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The dynamic features of microgrid operation, such as on-grid/off-grid operation mode, the intermittency of distributed generators, and its dynamic topology due to its ability to reconfigure itself, cause misfiring of conventional protection schemes. To solve this issue, adaptive protection schemes that use robust communication systems have been proposed for the protection of microgrids. However, the cost of this solution is significantly high. This paper presented an intelligent fault detection (FD) system for microgrids on the basis of local measurements and machine learning (ML) techniques. This proposed FD system provided a smart level to intelligent electronic devices (IED) installed on the microgrid through the integration of ML models. This allowed each IED to autonomously determine if a fault occurred on the microgrid, eliminating the requirement of robust communication infrastructure between IEDs for microgrid protection. Additionally, the proposed system presented a methodology composed of four stages, which allowed its implementation in any microgrid. In addition, each stage provided important recommendations for the proper use of ML techniques on the protection problem. The proposed FD system was validated on the modified IEEE 13-nodes test feeder. This took into consideration typical features of microgrids such as the load imbalance, reconfiguration, and off-grid/on-grid operation modes. The results demonstrated the flexibility and simplicity of the FD system in determining the best accuracy performance among several ML models. The ease of design’s implementation, formulation of parameters, and promising test results indicated the potential for real-life applications.

This paper deals with the problem of the optimal selection of capacitor banks in electrical AC distribution systems for minimizing the costs of energy losses during a year of operation through a discrete version of the vortex search algorithm (DVSA). This algorithm works with a hypersphere with a variable radius defined by an exponential function where a Gaussian distribution is used to generate a set of candidate solutions uniformly distributed around the center of this hypersphere. This center corresponds to the best solution obtained at the iteration t, which is initialized at the center of the solution space at the iterative search beginning. The main advantage of combining the exponential function with the Gaussian distribution is the correct balance between the exploration and exploitation of the solution space, which allows reaching the global optimal solution of the optimization problem with a low standard deviation, i.e., guaranteeing repeatability at each simulation. Two classical distribution networks composed of 33 and 69 nodes were used to validate the proposed DVSA algorithm. They demonstrated that the DVSA improves numerical reports found in specialized literature regarding the optimal selection and location of fixed-step capacitor banks with a low computational burden. All the simulations were carried out in MATLAB software.

A convex mathematical model based on second-order cone programming (SOCP) for the optimal operation in direct current microgrids (DCMGs) with high-level penetration of renewable energies and battery energy storage systems (BESSs) is developed in this paper. The SOCP formulation allows converting the non-convex model of economic dispatch into a convex approach that guarantees the global optimum and has an easy implementation in specialized software, i.e., CVX. This conversion is accomplished by performing a mathematical relaxation to ensure the global optimum in DCMG. The SOCP model includes changeable energy purchase prices in the DCMG operation, which makes it in a suitable formulation to be implemented in real-time operation. An energy short-term forecasting model based on a receding horizon control (RHC) plus an artificial neural network (ANN) is used to forecast primary sources of renewable energy for periods of 0.5h. The proposed mathematical approach is compared to the non-convex model and semidefinite programming (SDP) in three simulation scenarios to validate its accuracy and efficiency.

The problem of the output voltage regulation in a DC-DC boost converter feeding a DC microgrid is addressed in this research via the passivity-based control theory with a proportional–integral action (PI-PBC). Two external input estimators were implemented in conjunction with the proposed controller to make it sensorless and adaptive. The first estimator corresponds to the immersion & invariance (I&I) approach applied to calculate the expected value of the DC load, which is modeled as an unknown DC current. The second estimator is based on the disturbance–observer (DO) approach, which reaches the value of the voltage input. The main advantage of both estimators is that these ensure exponential convergence under steady-state operating conditions, and their parametrization only requires the definition of an integral gain. A comparative analysis with simulations demonstrates that the proposed PI-PBC approach is effective in regulating/controlling the voltage profile in unknown DC loads as compared to the adaptive sliding mode controller. Experimental validations have demonstrated that the proposed PI-PBC approach, in conjunction with the I&I and the DO estimators, allowed regulation of the voltage output profile in the terminals of the DC load with asymptotic stability properties and fast convergence times (1.87 ms) and acceptably overshoots (6.1%) when the voltage input varies its magnitude (from 10 to 12 V and from 10 to 8 V) considering that the DC load changed with a square waveform between 1 and 2 A with 100 Hz.

Photovoltaic (PV) systems are a clean energy source that allows for power generation integration into electrical networks without destructive environmental effects. PV systems are usually integrated into electrical networks only to provide active power during the day, without taking full advantage of power electronics devices, which can compensate for the reactive power at any moment during their operation. These systems can also generate dynamic reactive power by means of voltage source converters, which are called PV-STATCOM devices. This paper presents a convex formulation for the optimal integration (placement and sizing) of PV-STATCOM devices in electrical distribution systems. The proposed model considers reducing the costs of the annual energy losses and installing PV-STATCOM devices. A convex formulation was obtained to transform the hyperbolic relation between the products of the voltage into a second-order constraint via relaxation. Two simulation cases in the two IEEE test systems (33- and 69-node) with radial and meshed topologies were implemented to demonstrate the effectiveness of the proposed mixed-integer convex model. The results show that PV-STATCOM devices reduce the annual cost of energy losses of electrical networks in a more significant proportion than PV systems alone.

Thermoelectric generators (TEGs) have the potential to convert waste heat into electrical energy, making them attractive for energy harvesting applications. However, accurately estimating TEG parameters from industrial systems is a complex problem due to the mathematical complex non-linearities and numerous variables involved in the TEG modeling. This paper addresses this research gap by presenting a comparative evaluation of three optimization methods, Particle Swarm Optimization (PSO), Salps Search Algorithm (SSA), and Vortex Search Algorithm (VSA), for TEG parameter estimation. The proposed integrated approach is significant as it overcomes the limitations of existing methods and provides a more accurate and rapid estimation of TEG parameters. The performance of each optimization method is evaluated in terms of root mean square error (RMSE), standard deviation, and processing time. The results indicate that all three methods perform similarly, with average RMSE errors ranging from 0.0019 W to 0.0021 W, and minimum RMSE errors ranging from 0.0017 W to 0.0018 W. However, PSO has a higher standard deviation of the RMSE errors compared to the other two methods. In addition, we present the optimized parameters achieved through the proposed optimization methods, which serve as a reference for future research and enable the comparison of various optimization strategies. The disparities observed in the optimized outcomes underscore the intricacy of the issue and underscore the importance of the integrated approach suggested for precise TEG parameter estimation.

This paper presents a comprehensive study on the formulation and solution of the power flow problem in bipolar direct current (DC) distribution networks with unbalanced constant power loads. Using the nodal voltage method, a unified nonlinear model is proposed which accurately captures both monopolar and bipolar load configurations as well as the voltage coupling between conductors. The model assumes a solid grounding of the neutral conductor and known system parameters, ensuring reproducibility and physical consistency. Seven iterative algorithms are developed and compared, including three Newton–Raphson-based formulations and four quasi-Newton methods with constant Jacobian approximations. The proposed techniques are validated on two benchmark networks comprising 21 and 85 buses. Numerical results demonstrate that Newton-based methods exhibit quadratic convergence and high accuracy, while quasi-Newton approaches significantly reduce computational time, making them more suitable for large-scale systems. The findings highlight the trade-offs between convergence speed and computational efficiency, and they provide valuable insights for the planning and operation of modern bipolar DC grids.

This research addresses the optimal reactive power compensation problem in medium-voltage distribution networks by integrating Thyristor-based Switched Capacitors (TSCs) and applying the Artificial Hummingbird Algorithm (AHA). Using TSCs in distribution networks aims at reducing the annualized grid operating costs associated with energy losses while considering the costs of investment in reactive power compensators. The AHA-a bio-inspired metaheuristic optimization approach—is used to determine the optimal set of nodes and sizes for the TSCs. To estimate the expected annualized costs of energy losses, a classical power flow approach based on successive approximations is implemented, structured within a master-slave framework with the AHA. Numerical results on 33- and 69-bus systems demonstrate the effectiveness of the proposed approach compared to three other metaheuristic methods: the sine-cosine algorithm, the Chu & Beasley genetic algorithm, the particle swarm optimizer, and the black widow optimizer. All computational validations were performed using MATLAB software. Esta investigación aborda el problema de la compensación óptima de potencia reactiva en redes de distribución de media tensión mediante la integración de compensadores conmutados basados en tiristores (TSCs) y la aplicación del algoritmo artificial de colibrí (AHA). El uso de TSCs en redes de distribución busca reducir los costos operativos anualizados de la red que se relacionan con las pérdidas de energía, a la vez que se consideran los costos de inversión en compensadores de potencia reactiva. El AHA, un enfoque bioinspirado de optimización metaheurística, se utiliza para determinar el conjunto óptimo de nodos y tamaños para los TSCs. Para estimar los costos anualizados que se proyectan para las pérdidas de energía, se implementa un enfoque clásico de flujo de potencia basado en aproximaciones sucesivas, estructurado en el marco de una configuración maestro-esclavo con el AHA. Los resultados numéricos obtenidos en sistemas de 33 y 69 nodos demuestran la efectividad del enfoque propuesto del AHA en comparación con otros tres métodos metaheurísticos: el algoritmo seno-coseno, el algoritmo genético de Chu & Beasley, el optimizador de enjambre de partículas y el optimizador de viuda negra. Todas las validaciones computacionales se realizaron en el software MATLAB.

This paper addresses the voltage stability margin calculation in medium-voltage distribution networks in the context of exact mathematical modeling. This margin calculation is performed with a second-order cone (SOCP) reformulation of the classical nonlinear non-convex optimal power flow problems. The main idea around the SOCP approximation is to guarantee the global optimal solution via convex optimization, considering as the objective function the λ-coefficient associated with the maximum possible increment of the load consumption at all the nodes. Different simulation cases are considered in one test feeder, described as follows: (i) the distribution network without penetration of distributed generation; (ii) the distribution network with penetration of distributed generation; and (iii) the distribution grid with capacitive compensation. Numerical results in the test system demonstrated the effectiveness of the proposed SOCP approximation to determine the λ-coefficient. In addition, the proposed approximation is compared with nonlinear tools available in the literature. All the simulations are carried out in the MATLAB software with the CVX package and the Gurobi solver.

The optimal integration of photovoltaic (PV) systems and distribution static synchronous compensators (D-STATCOMs) in electrical distribution networks is important to reduce their operating costs, improve their voltage profiles, and enhance their power quality. To this effect, this paper proposes a mixed-integer convex (MI-Convex) optimization model for the optimal siting and sizing of PV systems and D-STATCOMs, with the aim of minimizing investment and operating costs in electrical distribution networks. The proposed model transforms the traditional mixed-integer nonlinear programming (MINLP) formulation into a convex model through second-order conic relaxation of the nodal voltage product. This model ensures global optimality and computational efficiency, which is not achieved using traditional heuristic-based approaches. The proposed model is validated on IEEE 33- and 69-bus test systems, showing a significant reduction in operating costs in both feeders compared to traditional heuristic-based approaches such as the vortex search algorithm (VSA), the sine-cosine algorithm (SCA), and the sech-tanh optimization algorithm (STOA). According to the results, the MI-convex model achieves cost savings of up to 38.95% in both grids, outperforming the VSA, SCA, and STOA.