10,081 research outputs found
Topologically Protected Loop Flows in High Voltage AC Power Grids
Geographical features such as mountain ranges or big lakes and inland seas
often result in large closed loops in high voltage AC power grids. Sizable
circulating power flows have been recorded around such loops, which take up
transmission line capacity and dissipate but do not deliver electric power.
Power flows in high voltage AC transmission grids are dominantly governed by
voltage angle differences between connected buses, much in the same way as
Josephson currents depend on phase differences between tunnel-coupled
superconductors. From this previously overlooked similarity we argue here that
circulating power flows in AC power grids are analogous to supercurrents
flowing in superconducting rings and in rings of Josephson junctions. We
investigate how circulating power flows can be created and how they behave in
the presence of ohmic dissipation. We show how changing operating conditions
may generate them, how significantly more power is ohmically dissipated in
their presence and how they are topologically protected, even in the presence
of dissipation, so that they persist when operating conditions are returned to
their original values. We identify three mechanisms for creating circulating
power flows, (i) by loss of stability of the equilibrium state carrying no
circulating loop flow, (ii) by tripping of a line traversing a large loop in
the network and (iii) by reclosing a loop that tripped or was open earlier.
Because voltage angles are uniquely defined, circulating power flows can take
on only discrete values, much in the same way as circulation around vortices is
quantized in superfluids.Comment: 12 pages 6 figures + Supplementary Material, Accepted for publication
in New Journal of Physic
Linear Approximations to AC Power Flow in Rectangular Coordinates
This paper explores solutions to linearized powerflow equations with
bus-voltage phasors represented in rectangular coordinates. The key idea is to
solve for complex-valued perturbations around a nominal voltage profile from a
set of linear equations that are obtained by neglecting quadratic terms in the
original nonlinear power-flow equations. We prove that for lossless networks,
the voltage profile where the real part of the perturbation is suppressed
satisfies active-power balance in the original nonlinear system of equations.
This result motivates the development of approximate solutions that improve
over conventional DC power-flow approximations, since the model includes ZIP
loads. For distribution networks that only contain ZIP loads in addition to a
slack bus, we recover a linear relationship between the approximate voltage
profile and the constant-current component of the loads and the nodal active
and reactive-power injections
Gradient and Passive Circuit Structure in a Class of Non-linear Dynamics on a Graph
We consider a class of non-linear dynamics on a graph that contains and
generalizes various models from network systems and control and study
convergence to uniform agreement states using gradient methods. In particular,
under the assumption of detailed balance, we provide a method to formulate the
governing ODE system in gradient descent form of sum-separable energy
functions, which thus represent a class of Lyapunov functions; this class
coincides with Csisz\'{a}r's information divergences. Our approach bases on a
transformation of the original problem to a mass-preserving transport problem
and it reflects a little-noticed general structure result for passive network
synthesis obtained by B.D.O. Anderson and P.J. Moylan in 1975. The proposed
gradient formulation extends known gradient results in dynamical systems
obtained recently by M. Erbar and J. Maas in the context of porous medium
equations. Furthermore, we exhibit a novel relationship between inhomogeneous
Markov chains and passive non-linear circuits through gradient systems, and
show that passivity of resistor elements is equivalent to strict convexity of
sum-separable stored energy. Eventually, we discuss our results at the
intersection of Markov chains and network systems under sinusoidal coupling
Moment-Based Relaxation of the Optimal Power Flow Problem
The optimal power flow (OPF) problem minimizes power system operating cost
subject to both engineering and network constraints. With the potential to find
global solutions, significant research interest has focused on convex
relaxations of the non-convex AC OPF problem. This paper investigates
``moment-based'' relaxations of the OPF problem developed from the theory of
polynomial optimization problems. At the cost of increased computational
requirements, moment-based relaxations are generally tighter than the
semidefinite relaxation employed in previous research, thus resulting in global
solutions for a broader class of OPF problems. Exploration of the feasible
space for test systems illustrates the effectiveness of the moment-based
relaxation.Comment: 7 pages, 4 figures. Abstract accepted, full paper in revie
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