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The AC power flow equations are fundamental in all aspects of power systems planning and operations. They are routinely solved using Newton-Raphson like methods. However, there is little theoretical understanding of when these algorithms…
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,…
This paper presents a new method for enhancing Alternating Current Power Flow (ACPF) analysis. The method integrates the Newton-Raphson (NR) method with Enhanced-Gradient Descent (GD) and computational graphs. The integration of renewable…
This paper presents a quadratic approximation for the optimal power flow in power distributions systems. The proposed approach is based on a linearized load flow which is valid for power distribution systems including three-phase unbalanced…
In recent years, the power system research community has seen an explosion of novel methods for formulating and solving power network optimization problems. These emerging methods range from new power flow approximations, which go beyond…
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…
The solution of potential-driven steady-state flow in large networks is a task which manifests in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear…
Discretization of non-linear Poisson-Boltzmann Equation equations results in a system of non-linear equations with symmetric Jacobian. The Newton algorithm is the most useful tool for solving non-linear equations. It consists of solving a…
We describe a three precision variant of Newton's method for nonlinear equations. We evaluate the nonlinear residual in double precision, store the Jacobian matrix in single precision, and solve the equation for the Newton step with…
To efficiently solve large scale nonlinear systems, we propose a novel Random Greedy Fast Block Kaczmarz method. This approach integrates the strengths of random and greedy strategies while avoiding the computationally expensive…
This short paper presents a Wirtinger's-Calculus based load-flow methodology for power distribution grids. This approach allows to obtain an algorithm which works directly on the complex domain maintaining some useful symmetries and a…
Understanding the feasible power flow region is of central importance to power system analysis. In this paper, we propose a geometric view of the power system loadability problem. By using rectangular coordinates for complex voltages, we…
Fast convergent, accurate, computationally efficient, parallelizable, and robust matrix inversion and parameter estimation algorithms are required in many time-critical and accuracy-critical applications such as system identification,…
This paper proposes and compares experimentally several methods to estimate the series resistance and reactance (i.e., the transversal components of the $\pi$-model of a line) of low-voltage lines in distribution grids. It first shows that…
Learning expressive probabilistic models correctly describing the data is a ubiquitous problem in machine learning. A popular approach for solving it is mapping the observations into a representation space with a simple joint distribution,…
A modification of Newton's method for solving systems of $n$ nonlinear equations is presented. The new matrix-free method relies on a given decomposition of the invertible Jacobian of the residual into invertible sparse local Jacobians…
We formulate a steady-state network flow problem for non-ideal gas that relates injection rates and nodal pressures in the network to flows in pipes. For this problem, we present and prove a theorem on uniqueness of generalized solution for…
Balanced steady operation state in power networks changes over time. Traditional power flow algorithm is focused on the steady operation state under a certain time point and calculates the corresponding voltage and power distributions for…
Coordinating growing grid flexibility under uncertainty is becoming increasingly important for efficient and reliable power-system operation. A core computational requirement is the efficient large-scale batched evaluation of AC power flow…
Proper traffic simulation of electric vehicles, which draw energy from overhead wires, requires adequate modeling of traction infrastructure. Such vehicles include trains, trams or trolleybuses. Since the requested power demands depend on a…