36 research outputs found
Synchronization and Transient Stability in Power Networks and Non-Uniform Kuramoto Oscillators
Motivated by recent interest for multi-agent systems and smart power grid
architectures, we discuss the synchronization problem for the network-reduced
model of a power system with non-trivial transfer conductances. Our key insight
is to exploit the relationship between the power network model and a
first-order model of coupled oscillators. Assuming overdamped generators
(possibly due to local excitation controllers), a singular perturbation
analysis shows the equivalence between the classic swing equations and a
non-uniform Kuramoto model. Here, non-uniform Kuramoto oscillators are
characterized by multiple time constants, non-homogeneous coupling, and
non-uniform phase shifts. Extending methods from transient stability,
synchronization theory, and consensus protocols, we establish sufficient
conditions for synchronization of non-uniform Kuramoto oscillators. These
conditions reduce to and improve upon previously-available tests for the
standard Kuramoto model. Combining our singular perturbation and Kuramoto
analyses, we derive concise and purely algebraic conditions that relate
synchronization and transient stability of a power network to the underlying
system parameters and initial conditions
An Extended Kalman Filter for Data-enabled Predictive Control
The literature dealing with data-driven analysis and control problems has
significantly grown in the recent years. Most of the recent literature deals
with linear time-invariant systems in which the uncertainty (if any) is assumed
to be deterministic and bounded; relatively little attention has been devoted
to stochastic linear time-invariant systems. As a first step in this direction,
we propose to equip the recently introduced Data-enabled Predictive Control
algorithm with a data-based Extended Kalman Filter to make use of additional
available input-output data for reducing the effect of noise, without
increasing the computational load of the optimization procedure
A power consensus algorithm for DC microgrids
A novel power consensus algorithm for DC microgrids is proposed and analyzed.
DC microgrids are networks composed of DC sources, loads, and interconnecting
lines. They are represented by differential-algebraic equations connected over
an undirected weighted graph that models the electrical circuit. A second graph
represents the communication network over which the source nodes exchange
information about the instantaneous powers, which is used to adjust the
injected current accordingly. This give rise to a nonlinear consensus-like
system of differential-algebraic equations that is analyzed via Lyapunov
functions inspired by the physics of the system. We establish convergence to
the set of equilibria consisting of weighted consensus power vectors as well as
preservation of the weighted geometric mean of the source voltages. The results
apply to networks with constant impedance, constant current and constant power
loads.Comment: Abridged version submitted to the 20th IFAC World Congress, Toulouse,
Franc
Voltage Stabilization in Microgrids via Quadratic Droop Control
We consider the problem of voltage stability and reactive power balancing in
islanded small-scale electrical networks outfitted with DC/AC inverters
("microgrids"). A droop-like voltage feedback controller is proposed which is
quadratic in the local voltage magnitude, allowing for the application of
circuit-theoretic analysis techniques to the closed-loop system. The operating
points of the closed-loop microgrid are in exact correspondence with the
solutions of a reduced power flow equation, and we provide explicit solutions
and small-signal stability analyses under several static and dynamic load
models. Controller optimality is characterized as follows: we show a one-to-one
correspondence between the high-voltage equilibrium of the microgrid under
quadratic droop control, and the solution of an optimization problem which
minimizes a trade-off between reactive power dissipation and voltage
deviations. Power sharing performance of the controller is characterized as a
function of the controller gains, network topology, and parameters. Perhaps
surprisingly, proportional sharing of the total load between inverters is
achieved in the low-gain limit, independent of the circuit topology or
reactances. All results hold for arbitrary grid topologies, with arbitrary
numbers of inverters and loads. Numerical results confirm the robustness of the
controller to unmodeled dynamics.Comment: 14 pages, 8 figure
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