786 research outputs found
On the Properties of the Compound Nodal Admittance Matrix of Polyphase Power Systems
Most techniques for power system analysis model the grid by exact electrical
circuits. For instance, in power flow study, state estimation, and voltage
stability assessment, the use of admittance parameters (i.e., the nodal
admittance matrix) and hybrid parameters is common. Moreover, network reduction
techniques (e.g., Kron reduction) are often applied to decrease the size of
large grid models (i.e., with hundreds or thousands of state variables),
thereby alleviating the computational burden. However, researchers normally
disregard the fact that the applicability of these methods is not generally
guaranteed. In reality, the nodal admittance must satisfy certain properties in
order for hybrid parameters to exist and Kron reduction to be feasible.
Recently, this problem was solved for the particular cases of monophase and
balanced triphase grids. This paper investigates the general case of unbalanced
polyphase grids. Firstly, conditions determining the rank of the so-called
compound nodal admittance matrix and its diagonal subblocks are deduced from
the characteristics of the electrical components and the network graph.
Secondly, the implications of these findings concerning the feasibility of Kron
reduction and the existence of hybrid parameters are discussed. In this regard,
this paper provides a rigorous theoretical foundation for various applications
in power system analysi
Synchronization of Nonlinear Circuits in Dynamic Electrical Networks with General Topologies
Sufficient conditions are derived for global asymptotic synchronization in a
system of identical nonlinear electrical circuits coupled through linear
time-invariant (LTI) electrical networks. In particular, the conditions we
derive apply to settings where: i) the nonlinear circuits are composed of a
parallel combination of passive LTI circuit elements and a nonlinear
voltage-dependent current source with finite gain; and ii) a collection of
these circuits are coupled through either uniform or homogeneous LTI electrical
networks. Uniform electrical networks have identical per-unit-length
impedances. Homogeneous electrical networks are characterized by having the
same effective impedance between any two terminals with the others open
circuited. Synchronization in these networks is guaranteed by ensuring the
stability of an equivalent coordinate-transformed differential system that
emphasizes signal differences. The applicability of the synchronization
conditions to this broad class of networks follows from leveraging recent
results on structural and spectral properties of Kron reduction---a
model-reduction procedure that isolates the interactions of the nonlinear
circuits in the network. The validity of the analytical results is demonstrated
with simulations in networks of coupled Chua's circuits
Output Impedance Diffusion into Lossy Power Lines
Output impedances are inherent elements of power sources in the electrical
grids. In this paper, we give an answer to the following question: What is the
effect of output impedances on the inductivity of the power network? To address
this question, we propose a measure to evaluate the inductivity of a power
grid, and we compute this measure for various types of output impedances.
Following this computation, it turns out that network inductivity highly
depends on the algebraic connectivity of the network. By exploiting the derived
expressions of the proposed measure, one can tune the output impedances in
order to enforce a desired level of inductivity on the power system.
Furthermore, the results show that the more "connected" the network is, the
more the output impedances diffuse into the network. Finally, using Kron
reduction, we provide examples that demonstrate the utility and validity of the
method
On the Properties of the Power Systems Nodal Admittance Matrix
This letter provides conditions determining the rank of the nodal admittance
matrix, and arbitrary block partitions of it, for connected AC power networks
with complex admittances. Furthermore, some implications of these properties
concerning Kron Reduction and Hybrid Network Parameters are outlined.Comment: Index Terms: Nodal Admittance Matrix, Rank, Block Form, Network
Partition, Kron Reduction, Hybrid Network Parameter
A Multiscale Pyramid Transform for Graph Signals
Multiscale transforms designed to process analog and discrete-time signals
and images cannot be directly applied to analyze high-dimensional data residing
on the vertices of a weighted graph, as they do not capture the intrinsic
geometric structure of the underlying graph data domain. In this paper, we
adapt the Laplacian pyramid transform for signals on Euclidean domains so that
it can be used to analyze high-dimensional data residing on the vertices of a
weighted graph. Our approach is to study existing methods and develop new
methods for the four fundamental operations of graph downsampling, graph
reduction, and filtering and interpolation of signals on graphs. Equipped with
appropriate notions of these operations, we leverage the basic multiscale
constructs and intuitions from classical signal processing to generate a
transform that yields both a multiresolution of graphs and an associated
multiresolution of a graph signal on the underlying sequence of graphs.Comment: 16 pages, 13 figure
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