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Power flow analysis is a fundamental tool for power system analysis, planning, and operational control. Traditional Newton-Raphson methods suffer from limitations such as initial value sensitivity and low efficiency in batch computation,…
The optimal power flow (OPF) problem is an important mathematical program that aims at obtaining the best operating point of an electric power grid. The optimization problem typically minimizes the total generation cost subject to certain…
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…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…
The increasing penetration of renewables in distribution networks calls for faster and more advanced voltage regulation strategies. A promising approach is to formulate the problem as an optimization problem, where the optimal reactive…
The solution to an optimal power flow (OPF) problem provides a minimum cost operating point for an electric power system. The performance of OPF solution techniques strongly depends on the problem's feasible space. This paper presents an…
The energy transition is driving the integration of large shares of intermittent power sources in the electric power grid. Therefore, addressing the AC optimal power flow (AC-OPF) effectively becomes increasingly essential. The AC-OPF,…
Certifying power flow solvability is important for reliable power system operations under volatile operating conditions, but solving power flow equations repeatedly can be costly and may encounter convergence issues. In this paper, we…
As a common practice, the direction of natural gas flow in every pipeline is determined ex-ante for simplification purposes, and treated as a given parameter within the scheduling problem. However, in integrated gas and electric power…
Deregulated energy markets, demand forecasting, and the continuously increasing share of renewable energy sources call---among others---for a structured consideration of uncertainties in optimal power flow problems. The main challenge is to…
The existence of multiple solutions to AC optimal power flow (ACOPF) problems has been noted for decades. Existing solvers are generally successful in finding local solutions, which satisfy first and second order optimality conditions, but…
The AC power flow equations underlie all operational aspects of power systems. They are solved routinely in operational practice using the Newton-Raphson method and its variants. These methods work well given a good initial "guess" for the…
Neuro-dynamic programming is a class of powerful techniques for approximating the solution to dynamic programming equations. In their most computationally attractive formulations, these techniques provide the approximate solution only…
We propose a new method for generating semidefinite relaxations of optimal power flow problems. The method is based on chordal conversion techniques: by dropping some equality constraints in the conversion, we obtain semidefinite…
The dramatic increase of network infrastructure comes at the cost of rapidly increasing energy consumption, which makes optimization of energy efficiency (EE) an important topic. Since EE is often modeled as the ratio of rate to power, we…
In recent years, the implementation of the demand response (DR) programs in the power systems scheduling and operation is increased. DR is used to improve the consumers' and power providers economic condition. That said, optimal power flow…
This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derive a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model is…
Unit Commitment (UC) and Optimal Power Flow (OPF) are two fundamental problems in short-term electric power systems planning that are traditionally solved sequentially. The state-of-the-art mostly uses a direct current flow approximation of…
This paper proposes a novel method for solving and tracing power flow solutions with changes of a loading parameter. Different from the conventional continuation power flow method, which repeatedly solves static AC power flow equations, the…
Modern power systems face a grand challenge in grid management due to increased electricity demand, imminent disturbances, and uncertainties associated with renewable generation, which can compromise grid security. The security assessment…