The primary goal of a power system is to provide consumers with reliable access to power at the most economical cost. Under the declining costs of renewable energy sources, the increasing cost of natural gas, and growing emissions control policies, investment in variable renewable energy (VRE) sources including wind and solar is accelerating. As a fundamental optimization tool in the operation and planning of electric power systems, the optimal power flow (OPF) is critical for setting the optimal state of control variables by minimizing desired objective while satisfying all related constraints. However, a comprehensive review of the generic OPF framework that includes all categories of objectives, control variables, and constraints will provide a valuable background to many of the integration studies that are necessary to facilitate the transition of energy systems. A comprehensive OPF framework is essential for researchers to identify the most critical challenges to their applications to develop new solution methods to improve computational efficiency and to take advantage of the increasing computing power to reduce the number of approximations in OPF models. In this work, we aim to provide a comprehensive survey and a generic OPF formulation, along with a detailed explanation of the major formulations for conventional OPF objective functions, control variables, and network constraints, in particular those related to the handling of VREs. This article also highlights the modeling and challenges in the distribution system, and potential formulations to incorporate with the significant variability and intermittency of VRE sources. In addition to a discussion of various formulations and foci for the OPF problem, we compare the implications of these decisions on a small case study to highlight differences.

Planning and operational systemwide analyses relying on a deterministic optimal power flow (OPF) are subject to the uncertainties associated with the stochasticity of non-conventional renewables such as solar and wind. In this context, forecasting techniques will be essential for future power grids. An accurate and reliable forecast can complement a conventional time series optimal power flow (TSOPF) formulation by tackling uncertainty via accurate estimates of the intermittent generation resources. By doing so, the need for complex forecasting models is bypassed, and the computational tractability of the TSOPF problem is significantly reduced. Our work introduces a method to produce realistic load profiles, together with solar and wind generation forecasts. The generated data records are then input to a conventional TSOPF problem to determine the impact of an increasing share of non-conventional renewables into the grid over five years; we analyze increased penetration levels of 12%, 20%, 25%, and 30%. Our case study corresponds to an adapted version of the IEEE 39 test case, tailored to match the ISONE region transmission system. Forecasts are made using a data-driven neural network technique that accounts for the weather conditions in distinct locations of the ISONE footprint. Our results show several benefits of increased penetration of renewables, such as reducing line overloading and preventing undervoltage scenarios. However, it also points out potential problems that system planners might have to address by expanding the system or commissioning new equipment in particular locations.

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 frequency and severity of disruptive weather events, such as windstorms and other high-impact low-probability (HILP) occurrences, emphasize the critical necessity for enhanced preparedness and resilience strategies in power systems. Operators face significant challenges in optimally deploying mobile generating resources to areas experiencing outages of crucial infrastructure components, including generators, transmission lines, and transformers. These disruptions often compromise the reliability and stability of power delivery, necessitating temporary load shedding to ensure grid stability until full restoration is achieved. This paper introduces quantum integrated resiliency for power systems (QUIRCY), a new resilience approach aimed at optimizing resource allocation in power systems. The proposed framework integrates a two-level quantum algorithm that combines the Harrow-Hassidim-Lloyd (HHL) algorithm for highly efficient quantum power flow analysis with quadratic unconstrained binary optimization (QUBO) to strategically allocate distributed energy resources (DERs). The HHL algorithm significantly outperforms classical fast decoupled load flow (FDLF) methods by requiring only $\log _{2} N$ qubits to effectively represent an N-dimensional system. Simulation case studies on IEEE test systems have demonstrated the effectiveness and efficiency of the proposed quantum approach, indicating consistent convergence to optimal solutions under various severe system constraints. These results highlight the significant promise of quantum computing approaches for improving power system resilience, particularly as advancements in noisy intermediate-scale quantum (NISQ) technology continue to evolve.

States in the US increasingly integrate renewable energies to facilitate the transition to carbon neutrality. However, there are still many operational challenges to their efficient integration. This paper presents an innovative approach to solve the day-ahead Markov-based stochastic unit commitment (MSUC) problem with distributed wind generation. The MSUC utilizes a Markovian uncertainty set to represent the uncertainties in wind and other distributed intermittent renewable energies. While the Markovian uncertainty set intricately captures the stochasticity via states and state transitions, the set grows exponentially under the multi-dimensional uncertainties of distributed intermittent resources, thus rendering the MSUC intractable for systems with five or more such resources. In order to reduce the MSUC’s complexity, the problem is decomposed into approximate area problems (AAP), where each AAP utilizes a reduced, area-centric uncertainty set created using principal component analysis. Furthermore, the AAPs consider the binary commitment variables of only the local units, thus rendering much reduced complexity than the original MSUC. The AAPs are iteratively solved, and their solutions are coordinated in a novel Surrogate Absolute-Value Lagrangian Relaxation-based framework. Numerical testing is performed on test cases based on the IEEE 118-bus system with up to ten distributed wind farms, and solutions are validated via Monte Carlo simulations with typical and extreme wind generation scenarios. The simulation results demonstrate the ability of our method to obtain robust and cost-effective solutions to the MSUC in a constrained time frame.