7,114 research outputs found
Critical slowing-down as indicator of approach to the loss of stability
We consider stochastic electro-mechanical dynamics of an overdamped power
system in the vicinity of the saddle-node bifurcation associated with the loss
of global stability such as voltage collapse or phase angle instability.
Fluctuations of the system state vector are driven by random variations of
loads and intermittent renewable generation. In the vicinity of collapse the
power system experiences so-called phenomenon of critical slowing-down
characterized by slowing and simultaneous amplification of the system state
vector fluctuations. In generic case of a co-dimension 1 bifurcation
corresponding to the threshold of instability it is possible to extract a
single mode of the system state vector responsible for this phenomenon. We
characterize stochastic fluctuations of the system state vector using the
formal perturbative expansion over the lowest (real) eigenvalue of the system
power flow Jacobian and verify the resulting expressions for correlation
functions of the state vector by direct numerical simulations. We conclude that
the onset of critical slowing-down is a good marker of approach to the
threshold of global instability. It can be straightforwardly detected from the
analysis of single-node autostructure and autocorrelation functions of system
state variables and thus does not require full observability of the grid.Comment: Shorter version submitted to IEEE SmartGridComm 2014; 6 pages, 4
figures, discussion of autostructure functions adde
Optimal Topology Design for Disturbance Minimization in Power Grids
The transient response of power grids to external disturbances influences
their stable operation. This paper studies the effect of topology in linear
time-invariant dynamics of different power grids. For a variety of objective
functions, a unified framework based on norm is presented to analyze the
robustness to ambient fluctuations. Such objectives include loss reduction,
weighted consensus of phase angle deviations, oscillations in nodal frequency,
and other graphical metrics. The framework is then used to study the problem of
optimal topology design for robust control goals of different grids. For radial
grids, the problem is shown as equivalent to the hard "optimum communication
spanning tree" problem in graph theory and a combinatorial topology
construction is presented with bounded approximation gap. Extended to loopy
(meshed) grids, a greedy topology design algorithm is discussed. The
performance of the topology design algorithms under multiple control objectives
are presented on both loopy and radial test grids. Overall, this paper analyzes
topology design algorithms on a broad class of control problems in power grid
by exploring their combinatorial and graphical properties.Comment: 6 pages, 3 figures, a version of this work will appear in ACC 201
Online Learning of Power Transmission Dynamics
We consider the problem of reconstructing the dynamic state matrix of
transmission power grids from time-stamped PMU measurements in the regime of
ambient fluctuations. Using a maximum likelihood based approach, we construct a
family of convex estimators that adapt to the structure of the problem
depending on the available prior information. The proposed method is fully
data-driven and does not assume any knowledge of system parameters. It can be
implemented in near real-time and requires a small amount of data. Our learning
algorithms can be used for model validation and calibration, and can also be
applied to related problems of system stability, detection of forced
oscillations, generation re-dispatch, as well as to the estimation of the
system state.Comment: 7 pages, 4 figure
Robust Decentralized Secondary Frequency Control in Power Systems: Merits and Trade-Offs
Frequency restoration in power systems is conventionally performed by
broadcasting a centralized signal to local controllers. As a result of the
energy transition, technological advances, and the scientific interest in
distributed control and optimization methods, a plethora of distributed
frequency control strategies have been proposed recently that rely on
communication amongst local controllers.
In this paper we propose a fully decentralized leaky integral controller for
frequency restoration that is derived from a classic lag element. We study
steady-state, asymptotic optimality, nominal stability, input-to-state
stability, noise rejection, transient performance, and robustness properties of
this controller in closed loop with a nonlinear and multivariable power system
model. We demonstrate that the leaky integral controller can strike an
acceptable trade-off between performance and robustness as well as between
asymptotic disturbance rejection and transient convergence rate by tuning its
DC gain and time constant. We compare our findings to conventional
decentralized integral control and distributed-averaging-based integral control
in theory and simulations
Performance tradeoffs of dynamically controlled grid-connected inverters in low inertia power systems
Implementing frequency response using grid-connected inverters is one of the
popular proposed alternatives to mitigate the dynamic degradation experienced
in low inertia power systems. However, such solution faces several challenges
as inverters do not intrinsically possess the natural response to power
fluctuations that synchronous generators have. Thus, to synthetically generate
this response, inverters need to take frequency measurements, which are usually
noisy, and subsequently make changes in the output power, which are therefore
delayed. This paper explores the system-wide performance tradeoffs that arise
when measurement noise, power disturbances, and delayed actions are considered
in the design of dynamic controllers for grid-connected inverters. Using a
recently proposed dynamic droop (iDroop) control for grid-connected inverters,
which is inspired by classical first order lead-lag compensation, we show that
the sets of parameters that result in highest noise attenuation, power
disturbance mitigation, and delay robustness do not necessarily have a common
intersection. In particular, lead compensation is desired in systems where
power disturbances are the predominant source of degradation, while lag
compensation is a better alternative when the system is dominated by delays or
frequency noise. Our analysis further shows that iDroop can outperform the
standard droop alternative in both joint noise and disturbance mitigation, and
delay robustness
- …