Coordinated Hybrid Approach Based on Firefly Algorithm and Particle Swarm Optimization for Distributed Secondary Control and Stability Analysis of Direct Current Microgrids

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Coordinated Hybrid Approach Based on Firefly Algorithm and Particle Swarm Optimization for Distributed Secondary Control and Stability Analysis of Direct Current Microgrids


1. Introduction

The amount of energy consumed worldwide has significantly increased in recent years, posing a significant threat to the economic sector and sustainable development in meeting current energy demands [1,2]. Proposals to increase energy resources to satisfy the increasing demand have been making the rounds; these include both fossil fuels and alternative energies [3]. However, to lessen the harmful effects of carbon dioxide on the environment, society has emphasised reducing its dependency on fossil fuels over the past decade [4]. This has encouraged the development of power plants that harness renewable energies. According to projections by the United States. International Energy Agency, there is an anticipated 50% surge in the utilization of clean energy resources between 2019 and 2024 [5]. Conversely, numerous regions, including rural areas, grapple with energy shortages, emphasizing factors such as consumption patterns, social standing, income, and restricted availability of clean, modern, and sustainable energy resources [6,7]. Therefore, in addressing concerns such as the economic aspects of power generation, environmental impact from fossil fuels, limited availability, and electricity shortages, researchers worldwide have developed an integrated approach. This approach combines conventional and non-conventional methods for electricity generation, aiming to promote renewable energy sources (RESs) and mitigate existing issues. However, integrating RESs into the conventional utility grid might incur significant expenses due to losses in unnecessary power conversion stages [8]. Hence, implementing a standalone microgrid—an autonomous system equipped with its own control framework, generation sources, storage systems, and loads—becomes essential in providing power to remote areas while reducing expenses and centralising these resources in a single location [9]. The idea of microgrids emerged over a decade ago; however, numerous associated challenges have prevented its widespread adoption, making it the focus of current research efforts [10]. In the current body of literature, diverse types of microgrids have been employed, encompassing hybrid AC/DC, AC, and DC configurations [11,12]. Presently, DC-based systems are considered to be a better choice for microgrid operation. Their higher efficiency, improved compatibility with consumer electronics, direct interface with various RESs, and energy storage systems (ESSs) contribute to the demand for them [8,13]. When operating in islanded mode, frequency and harmonic-related issues are non-existent. Also, there are no concerns regarding regulating reactive power, and synchronization is not required [14,15]. Addressing specific challenges is crucial to optimize the potential of this microgrid setup. These challenges encompass ensuring compatibility with AC loads and seamlessly transitioning between islanded and on-grid operations [16]. Protecting DC microgrids does present a challenge owing to the lack of zero-crossing current and ground limitations [17]. Sustaining stability in a direct current MG becomes significantly challenging during fault conditions. This difficulty primarily arises from the absence of inherent physical inertia and the resistive impedance characteristic of direct current MG configurations [16,18].
Power electronic converters are commonly used as interfaces in every microgrid. They enable the connection of each distributed energy resource to the shared DC bus [19]. The advent of direct current microgrid technology led to the widespread adoption of DC loads across diverse sectors, including fields like data centres and telecommunication facilities [20]. Many modern electronic devices like televisions, laptop or phone chargers, and LED bulbs require precise DC voltage levels for their operation. Hence, due to these characteristics, direct current MGs can potentially cater to the increasing needs of remote and small communities around the globe [21]. Highlighting the importance of regulating bus voltage and ensuring efficient current distribution within multi-source DC microgrids underscores a critical priority for ongoing research in this field. The traditional droop control method for direct current MGs has been employed in the literature due to its straightforward implementation, stemming from the absence of a communication network requirement [22]. However, this control technique encounters issues such as circulating current regulations, voltage fluctuations, and unbalanced current sharing due to line and droop resistance among the MG converters [9]. Voltage stability and current allocation accuracy are intricately linked to the droop resistance: increasing the droop resistance leads to greater voltage deviations but improves current sharing accuracy and vice versa [23]. Consequently, the traditional droop technique presents several limitations: it faces an inherent load-sharing and voltage control management trade-off, exhibits slow transient response, delivers suboptimal performance with distributed energy resources (DERs), and experiences impedance misalignment among parallel converters, affecting active power distribution. As a result, incorporating a secondary control loop alongside droop control can serve as an additional control layer for DC microgrids [14,18,24]. There are three primary categories of secondary control: decentralized, centralized, and distributed control. In centralized control, the microgrid relies on a single central controller that communicates with all distributed energy resources within the system. This controller must be able to handle all data from components operating within the microgrid [23]. This control method places a significant communication burden, leading to limited control reliability and heavy dependence on the central controller. If there is a communication breakdown or failure of the central controller, the entire system can become inoperative [23,25]. The decentralized control approach alleviates the limitations of centralized control by eliminating the necessity for communication among the DERs. Instead, only local measurements are utilized to implement the control loop for each operating distributed energy source within the microgrid. Deploying a secondary decentralized control system can pose challenges, potentially compromising the overall operational efficiency of the DC microgrid. This stems from the absence of a communication link, limiting access to global information. Consequently, the controller’s output might not adequately counterbalance the required deviation induced by the droop controls [16,23].
Distributed control techniques exhibit characteristics present in both decentralized and centralized control approaches, leveraging the benefits of both types of control approaches. Each active distributed energy source within the MG possesses its own secondary distributed controller, and they establish communication among themselves through digital communication interfaces, typically utilizing a power line or a low-bandwidth communication network to exchange data like bus voltage and DER current output, among other parameters [18,26]. This helps the microgrid sustain complete functionality, even in a controller malfunction or communication link failure scenario, as long as the network remains interconnected. As a result, distributed control can withstand the possibility of one point of failure, enabling the convenient plug-and-play operation of distributed energy resources [14,18]. Recent advancements in distributed control techniques have enabled the implementation of a secondary control loop to achieve its control objectives (current distribution and voltage restoration) in a consensus manner with enhanced levels of reliability, scalability, and robustness. An integral-type secondary distributed control technique, which utilizes event-triggered communication, is presented in [27] to facilitate a balanced distribution of current and guarantee voltage recovery in an autonomous direct current MG. This approach can accomplish control objectives with minimal reliance on aperiodic communication, significantly reducing communication costs. However, it becomes ineffective if the converters do not have access to the bus voltage. Furthermore, this approach considers resistive loads alone, rendering it incapable of accommodating other load types. A cooperative distributed control technique is introduced in [25] for voltage recovery and current allocation in a direct current MG. The approach utilizes a discrete consensus with sparse communication with neighbouring converters, considering the discrete nature of measurements, communication data exchange, and control system implementation. In [28], a supervisory distributed control is introduced, which enables smooth transitions between two separate secondary controls. These distributed controllers are engineered explicitly for current distribution and voltage recovery within the DC microgrid. The constraints associated with this method include transients arising from the constant switching circuit’s operation and the complexity of adjusting multiple control coefficients. A secondary distributed control based on a consensus protocol is introduced in [29] for addressing the issues of current allocation and voltage recovery within a direct current microgrid. The approach utilizes a duo of PI controllers; one focused on voltage recovery and the other assigned to ensure an equitable current allocation. The amendment signals generated by these secondary control loops are transmitted to their respective local primary control loops. While the implementation of this method is simple, it does not provide the precise correction term needed, which can result in a decline in control performance due to this mismatch. In [30], a secondary distributed control approach for DC microgrids is presented. The approach utilizes event-triggered communication to reduce costs. It breaks the secondary control and tertiary optimization hierarchy by simultaneously solving the voltage restoration and power regulation issues in the secondary layer. The practical implementation of the optimization algorithm utilized in this technique still faces certain challenges, such as communication delays, and the limitation of line capacity was also not considered. A fixed-time secondary distributed control approach based on virtual voltage drop was also introduced in [31]. Though the control system accomplished the control objectives associated with voltage control and current allocation within a predefined settling period, the influence of line impedance was not considered in the design. In [32], a distributed iterative algorithm utilizing a game theory approach has been formulated. The technique targets proportionate current allocation and voltage restoration control in a direct current MG. A downside of this approach is the significant computational workload it imposes; it demands an extensive dataset to effectively learn the operations of the direct current MG for optimal performance.
Drawing from the existing literature review, it is clear that designing the secondary control system requires integrating two control loops: one for current distribution and another for voltage recovery. Integrating the control signal at the output of the secondary control system into the primary control loop typically results in a trade-off between voltage restoration and current distribution. Therefore, this research aims to develop a control technique that concurrently achieves both current distribution and voltage recovery, striking a balance between these two objectives. In this article, a distributed control technique is proposed, relying on a linear integration of current allocation and voltage control loops within the layers of the secondary control for a standalone DC MG. The distributed nature ensures robustness in the microgrid’s operation. Each distributed energy resource (DER) within the microgrid has its secondary control system, fostering a distributed setup. However, there is information exchange among the DERs to ensure agreement in their operations. To balance control objectives between current distribution and voltage restoration, a weighting coefficient is introduced, resolving the control trade-off. This weighting coefficient is determined through a meta-heuristic optimization (MHO) technique. Recent findings indicate a significant lack of emphasis on utilizing MHO methods, which are notable for their effectiveness in tackling complex problems and optimizing controller parameters [33]. This oversight pertains to addressing the significant challenges identified in prior research within the secondary control layer of DC microgrids. Addressing these challenges can involve the application of a range of meta-heuristic algorithms. A handful of illustrative algorithms in this category include the gravitational search algorithm, the firefly optimization algorithm (FFA) [34], the particle swarm optimization (PSO) method [35], and the grey wolf optimization (GWO) algorithm [36], inspired from the hierarchical leadership structure observed in grey wolf packs. Other examples include the giant trevally optimizer (GTO) [37], designed based on the giant trevally hunting behaviours; elephant clan optimization (ECO) [38], which is developed by simulating a model of elephant behaviour; the barnacle mating optimizer (BMO) algorithm [39], created using barnacle mating behaviour as a model; the sewing-training-based optimization (STBO) algorithm [40], designed using the task of imparting sewing skills as a model; the ebola optimization search algorithm (EOSA) [41], inspired by the ebola virus transmission mechanism; and the Aquila optimizer (AO) [42], inspired by the Aquila’s strategy of capturing prey. Given their limitations and inherent strengths, it is crucial to emphasize that no individual optimization algorithm can ensure the optimum operational performance of the system. For instance, the strengths of PSO include its straightforward implementation, minimal computational demands, and rapid convergence. However, it also exhibits weaknesses like early convergence or becoming stuck in local optima, along with a slower rate of convergence during exploitation when particles cluster around each other or the global optimum [19]. On the other hand, the FFA is a nature-inspired optimization technique rooted in swarm intelligence, mirroring the behaviour of fireflies in the natural world. the FFA holds certain advantages over the PSO algorithm [34,43]. Specifically, the FFA lacks an individual or specific global best, thereby avoiding the drawbacks associated with becoming trapped in local minima or encountering early convergence. Furthermore, the fireflies within the FFA lack a velocity characteristic. Consequently, this absence helps prevent issues related to fast or slow velocities [34]. While the FFA exhibits strong characteristics in local searches, there are instances where it struggles to break free entirely from local searches, resulting in being trapped in a local minimum [43]. Prior research has proposed integrating multiple algorithms through hybridization to address these challenges with the goal of attaining optimal system performance. Adopting a hybrid FFA–PSO can harness the respective strengths of both the FFA and PSO. The hybrid algorithm under consideration leverages the light intensity operation mechanism from the FFA for local search and integrates a PSO operator for global exploration. This algorithm blend ensures a harmonious equilibrium between exploitation and exploration, harnessing the strengths of both the FFA and PSO algorithms to optimize performance [43]. The algorithm stands out due to its simplicity and user-friendly nature as a potent tool for problem-solving. Moreover, it demonstrates competitive performance when benchmarked against other optimization algorithms [34], and it has proven effective in solving optimization problems [44]. Implementing this method can notably enhance the performance of the secondary control loop in direct current microgrids. Hence, this paper addresses current allocation and voltage recovery challenges in DC MGs. It proposes employing the hybrid FFA–PSO algorithm to dynamically select the newly introduced weighting coefficient incorporated within the secondary control system. It is important to highlight that the proposed technique brings significant contributions, such as better bus voltage restoration within a 5% tolerance, improved current-sharing among parallel DERs in the MG, decreased settling time, and minimized undershoot/overshoot across diverse operating scenarios. Eigenvalue analysis was employed to evaluate the stability of the control method presented in this study. Furthermore, the proposed technique requires less communication bandwidth, resulting in decreased communication costs. To assess the robustness of the newly introduced secondary distributed control technique to guarantee voltage recovery and accurate current allocation within the MG and its practical application in real-world scenarios for direct current MGs, a real-time environment incorporating a Speedgoat real-time digital machine is utilized to develop the direct current MG and implement the proposed secondary control under diverse operating scenarios.

In summary, this study has made the following contributions:

  • A distributed secondary control strategy for a DC microgrid is proposed, incorporating a new weighting parameter that concurrently ensures fair current distribution and eliminates bus voltage variations across several DERs.

  • An innovative FFA-PSO is introduced to aid in the parameter selection for the distributed control approach. This algorithm helps in fulfilling the control objectives of the microgrid.

  • A DC microgrid state-space model that incorporates eigenvalue observation analysis is developed to evaluate the impacts of the optimized secondary distributed control on the stability of the microgrid. This analysis helps in understanding the stability of the system.

  • A real-time testing setup using MATLAB/Simulink® is built and implemented on a Speedgoat real-time machine to verify the practical performance of the proposed approach in real-world applications.

The research structure is shown in Figure 1, while the article has the following layout: Section 2 explores the direct current MG state-space models, incorporating the primary control loop model. The modelling of the newly introduced distributed secondary control technique is outlined in Section 3. Section 4 introduces and formulates the hybrid FFA–PSO tuning method for addressing the discussed problem. The outcomes of evaluating the proposed technique’s performance, along with stability analysis, are detailed in Section 5. Lastly, Section 6 summarizes the achievements attained in this study.

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