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Electricity markets often utilize the DC approximation of the AC power flow equations to facilitate solving an otherwise complex nonconvex optimization problem. These DC power flow equations have analogies to DC circuit laws such as…

This chapter presents recent solutions to the optimal power flow (OPF) problem in the presence of renewable energy sources (RES), {such} as solar photo-voltaic and wind generation. After introducing the original formulation of the problem,…

We consider a robust optimization problem in an electric power system under uncertain demand and availability of renewable energy resources. Solving the deterministic alternating current optimal power flow (ACOPF) problem has been…

To solve the optimal power flow (OPF) problem, reinforcement learning (RL) emerges as a promising new approach. However, the RL-OPF literature is strongly divided regarding the exact formulation of the OPF problem as an RL environment. In…

This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations…

An effective means for analyzing the impact of novel operating schemes on power systems is time domain simulation, for example for investigating optimization-based curtailment of renewables to alleviate voltage violations. Traditionally,…

Designing robust algorithms for the optimal power flow (OPF) problem is critical for the control of large-scale power systems under uncertainty. The chance-constrained OPF (CCOPF) problem provides a natural formulation of the trade-off…

Solving the power flow problem in a distributed fashion empowers different grid operators to compute the overall grid state without having to share grid models-this is a practical problem to which industry does not have off-the-shelf…

This paper explores the integration of renewable energy sources into power systems, highlighting the resulting complexities such as variability and intermittency that challenge traditional power flow dynamics. We delve into innovative…

HVDC is a critically important technology for the large-scale integration of renewable resources such as offshore wind farms. Currently, only point-to-point and multi-terminal HVDC connections exist in real-life operation. However, with the…

Stepwise controllable devices, such as switched capacitors or stepwise controllable loads and generators, transform the nonconvex AC optimal power flow (AC-OPF) problem into a nonconvex mixed-integer (MI) programming problem which is…

To figure out the stability issues brought by renewable energy sources (RES) with non-Gaussian uncertainties in isolated microgrids, this paper proposes a chance constrained stability constrained optimal power flow (CC-SC-OPF) model.…

The limitations of centralized optimization methods for power systems operation have led to the distributed computing paradigm, particularly in power distribution systems. The existing techniques reported in recent literature for solving…

In the course of the energy transition, the expansion of generation and consumption will change, and many of these technologies, such as PV systems, electric cars and heat pumps, will influence the power flow, especially in the distribution…

Recently, we proposed a capacity expansion approach for transmission grids that combines the upgrade of transmission capacity with a transition in system structure to improve grid operation. The key to this concept is a particular hybrid…

Managing uncertainty and variability in power injections has become a major concern for power system operators due to the increasing levels of fluctuating renewable energy connected to the grid. This work addresses this uncertainty via a…

This paper develops a branch-flow based optimal power flow (OPF) problem for multi-phase distribution networks that allows for tap selection of wye, closed-delta, and open-delta step-voltage regulators (SVRs). SVRs are assumed ideal and…

We propose a hidden convexity-based method to address distributed optimal energy flow (OEF) problems for transmission-level integrated electricity-gas systems. First, we develop a node-wise decoupling method to de-compose an OEF problem…

Consider a polynomial optimisation problem, whose instances vary continuously over time. We propose to use a coordinate-descent algorithm for solving such time-varying optimisation problems. In particular, we focus on relaxations of…

This paper proposes a data-driven approach for optimal power flow (OPF) based on the stacked extreme learning machine (SELM) framework. SELM has a fast training speed and does not require the time-consuming parameter tuning process compared…