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