Practical stability of approximating discrete-time filters with respect to model mismatch using relative entropy concepts

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Using local consistency assumption, the practical stability established is in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Significantly, these practical stability results do not require the approximating model to be of the same model type as the true system. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Practical stability with respect to model mismatch of approximate discrete-time output feedback control

This paper establishes a practical stability result for discrete-time output feedback control involving mismatch between the exact system to be stabilised and the approximating system used to design the controller. The practical stability is in the sense of an asymptotic bound on the amount of error bias introduced by the model approximation, and is established using local consistency properties of the systems. Importantly, the practical stability established here does not require the approximating system to be of the same model type as the exact system. Examples are presented to illustrate the nature of our practical stability result.

Practical stability of approximating discrete-time filters with respect to model mismatch

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Practical stability is established in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Filter and control performance bounds in the presence of model uncertainties with aerospace applications

This thesis establishes performance properties for approximate filters and controllers that are designed on the basis of approximate dynamic system representations. These performance properties provide a theoretical justification for the widespread application of approximate filters and controllers in the common situation where system models are not known with complete certainty. This research also provides useful tools for approximate filter designs, which are applied to hybrid filtering of uncertain nonlinear systems. As a contribution towards applications, this thesis also investigates air traffic separation control in the presence of measurement uncertainties.

Stability analysis based on birfurcation theory of the DSTATCOM operating in current control mode

This paper presents the stability analysis for a distribution static compensator (DSTATCOM) that operates in current control mode based on bifurcation theory. Bifurcations delimit the operating zones of nonlinear circuits and, hence, the capability to compute these bifurcations is of important interest for practical design. A control design for the DSTATCOM is proposed. Along with this control, a suitable mathematical representation of the DSTATCOM is proposed to carry out the bifurcation analysis efficiently. The stability regions in the Thevenin equivalent plane are computed for different power factors at the point of common coupling. In addition, the stability regions in the control gain space, as well as the contour lines for different Floquet multipliers are computed. It is demonstrated through bifurcation analysis that the loss of stability in the DSTATCOM is due to the emergence of a Neimark bifurcation. The observations are verified through simulation studies.

Stability analysis of STATCOM in distribution networks

This chapter presents the stability analysis based on bifurcation theory of the distribution static compensator (DSTATCOM) operating both in current control mode as in voltage control mode. The bifurcation analysis allows delimiting the operating zones of nonlinear power systems and hence the computation of these boundaries is of interest for practical design and planning purposes. Suitable mathematical representations of the DSTATCOM are proposed to carry out the bifurcation analyses efficiently. The stability regions in the Thevenin equivalent plane are computed for different power factors at the Point of Common Coupling (PCC). In addition, the stability regions in the control gain space are computed, and the DC capacitor and AC capacitor impact on the stability are analyzed in detail. It is shown through bifurcation analysis that the loss of stability in the DSTATCOM is in general due to the emergence of oscillatory dynamics. The observations are verified through detailed simulation studies.

Stability synthesis of power hardware-in-the-loop (PHIL) simulation

A virtual power system can be interfaced with a physical system to form a power hardware-in-the-loop (PHIL) simulation. In this scheme, the virtual system can be simulated in a fast parallel processor to provide near real-time outputs, which then can be interfaced to a physical hardware that is called the hardware under test (HuT). Stable operation of the entire system, while maintaining acceptable accuracy, is the main challenge of a PHIL simulation. In this paper, after an extended stability analysis for voltage and current type interfaces, some guidelines are provided to have a stable PHIL simulation. The presented analysis have been evaluated by performing several experimental tests using a Real Time Digital Simulator (RTDS™) and a voltage source converter (VSC). The practical test results are consistent with the proposed analysis.

Development of innovative robust stability enhancement algorithms for distribution systems containing distributed generators

This project was a step forward in improving the voltage profile of traditional low voltage distribution networks with high photovoltaic generation or high peak demand. As a practical and economical solution, the developed methods use a Dynamic Voltage Restorer or DVR, which is a series voltage compensator, for continuous and communication-less power quality enhancement. The placement of DVR in the network is optimised in order to minimise its power rating and cost. In addition, new approaches were developed for grid synchronisation and control of DVR which are integrated with the voltage quality improvement algorithm for stable operation.