Fine Tuning of On-Board Traction Converters for High-Speed Electric Multiple Units at Depot

This article presents a meticulous exploration of on-board traction converters deployed in Electric Multiple Units (EMUs). The study involves the development of a comprehensive traction converter and control system, encompassing essential elements such as transformers, front-end rectifiers, and DC link capacitors. The precise control of the front-end rectifier’s switching states is crucial for achieving high-quality power. A new application of the advanced Hybrid Particle Swarm Optimization (Hybrid PSOS) technique for the optimization of controller parameters is presented. This parameter tuning process aims to minimize the integral time absolute error (ITAE), a critical metric governing the regulation of DC-link capacitor voltage. Simulation results showcase the impressive attributes of on-board traction converters, including low harmonic content, a high-power factor, and stable DC voltage. Additionally, a rigorous comparative analysis is conducted between Hybrid PSOS and other established algorithms like Symbiotic Organisms Search (SOS) and Particle Swarm Optimization (PSO). Hybrid PSOS traction unit outperforms SOS and PSO, with a minimal overshoot of 1.3401%, faster settling time of 0.2413 seconds, compared to SOS (0.3884 seconds) and PSO (0.5531 seconds). Total Harmonic Distortion (THD) for secondary line currents, the values are 12.48% for PSO, 2.17% for SOS, and 1.08% for Hybrid PSOS. Hybrid PSOS consistently demonstrates its superiority, significantly enhancing system performance and stability. This research underscores the substantial potential of on-board traction converters, emphasizing their role in facilitating efficient and stable electric multiple unit (EMU) operations.

A robust and efficient transportation system plays a pivotal role in a nation's holistic development.Railway transportation (RWT) offers numerous advantages over alternative modes of travel.It excels in terms of precise control over travel schedules, reducing exposure to heavy traffic congestion, and mitigating the risk of road accidents commonly associated with road transportation.Moreover, it serves as an economical, swift, and comfortable mode of travel, making substantial contributions to both the environment and the economy.Notably, road transportation is a significant contributor to pollution, with light vehicles (LV) like personal cars and light trucks comprising a substantial 74% of all road-based modes.Of this, cars and trucks account for 40% and 34%, respectively.In contrast, air and marine transportation (including planes and boats) collectively contribute to about 22% of the overall pollution associated with transportation methods.Remarkably, the railway sector emerges as a relatively eco-friendly option, responsible for only about 4% of the total pollution generated by various transportation modes [1].This underscores the environmental advantages of railway transportation and its potential to contribute to a cleaner, more sustainable transportation landscape.
Many countries have recently turned their attention to the development of high-speed railways, recognizing their myriad advantages over alternative modes of transportation.The advent of high-speed railways has ushered in the use of Electric Multiple Units (EMUs).However, this transition has introduced a challenge in the form of Low-Frequency Oscillations (LFOs) within the network.LFOs are the result of intricate interactions between the traction locomotive (TL) and the electric traction network (ETN) [2], [3], [4].A notable issue emerging worldwide is voltage LFO within high-speed traction networks.Numerous studies [4], [5] have pinpointed the prevalence of these LFO problems primarily within depots when EMUs are stationary.Consequently, these issues are often referred to as ''depot problems'' [6], as they manifest when a substantial number of EMUs enter the depot or remain stationary in the stabling yard area.
These LFOs typically occur due to electrical mismatches between the power source and the ETN.Research [7] has shown that during LFO incidents, load-side inverters and motors become non-operational, with stability concerns arising predominantly under light load conditions rather than heavy ones, as mentioned in [5] and [8].Additionally, LFOs can trigger protective devices within EMUs, potentially leading to blockades within the depot.This operational delay subsequently impacts railway services and the overall stability of the ETN.
High-speed EMUs are equipped with a range of components, including single-phase interleaved four-quadrant converters (4QCs), a DC link capacitor, three-phase inverters, three-phase induction motors, and auxiliary loads like condensers and cooling systems.Among these components, it's important to note that only the front-end rectifiers (FERs)/4QCs and auxiliary loads draw power from the ETN.The issue of LFOs first came to light in 1996 on the Norwegian railways [9].Subsequently, similar problems were observed in France, the USA, Germany, and Switzerland [10], [11].To address these challenges, researchers have explored various methodologies: in [12] and [13], advanced synchronization methods employing Phase-Locked Loops (PLL) and closed-loop input impedance techniques for FERs were discussed.Reference [14] focused on a dq-based control strategy to model FERs and highlighted the impact of different parameters on the ETN.LFO problems for single-phase FERs were derived from dq decomposition methods based on the forbidden region criterion in [7].Jiang et al. [15] investigated how converter controller parameters negatively affect the ETN.In the field of LFO control strategies, various approaches have been adopted to enhance system dynamics under different operational conditions.Further investigations into the influence of controller parameters were carried out in [16] and [17].These studies collectively contribute to a deeper understanding of LFOs and the development of control strategies to improve system performance within the realm of high-speed EMUs.
In recent decades, the complexity of high-speed ETNs has significantly grown, primarily attributed to the integration of various nonlinear devices, particularly power electronics components.This heightened nonlinearity and intricate nature have made mathematical modeling of these systems considerably more intricate.Traditional optimization techniques often rely on approximations to reach feasible solutions, which frequently yield suboptimal results due to the increased system complexity and nonlinearity.To address these challenges, evolutionary algorithms (EAs) have gained prominence across various engineering design domains for optimization purposes.EAs offer a versatile and effective approach, drawing inspiration from natural organisms' behaviors.It is important to note, as highlighted by Wolpert and Macready in their ''no free lunch theorem'' [18], that no single meta-heuristic algorithm can universally excel in solving all problems.Consequently, there exists a perpetual need for the development and application of novel algorithms tailored to specific problems, with the aspiration of achieving superior outcomes.In essence, as high-speed ETNs become increasingly intricate, the utilization of evolutionary algorithms represents a pragmatic approach to navigate the complexities and nonlinearities of these systems while striving for optimized solutions.
A thorough examination of the existing literature has unveiled some crucial observations.While the implementation of PI controllers is known for its relative ease, it becomes apparent that the overall system's dynamic performance may encounter significant challenges while interacting with the traction networks.In light of these considerations, this paper places its primary emphasis on the application of recently developed optimization algorithms.Specifically, we explore the potential of algorithms like Hybrid PSOS, SOS, and traditional PSO in fine-tuning controller parameters.The principal objective is to effectively enhance power quality, and maintain precise regulation of the DC link capacitor voltage which eventually mitigate LFOs in the traction network.Therefore, this entire study mainly focused on the onboard converter performance.
Section II introduces the concept of in-depth modeling for a typical EMU, that includes Conventional PI controller of active rectifier.Section III describes the objective function to address all the issues related to EMUs.In Section IV, the various evolutionary techniques employed in this research endeavor are explored in depth.Additionally, this section elaborates on the precise steps undertaken to fine-tune the parameters of the PI controller utilizing these techniques.In Section V, the study presents simulation results with a specific emphasis on LFOs, accompanied by detailed discussions.To optimize controller parameters, three distinct meta-heuristic algorithms-Hybrid PSOS, SOS, and PSO have been effectively utilized.The paper offers an extensive comparative analysis of the results generated by these algorithms.To evaluate the proposed algorithm's robustness in addressing this matter, a comprehensive statistical analysis of the test results has been performed.This analysis provides valuable insights into the algorithm's performance and its effectiveness in addressing the issue at hand.

II. MODELING OF EMUS
As previously stated in the introduction, LFOs primarily manifest when multiple EMUs are stationary in the depot.Consequently, under conditions of light load, it becomes feasible to model the entire load side, comprising the inverter and motor, as a resistive load.Fig. 1 illustrates the equivalent circuit for the traction locomotive.The state-space representation corresponding to Fig. 1 can be expressed as follows [27].
Expressions ( 1) and ( 2) can be further reformulated using the dq reference frame [9] as follows: where, i ud , i uq , v ud , v uq , S wabd , and S wabq are all dq components of i u , v u , and S wab respectively.i uα , i uβ , v uα , and v uβ are αβ components of i u , and v u respectively.Fig. 2 illustrates the controller designed for the Front-End Converter (FEC) tasked with regulating the DC link capacitor voltage, which is essential for powering auxiliary loads like capacitors, cooling systems, and batteries.This, includes a voltage control loop.The voltage control loop samples the output, V DC , with respect to the predefined reference DC link capacitor voltage, V DCref , to produce the reference interfacing current, i udref .In this process, a single-phase, phase-locked loop (PLL) is also incorporated to keep the input current to the converter sinusoidal and in phase with the input voltage to the converter, to achieve the unity PF.Furthermore, the obtained i udref is sampled with the input converter current in current control loop.The obtained voltage reference from the current control loop is provided to a unipolar sinusoidal pulse width modulation (PWM) signal with the 10 kHz triangular carrier signal to achieve the gate pulses.These gate pulses are provided to the switches of the front-end rectifier for rectification process.This controller ensures the system operates at unity power factor to prevent the occurrence of LFOs.The utilization of a PI controller is widespread due to its ease of implementation.However, despite the availability of various controllers for this purpose, the precise tuning of controller parameters remains a formidable challenge.It is in this context that evolutionary algorithms emerge as valuable tools for achieving optimal parameter settings.

III. OBJECTIVE FUNCTION
The DC-link capacitor plays a pivotal role in maintaining its voltage level at 3600 V.This voltage stability is crucial to harness the stored energy within the DC-link capacitor, which is then utilized by the 3-phase inverter to drive the 3-phase induction motor and power auxiliary loads such as batteries and cooling systems.Concerning Low-Frequency Oscillations (LFOs), they typically occur when the Traction Locomotive (TL) is at a standstill or when the 3-phase inverters are not in operation.To effectively regulate the DC-link capacitor voltage and mitigate LFOs, the Integral Time Absolute Error (ITAE) is minimized.This optimization is achieved through the fine-tuning of control parameters within the PI controller.The mathematical representation for optimizing these controller parameters is provided below: where, V DC = V DCref − V DC In this study, the optimization methods employed have been implemented to optimize the objective function outlined in equation ( 6) while adhering to the subsequent inequality constraints: K vp , K vi , K pi , and K i are the PI controller gains ranging from 0.1 to 500.

IV. OVERVIEW ON RECENTLY DEVELOPED EVOLUTIONARY ALGORITHMS
In recent years, several optimization algorithms, including Hybrid PSOS, SOS, and PSO, have emerged, demonstrating their proficiency in tackling intricate optimization challenges.These optimization algorithms have proven their effectiveness in addressing a wide range of complex optimization problems, each offering unique strengths and approaches to finding optimal solutions.Brief explanation of these algorithms are provided below: The PSO algorithm, introduced by Kennedy and Eberhart in 1995 [19], is a nature-inspired optimization technique that emulates the behaviour of a flock of birds searching for prey.
In PSO, particles are distributed across the search space of a problem, with each particle assessing the objective function associated with its current location.Subsequently, each particle calculates its movement within the search space by considering the historical information about its own current and best locations, along with that of one or more fellow particles within the swarm, while introducing some random perturbations.The next iteration commences after all particles have completed their movements.Eventually, the swarm as a whole tends to converge toward an optimal value of the fitness function.The key steps of the PSO algorithm are succinctly outlined below: Step 1: Initialize a population of particles (K vp , K vi , K pi , K i ) with random positions and velocities, taking into account the predefined dimensions within the search space.
Step 2: For each particle, assess the desired optimization objective function using (6).
Step 3: Compare the particle's fitness evaluation with its own particle best.If the current value proves superior, update the particle best with the current value and proceed to the next step.
Step 4: Adjust the particle's velocity and position based on the principles outlined in [19], and evaluate the objective function value.
Step 5: Repeat steps 2 to 4 until the termination criteria are met.
In summary, the PSO algorithm, inspired by the coordinated movement of birds in search of prey, leverages particle interactions within a swarm to guide optimization toward achieving optimal fitness values.
Flowchart of PSO is given below in Fig. 3:

B. SYMBIOTIC ORGANISMS SEARCH (SOS)
The SOS algorithm, developed by Min-Yuan Cheng and Doddy Prayogo, is a meta-heuristic approach that emulates the interactive behavior of organisms within an ecosystem to survive and propagate [20].This interplay among organisms in their struggle for survival is referred to as symbiosis, which encompasses three distinct phases: mutualism, commensalism, and parasitism.The SOS algorithm can be summarized through the following steps: Step 1: Begin by randomly initializing the ecosystem with a specified size (ecosize).Set the control parameters (number of organisms) within their defined upper and lower bounds.Establish the maximum fitness evaluation (FE).
Step 2: Calculate the objective function value for each organism set within the current ecosystem, tracking the total number of fitness evaluations (FE).
Step 3: Determine the best organism set within the present ecosystem based on their respective objective function values.
Step 4: Update the ecosystem by applying mutualism, commensalism, and parasitism phases of the SOS algorithm, following the guidelines outlined in [20], and guided by the objective function values.
Step 5: Identify the best fitness value as the minimum objective function value among all solution sets, and determine the corresponding best organism set that achieves this optimal fitness.
Step 6: Return to step 4 and continue iterating until the total number of fitness evaluations reaches the predefined maximum (maxFE).
The SOS algorithm, inspired by ecological symbiosis, seeks to optimize solutions through the dynamic interaction of organisms in a simulated ecosystem.
Flowchart of SOS is given below in Fig. 4:

C. HYBRID PSOS ALGORITHM
The hybrid metaheuristic algorithm for global optimization, known as Hybrid PSOS [21], is designed by merging the PSO and SOS algorithms.This hybridization serves the purpose of addressing certain challenges that neither SOS nor PSO can independently overcome.The primary enhancement driving this approach stems from the adjustments made within the SOS component of the proposed algorithm.These refinements play a vital role in averting entrapment within local solutions, thereby enhancing the algorithm's success rate.Notably, since the SOS algorithm operates without requiring any external parameters, the Hybrid PSOS algorithm minimizes the utilization of additional parameters, relying predominantly on those derived from the PSO.In this hybrid algorithm, the PSO undertakes the responsibility of accumulating valuable experiences and discerning the most promising ones for application during the SOS interaction phases.This collaborative approach significantly contributes to the algorithm's rapid convergence.The steps of the algorithm are briefly discussed below: Step 1: Initialize a population of particles (K vp , K vi , K pi , K i ) with random positions and velocities, taking into account the predefined dimensions within the search space.
Step 2: For each particle, assess the desired optimization objective function using (6).
Step 3: Compare the particle's fitness evaluation with its own particle best.If the current value proves superior, update the particle best with the current value and proceed to the next step.
Step 4: Adjust the particle's velocity and position based on the principles outlined in [21], and evaluate the objective function value.
Step 5: Update the search space by applying mutualism, commensalism, and parasitism phases of the SOS algorithm, following the guidelines outlined in [21] and evaluate the objective function using (6).
Step 6: Identify the best fitness value as the minimum objective function value among all solution sets, and determine the corresponding best organism set/search agent that achieves this optimal fitness.
Step 7: Return to step 4 and continue iterating until the total number of fitness evaluations reaches the predefined maximum (maxFE).
Flowchart of Hybrid PSOS is given below in Fig. 5:

V. RESULTS AND DISCUSSION
The study involves a comparative analysis of the optimization algorithms mentioned above, utilizing a simulation model of a single traction drive unit in EMUs.All simulations were conducted on a personal computer with a 1.7 GHz processor and 16 GB of RAM, using the MATLAB/Simulink R2022b platform.

A. SINGLE TRACTION DRIVE UNIT OF EMUS
Within this section, we focus on the evaluation of Hybrid PSOS's effectiveness in comparison to SOS and PSO, using a single traction drive as an illustrative example.Fig. 6 presents the simulation model that encompasses all three algorithms.For a detailed list of system parameters, please refer to Appendix A (Table 3).The responses of the system, including v u , i u and V DC were analyzed using the three algorithms, as illustrated in Figs. 7, 8, and 9. Notably, in Fig. 8, it is evident that the proposed Hybrid PSOS-based traction unit exhibits a remarkably low overshoot of just 1.3401%.In contrast, the overshoot values for the SOS and PSO-based algorithms are notably higher at 6.4542% and 20.6166%, respectively.Furthermore, the stability of the newly proposed Hybrid PSOS algorithm surpasses that of the other two algorithms, as it achieves a settling time of 0.2413 seconds to reach a steady-state condition.In comparison, SOS takes 0.3884 seconds, and PSO takes 0.5531 seconds to achieve the same.Fig. 7 provides the results of the FFT analysis for all three algorithms.
The Total Harmonic Distortion (THD) values for the line currents on the TT's secondary side were checked using three algorithms.The results show 12.48% for PSO, 2.17% for SOS, and only 1.08% for Hybrid PSOS.What's interesting is that when we compare Hybrid PSOS to SOS and PSO, we can see that Hybrid PSOS significantly lowers distortion in the line currents.This means the Hybrid PSOS algorithm is really good at reducing noise in the electrical currents, making it a promising choice for improving overall system performance.
To demonstrate the robustness of the Hybrid PSOS algorithm, PI controller parameters were fine-tuned under steady-state conditions.Subsequently, tuned parameters were applied to analyze the system's performance across various operating conditions, with supporting evidence provided in Figs.7 and 8. Table 1 lists the tuned PI controller parameters for different algorithms.In all algorithm scenarios, a consistent population size of 50 was employed, and the convergence behaviors of these algorithms were observed over a span of 50 iterations.The convergence profiles for the PSO, SOS, and Hybrid PSOS-based traction drives are visually represented in Fig. 9.
To assess the enhanced robustness of the proposed methodology, simulations were conducted to evaluate the system's response to load step changes.The simulation results depicted in Fig. 10 and Fig. 11 showcase the behavior of V DC as the load is incrementally raised by 20% and 50%, respectively, at the 2-second mark for all three algorithms.
In the case of PSO, a commendable dynamic response is observed prior to the load alteration; however, it exhibits a prolonged duration before returning to the predefined setpoint of the dc-link voltage at 3600 V.
Conversely, the V DC response derived from the Hybrid PSOS algorithm, as illustrated in Fig. 10 and Fig. 11, demonstrates a marginally higher voltage than the setpoint following a step load change.Yet, it accomplishes this with a reduced duration, swiftly converging back to the target voltage of 3600 V.This expedited recovery surpasses the performance observed in both the PSO and SOS algorithms.
In summary, comparative analysis with PSO and SOS establishes that the Hybrid PSOS algorithm manifests superior dynamic performance and a more rapid dynamic response, reinforcing its efficacy in scenarios involving load variations.
Observations drawn from Figs. 7, 8, 10 and 11, for the single traction drive unit of EMUs include: 1.The Hybrid PSOS-based controller effectively maintains the DC link capacitor voltage to 3600 V through proper PI controller tuning.2. In the Hybrid PSOS-based controller, v u , and i u exhibit in-phase behaviour, unlike the PSO and SOS-based controllers.

VI. BEST PARAMETER SETTINGS FOR THE ALGORITHMS STUDIED
The optimal configurations for each of the optimization algorithms were determined as follows: For Hybrid PSOS, the best results were achieved with a population size of 40, a benefit factors (BF1 = BF2 = 1) [21].SOS yielded its best results with a population size of 50 [20].In the case of PSO, the most favourable outcomes were obtained with a population size of 40, an inertia weight of 0.6, and an acceleration coefficient value of 1.5 [19].

VII. STATISTICAL ANALYSIS OF THE SIMULATED RESULTS
To assess the robustness of the Hybrid PSOS algorithm in comparison to other meta-heuristic optimization methods, namely PSO and SOS, a comprehensive statistical analysis was conducted using Wilcoxon's Signed Rank test [24], [25].This analysis was performed on a dataset comprising 50 trials, aimed at evaluating the performance of Hybrid PSOS.
The Wilcoxon's Signed Rank test is a pairwise examination designed to discern behavioral distinctions among various optimization algorithms, as elucidated by Derrac et al. [26].
In practical terms, an algorithm can be deemed robust if it provides compelling evidence against the null hypothesis [27].
In this context, the Wilcoxon's Signed Rank test was applied to the solution sets generated by each of the algorithms, affirming the robustness of the Hybrid PSOS algorithm.A p-value below 0.05 signifies substantial evidence against the null hypothesis.minimal deviation from mean values, underscoring the robustness of this algorithm.

VIII. LIMITATIONS OF THE PRESENT WORK
For the optimization techniques used, they present the certain limitations.The limitations of PSO are as follows: • PSO may converge to local optima and struggle to escape them, especially in complex optimization problems with multiple local optima.
• The performance of PSO is sensitive to its parameters (inertia weight, acceleration coefficients, etc.), and finding the optimal parameter values can be challenging.
• PSO may have limited global exploration capabilities, particularly in problems with a large search space.
• The algorithm may converge too quickly, stopping the search before the global optimum is found.The limitations of SOS are as follows: • Like PSO and many other optimization algorithms, SOS requires tuning of its parameters for different problem instances, and finding the right parameter values can be challenging.
• SOS may not perform well on all types of optimization problems, and its effectiveness can be influenced by the characteristics of the problem.
• The performance of SOS can be sensitive to the initial solutions generated, and poor initial solutions may lead to suboptimal results.
• SOS may face challenges when applied to high-dimensional optimization problems, and its efficiency might decrease with an increase in dimensionality.

IX. CONCLUSION
Three meta-heuristic optimization algorithms PSO, SOS, and Hybrid PSOS were applied to optimize and fine-tune PI controller parameters.The Hybrid PSOS algorithm yielded the best-tuned parameters.The algorithm-based traction unit developed using Hybrid PSOS exhibited a mere 1.3401% overshoot, in stark contrast to the considerably higher overshoots of 6.4542% for SOS and 20.6166% for PSO-based algorithms.Moreover, Hybrid PSOS demonstrated superior stability, achieving a steady-state condition with a settling time of just 0.2413 seconds, as opposed to 0.3884 seconds for SOS and 0.5531 seconds for PSO.The Hybrid PSOS-based controller effectively maintains the DC link capacitor voltage to 3600 V and also, v u , and i u are in-phase, signifying unity power factor, unlike the PSO and SOS-based controllers.This study also conducted harmonic analysis of input current to the converter, revealing a significantly lower THD of 1.08% for the Hybrid PSOS-based traction drive unit, compared to 12.48% for the PSO-based unit and 2.17% for the SOS-based unit.Simulations for load step changes affirm the robustness improvement of the proposed method.In summary, the simulations for load step changes confirm the enhanced robustness of the proposed method.V DC exhibits responses to 20% and 50% load increases at 2 seconds for all three algorithms.Notably, when compared with PSO and SOS, Hybrid PSOS showcases superior dynamic performance and a faster response.Finally, the robustness of the designed controller was rigorously established using Wilcoxon's Signed Rank test, affirming Hybrid PSOS's superiority over the PSO and SOS optimization algorithms in enhancing system performance and stability.

FUTURE SCOPE
The experimentation was conducted utilizing a simulation model, and the outcomes achieved have demonstrated a high level of satisfaction.The reliability and accuracy of these results can be further verified through the implementation of a practical hardware setup.This approach will ensure not only the robustness of the simulated findings but also the real-world applicability and validation of the proposed methodology.

APPENDIX A
See Table 3.

FIGURE 1 .
FIGURE 1. Equivalent circuit representation for an electric multiple unit (EMU).

FIGURE 2 .
FIGURE 2. Traditional PI controller for an active rectifier.

FIGURE 6 .
FIGURE 6. Simulation model of single traction drive unit of EMUs [1].

FIGURE 7 .
FIGURE 7. Simulation results for a single traction drive unit in electric multiple units (EMUs).

FIGURE 8 .
FIGURE 8. V DC for a single traction drive unit comparing PSO, SOS, and Hybrid PSOS.

FIGURE 10 .FIGURE 11 .
FIGURE 10.V DC for a single traction drive unit comparing PSO, SOS, and Hybrid PSOS for step load is increased by 20%.

TABLE 1 .
Tuned PI parameters for various algorithms when single unit is accessed to the ETN.

Table 2
furnishes p-values resulting this test, alongside maximum, average, and standard deviation (SD) values.Notably, the p-values for all algorithms were considerably lower than the desired

TABLE 2 .
Wilcoxon Signed Rank test for various algorithms when single unit is accessed to ETN.