70 research outputs found
Sensitivity Function Trade-offs for Networks with a String Topology
We present two sensitivity function trade-offs that apply to a class of
networks with a string topology. In particular we show that a lower bound on
the H-infinity norm and a Bode sensitivity relation hold for an entire family
of sensitivity functions associated with growing the network. The trade-offs we
identify are a direct consequence of growing the network, and can be used to
explain why poorly regulated low frequency behaviours emerge in long vehicle
platoons even when using dynamic feedback
Robust Scale-Free Synthesis for Frequency Control in Power Systems
The AC frequency in electrical power systems is conventionally regulated by
synchronous machines. The gradual replacement of these machines by asynchronous
renewable-based generation, which provides little or no frequency control,
increases system uncertainty and the risk of instability. This imposes hard
limits on the proportion of renewables that can be integrated into the system.
In this paper we address this issue by developing a framework for performing
frequency control in power systems with arbitrary mixes of conventional and
renewable generation. Our approach is based on a robust stability criterion
that can be used to guarantee the stability of a full power system model on the
basis of a set of decentralised tests, one for each component in the system. It
can be applied even when using detailed heterogeneous component models, and can
be verified using several standard frequency response, state-space, and circuit
theoretic analysis tools. Furthermore the stability guarantees hold
independently of the operating point, and remain valid even as components are
added to and removed from the grid. By designing decentralised controllers for
individual components to meet these decentralised tests, every component can
contribute to the regulation of the system frequency in a simple and provable
manner. Notably, our framework certifies the stability of several existing
(non-passive) power system control schemes and models, and allows for the study
of robustness with respect to delays.Comment: 10 pages, submitte
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
A Damping Ratio Bound for Networks of Masses and Springs
The damping ratio is a key performance measure in systems that can be modelled as networks of masses and springs. We derive a lower bound on this quantity that applies to such networks when the masses are subject to viscous damping. The result allows the size of the damping ratio to be understood as a function of the system parameters. We use this to derive a decentralised criterion which, if satisfied, guarantees that all the modes of a swing equation power system model are sufficiently well damped, independently of its operating point and size
Scale Free Bounds on the Amplification of Disturbances in Mass Chains
We give a method for designing a mechanical impedance to suppress the
propagation of disturbances along a chain of masses. The key feature of our
method is that it is scale free. This means that it can be used to give a
single, fixed, design, with provable performance guarantees in mass chains of
any length. We illustrate the approach by designing a bidirectional control law
in a vehicle platoon in a manner that is independent of the number of vehicles
in the platoon
A Frequency Domain Analysis of Slow Coherency in Networked Systems
Network coherence generally refers to the emergence of simple aggregated
dynamical behaviours, despite heterogeneity in the dynamics of the subsystems
that constitute the network. In this paper, we develop a general frequency
domain framework to analyze and quantify the level of network coherence that a
system exhibits by relating coherence with a low-rank property of the system's
input-output response. More precisely, for a networked system with linear
dynamics and coupling, we show that, as the network's \emph{effective algebraic
connectivity} grows, the system transfer matrix converges to a rank-one
transfer matrix representing the coherent behavior. Interestingly, the non-zero
eigenvalue of such a rank-one matrix is given by the harmonic mean of
individual nodal dynamics, and we refer to it as the coherent dynamics. Our
analysis unveils the frequency-dependent nature of coherence and a non-trivial
interplay between dynamics and network topology. We further show that many
networked systems can exhibit similar coherent behavior by establishing a
concentration result in a setting with randomly chosen individual nodal
dynamics.Comment: arXiv admin note: substantial text overlap with arXiv:2101.0098
Hydraulic Parameter Estimation in District Heating Networks
Using hydraulic models in control design in district heating networks can
increase pumping efficiency and reduce sensitivity to hydraulic bottlenecks.
These models are usually white-box, as they are obtained based on full
knowledge of the district heating network and its parameters. This type of
model is time-consuming to obtain, and might differ from the actual behavior of
the system. In this paper, a method is proposed to obtain a grey-box hydraulic
model for tree-shaped district heating systems: hydraulic parameters are
estimated based on pressure measurements in only two locations. While previous
works only estimate parameters related to pressure losses in pipes, this work
also includes customers valves in the grey-box model structure, an important
inclusion for control-oriented applications. Finally, a numerical example
illustrates the proposed method on a small district heating network, showing
its ability to obtain an accurate model on the basis of noisy measurements
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