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Over the past half-century, Optimal Power Flow (OPF) has become one of the most important and widely studied nonlinear optimization problems. In general, OPF seeks to optimize the operation of electric power generation, transmission, and distribution networks subject to system constraints and control limits. Within this framework, however, there is an extremely wide variety of OPF formulations and solution methods. Moreover, the nature of OPF continues to evolve due to modern electricity markets and renewable resource integration. In this two-part survey, we survey both the classical and recent OPF literature in order to provide a sound context for the state of the art in OPF formulation and solution methods. The survey contributes a comprehensive discussion of specific optimization techniques that have been applied to OPF, with an emphasis on the advantages, disadvantages, and computational characteristics of each. Part I of the survey (this article) provides an introduction and surveys the deterministic optimization methods that have been applied to OPF. Part II of the survey examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF.

This paper focuses on the state-of-the-art of unit commitment (UC) and economic dispatch (ED) algorithms suitable for the Italian electricity market. In view of the spread of renewable energy systems (RES), the desired UC algorithm should be able to properly consider the uncertainty affecting key input variables into the formulation of the problem, as well as the different capabilities of dispatched power plants to provide ancillary services (e.g., voltage regulation). The goal of this paper is to resume the developments in UC and ED algorithms which occurred in the last decades, having a particular focus on alternating current (AC) security constrained (SC) approaches and stochastic ones, highlighting the advantages and weakness of each technique. This review is useful for the Italian TSO (Terna) to investigate what is the best solution to formulate a new algorithm to be potentially adopted in the framework of the Italian Ancillary Service Market, striving for an explicit modelization of stochastic variables and voltage constraints. This review is also useful to all system operators (SOs), independently to the market environment in which they operate, because UC algorithms are widely adopted to ensure real-time security of power systems. In conclusion, an SC-UC algorithm which takes into account both stochastic variables and AC formulation does not exist.

Flexible distributed energy resources, such as energy storage systems (ESSs), are increasingly considered as means for mitigating challenges introduced by the integration of stochastic, variable distributed generation (DG). The optimal operation of a distribution system with ESS can be formulated as a multi-period optimal power flow (MPOPF) problem which involves scheduling of the charging/discharging of the ESS over an extended planning horizon, e.g., for day-ahead operational planning. Although such problems have been the subject of many works in recent years, these works very rarely consider uncertainties in DG, and almost never explicitly consider uncertainties beyond the current operational planning horizon. This article presents a framework of methods and models for accounting for uncertainties due to distributed wind and solar photovoltaic power generation beyond the planning horizon in an AC MPOPF model for distribution systems with ESS. The expected future value of energy stored at the end of the planning horizon is determined as a function of the stochastic DG resource variables and is explicitly included in the objective function. Results for a case study based on a real distribution system in Norway demonstrate the effectiveness of an operational strategy for ESS scheduling accounting for DG uncertainties. The case study compares the application of the framework to wind and solar power generation. Thus, this work also gives insight into how different approaches are appropriate for modeling DG uncertainty for these two forms of variable DG, due to their inherent differences in terms of variability and stochasticity.

Manta Ray Foraging Optimization Algorithm (MRFO) is a new bio-inspired, meta-heuristic algorithm. MRFO algorithm has been used for the first time to optimize a multi-objective problem. The best size and location of distributed generations (DG) units have been determined to optimize three different objective functions. Minimization of active power loss, minimization of voltage deviation, and maximization of voltage stability index has been achieved through optimizing DG units under different power factor values, unity, 0.95, 0.866, and optimum value. MRFO has been applied to optimize DGs integrated with two well-known radial distribution power systems: IEEE 33-bus and 69-bus systems. The simulation results have been compared to different optimization algorithms in different cases. The results provide clear evidence of the superiority of MRFO that defind before (Manta Ray Foraging Optimization Algorithm. Quasi-Oppositional Differential Evolution Lévy Flights Algorithm (QODELFA), Stochastic Fractal Search Algorithm (SFSA), Genetics Algorithm (GA), Comprehensive Teaching Learning-Based Optimization (CTLBO), Comprehensive Teaching Learning-Based Optimization (CTLBO (ε constraint)), Multi-Objective Harris Hawks Optimization (MOHHO), Multi-Objective Improved Harris Hawks Optimization (MOIHHO), Multi-Objective Particle Swarm Optimization (MOPSO), and Multi-Objective Particle Swarm Optimization (MOWOA) in terms of power loss, Voltage Stability Index (VSI), and voltage deviation for a wide range of operating conditions. It is clear that voltage buses are improved; and power losses are decreased in both IEEE 33-bus and IEEE 69-bus system for all studied cases. MRFO algorithm gives good results with a smaller number of iterations, which means saving the time required for solving the problem and saving energy. Using the new MRFO technique has a promising future in optimizing different power system problems.

Contingency Constrained Optimal Power Flow (CCOPF) differs from traditional Optimal Power Flow (OPF) because its generation dispatch is planned to work with state variables between constraint limits, considering a specific contingency. When it is not desired to have changes in the power dispatch after the contingency occurs, the CCOPF is studied with a preventive perspective, whereas when the contingency occurs and the power dispatch needs to change to operate the system between limits in the post-contingency state, the problem is studied with a corrective perspective. As current power system software tools mainly focus on the traditional OPF problem, having the means to solve CCOPF will benefit power systems planning and operation. This paper presents a Quadratically Constrained Quadratic Programming (QCQP) formulation built within the matpower environment as a solution strategy to the preventive CCOPF. Moreover, an extended OPF model that forces the network to meet all constraints under contingency is proposed as a strategy to find the power dispatch solution for the corrective CCOPF. Validation is made on the IEEE 14-bus test system including photovoltaic generation in one simulation case. It was found that in the QCQP formulation, the power dispatch calculated barely differs in both pre- and post-contingency scenarios while in the OPF extended power network, node voltage values in both pre- and post-contingency scenarios are equal in spite of having different power dispatch for each scenario. This suggests that both the QCQP and the extended OPF formulations proposed, could be implemented in power system software tools in order to solve CCOPF problems from a preventive or corrective perspective.

An optimal power flow algorithm for unbalanced three-phase distribution grids is presented in this paper as a new tool for grid planning on low voltage level. As additional equipment like electric vehicles, heat pumps or solar power systems can sometimes cause unbalanced power flows, existing algorithms have to be adapted. In comparison to algorithms considering balanced power flows, the presented algorithm uses a complete model of a three-phase four-wire low voltage grid. Additionally, a constraint for the voltage unbalance in the grid is introduced. The algorithm can be used to optimize the operation of energy storage systems in unbalanced systems. The used grid model, constraints, objective function and solver are explained in detail. A validation of the algorithm using a commercial tool is done. Additionally, three exemplary optimizations are performed to show possible applications for this tool.

Renewable energy sources including wind farms and solar sites, have been rapidly integrated within power systems for economic and environmental reasons. Unfortunately, many renewable energy sources suffer from variability and uncertainty, which may jeopardize security and stability of the power system. To face this challenge, it is necessary to develop new methods to manage increasing supply-side uncertainty within operational strategies. In modern power system operations, the optimal power flow (OPF) is essential to all stages of the system operational horizon; underlying both day-ahead scheduling and real-time dispatch decisions. The dispatch levels determined are then implemented for the duration of the dispatch interval, with the expectation that frequency response and balancing reserves are sufficient to manage intra-interval deviations. To achieve more accurate generation schedules and better reliability with increasing renewable resources, the OPF must be solved faster and with better accuracy within continuous time intervals, in both day-ahead scheduling and real-time dispatch. To this end, we formulate a multi-period dispatch framework, that is, progressive period optimal power flow (PPOPF), which builds on an interval optimal power flow (IOPF), which leverages median and endpoints on the interval to develop coherent coordinations between day-ahead and real-time period optimal power flow (POPF). Simulation case studies on a practical PEGASE 13,659-bus transmission system in Europe have demonstrated implementation of the proposed PPOPF within multi-stage power system operations, resulting in zero dispatch error and violation compared with traditional OPF.

The increasing penetration of renewable energy resources has amplified variability and uncertainty in power systems, reducing the effectiveness of conventional single-period Optimal Power Flow (OPF) strategies. Multi-period AC-OPF offers a more comprehensive framework by incorporating inter-temporal constraints and resource flexibility, but its high computational complexity and strong temporal coupling make large-scale applications challenging, often causing scalability issues and convergence difficulties in conventional solvers. We address these issues with a spatio-temporal deep learning model that combines a Graph Attention Network (GAT) for topology-aware feature learning with a Temporal Convolutional Network (TCN) for multi-period temporal modeling. The proposed model is trained on large-scale 500-bus and 1354-bus systems under both 8-period and 24-period settings, and it achieves robust scalability with consistently high prediction accuracy. Using the model’s predictions, we construct an initial solution and provide it to a conventional OPF solver, which improves convergence performance and demonstrates the model’s effectiveness as an auxiliary tool for complex MP-ACOPF problems.

Optimal power dispatch is essential to improve the power system’s safety, stability, and optimal operation. The present research proposes a multi-objective optimization methodology to solve the real and reactive power dispatch problem by minimizing the active power losses and generation costs based on mixed-integer nonlinear programming (MINLP) using the epsilon constraint method and fuzzy satisficing approach. The proposed methodology was tested on the IEEE 30-bus system, in which each objective function was modeled and simulated independently to verify the results with what is obtained via Digsilent Power Factory and then combined, which no longer allows for the simulation of Digsilent Power Factory. One of the main contributions was demonstrating that the proposed methodology is superior to the one available in Digsilent Power Factory, since this program only allows for the analysis of single-objective problems.

This article presents a new algorithm aimed toward effective handling of the transient-stability-constrained optimal power flow (TSC_OPF) problem. The algorithm is a hybridized version of the existing differential evolution (DE) and symbiotic organism search (SOS) algorithms. It combines exploration and exploitation ability of both algorithms which results in its better performance as compared to DE and SOS acting alone. It was tested on IEEE 30 bus test system and the New England 39 bus test system. The results obtained by the proposed approach were compared with conventional TSC_OPF and also with other algorithms available in the literature. Results obtained using the proposed approach demonstrates superiority in comparison with other available algorithms in the literature.