optimally controlled parameters: Novel method is proposed for optimizing the proportional and integral gain parameters and for tuning the phase shift of DAB effectively under transient condition by using PSO, ABC, HHO algorithm. This method significantly enhances the system’s accuracy and responsiveness.

• Addressing PI controller limitations: The proposed work overcomes the shortcomings of conventional PI controller, especially the problem of significant overshoot in output voltage. The proposed method provides improved performance, making it a strong alternative to traditional PI controller.

• Comparative performance analysis - Conducts an in-depth comparison of the proposed controller, tuned using PSO, ABC, HHO across different scenarios. This study highlights the strengths and limitations of algorithm, aiding researchers, developers for selecting the most effective optimization strategy for similar applications.

• Performance indices such integral of time absolute error (ITAE), integral absolute error (IAE), integral square error (ISE) analysis are compared for PSO, artificial bee colony (ABC), HHO algorithms.

The article is structured as follows: section 1 explains the literature review about the converter and the various controllers as well as the justification of the work done and some of the difficulties faced and achievements made. Section 2 focuses on describing how the converter functions and the formulae used. Section 3 provides an overview of the system, including its description and the algorithms applied. This is followed by the section 4, exploring various algorithms. The subsequent section 5 presents the results and engages in discussion. Finally, the section 6 summarizes the findings and discusses the future scope of the work.

2. Materials and Methods

Fig. 1 shows the circuit configuration of the DAB converter, which is extensively used in various applications, such as renewable energy systems, battery management, EVs, and power supply systems (Mounica et al., 2024; Konara et al., 2023; Vishnuram, 2024). It is valued for its high efficiency, power density, and ability to handle high power levels while providing galvanic isolation. Each bridge is composed of four switches (typically MOSFETs or IGBTs) arranged in a H-bridge topology. Galvanic isolation is provided by HFT between the primary and secondary. The direction and amount of power transferred are based on the control of the phase shift between the voltages of the sending and receiving sides. The operation of a converter using SPS modulation has been discussed in Ai et al. (2022), where the duty ratio of the switches is fixed at 50%. The most challenging area in DAB is the control part, which requires sophisticated control algorithms to obtain optimum phase shift and ensure stable operation under varying load conditions. In this work, a 10kW DAB model is designed with an output of 500V/20A. Table 1 shows the system parameters. Here, the G2V mode is considered, where the power flows from the grid to the load side. The generalized power expression is given by:

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Fig. 1.

Converter configuration.

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Where,

V_in: Primary voltage

V_out: Secondary voltage

$\phi$: Phase shift

L_k: Leakage inductance

f_s: Switching frequency

Leakage inductance:

Phase shift:

3. Controller

The schematic of the DAB with the proposed controller has been shown in Fig. 2. The system comprises a 10kW DAB, where the switches are controlled using the SPS modulation technique and the phase shift is controlled using the optimal PI parameters obtained using the meta-heuristic optimization algorithm. The modes of operation of the converter have been well explained in Deepti et al. ( 2025, 2024). Choosing the right error criteria is essential when applying optimization techniques to tune PI controllers for DAB. These standards aid in assessing the controller’s performance and direct the optimization procedure in determining the ideal or nearly ideal PI settings. Various error criteria, including ITAE, ISE, and IAE, might be employed in accordance with the application and intended performance goals. For example:

• If the goal is to reduce the total accumulated error over time, IAE might be appropriate.

• If it is crucial to avoid large deviations from the setpoint, ISE could be more suitable.

• For applications where it is important to settle quickly and reduce persistent errors, ITAE is a good choice.

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Fig. 2.

Proposed controller.

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Here, the ITAE criteria for the error signal e(t) are used as a performance index. The Integral Time Weighted Absolute Error (ITAE) is defined as:

Where, $e\left(t\right)=V_{ref}- V_{out}$

The PI parameters are optimized using PSO, ABC, and HHO. The following subsections explain the optimization algorithm for selecting the PI parameters.

3.1 Partial swarm optimization

The method was initially created by studying the swarming behaviors of real animals, for e.g., a shoal of fish and a brace of birds. PSO operates on the fundamental concept that every particle in the swarm will travel at its own speed through a designated search zone (Shukla et al., 2022; BGad, 2022). This particle’s velocity is dynamically changed based on both its own and other particles’ flight experiences. Every time a particle finds the optimal coordinates as defined by the fitness function that was applied, it would also record its coordinates in its search space. P_best is the individual best coordinate. Additionally, every particle is tracking a different position, where the best particle among all of them is also recorded. G_best is termed as the best position. The optimal solution the swarm has been looking for will be termed by the final G_best, which is determined by repeatedly measuring the velocity, P_best, and G_best of each particle. The generalized flowchart of PSO has been shown in Fig. 3, where each particle’s seeking space is further improved by weighting the acceleration between each particle’s velocity with a random coefficient. The following equation represents the velocity update:

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Fig. 3.

PSO flowchart.

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(6)

$v_i\left(n+1\right)=w{v}_i\left(n\right)+p_1{l}_1\left(P_{bes{t}_i}-x_i\left(n\right)\right)+ p_2{l}_2\left(G_{best}-x_i\left(n\right)\right)$

(7)

$x_i\left(n+1\right)= x_i\left(n\right)+v_i\left(n+1\right)$

Here, w defines the inertia weight, l₁, l₂ denote the random numbers in the range [0,1]. p₁, p₂ are the acceleration coefficients.

3.2 Artificial bee colony optimization

Karaboga was the first to introduce the ABC algorithm for numerical optimization issues based on the honeybee swarm’s foraging behavior (Karaboga, 2010; Kaya et al., 2022). The grazing bees are classified as follows: workers, onlookers, and scouts. A worker bee finds an edible source to utilize. Onlookers wait for the data regarding the food source in the hive. And scouts randomly search for new food sources around the hive. Fig. 4 shows the flowchart of the ABC algorithm. The sap content of the food source serves as an indication of the solution’s fitness, and the algorithm treats the source location as the potential answer for the problem. The number of food sources is equal to the number of employed bees in this colony. The bees are mostly separated into employed bees and onlookers. The worker bee of a food source turns into a scout and conducts a scattered search after leaving the food source. In the initialization phase the following definition is used:

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Fig. 4.

ABC flowchart.

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(8)

$x_{mi}= l_i+rand\left(0,1\right)*\left(u_i-l_i\right)$

Where, l_i and u_i are the lower and upper bound values of the parameter x_mi. Initial phase is done, the prime condition of the process is repeated for a defined number of cycles or until a termination condition is achieved. Initially, the employed bee phase to determine the neighborhood food source v_m is defined as:

(9)

$v_{mi}=x_{mi}+{\phi }_{mi}\left(x_{mi}-x_{ki}\right)$

Where, x_k is the randomly selected food source, m is {1, 2, D}, i is the randomly chosen parameter index, φ_mi is the random number chosen from

a range of (-1,1). Following this, the onlooker bees choose a new value and start searching for new food sources surrounding the new solution. This selection process is probabilistic, utilizing a mechanism like a roulette wheel based on the fitness of all current solutions (derived from the objective function or a similar measure). A uniform random number generator helps determine the solution to explore.

(10)

$p_i= \frac{fi{t}_i}{{\sum }_{n=1}^{SN}fi{t}_n}$

Notably, some onlooker bees may end up searching around the same solutions. Once these solutions are chosen, new candidate solutions are generated in the same way employed bees do, as outlined in equation (8). The food sources are updated through the process, checking the obtained value from onlookers with the existing ones. Various methods have been proposed for assigning fitness to solutions, especially when using a maximization algorithm like ABC for minimization tasks or when dealing with negative objective function values. Karaboga introduced a commonly used method, which this paper also adopts

(11)

$f_{ti}= \left(\begin{array}{c}\frac{1}{1+f_i} f_i\ge 0\\ 1+\left(f_i\right) f_i\le 0\end{array}\right)$

Where, f_i is the objective function of solution x_i. In this study, the key function is to minimize the weighted sum of the ITAE. The dimension D is 2, representing the two variables K_p and K_i. The performance indices were calculated using model-based analysis on the MATLAB platform.

3.3 Harris hawk optimization

Nature-inspired algorithm that imitates the cooperative hunting pattern of Harris hawks. It was introduced to solve complex optimization problems by leveraging the hawks’ strategies for hunting prey in nature. The key feature of this algorithm is that it alternates between exploration and exploitation phases to balance the search process (Alabool et al., 2021; Heidari et al., 2019). Fig. 5 shows the overall operation of the HHO algorithm.

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Fig. 5.

HHO flowchart.

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Exploration: Involves global search strategies where hawks explore the search space more broadly. Prevents getting trapped in local optima. Exploitation: Involves local search strategies where hawks focus on refining and improving current solutions. This phase homes in on the promising areas identified during exploration.

Exploration Phase. Randomly searches specific regions for locating the feed using two strategies. The location of each hawk is attuned according to equation (9). Here, the prey is the K_p, K_i controller parameters, while the hawks represent the proposed search agents.

(12)

$X\left(t+1\right)= \left(\begin{array}{c}\left(x_{prey}\left(t\right)- x_m\left(t\right)-c_3(l_b+c_4(u_b-l_b\right)), K<0.5\\ x_{rand}\left(t\right)-c_1\left(x_{rand}\left(t\right)-2c_{2}x\left(t\right)\right), K\ge 0.5 \end{array}\right)$

Where,

$X\left(t+1\right)$Hawk location for the succeeding cycle

$x_{prey}\left(t\right)$ Location of variables (K_p, K_i)

K, c₁, c₂, c₃, c₄ Random variables in the limit (0,1)

u_b and l_b Upper and lower bound limit of the PI parameters

$x_{rand}\left(t\right)$ Hawk chosen randomly

$x\left(t\right)$ Is the current position vector of Hawks c₁, c₂, c₃, c₄

Typical location of the Hawks is defined as:

(13)

$x_m\left(t\right)= \frac{1}{N}\sum _{i=1}^N{x}_i\left(t\right)$

$x_m\left(t\right)$ Average position of hawk

$x_i\left(t\right)$ Position of hawk at repetition t

N Total number of hawk, here N = 25, 50

4. Problem Design

Here, the PI controller is optimally tuned using the algorithms mentioned earlier. For the proposed DAB, the key function focuses on minimizing the ITAE performance index, as defined by the objective function in equation (4). The control variables for the mentioned optimization algorithm have been listed in Table 2, mentioning the dimension, objective function, and range. Table 3 presents the selected results of the optimal solutions for PSO, ABC, and HHO optimization methods for tuning PI parameters of the DAB for the constant load, and Table 4 presents the analysis of the algorithm under step load conditions. The analysis indicates that the HHO algorithm outperforms PSO and ABC in tuning PI controller parameters, providing the best results with the least overshoot, shortest settling time, and minimal steady-state error. PSO also performs well but is slightly less optimal than HHO, while ABC, despite its broader parameter exploration, does not achieve the same level of optimization in this context. Thus, for applications requiring precise and rapid tuning of PI parameters, HHO is the preferred choice.

5. Results and Discussion

The PI parameters are tuned using the above-mentioned algorithms, and the convergence rate and time domain parameters were analyzed based on the iteration and population size. Population sizes chosen are 50 and 25, with an iteration of 5, 10, and 15.

5.1 Convergence analysis

5.1.1 Using the particle swarm optimization algorithm

Fig. 6(a-c) shows the PSO-based optimized value of the fitness function ITAE for the swarm size of 25 with iterations 5, 10, and 15 under step load conditions with 70% of the rated load. Similarly, In Figs. 6(d-f) shows the analysis with a swarm size of 50. From the fitness function curves, the convergence rate for different population sizes and iteration counts is analyzed. The analysis shows that a higher population size tends to have a faster convergence rate. For a smaller population size, the curve exhibits more fluctuation, and there is a noticeable variability in the best cost values, indicating less stable optimization. Table 5 depicts the optimal PI parameters and the cost function obtained by varying the population size and iteration.

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Fig. 6.

(a-f) Fitness curves using PSO algorithm under step load condition. (a)-(c) Convergence curve using PSO under step load condition for N=25. (d)-(f) For N=50.

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Table 5. Optimal parameters attained under step load condition.

Optimal parameters	Population size - 50			Population size - 25
	Iteration - 5	Iteration - 10	Iteration - 15	Iteration - 5	Iteration - 10	Iteration - 15
Kp	0.552	0.539	0.543	0.529	0.524	0.542
Ki	90	90	90	90	89.96	90
Cost Function	1.408	1.399	1.399	1.403	1.408	1.402

Figs. 7(a-c) shows the fitness function results of ITAE for the proposed model under rated load conditions with a swarm size of 25, and Figs. 7(d-f) shows the fitness curve by considering the swarm size of 50.

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Fig 7.

(a-f) Fitness curves using the PSO algorithm under the rated load condition. (a)-(c) Convergence curve using PSO under rated load condition for N=25.(d)-(f) For N=50.

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Table 6 depicts the optimal PI parameters and the cost function obtained by varying the population size and iteration.

Table 6. Optimal parameters attained under rated load condition.

Optimal parameters	Population Size - 50			Population Size - 25
	Iteration - 5	Iteration - 10	Iteration - 15	Iteration - 5	Iteration - 10	Iteration - 15
Kp	0.2944	0.3263	0.3271	0.2944	0.2762	0.289
Ki	90	89.998	89.82	90	90	90
Cost function	0.413	0.412	0.407	0.413	0.414	0.412

5.1.2 Using the ABC algorithm

From the Figs. 8(a-c) shows the convergence curve for a swarm size of 25, under a step load condition with 70% of the rated load. In a similar vein, the study with a population size of 50 and the same number of iterations is displayed in Figs. 8(d-f). The optimized PI parameters and fitness value under the specified iterations have been listed in Table 7.

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Fig. 8.

(a-f) Fitness curves using the ABC algorithm under step load conditions. (a)-(c) Convergence curve using ABC under step load condition for N=25.(d)-(f) For N=50.

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Table 7. Optimal parameters attained under step load conditions

Optimal parameters	Population Size - 50			Population Size - 25
	Iteration - 5	Iteration - 10	Iteration - 15	Iteration - 5	Iteration - 10	Iteration - 15
Kp	1.1722	1.289	1.547	1.058	1.289	1.546
Ki	172.551	173.589	178.467	162.98	173.589	214.895
Cost Function	1.095	1.101	1.088	1.106	1.101	1.081

Figs. 9(a-f) shows the proposed model’s fitness function results under rated load conditions with a population size of 25. The cost function and ideal PI parameters that are produced by adjusting the population size and iteration have been shown in Table 8.

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Fig 9.

(a-f) Fitness curves using the ABC algorithm under the rated load condition. Convergence curve using ABC under rated load condition for N=25.(d)-(f) For N=50.

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Table 8. Optimal parameters attained under rated load condition.

Optimal parameters	Population Size - 50			Population Size - 25
	Iteration - 5	Iteration - 10	Iteration - 15	Iteration - 5	Iteration - 10	Iteration - 15
Kp	0.282	0.198	0.326	0.297	0.309	0.328
Ki	94.155	92.55	116.97	89.323	102.65	116.513
Cost function	0.404	0.345	0.345	0.417	0.381	0.347

5.1.3 Using the HHO algorithm

Based on the HHO algorithm, Fig. 10 shows the optimum value of the fitness function ITAE. The convergence curve for a swarm size of 25 has been depicted in Figs. 10(a-c), under step load conditions at 70% of the rated load. Complementing this, Figs. 10(d-f) shows the study with 50 participants. For a smaller population of 25, the final solution quality does not change significantly within the same iteration constraints, with the exception of iteration 10. Greater stability is attained with bigger population sizes.

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Fig. 10.

(a-f) Fitness curves using the HHO algorithm under step load conditions. (a)-(c) convergence curve using HHO under step load condition for N=25.(d)-(f) For N=50.

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Table 9 displays the cost function and optimal PI parameters that are obtained by varying the population size and iteration.

Table 9. Optimal parameters attained under step load conditions.

Optimal parameters	Population Size - 50			Population Size - 25
	Iteration - 5	Iteration - 10	Iteration - 15	Iteration - 5	Iteration - 10	Iteration - 15
Kp	0.538	0.562	0.534	0.568	0.567	0.532
Ki	90	89.994	90	90	90	89.973
Cost Function	1.409	1.403	1.399	1.405	1.407	1.405

The fitness function findings for the proposed model with a population size of 25 under-rated load conditions have been shown in Figs. 11(a-c), and the fitness curve for a population size of 50 has been shown in Figs. 11(d-f).

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Fig. 11.

(a-f) Fitness curves using the HHO algorithm under rated load conditions. Convergence curve using HHO under rated load condition for N=25.(d)-(f) For N=50.

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Populations of 50 or more typically show faster initial convergence and higher levels of stability, whereas populations of 25 or fewer show more gradual improvements and take longer to reach stability. Table 10 displays the cost function and optimal PI parameters that are obtained by varying the population size and iteration.

Table 10. Optimal parameters attained under rated load condition.

Optimal parameters	Population size - 50			Population size - 25
	Iteration - 5	Iteration - 10	Iteration - 15	Iteration - 5	Iteration - 10	Iteration - 15
Kp	0.2916	0.327	0.326	0.286	0.285	0.327
Ki	90	90	90	90	90	90
Cost Function	0.412	0.408	0.405	0.413	0.414	0.408

5.2 Stability analysis

The stability evaluation of the algorithms over the PI and FOPI controller (Deepti et al., 2024), in terms of time domain response, has been shown in Table 11. By varying the population size, how the time domain parameters are affected is also analyzed in this section. From Table 11, we can see that the PSO shows lower overshoot across most cases, especially in higher iterations and large population sizes. ABC tends to have higher overshoot, particularly noticeable with increasing iterations. HHO generally has a moderate overshoot, lower than ABC but occasionally higher than PSO. Lower overshoot contributes to the stability and precision, indicating fewer oscillations around the set point. All the algorithms show a consistent rise time of 5.1 ms and settling time of 5.29 ms under all configurations, with slight variation in some iterations. Transient time is mostly stable across different configurations, with PSO and HHO showing a lower value compared to ABC. Steady state error is quite low for all algorithms, with HHO generally showing the lowest error across most ABC. Lower peak value of 502.773 V indicates that the system with lower peak values typically exhibits better damping configurations compared to PSO and ABC.

Table 11. Stability analysis of output voltage.

Population size	Iteration	Algorithm/Controller	Overshoot (%)	Rise time (ms)	Settling time (ms)	Transient time (ms)	Steady- state error (%)	Peak (V)
25	5	PSO	0.9218	5.1	5.29	5.93	0.085	505.036
		ABC	0.912	5.1	5.29	5.93	0.096	505.047
		HHO	0.8921	5.1	5.29	5.91	0.074	501.883
	10	PSO	0.9585	5.1	5.3	5.93	0.0831	505.212
		ABC	1.1879	5.1	5.27	5.94	0.11	506.193
		HHO	0.8879	5.1	5.27	5.94	0.12	502.193
	15	PSO	0.8519	5.1	5.29	5.88	0.05	504.814
		ABC	1.4248	5.1	5.25	5.53	0.031	507.282
		HHO	0.7066	5.1	5.29	5.85	0.048	503.773
50	5	PSO	0.9218	5.1	5.29	5.93	0.152	505.036
		ABC	0.996	5.1	5.29	5.92	0.096	505.466
		HHO	0.8523	5.1	5.29	5.93	0.096	502.745
	10	PSO	0.6735	5.1	5.29	5.82	0.087	503.804
		ABC	1.917	5.12	5.32	6.05	0.067	509.939
		HHO	0.6066	5.1	5.29	5.85	0.048	502.773
	15	PSO	0.7028	5.1	5.29	5.86	0.058	503.704
		ABC	1.398	5.1	5.25	5.9	0.075	507.372
		HHO	0.6125	5.1	5.29	5.86	0.037	503.051
N/A	N/A	PI	1.4258	5.6	9.1	18.8	0.092	507.428
		FOPI	0.537	3.2	6.6	13.2	0.089	503.012

Fig 12 shows the system’s response under load variation, where the resistive load is varied at specified time intervals of 0.05 and 0.15 s. The output voltage response shows that PI parameters tuned using the HHO algorithm give efficient performance with lesser overshoot, settling time, compared to the other algorithms and conventional PI and FOPI. HHO and PSO algorithm shows almost similar results with a slight variation, whereas the response from the PI parameters tuned using the ABC algorithm has a higher overshoot and a higher settling time. Table 12 and Fig. 13 provide the pictorial representation and the analysis of the controller at load transients.

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Fig. 12.

Output voltage response under load variation.

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Table 12. Comparison of controllers based on settling time and peak value.

Controller	Settling time (msec)	Peak value (V)
HHO- PI	6.34	503.5
PSO- PI	7.661	504.3
ABC- PI	11.452	505
FOPI	7.841	505.5
PI	11.961	506

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Fig. 13.

Response analysis under load variation.

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The output response at load transients by varying the input voltage from 750V to 850 V at the respective time instant of 0.05 s and 0.15 s and the rated input voltage is 800 V, has been shown in Fig. 14.

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Fig. 14.

Output voltage response under line variation.

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From the output voltage response, HHO also shows a good response in terms of lesser overshoot and lesser settling time compared to other algorithms and controllers. HHO-PI offers the shortest settling time among the compared controllers, indicating the output voltage quickly stabilizes under load variations, where rapid response is needed. Similarly, the lesser voltage drop indicates excellent voltage regulation, which is both crucial in maintaining the performance and efficiency of the EV’s powertrain and battery system.

5.2.1 Performance indices analysis

Performance indices such as IAE, ITAE, and ISE are essential tools in control system engineering and process optimization. These indices quantify the performance of control systems, providing insights into the accuracy, stability, and responsiveness of the system. Here, the following performance indices are also analyzed with the algorithms. Table 13 compares the performance indices across various control methodologies such as PSO, ABC, HHO algorithms, and existing controllers such as FOPI, PI. The FOPI and HHO methods exhibit the lowest ITAE values, indicating superior long-term error performance. ABC has the lowest ISE value, indicating the best performance in minimizing large errors. PSO and HHO also show significantly lower ISE values compared to conventional PI and FOPI controllers. The conventional PI controller has the highest ISE, indicating poor performance in terms of large error minimization. HHO demonstrates the lowest IAE value, indicating the best overall error magnitude performance. PSO and ABC also show good performance with relatively low IAE values. Conventional PI and FOPI have higher IAE values, indicating less efficiency in minimizing the total error magnitude. The analysis indicates that optimization-based methodologies like ABC, HHO, and PSO beat conventional PI and FOPI controllers in minimizing performance indices. HHO shows the best overall performance, particularly excelling in ITAE and IAE. This suggests that adopting advanced optimization algorithms can significantly enhance control system performance.

Table 13. Performance comparison of different methodologies.

Methodologies	ITAE	ISE	IAE
Conventional PI	0.04538	43.56	0.6871
FOPI	0.02143	21.61	0.3814
PSO	0.01368	5.226	0.3256
ABC	0.01518	2.245	0.3242
HHO	0.01362	5.086	0.2141

Fig. 15 shows the efficiency plot of the system with the PSO, ABC, HHO algorithms. Using the HHO technique, the system achieves higher efficiency compared to the conventional PI and PSO, ABC-based technique. The system achieves an efficiency of 97.2% at the rated load and a maximum efficiency of 98.27% at half of the rated load. However, both PSO and HHO shows better performance under various load conditions.

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Fig. 15.

Efficiency analysis.

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Table 14 presents a comparative statistical analysis of PSO, ABC, and HHO based on the ITAE cost function.

Table 14. Statistical analysis of fitness value.

Algorithm (sec)	Cost function	Best value	Min	Max	Mean	RMS Deviation	Computation time
PSO	ITAE	0.408278719	0.408278719	0.458429294	0.4145713821	0.0122631542	545
ABC	ITAE	0.411839741	0.411839741	0.458956662	0.4229113947	0.0137556400	975
HHO	ITAE	0.405300749	0.405300749	0.459933107	0.4102545888	0.0141508578	580

Among the three, the HHO achieves the lowest mean of 0.4192 and RMS deviation of 0.0141, indicating superior convergence accuracy and stability. It also records the best fitness value of 0.4053, outperforming PSO and ABC in minimizing error. Although HHO requires a slightly higher computation time of 580 sec than PSO, it remains significantly faster than ABC. Overall, HHO offers the best trade-off between computational efficiency and optimization performance, making it the most effective algorithm for PI controller tuning in this study.

Fig. 16 shows the convergence analysis of PSO, ABC, and HHO. Compares the convergence characteristics of PSO, ABC, and HHO when tuning the PI controller parameters. It can be observed that HHO reaches the optimal fitness value more rapidly and stabilizes within the first 3 to 4 iterations, indicating faster convergence and reduced fluctuation. PSO also converges to a good solution, but with slightly slower progress compared to HHO. In contrast, ABC shows a slower decline in the cost function and requires more iterations to approach stability. This analysis highlights the efficiency of HHO in quickly identifying near-optimal controller parameters, which is advantageous for offline optimization tasks.

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Fig. 16.

Convergence analysis- HHO, PSO, and ABC under rated load condition.

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6. Conclusions

As future work, the proposed PI controller using HHO optimization can be applied in the DC fast charging, enhancing efficiency and robustness, which may result in faster charging, greater stability, and lower battery stress. The enhancement of the HHO algorithm can contribute to the DAB operation for EV applications by optimizing efficiency, improving dynamic response, managing trade-offs in multi-objective scenarios, enhancing control strategies, and improving thermal management. These improvements can lead to better performance, increased reliability, and longer lifespan of the EV’s power conversion system. Optimization techniques can significantly improve the performance of DC-DC converters, they come with limitations related to complexity, computational requirements, real-time challenges, sensitivity to parameter variations, and practical implementation issues. Balancing these factors is crucial for achieving the desired outcomes in practical applications. This paper introduced the optimized PI controller for the DAB converter for EV applications. PSO, ABC, and HHO optimization algorithms were implemented to tune the PI parameters of the DAB. The primary objective of the algorithms was to minimize the ITAE performance indices and improve the overall response of the system. The system is designed and simulated in the Simulink platform. Results are validated with FOPI, PI under load variations, and line variation. From the above algorithms, HHO offers more optimized PI tuning parameters with lower performance indices and good time domain characteristics under transient conditions.

The primary limitations of the proposed optimization-based PI controller include scalability, tuning stability, and convergence reliability. The scalability of the approach is influenced by converter rating and system nonlinearity, which may require reconfiguration of algorithmic parameters when applied to higher power or multi-converter EV systems. Tuning stability may be affected under dynamic operating conditions or parameter uncertainties, where the optimized gains might deviate from optimal performance. Furthermore, the metaheuristic algorithms (PSO, ABC, and HHO) exhibit inherent stochastic behavior, and hence, convergence reliability can vary with population size, iteration count, and initialization.