Search Results (12)

This paper presents a comprehensive framework for real-time energy management in microgrids integrating distributed renewable energy sources and demand response (DR) programs. To address the inherent uncertainties in key operational variables—such as load demand, wind speed, solar irradiance, and electricity market prices—this study employs a probabilistic modeling approach. A two-stage stochastic optimization method, combining mixed-integer linear programming and optimal power flow (OPF), is developed to minimize operational costs while ensuring efficient system operation. Real-time dynamic pricing mechanisms are incorporated to incentivize consumer load shifting and promote energy-efficient consumption patterns. Three microgrid scenarios are analyzed using one year of real historical data: (i) a grid-connected microgrid without DR, (ii) a grid-connected microgrid with 10% and 20% DR-based load shifting, and (iii) an islanded microgrid operating under incentive-based DR contracts. Results demonstrate that incorporating DR strategies significantly reduces both operating costs and reliance on grid imports, especially during peak demand periods. The islanded scenario, while autonomous, incurs higher costs and highlights the challenges of self-sufficiency under uncertainty. Overall, the proposed model illustrates how the integration of real-time pricing with stochastic optimization enhances the flexibility, resilience, and cost-effectiveness of smart microgrid operations, offering actionable insights for the development of future grid-interactive energy systems. Full article

The expanding complexity of power systems—driven by the motivation to reduce their carbon footprint by integrating renewable energy sources (RESs) in the grid, the increasing energy demand, grid scalability, and the necessity for reliable and sustainable operation—has made the optimal power flow (OPF) problem the main issue in power systems. Hence, the concept of muti-objective optimal power flow (MOOPF) in power systems has become a crucial tool for power system management and planning. This article provides an overview of recent optimization techniques in power systems that have MOOPF as their central problem, as well as their applications in power systems, with the purpose of identifying significant approaches, challenges and trends when it comes to large-scale probabilistic MOOPF. This overview was developed based on an in-depth analysis of MOOPF techniques, the classification of their applications, and the formulation of the problem in power systems. This overview contributes to the existing literature by highlighting the evolution of optimization techniques, and the need for robust, probabilistic hybrid optimization techniques that can address variability, uncertainty, reliability, and sustainability in power systems. These findings are significant because they emphasize the current transition towards more adaptive and intelligent optimization strategies, which are essential to developing sustainable, dependable, and effective power systems, especially as we move towards smart grids and low-carbon energy systems. Full article

As electric grids decarbonize and distributed energy resources (DERs) become increasingly prevalent, interconnection assessments must evolve to reflect operational variability and control flexibility. This paper highlights key modeling limitations observed in practice and reviews approaches for modeling uncertainty. It then introduces a Probabilistic Deliverability Assessment (PDA) framework designed to complement and extend existing procedures. The framework integrates scenario-based AC optimal power flow (AC OPF), corrective dispatch, and optional multi-temporal constraints. Together, these form a structured methodology for quantifying DER utilization, deliverability, and reliability under uncertainty in load, generation, and topology. Outputs include interpretable metrics with confidence intervals that inform siting decisions and evaluate compliance with reliability thresholds across sampled operating conditions. A case study on Puerto Rico’s publicly available bulk power system model demonstrates the framework’s application using minimal input data, consistent with current interconnection practice. Across staged fossil generation retirements, the PDA identifies high-value DER sites and regions requiring additional reactive power support. Results are presented through mean dispatch signals, reliability metrics, and geospatial visualizations, demonstrating how the framework provides transparent, data-driven siting recommendations. The framework’s modular design supports incremental adoption within existing workflows, encouraging broader use of AC OPF in interconnection and planning contexts. Full article

As offline control photovoltaic (PV) plants are not equipped with online communication and remote control systems, they cannot adjust their power in real-time. Therefore, in a distribution network saturated with offline control PVs, the distribution system operator (DSO) should schedule the distributed energy resources (DERs) considering the uncertainty of renewable energy to prevent curtailment due to overvoltage. This paper presents a day-ahead network operation strategy using a mobile energy storage system (MESS) and offline control PVs to minimize power curtailment. The MESS model efficiently considers the transportation time and power loss of the MESS, and models various operating modes, such as the charging, discharging, idle, and moving modes. The optimization problem is formulated based on mixed-integer linear programming (MILP) considering the spatial and temporal operation constraints of MESSs and is performed using chanced constrained optimal power flow (CC-OPF). The upper limits for offline control PVs are set based on the probabilistic approach, thus mitigating overvoltage due to forecasting errors. The proposed operation strategy was tested in the IEEE 33-node distribution system coupled with a 15-node transportation system. The test results show the effectiveness of the proposed method for minimizing curtailment in offline control PVs. Full article

The conventional optimal power flow (OPF) is confronted with challenges in tackling more than three objectives and the stochastic characteristics due to the uncertainty and intermittence of the RESs. However, there are few methods available that simultaneously address high-dimensional objective optimization and uncertainty handling. This paper proposes a set-based group search optimizer (SetGSO) to tackle the stochastic many-objective optimal power flow (MaOPF) of power systems penetrated with renewable energy sources. The proposed SetGSO depicts the original stochastic variables by set-based individuals under the evolutionary strategy of the basic GSO, without using repeated sampling or probabilistic information. Consequently, two metrics, hyper-volume and average imprecision, are introduced to transform the stochastic MaOPF into a deterministic bi-objective OPF, guaranteeing a much superior Pareto-optimal front. Finally, our method was evaluated on three modified bus systems containing renewable energy sources, and compared with the basic GSO using Monte Carlo sampling (GSO-MC) and a set-based genetic algorithm (SetGA) in solving the stochastic MaOPF. The numerical results demonstrate a saving of 90% of the computation time in the proposed SetGSO method compared to sampling-based approaches and it achieves improvements in both the hyper-volume and average imprecision indicators, with a maximum enhancement of approximately 30% and 7% compared to SetGA. Full article

In this study, the Giant Trevally Optimizer (GTO) is employed to solve the probabilistic optimum power flow (P-OPF) issue, considering Renewable Energy Source (RES) uncertainties, achieving notable cost reduction. The objective function is established to minimize the overall generation cost, including the RES cost, which significantly surpassing existing solutions. The uncertain nature of the RES is represented through the employment of a Monte Carlo Simulation (MCS), strengthened by the K-means Clustering approach and the Elbow technique. Various cases are investigated, including various combinations of PV systems, WE systems, and both fixed and fluctuating loads. The study demonstrates that while considering the costs of solar, wind, or both might slightly increase the total generation cost, the cumulative generation cost remains significantly less than the scenario that does not consider the cost of RESs. The superior outcomes presented in this research underline the importance of considering RES costs, providing a more accurate representation of real-world system dynamics and enabling more effective decision making. Full article

This paper proposes a new, metaheuristic optimization technique, Artificial Gorilla Troops Optimization (GTO), for a hybrid power system with photovoltaic (PV) and wind energy (WE) sources, solving the probabilistic optimum power flow (POPF) issue. First, the selected algorithm is developed and evaluated such that it applies to solve the classical optimum power flow (OPF) approach with the total fuel cost as the objective function. Second, the proposed algorithm is used for solving the POPF, including the PV and WE sources, considering the uncertainty of these renewable energy sources (RESs). The performance of the suggested algorithm was confirmed using the standard test systems IEEE 30-bus and 118-bus. Different scenarios involving different sets of the PV and WE sources and fixed and variable loads were considered in this study. The comparison of the obtained results from the suggested algorithm with other algorithms mentioned in this literature has confirmed the efficiency and performance of the proposed algorithm for providing optimal solutions for a hybrid power system. Furthermore, the results showed that the penetration of the PV and WE sources in the system significantly reduces the total cost of the system. Full article

Integrating renewable energy sources (RESs) into modern electric power systems offers various techno-economic benefits. However, the inconsistent power profile of RES influences the power flow of the entire distribution network, so it is crucial to optimize the power flow in order to achieve stable and reliable operation. Therefore, this paper proposes a newly developed circle search algorithm (CSA) for the optimal solution of the probabilistic optimal power flow (OPF). Our research began with the development and evaluation of the proposed CSA. Firstly, we solved the OPF problem to achieve minimum generation fuel costs; this used the classical OPF. Then, the newly developed CSA method was used to deal with the probabilistic power flow problem effectively. The impact of the intermittency of solar and wind energy sources on the total generation costs was investigated. Variations in the system’s demands are also considered in the probabilistic OPF problem scenarios. The proposed method was verified by applying it to the IEEE 57-bus and the 118-bus test systems. This study’s main contributions are to test the newly developed CSA on the OPF problem to consider stochastic models of the RESs, providing probabilistic modes to represent the RESs. The robustness and efficiency of the proposed CSA in solving the probabilistic OPF problem are evaluated by comparing it with other methods, such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and the hybrid machine learning and transient search algorithm (ML-TSO) under the same parameters. The comparative results showed that the proposed CSA is robust and applicable; as evidence, an observable decrease was obtained in the costs of the conventional generators’ operation, due to the penetration of renewable energy sources into the studied networks. Full article

This paper proposes a novel hybrid optimization technique based on a machine learning (ML) approach and transient search optimization (TSO) to solve the optimal power flow problem. First, the study aims at developing and evaluating the proposed hybrid ML-TSO algorithm. To do so, the optimization technique is implemented to solve the classical optimal power flow problem (OPF), with an objective function formulated to minimize the total generation costs. Second, the hybrid ML-TSO is adapted to solve the probabilistic OPF problem by studying the impact of the unavoidable uncertainty of renewable energy sources (solar photovoltaic and wind turbines) and time-varying load profiles on the generation costs. The evaluation of the proposed solution method is examined and validated on IEEE 57-bus and 118-bus standard systems. The simulation results and comparisons confirmed the robustness and applicability of the proposed hybrid ML-TSO algorithm in solving the classical and probabilistic OPF problems. Meanwhile, a significant reduction in the generation costs is attained upon the integration of the solar and wind sources into the investigated power systems. Full article

The traditional cumulant method (CM) for probabilistic optimal power flow (P-OPF) needs to perform linearization on the Karush–Kuhn–Tucker (KKT) first-order conditions, therefore requiring input variables (wind power or loads) varying within small ranges. To handle large fluctuations resulting from large-scale wind power and loads, a novel P-OPF method is proposed, where the correlations among input variables are also taken into account. Firstly, the inverse Nataf transformation and Cholesky decomposition are used to obtain samples of wind speeds and loads with a given correlation matrix. Then, the K-means algorithm is introduced to group the samples of wind power outputs and loads into a number of clusters, so that in each cluster samples of stochastic variables have small variances. In each cluster, the CM for P-OPF is conducted to obtain the cumulants of system variables. According to these cumulants, the moments of system variables corresponding to each cluster are computed. The moments of system variables for the total samples are obtained by combining the moments for all grouped clusters through the total probability formula. Then, the moments for the total samples are used to calculate the corresponding cumulants. Finally, Cornish–Fisher expansion is introduced to obtain the probability density functions (PDFs) of system variables. IEEE 9-bus and 118-bus test systems are modified to examine the proposed method. Study results show that the proposed method can produce more accurate results than traditional CM for P-OPF and is more efficient than Monte Carlo simulation (MCS). Full article

This study tackles a risk-limiting scheduling problem of non-renewable power generation for large power systems, and addresses potential violations of the security constraints owing to the volatility of renewable power generation and the uncertainty of load demand. To cope with the computational challenge that arises from the probabilistic constraints in the considered problem, a computationally efficient solution algorithm that involves a bisection method, an off-line constructed artificial neural network (ANN) and an on-line point estimation method is proposed and tested on the IEEE 118-bus system. The results of tests and comparisons reveal that the proposed solution algorithm is applicable to large power systems in real time, and the solution obtained herein is much better than the conventional optimal power flow (OPF) solution in obtaining a much higher probability of satisfying the security constraints. Full article

This paper presents a novel probabilistic optimization algorithm for simultaneous active and reactive power dispatch in power systems with significant wind power integration. Two types of load and wind-speed uncertainties have been assumed that follow normal and Weibull distributions, respectively. A PV bus model for wind turbines and the wake effect for correlated wind speed are used to achieve accurate AC power flow analysis. The power dispatch algorithm for a wind-power integrated system is modeled as a probabilistic optimal power flow (P-OPF) problem, which is operated through fixed power factor control to supply reactive power. The proposed P-OPF framework also considers emission information, which clearly reflects the impact of the energy source on the environment. The P-OPF was tested on a modified IEEE 118-bus system with two wind farms. The results show that the proposed technique provides better system operation performance evaluation, which is helpful in making decisions about power system optimal dispatch under conditions of uncertainty. Full article