551 research outputs found
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
A scalable line-independent design algorithm for voltage and frequency control in AC islanded microgrids
We propose a decentralized control synthesis procedure for stabilizing
voltage and frequency in AC Islanded microGrids (ImGs) composed of Distributed
Generation Units (DGUs) and loads interconnected through power lines. The
presented approach enables Plug-and-Play (PnP) operations, meaning that DGUs
can be added or removed without compromising the overall ImG stability. The
main feature of our approach is that the proposed design algorithm is
line-independent. This implies that (i) the synthesis of each local controller
requires only the parameters of the corresponding DGU and not the model of
power lines connecting neighboring DGUs, and (ii) whenever a new DGU is plugged
in, DGUs physically coupled with it do not have to retune their regulators
because of the new power line connected to them. Moreover, we formally prove
that stabilizing local controllers can be always computed, independently of the
electrical parameters. Theoretical results are validated by simulating in PSCAD
the behavior of a 10-DGUs ImG
Plug-and-play and coordinated control for bus-connected AC islanded microgrids
This paper presents a distributed control architecture for voltage and
frequency stabilization in AC islanded microgrids. In the primary control
layer, each generation unit is equipped with a local controller acting on the
corresponding voltage-source converter. Following the plug-and-play design
approach previously proposed by some of the authors, whenever the
addition/removal of a distributed generation unit is required, feasibility of
the operation is automatically checked by designing local controllers through
convex optimization. The update of the voltage-control layer, when units plug
-in/-out, is therefore automatized and stability of the microgrid is always
preserved. Moreover, local control design is based only on the knowledge of
parameters of power lines and it does not require to store a global microgrid
model. In this work, we focus on bus-connected microgrid topologies and enhance
the primary plug-and-play layer with local virtual impedance loops and
secondary coordinated controllers ensuring bus voltage tracking and reactive
power sharing. In particular, the secondary control architecture is
distributed, hence mirroring the modularity of the primary control layer. We
validate primary and secondary controllers by performing experiments with
balanced, unbalanced and nonlinear loads, on a setup composed of three
bus-connected distributed generation units. Most importantly, the stability of
the microgrid after the addition/removal of distributed generation units is
assessed. Overall, the experimental results show the feasibility of the
proposed modular control design framework, where generation units can be
added/removed on the fly, thus enabling the deployment of virtual power plants
that can be resized over time
Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators
This paper examines the dynamics of power-electronic inverters in islanded
microgrids that are controlled to emulate the dynamics of Van der Pol
oscillators. The general strategy of controlling inverters to emulate the
behavior of nonlinear oscillators presents a compelling time-domain alternative
to ubiquitous droop control methods which presume the existence of a
quasi-stationary sinusoidal steady state and operate on phasor quantities. We
present two main results in this work. First, by leveraging the method of
periodic averaging, we demonstrate that droop laws are intrinsically embedded
within a slower time scale in the nonlinear dynamics of Van der Pol
oscillators. Second, we establish the global convergence of amplitude and phase
dynamics in a resistive network interconnecting inverters controlled as Van der
Pol oscillators. Furthermore, under a set of non-restrictive decoupling
approximations, we derive sufficient conditions for local exponential stability
of desirable equilibria of the linearized amplitude and phase dynamics
Harmonic synchronization under all three types of coupling: position, velocity, and acceleration
Synchronization of identical harmonic oscillators interconnected via
position, velocity, and acceleration couplings is studied. How to construct a
complex Laplacian matrix representing the overall coupling is presented. It is
shown that the oscillators asymptotically synchronize if and only if this
matrix has a single eigenvalue on the imaginary axis. This result generalizes
some of the known spectral tests for synchronization. Some simpler Laplacian
constructions are also proved to work provided that certain structural
conditions are satisfied by the coupling graphs.Comment: 9 pages, 2 figure
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
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