Search Results (253)

A deterministic Mixed-Integer Nonlinear Programming (MINLP) model for the Integrated Generation and Transmission Expansion Planning (IGTEP) problem is presented. The proposed framework is distinguished by its foundation on the complete AC power flow formulation, which is solved to global optimality using BARON, a deterministic MINLP solver, which ensures the identification of truly optimal expansion strategies, overcoming the limitations of heuristic approaches that may converge to local optima. This approach is employed to establish a definitive, high-fidelity economic and technical benchmark, addressing the limitations of commonly used DC approximations and metaheuristic methods that often fail to capture the nonlinearities and interdependencies inherent in power system planning. The co-optimization model is formulated to simultaneously minimize the total annualized costs, which include investment in new generation and transmission assets, the operating costs of the entire generator fleet, and the cost of unsupplied energy. The model’s effectiveness is demonstrated on the IEEE 14-bus system under various dynamic load growth scenarios and planning horizons. A key finding is the model’s ability to identify the most economic expansion pathway; for shorter horizons, the optimal solution prioritizes strategic transmission reinforcements to unlock existing generation capacity, thereby deferring capital-intensive generation investments. However, over longer horizons with higher demand growth, the model correctly identifies the necessity for combined investments in both significant new generation capacity and further network expansion. These results underscore the value of an integrated, AC-based approach, demonstrating its capacity to reveal non-intuitive, economically superior expansion strategies that would be missed by decoupled or simplified models. The framework thus provides a crucial, high-fidelity benchmark for the validation of more scalable planning tools. Full article

In this paper, a very fast and reliable strategy for load restoration utilizing optimal distribution feeder reconfiguration (DFR) is developed. The automated network configuration switches can improve the resilience of a microgrid (MG) equipped with a centralized and coordinated energy management system (EMS). The EMS has the authority to reconfigure the distribution network to fulfil high priority loads in the entire network, at the lowest cost, while maintaining the voltage at desirable bounds. In the case of islanded operation, the EMS is responsible for serving the high priority loads, including the establishment of new MGs, if necessary. This paper discusses the main functionality of the EMS in both grid-connected and islanded operation modes of MGs. The proposed model is developed based on a mixed-integer quadratically constrained program (MIQCP), including an optimal power flow (OPF) problem to minimize the power losses in normal operation and the load shedding in islanded operation, while keeping voltage and capacity constraints. The proposed framework is implemented on a modified IEEE 33-bus test system and the results show that the model is fast and accurate enough to be utilized in real-life situations without a loss of accuracy. Full article

With the rapid development of artificial intelligence technology, DRL has shown great potential in solving complex real-time optimal power flow problems of modern power systems. Nevertheless, traditional DRL methodologies confront dual bottlenecks: (a) suboptimal coordination between exploratory behavior policies and experience-based data exploitation in practical applications, compounded by (b) users’ distrust from the opacity of model decision mechanics. To address these, a model–data hybrid-driven physics-informed reinforcement learning (PIRL) algorithm is proposed in this paper. Specifically, the proposed methodology uses the proximal policy optimization (PPO) algorithm as the agent’s foundational framework and constructs a PI-actor network embedded with prior model knowledge derived from power flow sensitivity into the agent’s actor network via the PINN method, which achieves dual optimization objectives: (a) enhanced environmental perceptibility to improve experience utilization efficiency via gradient-awareness from model knowledge during actor network updates, and (b) improved user trustworthiness through mathematically constrained action gradient information derived from explicit model knowledge, ensuring actor updates adhere to safety boundaries. The simulation and validation results show that the PIRL algorithm outperforms the baseline PPO algorithm in terms of training stability, exploration efficiency, economy, and security. Full article

The proactive involvement of photovoltaic (PV) smart inverters (PVSIs) in grid management facilitates voltage regulation and enhances the integration of distributed energy resources (DERs) within distribution networks. However, to fully exploit the capabilities of PVSIs, it is essential to achieve optimal control of their operations and effective coordination with voltage-regulating devices in the distribution network. This study developed a dual strategy approach to forecast the optimal setpoints of onload tap changers (OLTCs), PVSIs, and distribution static synchronous compensators (DSTATCOMs) to improve the voltage profiles in power distribution systems. The study began by running a centralized AC optimal power flow (CACOPF) and using the hourly PV output power and the load demand to determine the optimal active and reactive power of the PVSIs, the setpoint of the DSTATCOM, and the optimal tap setting of the OLTC. Furthermore, Machine Learning (ML) models were trained as controllers to determine the reactive-power setpoints for the PVSIs and DSTATCOMs as well as the optimal OLTC tap position required for voltage stability in the network. To assess the effectiveness of the method, comprehensive evaluations were carried out on a modified IEEE 33 bus with a high penetration of PV energy. The results showed that deep neural networks (DNNs) outperformed other ML models used to mimic the coordination method based on CACOPF. Furthermore, when the DNN-based controller was tested and compared with the optimizer approach under different loading and PV conditions, the DNN-based controller was found to outperform the optimizer in terms of computational time. This approach allows predictive control in power systems, helping system operators determine the action to be initiated under uncertain PV energy and loading conditions. The approach also addresses the computational inefficiency arising from contingencies in the power system that may occur when optimal power flow (OPF) is run multiple times. Full article

Understanding the dynamic carbon emission status is vital for turning a power system into a low-carbon system. However, the existing research has normally considered the average carbon emissions as the indicator for the operation and planning of power systems. Detailed carbon emission responsibility is not well allocated to different demands within power systems, leading to inefficient emission control. To address this problem, this paper develops a data-driven method for accurately finding the characteristics of the nodal marginal emission factor without the requirement of real-time optimal power flow (OPF) simulation. First, the nodal marginal emission factor system is derived based on actual data covering a timespan of one year on top of the IEEE 118 system. Then, a Graphical Neural Network (GNN) is adopted to map both the spatial and temporal relationship between nodal marginal emission and other features, thereby identifying the marginal emission characteristics for different nodes of power transmission systems. Through case studies, fine-tuned GNNs estimate all nodal marginal emission factor (NMEF) values for power systems without the requirement of OPF simulation and achieve a 5.75% Normalized Root Mean Squared Error (nRMSE) and 2.52% Normalized Mean Absolute Error (nMAE). Last but not least, this paper brings a new finding: a strong inclination to reduce marginal emission rates would compromise economic operation for power systems. Full article

Transmission lines in electrical power systems are studied and analyzed to improve the electrical system’s safety, stability, and optimal operation. Past research has proposed various optimization methods to address the problem of active and reactive power; however, they do not consider the voltage at the nodes, which causes losses in the system. By proposing a reduction in voltage at the nodes of the electrical system, it is possible to minimize voltage variation in the system using mixed integer nonlinear programming. The proposed methodology was tested on the IEEE 30-bus test system, where the objective function was modeled and simulated independently to test the results achieved through an AC OPF and reducing energy loss in the system. One of the most important investments was to demonstrate that the proposed methodology reduces voltage deviation at the system nodes, effectively confirming and maintaining lower active and reactive power production losses, resulting in a new type of energy planning that effectively benefits the electrical system voltage. Full article

The increasing integration of renewable energy sources (RESs) introduces significant uncertainties in both generation and demand, presenting critical challenges to the convergence, feasibility, and real-time performance of optimal power flow (OPF). To address these challenges, a multi-agent deep reinforcement learning (DRL) model is proposed to solve the OPF while ensuring constraints are satisfied rapidly. A heterogeneous multi-agent proximal policy optimization (H-MAPPO) DRL algorithm is introduced for multi-area power systems. Each agent is responsible for regulating the output of generation units in a specific area, and together, the agents work to achieve the global OPF objective, which reduces the complexity of the DRL model’s training process. Additionally, a graph neural network (GNN) is integrated into the DRL framework to capture spatiotemporal features such as RES fluctuations and power grid topological structures, enhancing input representation and improving the learning efficiency of the DRL model. The proposed DRL model is validated using the RTS-GMLC test system, and its performance is compared to MATPOWER with the interior-point iterative solver. The RTS-GMLC test system is a power system with high spatial–temporal resolution and near-real load profiles and generation curves. Test results demonstrate that the proposed DRL model achieves a 100% convergence and feasibility rate, with an optimal generation cost similar to that provided by MATPOWER. Furthermore, the proposed DRL model significantly accelerates computation, achieving up to 85 times faster processing than MATPOWER. Full article

The integration of Distributed Energy Resources (DERs) into power grids presents significant challenges to grid performance, requiring innovative solutions for effective operation. Dynamic Operating Envelopes (DOEs) offer a promising approach by optimizing the use of existing infrastructure while ensuring compliance with network constraints. This paper reviews various DOE calculation methodologies, focusing on Optimal Power Flow (OPF)-based methods. Key findings include the role of DOEs in optimizing import and export limits, with critical factors such as forecast accuracy, network modelling, and the effects of mutual phase coupling in unbalanced networks identified as influencing DOE performance. The paper also explores the integration of DOEs into smart grid frameworks, examining both centralized and decentralized control strategies, as well as their potential for providing ancillary services. Challenges in scaling DOEs are also discussed, particularly regarding the need for accurate forecasts, computational resources, communication infrastructure, and balancing efficiency and fairness in resource allocation. Lastly, future research directions are proposed, focusing on the practical application of DOEs to improve grid performance and support network operations, as well as the development of more robust DOE calculation methodologies. This review provides a comprehensive overview of current DOE research and identifies avenues for further exploration and advancement. Full article

The development of smart grids has led to an increased focus by transmission and distribution network operators on the Optimal Power Flow (OPF) problem. The solutions identified for an OPF problem are vital to ensure the real-time optimal control and operation of electric networks and can help enhance their efficiency. In this context, this paper proposed an original solution to the OPF problem, represented by optimal voltage control in electric networks integrating wind farms. Based on a fuzzy inference system (FIS) built in the Fuzzy Logic Designer of the Matlab environment, where the fuzzification process was improved through fuzzy K-means clustering, two approaches were developed, representing novel tools for OPF analysis. The decision-maker can use these two approaches only successively. The FIS-based first approach considers the load requested at the PQ-type buses and the powers injected by the wind farms as the fuzzy input variables. Based on the fuzzy inference rules, the FIS determines the suitable tap positions for power transformers to minimise active power losses. The second approach (I-FIS), representing an improved variant of FIS, calculates the steady-state regime to determine power losses based on the suitable tap positions for power transformers, as determined with FIS. A real 10-bus network integrating two wind farms was used to test the two proposed approaches, considering comprehensive characteristic three-day tests to thoroughly highlight the performance under different injection active power profiles of the wind farms. The results obtained were compared with those of the best methods in constrained nonlinear mathematical programming used in OPF analysis, specifically sequential quadratic programming (SQP). The errors calculated throughout the analysis interval between the SQP-based approach, considered as the reference, and the FIS and I-FIS-based approaches were 5.72% and 2.41% for the first day, 1.07% and 1.19% for the second day, and 1.61% and 1.33% for the third day. The impact of the OPF, assessed by calculating the efficiency of the electric network, revealed average percentage errors between 0.04% and 0.06% for the FIS-based approach and 0.01% for the I-FIS-based approach. Full article

The increasing integration of distributed energy resources into distribution feeders introduces significant uncertainties, stemming from volatile renewable sources and other fluctuating electrical elements, which pose substantial challenges for optimal power flow (OPF) analysis. This paper introduces a data-driven distributionally robust chance-constrained (DRCC) approach to address the stochastic Alternating Current (AC) OPF problem in distribution grids, where the exact probability distributions of uncertainties are unknown. The proposed method utilizes the Wasserstein metric to construct an ambiguity set based on empirical distributions derived from historical data, eliminating the need for prior knowledge of the underlying probability distributions. Notably, the size of the Wasserstein ball within the ambiguity set is inversely related to the volume of available data, allowing for adaptive robustness. Moreover, a computationally efficient reformulation of the DRCC-OPF model is developed using the LinDistFlow AC power flow approximation. The effectiveness and precision of the developed method are validated through multiple IEEE distribution test cases, demonstrating higher reliability of the security constraints compared with other methods. As more data become available, this reliability is systematically and securely adjusted to achieve greater economic efficiency. Full article

The optimal power flow (OPF) problem is a critical component in the design and operation of power transmission systems. Various optimization algorithms have been developed to address this issue. This paper expands the use of the coronavirus disease optimization algorithm (COVIDOA) to solve a multi-objective OPF problem (MO-OPF), incorporating renewable energy sources as distributed generation (DG) across multiple scenarios. The main objective is to minimize fuel costs, emissions, voltage deviations, and power losses. Due to its non-convex nature and computational complexity, OPF poses significant challenges. While COVIDOA has been utilized to solve engineering problems, it faces difficulties with non-linear and non-convex issues. This paper introduces an enhanced version, the enhanced COVID-19 optimization algorithm (ENHCOVIDOA), designed to improve the performance of the original method. The effectiveness of the proposed algorithm is validated through testing on IEEE 30-bus, 57-bus, and 118-bus systems, as well as a real-world 28-bus system representing Iraq’s standard Iraq super grid high voltage (SISGHV 28-bus). The two-point estimation method (TPEM) is also applied to manage uncertainties in renewable energy sources in some cases, leading to cost reductions and annual savings of ($70,909.344, $817,676.64, and $5,608,782.144) for the IEEE 30-bus, 57-bus, and reality 28-bus systems, respectively. Thirteen different cases were analyzed, and the results demonstrate that ENHCOVIDOA is notably more efficient and effective than other optimization algorithms in the literature. Full article

A growing interest in offshore wind energy in the Mediterranean Sea has been recently observed thanks to the potential for scale-up and recent advances in floating technologies and dynamic cables: in the Italian panorama, the offshore wind connection requests to the National Transmission Grid (NTG) reached almost 84 GW at the end of September 2024. Starting from a realistic estimate of the offshore wind power plants (OWPPs) to be realized off the southern coasts in a very long-term scenario, this paper presents a novel optimization procedure for meshed AC offshore network configuration, aiming at minimizing the offshore wind generation curtailment based on the DC optimal power flow approximation, assessing the security condition of the whole onshore and offshore networks. The reactive power compensation aspects are also considered in the optimization procedure: the optimal compensation sizing for export cables and collecting stations is evaluated via the AC optimal power flow (OPF) approach, considering a combined voltage profile and minimum short circuit power constraint for the onshore extra-high voltage (EHV) nodes. The simulation results demonstrate that the obtained meshed network configuration and attendant re-active compensation allow most of the offshore wind generation to be evacuated even in the worst-case scenario, i.e., the N1 network, full offshore wind generation output, and summer line rating, testifying to the relevance of the proposed methodology for real applications. Full article

This work proposes multi-objective two-stage distribution optimal power flow (D-OPF) to coordinate the use of smart inverters (SIs) and existing voltage control legacy devices. The first stage of multi-objective D-OPF aims to solve a mixed-integer nonlinear programming (MINLP) formulation that minimizes both voltage variation and active power loss, with SI modes, SI settings, voltage regulator (VR) taps, and capacitor bank (CB) status as control variables. The Pareto Optimal Solutions obtained from the first-stage MINLP are used to determine the optimal active–reactive power dispatch from the SIs by solving a nonlinear programming formulation in the second stage of the proposed D-OPF. This model guarantees that the setpoints for active–reactive power align with the droop characteristics of the SIs, ensuring practicability and the autonomous dispatch of active–reactive power by the SIs according to IEEE 1547-2018. The effectiveness of the proposed method is tested on the IEEE 123 distribution network by contrasting the two proposed D-OPF models, with one prioritizing SIs for voltage control and power loss minimization and the other not prioritizing SIs. The simulation results demonstrate that prioritizing SIs with optimal mode and droop settings can improve voltage control and power loss minimization. The proposed model (with SI prioritization) also reduces the usage of traditional grid control devices and optimizes the dispatch of active–reactive power. The POS also shows that the SI modes, droops, and legacy device settings can be effectively obtained based on the desired objective priority. Full article

With the development of renewable energy, renewable power generation has become an increasingly important component of the power system. However, it also introduces uncertainty into the analysis of the power system. Therefore, to accelerate the solution of the OPF problem, this paper proposes a novel Hybrid Stacked Ensemble Method (HSEM), which incorporates explainable warm-start point learning for AC optimal power flow. The HSEM integrates conventional machine learning techniques, including regression trees and random forests, with gradient boosting trees. This combination leverages the individual strengths of each algorithm, thereby enhancing the overall generalization capabilities of the model in addressing AC-OPF problems and improving its interpretability. Experimental results indicate that the HSEM model achieves superior accuracy in AC-OPF solutions compared to traditional Deep Neural Network (DNN) approaches. Furthermore, the HSEM demonstrates significant improvements in both the feasibility and constraint satisfaction of control variables. The effectiveness of the proposed HSEM is validated through rigorous testing on the IEEE-30 bus system and the IEEE-118 bus system, demonstrating its ability to provide an explainable warm-start point for solving AC-OPF problems. Full article

The utilization of Harris Hawks Optimization (HHO) for Multi-Objective Optimal Power Flow (MaO-OPF) challenges presented in this paper is both novel and compelling, as this approach has not been previously applied to these types of optimization problems. HHO, which shares characteristics with ant behavior, demonstrates significant strength in addressing high-dimensional, nonlinear optimization issues within power systems. In this study, HHO is implemented on an IEEE 30-bus power system, optimizing six competing objectives: minimizing total fuel cost, emissions, active power loss, reactive power loss, reducing voltage deviation, and enhancing voltage steady state. The effectiveness of HHO is assessed by comparing its performance to two alternative methods, MOEA/D-DRA and NSGA-III. Experimental results reveal that solutions derived from HHO exhibit superior convergence, enhanced diversity maintenance, and higher quality Pareto-optimal solutions compared to the MOEA/D trail algorithms. The research breaks new ground in the application of the Harris Hawks Optimization (HHO) algorithm to the Multi-Objective Optimal Power Flow (MaO-OPF) problem. The restructuring not only incorporates self-adaptive constraint-handling techniques and dynamic exploration exploitation strategies, but also addresses the more pressing requirements of modern power systems with even better convergence, and both sequential and global computational efficiency than existing skill. This approach proves to be a powerful and effective solution for addressing the complex challenges associated with MaO, enabling power systems to manage multiple conflicting objectives more efficiently. Full article