This paper presents an advanced numerical approach for solving the direct-current (DC) power flow equations in distribution networks, which leverages the high-order ACT5S iterative method. The unique nonlinear formulations of the DC power flow problem are outlined, and their Jacobian structures are derived to facilitate the development of efficient solution strategies. The proposed methodology integrates the ACT5S scheme, known for its fifth-order convergence, to improve convergence speed and robustness when compared to the traditional Newton-Raphson method. Extensive numerical tests on the 33-bus and 69-bus systems demonstrate that the ACT5S method significantly reduces the number of iterations required, with comparable computation times and high solution accuracy. The results highlight the potential of high-order iterative algorithms for reliable and efficient power flow analysis in modern DC distribution networks, which is increasingly critical in applications involving renewable energy, energy storage, and electrification initiatives.

This paper presents a robust data-driven methodology for estimating transmission loss coefficients (B-coefficients) in power systems using linear and quadratic programming (LP and QP), both of which belong to the family of convex optimization models. The first model employs a linear objective function with linear constraints, ensuring computational efficiency for simpler scenarios. The second model utilizes a quadratic objective function, also under linear constraints, to better capture more complex nonlinear relationships. By framing the estimation problem as a parameter identification task, both methodologies minimize the cost functions that quantify the mismatch between measured and modeled power losses. By considering a broad range of operational scenarios, our approach effectively captures the stochastic behavior inherent in power system operations. The effectiveness of both the LP and QP models is validated in terms of their ability to accurately extract physically meaningful B-coefficients from diverse simulation datasets. This study underscores the potential of integrating linear and quadratic programming as powerful and scalable tools for data-driven parameter estimation in modern power systems, especially in environments characterized by uncertainty or incomplete information.

Voltage stability under transmission line contingencies is a critical concern in modern power systems, as the growing electricity demand and the large-scale integration of renewable energy sources increasingly challenge the security of network operation. This paper addresses the problem of estimating the voltage stability margin under N−1 transmission line contingencies through three solution methodologies: a nonlinear programming formulation solved via an interior-point algorithm (IPOPT) with a multi-start strategy, a recursive heuristic approach based on successive Newton–Raphson power flow solutions with progressive load scaling, and a convex second-order cone programming relaxation. The proposed methods are validated on the IEEE 9-, 14-, 30-, and 57-bus test systems, thereby covering networks of varying topological complexity and redundancy. A comparative analysis evaluates the accuracy of each approach against a nonlinear programming reference, as well as their computational efficiency under a comprehensive set of contingency scenarios. The results indicate that the heuristic method achieves higher precision, while the convex formulation offers a substantially faster solution, with both approaches demonstrating robustness in cases where the nonlinear programming method fails to converge.

This study presents a cost-oriented energy management framework for the coordinated scheduling of wind turbines and battery energy storage systems in a distribution microgrid. Each generation node includes a co-located wind turbine and battery unit, and the optimization model determines their hourly active and reactive power dispatch over a 24-hour horizon. The objective is to minimize daily operating cost while satisfying network constraints, converter apparent power limits, and battery state-of-charge restrictions in both grid-connected and isolated operating modes. The proposed solution strategy is based on a population-based genetic algorithm and is benchmarked against particle swarm optimization and the multiverse optimizer. Representative demand and wind generation profiles from a Colombian region are considered. In the studied configuration, the wind turbines contribute renewable active power and voltage support, while the battery systems provide energy shifting, peak shaving, and reactive power support. Each optimization method is executed 100 independent times to assess solution quality, repeatability, and robustness. The results show that the proposed genetic algorithm achieves the best average performance and the lowest variability among the methods compared, while preserving the microgrid’s technical feasibility and all battery operating constraints. These findings show that coordinated WT and BESS scheduling is an effective strategy for reducing operating cost and supporting the secure integration of wind generation in distribution microgrids.

The optimal expansion of unbalanced three-phase distribution networks in non-interconnected zones requires the simultaneous resolution of two highly complex planning decisions: the selection of feeder routes and the sizing of conductors. This problem, formulated as a non-convex mixed-integer nonlinear program (MINLP), poses significant computational challenges due to the combinatorial explosion of radial topologies, discrete conductor choices, and the nonlinearity of three-phase power-flow equations. While metaheuristics offer flexible exploration, they lack optimality guarantees and repeatability, whereas exact MINLP solvers provide rigorous solutions but become computationally intractable for systems of realistic size. To overcome these limitations, this paper introduces a novel hybrid exact–metaheuristic framework that synergistically combines the global exploration capabilities of the Equilibrium Optimizer (EO) with the rigorous evaluation power of an exact MINLP model. In this cascade architecture, EO efficiently navigates the discrete space of radial topologies, while the exact MINLP stage, solved using BONMIN with an interior-point branch-and-bound scheme, optimizes conductor selection and evaluates the full annualized cost, rigorously enforcing voltage, ampacity, and physical constraints. The proposed methodology was validated on 10-, 30-, 50-, and 110-node test systems derived from real Colombian non-interconnected zones (Nuquí, Leticia, San Andrés, and a large-scale urban case). Comparative analysis against pure metaheuristics (SSA, GWO, VSA) and standalone MINLP demonstrates that EO-MINLP consistently yields the lowest total annualized costs, achieving savings of up to 0.42%, 0.71%, and 1.36% over the best pure metaheuristic for the 10-, 30-, and 50-node systems, respectively. Crucially, the hybrid strategy dramatically enhances scalability, reducing the standalone MINLP computational time by 15.79%, 78.68%, and 88.95% for these cases, while preserving solution quality and improving repeatability (standard deviation reduced from over 1.2% to as low as 0.11%). For the challenging 110-node system, where the standalone MINLP proved computationally infeasible, the proposed method successfully delivered a feasible, high-quality solution with a standard deviation of just 0.43%, confirming its practical applicability to large-scale planning. These results demonstrate that the EO-MINLP framework provides a robust, scalable, and economically superior tool for the cost-effective design of unbalanced distribution networks, effectively bridging the gap between the flexibility of stochastic search and the rigor of mathematical programming.

This study focuses on estimating the nine parameters of the three-diode model (3DM) for photovoltaic (PV) cells by integrating the Atan-Sinc Optimization Algorithm (ASOA) with the Newton-Raphson (NR) method. The ASOA, a population-based metaheuristic approach inspired by the behaviors of the Sech and Tanh functions, systematically generates candidate solutions for the complete set of parameters in the 3DM. For each of these solutions, the NR method is employed to solve the transcendental equation governing the solar cell model, facilitating a precise evaluation of the associated objective function. To guide the parameter estimation process, experimental current-voltage (I-V) and voltage-power (V-P) curves are utilized. The robustness of the proposed methodology is validated through studies on both monocrystalline and polycrystalline solar cells. Computational results reveal that the ASOA effectively navigates the parameter space, while the NR method provides accurate evaluations, resulting in reliable and precise parameter estimations. All numerical validations were conducted using MATLAB software, version 2024b.

This research presents a coordinated short-term operational dispatch framework for photovoltaic generators and distribution static synchronous compensators (D-STATCOM) in radial distribution networks. The problem is formulated as a large-scale distribution-level optimal power flow with a 24 h horizon and 30 min resolution, where the active power of pre-installed photovoltaic units and the reactive power of D-STATCOM devices are optimally dispatched. Two objective functions are investigated independently: the minimization of daily active power losses and the minimization of daily carbon dioxide emissions. All operational constraints related to AC power flow, voltage limits, and line thermal capacities are explicitly considered. Five population-based metaheuristic algorithms, including Particle Swarm Optimization, Vortex Search Algorithm, Sine Cosine Algorithm, Crow Search Algorithm, and a Continuous Genetic Algorithm (CGA), are implemented and compared under identical simulation conditions. The methodology is validated on the IEEE 33-bus and IEEE 69-bus distribution test systems using realistic hourly load and solar generation profiles. Numerical results demonstrate that coordinated control of photovoltaic generation and D-STATCOM reactive power significantly improves both technical and environmental performance. In the loss minimization case, CGA achieves reductions exceeding 55 % and 66 % in the 33-bus and 69-bus systems, respectively. For the emission minimization objective, CGA attains carbon dioxide reductions of approximately 31 % and 48 % in the same networks while preserving voltage and current constraints. The obtained results indicate that the proposed multi-period scheduling framework yields consistent improvements on the test system radial feeders, with CGA showing the best balance between solution quality and dispersion among the tested stochastic methods.

This paper presents a novel master–slave stochastic optimization framework for the optimal siting and sizing of fixed-step capacitor banks in medium-voltage distribution networks, explicitly addressing the inherent variability of load demand that is typically neglected in conventional deterministic approaches. The proposed methodology integrates a scenario-based stochastic optimization model with a Chu and Beasley genetic algorithm (CBGA) as the master stage, which handles discrete placement decisions, and a successive-approximation power flow method (SAPF) as the slave stage, which evaluates the technical and economic performance of each candidate solution under multiple load scenarios. To capture demand uncertainties, 365 daily load realizations are generated using independent Gaussian noise with a relative standard deviation of 10% applied to each load point. These are subsequently reduced to ten representative scenarios via k-means clustering, reducing the number of power-flow evaluations per candidate solution from 365 to 10 (a 36.5-fold reduction); the reduced scenarios exhibit a low mean absolute error (MAE: <2%) with respect to the original mean, indicating faithful representation of the average load behavior, while the silhouette score is modest (approximately 0.25), consistent with the unimodal nature of the generated data and implying that the clusters are not well separated. Extensive simulations on a 33-bus test feeder considering three energy-cost-escalation scenarios (0%, 10%, and 20%) over a 20-year planning horizon demonstrate that both the deterministic and stochastic approaches reduce the total net present cost by 16.52% to 17.34% compared to the uncompensated network; the stochastic approach consistently delivers solutions that are either superior or comparable to deterministic planning (yielding up to approximately 0.16% additional cost reduction) while offering enhanced robustness against load variability. The stochastic framework offers distinct advantages, including robust solutions across a wide range of operating conditions, an inherent ability to adjust investment levels in response to probabilistic load distributions, and the ability to quantify uncertainty in decision making, with the most significant benefits observed when energy costs are low and load variability is high. The convergence of both approaches at a 20% escalation level further validates the reliability of high-resolution deterministic modeling when economic factors strongly dominate the optimization objective. This study underscores the importance of probabilistic modeling for modern distribution network planning, providing a practical and computationally efficient decision-support tool for utility planners to enhance grid resilience and operational efficiency in the context of increasing demand variability and renewable energy integration.

This paper presents a convex reformulation of the optimal power flow problem for monopolar DC distribution networks with integrated distributed energy resources, including photovoltaic generators, wind turbines, and battery storage systems. The non-convexity introduced by bilinear voltage terms in the power balance and loss equations is addressed using an exponential cone-based transformation. By introducing logarithmic auxiliary variables, the bilinear terms are embedded into the convex domain, enabling the use of efficient conic optimization solvers. The proposed model is implemented using the JuMP modeling framework in Julia and evaluated on benchmark DC feeders ranging from 27 to 123 buses. The results demonstrate that the exponential cone-based formulation achieves highly accurate approximations of the exact nonlinear solution, with relative errors as low as 10−5, while significantly outperforming standard second-order cone programming relaxations in terms of both accuracy and scalability. The proposed approach offers a reliable and computationally tractable tool for the optimal dispatch and voltage regulation of large-scale DC networks.

The increasing penetration of renewable generation and dynamic electricity tariffs creates new challenges for household energy management, requiring strategies that minimize costs while preserving user comfort. This paper proposes a stochastic home energy management model for the optimized scheduling of controllable appliances, formulated as a mixed-integer linear programming problem. The model incorporates dynamic pricing, photovoltaic (PV) generation, and battery storage, while fixed loads are assumed to be non-controllable. To capture the variability of electricity prices and solar irradiance, a K-means clustering technique is employed in order to generate representative scenarios from historical data. The methodology is applied to a representative household equipped with four controllable appliances, three solar panels, and a battery system. Four scenarios are analyzed: (i) a benchmark with fixed schedules, (ii) stochastic scheduling of appliances, (iii) stochastic scheduling with solar generation, and (iv) stochastic scheduling with PV generation and battery storage. The results show that, compared to the benchmark case (US$ 2.8895), stochastic scheduling alone reduces costs by 7.18%, while including PV generation yields savings of 55.61%. The most favorable configuration combines PV generation and storage, lowering the electricity bill to US$ 1.2824 (55.62% savings). The battery state of energy profile confirms its role in peak shaving, charging during midday and discharging during tariff peaks. These findings demonstrate that integrating stochastic optimization with solar panels and battery storage significantly enhances household energy flexibility and reduces costs, underscoring the importance of advanced energy management strategies for sustainable and cost-efficient residential consumption.

This research aims to accurately estimate the nine parameters of the three-diode photovoltaic model (3DM) by employing a hybrid optimization strategy that integrates the atan-sinc optimization algorithm (ASOA) with the Newton-Raphson method (NRM). The ASOA, inspired by the mathematical properties of the arctangent and sinc functions, serves as a population-based metaheuristic to generate candidate parameter sets for the comprehensive 3DM. To ensure a precise evaluation of each candidate, the NRM is entrusted with solving the complex transcendental equations typically associated with photovoltaic cell modeling, enabling a reliable computation of the objective function. The parameter estimation process is guided by experimental current-voltage (I-V) and power-voltage (P-V) curves collected from both monocrystalline and polycrystalline solar modules, which help to validate the robustness of the proposed methodology. The results demonstrate that the ASOA effectively explores the parameter space, while the NRM guarantees high accuracy with regard to solution evaluation, thereby producing dependable parameter estimates. All computational procedures and analyses were performed using MATLAB R2025b.

This article presents a hybrid optimization model designed to determine the optimal location and operation of capacitor banks in medium-voltage distribution networks, aiming to reduce energy losses and enhance the system's economic efficiency. The use of reactive power compensation through fixed-step capacitor banks is highlighted as an effective and cost-efficient solution; however, their optimal placement and sizing pose a mixed-integer nonlinear programming optimization challenge of a combinatorial nature. To address this issue, a multi-objective optimization methodology based on the Sine Cosine Algorithm (SCA) is proposed to identify the ideal location and capacity of capacitor banks within distribution networks. This model simultaneously focuses on minimizing technical losses while reducing both investment and operational costs, thereby producing a Pareto front that facilitates the analysis of trade-offs between technical performance and economic viability. The methodology is validated through comprehensive testing on the 33- and 69-bus reference systems. The results demonstrate that the proposed SCA-based approach is computationally efficient, easy to implement, and capable of effectively exploring the search space to identify high-quality Pareto-optimal solutions. These characteristics render the approach a valuable tool for the planning and operation of efficient and resilient distribution networks.

This study introduces a comparative analysis of the Newton-Raphson and quasi-Newton techniques for addressing the power flow problem in monopolar DC distribution networks within a quasi-dynamic framework. The proposed approach is tailored for simulations with a time resolution of one minute, facilitating real-time or large-scale system assessments. Two variants of the Newton-Raphson method, differing in their Jacobian structures, are evaluated alongside three quasi-Newton algorithms employing constant Jacobian approximations. Validation is performed on the DC equivalents of test systems comprising 33 and 69 nodes, considering performance metrics such as convergence speed, computational efficiency, and precision in power losses estimation. The results indicate that, while Newton-Raphson methods tend to converge in fewer iterations, quasi-newton approaches—especially those using fixed Jacobian matrices—achieve reduced computation times, demonstrating their suitability for fast, quasi-dynamic power system analysis.

This research introduces a novel convex methodology for estimating transmission loss coefficients (B-coefficients) in power systems using a data-driven approach based on power system measurements. To enhance estimation accuracy and practical relevance, the model is evaluated across a wide spectrum of operating conditions, incorporating random variations in active power injections and demand profiles modeled via uniform and Gaussian distributions. A semi-definite programming (SDP) model leveraging p-norm formulations is proposed to derive the B-coefficients efficiently. Numerical evaluations on IEEE 14-, 39-, 57-, and 118-bus test feeders demonstrate the effectiveness and robustness of the approach, yielding average estimation errors between [Formula: see text] and [Formula: see text] across diverse scenarios. These results confirm the reliability of the proposed methodology, contributing to improved accuracy in transmission loss modeling and supporting more efficient power system operations.

This work develops a methodology for operating Battery Energy Storage Systems (BESSs) in distribution networks, connected in parallel with a medium- and small-scale photovoltaic Distributed Generator (PMGD), focusing on a real project located in the O'Higgins region of Chile. The objective is to increase energy sales by the PMGD while ensuring compliance with operational constraints related to the grid, PMGD, and BESSs, and optimizing renewable energy use. A real distribution network from Compa & ntilde;& iacute;a General de Electricidad (CGE) comprising 627 nodes was simplified into a validated three-node, two-line equivalent model to reduce computational complexity while maintaining accuracy. A mathematical model was designed to maximize economic benefits through optimal energy dispatch, considering solar generation variability, demand curves, and seasonal energy sales and purchasing prices. An energy management system was proposed based on a master-slave methodology composed of Particle Swarm Optimization (PSO) and an hourly power flow using the successive approximation method. Advanced optimization techniques such as Monte Carlo (MC) and the Genetic Algorithm (GAP) were employed as comparison methods, supported by a statistical analysis evaluating the best and average solutions, repeatability, and processing times to select the most effective optimization approach. Results demonstrate that BESS integration efficiently manages solar generation surpluses, injecting energy during peak demand and high-price periods to maximize revenue, alleviate grid congestion, and improve operational stability, with PSO proving particularly efficient. This work underscores the potential of BESS in PMGD to support a more sustainable and efficient energy matrix in Chile, despite regulatory and technical challenges that warrant further investigation.

Three-phase induction motors account for nearly two-thirds of industrial electricity consumption, making accurate parameter identification essential for efficiency optimization, predictive maintenance, and digital twin calibration. This paper introduces the stochastic spheric navigator algorithm (SSNA) for estimating the equivalent circuit parameters (stator and rotor resistances, leakage reactances, and magnetizing reactance) of induction motors by minimizing the normalized squared error between manufacturer-provided torque characteristics (starting, peak, and full-load) and their analytical counterparts derived from the steady-state Th & eacute;venin model. The SSNA employs an adaptive spherical search mechanism with a decaying radius schedule that progressively narrows the exploration neighborhood, enabling a balanced transition from global exploration to local refinement. Validated on 5 hp and 25 hp motors against the genetic algorithm (GA), particle swarm optimizer (PSO), hybrid GA-PSO, and sine-cosine algorithm (SCA), the SSNA demonstrates distinct advantages. For the 5 hp motor, it achieves the lowest errors in maximum torque (1.34 & times;10-4%) and full-load torque (5.08 & times;10-4%). For the previously unreported 25 hp motor, the SSNA yields an objective function value of 4.68 & times;10-12-six orders of magnitude lower than the SCA-and reduces magnetizing reactance estimation error from 46.55% (SCA) to 16.18%. Statistical analysis over 100 independent runs reveals that the SSNA uniquely combines the lowest minimum (best) value, the lowest maximum (worst) value, and the lowest standard deviation, demonstrating superior accuracy, reliability, and consistency. These results position the SSNA as a highly competitive optimization framework for induction motor parameter identification, with particular suitability for applications demanding high precision and robust performance.

The large-scale integration of photovoltaic generation into distribution grids has introduced significant operational challenges, including voltage excursions, reverse power flows, and increased variability. Battery energy storage systems (BESSs) offer a versatile solution by providing coordinated active- and reactive-power support. However, their scheduling in active distribution networks is challenging because of the non-convex alternating-current (AC) power-flow equations, the nondifferentiability of battery-degradation modeling, and uncertainty in renewable generation and demand. This paper proposes a two-stage methodology for the day-ahead operation of BESSs in ADNs. In the first stage, parallel particle swarm optimization (PPSO) determines the hourly active- and reactive-power schedules of the BESS units. In the second stage, a matrix-based multi-period AC power flow based on successive approximations evaluates the schedules and verifies voltage, thermal, converter-capability, and state-of-charge (SoC) constraints. A rainflow-counting degradation model is incorporated into the objective function to account for cycling and calendar aging costs. The methodology is assessed through ablation analyses comparing active-power-only and coordinated P–Q dispatches, degradation-unaware and degradation-aware scheduling, and serial and parallel PSO implementations. It is validated on modified 33-, 69-, and 136-node systems under deterministic and uncertainty-based operating conditions, including 100 demand and PV-generation scenarios. PPSO is compared with parallel versions of the adaptive Jaya algorithm (AJAYA), genetic algorithm (GA), multi-verse optimizer (MVO), salp swarm algorithm (SSA), grey wolf optimizer (GWO), and vortex search algorithm (VSA), using operating-cost reduction, computational time, solution variability, feasibility indicators, BESS lifetime, and weekly cost analysis. Additionally, exact one-sided Wilcoxon signed-rank tests with Holm adjustment are used to assess the statistical significance of the economic differences between PPSO and the benchmark methods. Results show that PPSO provides the lowest or most competitive operating costs and the shortest computational time in the evaluated cases, while all network and storage constraints remain satisfied.

This paper presents an adaptive one-step model predictive control (MPC) strategy for optimal load-sharing and voltage regulation in isolated direct current (DC) microgrids. Utilizing a port-Hamiltonian representation within a reduced model, the proposed secondary control method ensures physically consistent actions and incorporates a recursive least-squares algorithm for real-time estimation of the reduced conductance matrix. The one-step formulation enables the analytical derivation of the optimal control law, ensuring convexity and global optimality for real-time implementation. Additionally, a convex optimization procedure is introduced to compute droop control gains, maintaining the passivity properties of the system while balancing current sharing and voltage regulation within operational constraints. Dynamic simulations on a realistic DC microgrid benchmark validate the method’s effectiveness, demonstrating enhancements in load-sharing accuracy, voltage regulation, and responsiveness to abrupt demand changes. These results highlight the potential of the proposed MPC framework to improve the reliability and efficiency of DC microgrid operations.

The proliferation of distributed photovoltaic (PV) generation introduces significant operational challenges for distribution networks, including voltage instability and elevated technical losses. While modern PV inverters capable of static synchronous compensator (STATCOM) functionality—forming PV-STATCOM systems—offer a promising solution, their optimal integration remains a complex mixed-integer non-linear programming (MINLP) problem. This paper addresses this gap by proposing a novel hybrid evaluator–optimizer framework for the optimal daily placement and sizing of PV-STATCOM devices. The framework synergistically integrates the metaheuristic crow search algorithm (CSA) for global exploration of discrete device locations with a high-fidelity, multi-period optimal power flow (OPF) model—implemented efficiently in Julia with the Ipopt solver—for continuous operational evaluation and constraint validation. The methodology incorporates realistic 24 h load and solar irradiance profiles. Extensive validation on standard IEEE 33- and 69-bus test systems demonstrates the efficacy of the proposed approach. The results indicate substantial reductions in daily energy losses—by up to 70.4% and 72.9% for the 33- and 69-bus systems, respectively—and corresponding operational costs, outperforming recent state-of-the-art metaheuristic and convex optimization methods reported in the literature. The CSA also exhibits robust convergence and repeatability across multiple independent runs. This work contributes a computationally efficient, open-source planning tool that leverages modern optimization solvers, providing a scalable and effective strategy for enhancing the power quality and economic performance of PV-rich distribution networks.