This paper presents a detection algorithm for identifying when a sinusoidal signal becomes zero, which can provide information about its amplitude. This method can be used to detect voltage interruptions in a single-phase sinusoidal waveform, which may be applied in the rapid recognition of power outages in single-phase electrical systems. The method requires the measurement of a voltage signal. Other analysis methods, like calculating the Root Mean Square (RMS), are based on window sampling and require storing a relatively larger amount of samples in the system memory; an advantage of the proposed method is that it does not require as many samples, but its main advantage is its ability to reduce the detection time compared to other approaches. Techniques like the RMS value or amplitude detection through FFT typically require one full AC cycle to change from a 100% to 0% output signal and then detect a blackout, whereas the proposed method achieves detection within only a quarter cycle without considering additional rate-of-change enhancements, which can be further applied. The algorithm treats the measured single-phase voltage as the α component of an αβ Clarke pair and generates the β component by introducing a 90° electrical delay through a delayed replica of the original signal. The resulting αβ signals are then transformed into the dq reference frame in which the d component is used for outage detection, as it rapidly decreases from 100% to 0% within a quarter cycle following an interruption. This rapid response makes the proposed method suitable for applications that demand minimal detection latency, such as battery backup systems. Both simulation and experimental results validate the effectiveness of the approach.

This paper presents the implementation of the Grid-Forming (GFM) control technique in renewable energy source inverters to synchronize with the grid and provide frequency support. Specifically, the GFM Droop Control technique, based on the Power–Frequency relationship, is employed. The proposed model was developed and validated in the Matlab-Simulink environment. By using electromagnetic transient (EMT) simulations, we were able to precisely monitor and analyze voltage and current waveforms, thereby confirming the approach’s effectiveness in enhancing grid stability and power quality. The implementation of the GFM control technique in islanded mode demonstrated high system frequency stability. In response to sudden load changes up to 5 MW (equivalent to over 30% of the total load), a maximum frequency deviation of 0.04 Hz and a maximum Rate of Change of Frequency (RoCoF) of 4 Hz/s were observed. The system ensured the frequency’s return to its nominal value of 60 Hz, thanks to the virtual inertia and frequency regulation provided by the GFM. The total harmonic distortion (THD) of current and voltage in steady-state operation consistently remained below 1%, thus complying with IEEE 1547 standards. In tests with the GFM interconnected to the grid, the droop+LPF control provided dynamic support to the external system, effectively mitigating both frequency deviations and RoCoF. The GFM contributes to the grid’s frequency stability by providing virtual inertia. The power quality at the point of common coupling (PCC) was excellent, as the voltage distortion was maintained below 0.5%, confirming that the injection of harmonic currents does not violate established limits.

Electricity expansion planning is inherently subject to uncertainty, shaped by climatic, regulatory, and economic risks. In Brazil, this challenge is compounded by recurrent crises that have repeatedly reduced electricity demand. This study proposes a complementary decision-support approach to make planning more resilient to such crises. Using Brazil’s official optimization models (NEWAVE), we introduce two analytical elements: (i) a regret-minimization screen for choosing between conservative and optimistic demand trajectories and (ii) a flexibility stress test that evaluates the cost impact of compulsory-dispatch shares in generation portfolios. Key findings show that conservative demand projections systematically minimize consumer-cost regret when crises occur, while portfolios with lower compulsory-dispatch shares reduce total system cost and improve adaptability across 2000 hydro inflow scenarios. These results highlight that crisis-robust planning requires combining cautious demand assumptions with flexible supply portfolios. Although grounded in the Brazilian context, the methodological contributions are generalizable and provide practical guidance for other electricity markets facing deep and recurrent uncertainty.

Peer-to-peer (P2P) energy trading has emerged as a novel approach to enhancing the coordination and utilization of distributed energy resources (DERs) within modern power distribution networks. This study presents a techno-economic analysis of different DER characteristics, focusing on the integration of photovoltaic (PV) systems and energy storage systems (ESS) within a community-based P2P energy trading framework in Aswan, Egypt, under a time-of-use (ToU) electricity tariff. Eight distinct cases are evaluated to assess the impact of different DER characteristics on P2P energy trading performance and an unbalanced low-voltage (LV) distribution network by varying the PV capacity, ESS capacity, and ESS charging power. To the best of the authors’ knowledge, this is the first study to comprehensively examine the effects of different DER characteristics on P2P energy trading and the associated impacts on an unbalanced distribution network. The findings demonstrate that integrating PV and ESS can substantially reduce operational costs—by 37.19% to 68.22% across the analyzed cases—while enabling more effective energy exchanges among peers and with the distribution system operator (DSO). Moreover, DER integration reduced grid energy imports by 30.09% to 63.21% and improved self-sufficiency, with 30.10% to 63.21% of energy demand covered by community DERs. However, the analysis also reveals that specific DER characteristics—particularly those with low PV capacity (1.5 kWp) and high ESS charging rates (e.g., ESS 13.5 kWh with 2.5 kW inverter)—can significantly increase transformer and line loading, reaching up to 19.90% and 58.91%, respectively, in Case 2. These setups also lead to voltage quality issues, such as increased voltage unbalance factors (VUFs), peaking at 1.261%, and notable phase voltage deviations, with the minimum Vb dropping to 0.972 pu and maximum Vb reaching 1.083 pu. These findings highlight the importance of optimal DER sizing and characteristics to balance economic benefits with technical constraints in P2P energy trading frameworks.

This article presents an optimized approach to battery sizing and economic dispatch in wind-powered microgrids. The primary focus is on integrating battery depth of discharge (DoD) constraints to prolong battery life and ensure cost-effective energy storage management. Because of the intermittent nature of wind energy, wind-powered microgrids require sophisticated energy storage systems to ensure stable operation. This study develops a metaheuristic optimization method that balances power supply, battery lifespan, and economic dispatch in a microgrid. The proposed method optimizes both battery size and dispatch strategy while considering wind energy variability and the impact of DoD on battery lifespan. Case studies conducted on a wind-powered microgrid under varying load conditions show that the developed approach achieves a 40 to 50% reduction in operating costs and cost of electricity (CoE) compared to other approaches. The results also reveal that the inclusion of DoD constraints enhances battery lifespan. The proposed method offers a practical solution for improving the economic and operational efficiency of wind-powered microgrids, providing valuable understanding for energy planners and grid operators in renewable energy systems.

The Economic Dispatch Problem (EDP) plays a critical role in power system operations by trying to allocate power generation across multiple units at minimal cost while satisfying complex operational constraints. Traditional optimization techniques struggle with the non-convexities introduced by factors such as valve-point effects, prohibited operating zones, and spinning reserve requirements. While metaheuristics methods have shown promise, they often suffer from convergence issues and constraint-handling limitations. In this study, we introduce a novel application of Group Relative Policy Optimization (GRPO), a reinforcement learning framework that extends Proximal Policy Optimization by integrating group-based learning and relative performance assessments. The proposed GRPO approach incorporates smart initialization, adaptive exploration, and elite-guided updates tailored to the EDP’s structure. Our method consistently produces high-quality, feasible solutions with faster convergence compared to state-of-the-art metaheuristics and learning-based methods. For instance, in the case of the 15-unit system, GRPO achieved the best cost of USD 32,421.67/h with full constraint satisfaction in just 4.24 s, surpassing many previous solutions. The algorithm also demonstrates excellent scalability, generalizability, and stability across larger-scale systems without requiring parameter retuning. These results highlight GRPO’s potential as a robust and efficient tool for real-time energy scheduling in smart grid environments.

This study presents a novel methodology for determining zonal electricity generation and capacity requirements corresponding to forecasted annual production in an integrated power system (IPS). The proposed model combines the statistical analysis of historical daily load patterns with a calibration technique to translate forecast total demand into zonal powers (base, semi-peak and peak). A representative reference daily electrical load graph (ELG) is selected from retrospective data using least squares criteria, and a calibration factor α = Wx/Wie scales its zonal outputs to match the forecasted annual generation Wx. The innovation lies in this combination of historical ELG identification and calibration for accurate zonal power prediction. Applying the model to Ukrainian IPS data yields high accuracy: a zonal power error below 1.02% and a generation error below 0.39%. Key contributions include explicitly stating the research questions and hypotheses, providing a schematic procedural description and discussing model limitations (e.g., treatment of renewable variability and omission of meteorological/astronomical factors). Future work is outlined to incorporate unforeseen factors (e.g., post-war demand shifts, electric vehicle adoption) into the forecasting framework.

Power systems are equipped with a set of equipment for the generation, transmission, and distribution of electrical energy to consumption centers in a continuous manner and with quality indices [...]

This paper proposes the integration and operation of lithium-ion battery energy storage systems (ESS) in active distribution networks with high penetration of distributed generation based on renewable energy. The goal is to minimize total system costs, including energy purchasing at the substation node, as well as ESS integration, maintenance, and replacement costs over a 20-year planning horizon. The proposed master–slave methodology uses the Salp Swarm Optimization Algorithm to determine ESS location, technology, and daily operation schemes, combined with a successive approximation power flow to compute the objective function value and enforce constraints. This approach employs a discrete–continuous encoding, reducing processing times and increasing the likelihood of finding the global optimum. Validated on a 33-node test system adapted to Medellín, Colombia, the methodology outperformed five metaheuristic algorithms, achieving the highest annual savings (USD 16,605.77), the lowest average cost (USD 2,964,139.99), and the fastest processing time (345.71 s). The results demonstrate that the proposed methodology enables network operators to reduce distribution network costs effectively, offering high repeatability, solution quality, and computational efficiency.

This article presents two novel mixed-integer nonlinear programming (MINLP) formulations in the complex variable domain to address the optimal phase-balancing problem in asymmetric three-phase distribution networks. The first employs a matrix-based load connection model (M-MINLP), while the second uses a compact vector-based representation (V-MINLP). Both integrate the power flow equations through the current injection method, capturing the nonlinearities of Delta and Wye loads. These formulations, solved via an interior-point optimizer and the branch-and-cut method in the Julia software, ensure global optima and computational efficiency. Numerical validations on 8-, 25-, and 37-node feeders showed power loss reductions of 24.34%, 4.16%, and 19.26%, outperforming metaheuristic techniques and convex approximations. The M-MINLP model was 15.6 times faster in the 25-node grid and 2.5 times faster in the 37-node system when compared to the V-MINLP approach. The results demonstrate the robustness and scalability of the proposed methods, particularly in medium and large systems, where current techniques often fail to converge. These formulations advance the state of the art by combining exact mathematical modeling with efficient computation, offering precise, scalable, and practical tools for optimizing power distribution networks. The corresponding validations were performed using Julia (v1.10.2), JuMP (v1.21.1), and AmplNLWriter (v1.2.1).