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.

The main purpose of this paper is to present a novel algorithmic reinforcement learning (RL) method for damping the voltage and frequency oscillations in a micro-grid (MG) with penetration of wind turbine generators (WTG). First, the continuous-time environment of the system is discretized to a definite number of states to form the Markov decision process (MDP). To solve the modeled discrete RL-based problem, Q-learning method, which is a model-free and simple iterative solution mechanism is used. Therefore, the presented control strategy is adaptive and it is suitable for the realistic power systems with high nonlinearities. The proposed adaptive RL controller has a supervisory nature that can improve the performance of any kind of controllers by adding an offset signal to the output control signal of them. Here, a part of Denmark distribution system is considered and the dynamic performance of the suggested control mechanism is evaluated and compared with fuzzy-proportional integral derivative (PID) and classical PID controllers. Simulations are carried out in two realistic and challenging scenarios considering system parameters changing. Results indicate that the proposed control strategy has an excellent dynamic response compared to fuzzy-PID and traditional PID controllers for damping the voltage and frequency oscillations.

This article deals with the stochastic scheduling of a microgrid (MG) to balance the economical and resilience metrics. In the proposed model, the MG resilience indices are integrated into the economic criteria to ensure the resilience of MG operation alongside the main MG actors' profit/loss. The MG fragility index, recovery efficiency index, MG voltage index, and lost load index are considered in the proposed planning model. Further, to make the results more realistic, the uncertainties associated with energy price and wind production, alongside with planning of energy storage systems and electric vehicles parking lots are considered. To achieve a better solution for the security-constraint operation of MG, AC network equations are included in the system modeling. Finally, a large-scale MG based on the IEEE-33 bus testbed is utilized to evaluate the effectiveness of the proposed stochastic scheduling program.