An official website of the United States government
Power flow computations are fundamental to many power system studies. Obtaining a converged power flow case is not a trivial task especially in large power grids due to the non-linear nature of the power flow equations. One key challenge is that the widely used Newton based power flow methods are sensitive to the initial voltage magnitude and angle estimates, and a bad initial estimate would lead to non-convergence. This paper addresses this challenge by developing a random-forest (RF) machine learning model to provide better initial voltage magnitude and angle estimates towards achieving power flow convergence. This method was implemented on a real ERCOT 6102 bus system under various operating conditions. By providing better Newton-Raphson initialization, the RF model precipitated the solution of 2,106 cases out of 3,899 non-converging dispatches. These cases could not be solved from flat start or by initialization with the voltage solution of a reference case. Results obtained from the RF initializer performed better when compared with DC power flow initialization, Linear regression, and Decision Trees.
more »
« less
Uniqueness of Power Flow Solutions Using Monotonicity and Network Topology
This article establishes sufficient conditions for the uniqueness of AC power flow solutions via the monotonic relationship between real power flow and the phase angle difference. More specifically, we prove that the P-Θ power flow problem has at most one solution for any acyclic or GSP graph. In addition, for arbitrary cyclic power networks, we show that multiple distinct solutions cannot exist under the assumption that angle differences across the lines are bounded by some limit related to the maximal girth of the network. In these cases, a vector of voltage phase angles can be uniquely determined (up to an absolute phase shift) given a vector of real power injections within the realizable range. The implication of this result for the classical power flow analysis is that under the conditions specified above, the problem has a unique physically realizable solution if the phasor voltage magnitudes are fixed. We also introduce a series-parallel operator and show that this operator obtains a reduced and easier-to-analyze model for the power system without changing the uniqueness of power flow solutions.
more »
« less
- Award ID(s):
- 1808859
- PAR ID:
- 10282185
- Date Published:
- Journal Name:
- IEEE transactions on control of network systems
- ISSN:
- 2325-5870
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
When a plane shock hits a two-dimensional wedge head on, it experiences a reflection-diffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The experimental, computational, and asymptotic analysis has indicated that various patterns occur, including regular reflection and Mach reflection. The von Neumann's conjectures on the transition from regular to Mach reflection involve the existence, uniqueness, and stability of regular shock reflection-diffraction configurations, generated by concave cornered wedges for compressible flow. In this paper, we discuss some recent developments in the study of the von Neumann's conjectures. More specifically, we discuss the uniqueness and stability of regular shock reflection-diffraction configurations governed by the potential flow equation in an appropriate class of solutions. We first show that the transonic shocks in the global solutions obtained in Chen-Feldman [19] are convex. Then we establish the uniqueness of global shock reflection-diffraction configurations with convex transonic shocks for any wedge angle larger than the detachment angle or the critical angle. Moreover, the solution under consideration is stable with respect to the wedge angle. Our approach also provides an alternative way of proving the existence of the admissible solutions established first in [19].more » « less
-
Abstract We study the problem of finding the resistors in a resistor network from measurements of the power dissipated by the resistors under different loads. We give sufficient conditions for local uniqueness, i.e. conditions that guarantee that the linearization of this non-linear inverse problem admits a unique solution. Our method is inspired by a method to study local uniqueness of inverse problems with internal functionals in the continuum, where the inverse problem is reformulated as a redundant system of differential equations. We use our method to derive local uniqueness conditions for other discrete inverse problems with internal functionals including a discrete analogue of the inverse Schrödinger problem and problems where the resistors are replaced by impedances and dissipated power at the zero and a positive frequency are available. Moreover, we show that the dissipated power measurements can be obtained from measurements of thermal noise induced currents.more » « less
-
This paper develops a finite approximation approach to find a non-smooth solution of an integral equation of the second kind. The equation solutions with non-smooth kernel having a non-smooth solution have never been studied before. Such equations arise frequently when modeling stochastic systems. We construct a Banach space of (right-continuous) distribution functions and reformulate the problem into an operator equation. We provide general necessary and sufficient conditions that allow us to show convergence of the approximation approach developed in this paper. We then provide two specific choices of approximation sequences and show that the properties of these sequences are sufficient to generate approximate equation solutions that converge to the true solution assuming solution uniqueness and some additional mild regularity conditions. Our analysis is performed under the supremum norm, allowing wider applicability of our results. Worst-case error bounds are also available from solving a linear program. We demonstrate the viability and computational performance of our approach by constructing three examples. The solution of the first example can be constructed manually but demonstrates the correctness and convergence of our approach. The second application example involves stationary distribution equations of a stochastic model and demonstrates the dramatic improvement our approach provides over the use of computer simulation. The third example solves a problem involving an everywhere nondifferentiable function for which no closed-form solution is available.more » « less
-
Emerging distribution systems with a proliferation of distributed energy resources are facing with new challenges, such as voltage collapse and power flow congestion in unsymmetrical network configurations. As a fundamental tool that could help quantify these new challenges and further mitigate their impacts on the secure and economic operation of distribution systems, effective AC optimal power flow (ACOPF) models and solution approaches are in urgent need. This study focuses on ACOPF of three‐phase four‐conductor configured distribution systems, in which neutral conductors and ground resistances are modelled explicitly to reflect practical situation. In addition, by leveraging the Kirchhoff's current law (KCL) theorem and the effect of zero injections, voltage variables of neutrals and zero‐injection phases can be effectively eliminated. The ACOPF problem is formulated as a convex semidefinite programming (SDP) relaxation model in complex domain. In recognising possible solution inexactness of SDP relaxation model, a Karush–Kuhn–Tucker condition based process is further proposed to effectively recover feasible solutions to the original ACOPF problem by calculating a set of computational‐inexpensive non‐linear equations. Numerical studies on a modified IEEE 123‐bus system show the effectiveness of the proposed SDP relaxation model with variable reductions and the feasible solution recovery process for three‐phase four‐conductor configured distribution systems.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- The DOI is not currently available.
