Scattering theory and linear optimal control: Regulator and servo problems

In this paper, several known computational solutions are readily obtained in a very natural way for the linear regulator, fixed end-point and servo-mechanism problems using a certain frame-work from scattering theory. The relationships between the solutions to the linear regulator problem with different terminal costs and the interplay between the forward and backward equations have enabled a concise derivation of the partitioned equations, the forward-backward equations, and Chandrasekhar equations for the problem. These methods have been extended to the fixed end-point, servo, and tracking problems.

Control technique for non-linear and unbalance compensation of an integrated magnetics-based three-phase series-shunt-compensated uninterruptible power supply

Handling unbalanced and non-linear loads in a three-phase AC power supply has always been a difficult issue. This has been addressed in the literature by either using fast controllers in the fundamental rotating reference frame or using separate controllers in reference frames specific to the harmonics. In the former case, the controller needs to be fast and in the latter case, besides the need for many controllers, negative-sequence components need to be extracted from the measured signal. This study proposes a control scheme for harmonic and unbalance compensation of a three-phase uninterruptible power supply wherein the problems mentioned above are addressed. The control takes place in the fundamental positive-sequence reference frame using only a set of feedback and feed-forward compensators. The harmonic components are extracted by a process of frame transformations and used as feed-forward compensation terms in the positive-sequence fundamental reference frame. This study uses a method wherein the measured signal itself is used for fundamental negative-sequence compensation. As the feed-forward compensator handles the high-bandwidth components, the feedback compensator can be a simple low-bandwidth one. This control algorithm is explained and validated experimentally.

Control technique for non-linear and unbalance compensation of an integrated magnetics-based three-phase series-shunt-compensated uninterruptible power supply

Handling unbalanced and non-linear loads in a three-phase AC power supply has always been a difficult issue. This has been addressed in the literature by either using fast controllers in the fundamental rotating reference frame or using separate controllers in reference frames specific to the harmonics. In the former case, the controller needs to be fast and in the latter case, besides the need for many controllers, negative-sequence components need to be extracted from the measured signal. This study proposes a control scheme for harmonic and unbalance compensation of a three-phase uninterruptible power supply wherein the problems mentioned above are addressed. The control takes place in the fundamental positive-sequence reference frame using only a set of feedback and feed-forward compensators. The harmonic components are extracted by a process of frame transformations and used as feed-forward compensation terms in the positive-sequence fundamental reference frame. This study uses a method wherein the measured signal itself is used for fundamental negative-sequence compensation. As the feed-forward compensator handles the high-bandwidth components, the feedback compensator can be a simple low-bandwidth one. This control algorithm is explained and validated experimentally.

Control technique for non-linear and unbalance compensation of an integrated magnetics-based three-phase series-shunt-compensated uninterruptible power supply

Handling unbalanced and non-linear loads in a three-phase AC power supply has always been a difficult issue. This has been addressed in the literature by either using fast controllers in the fundamental rotating reference frame or using separate controllers in reference frames specific to the harmonics. In the former case, the controller needs to be fast and in the lattercase, besides the need for many controllers, negative-sequence components need to be extracted from the measured signal.This study proposes a control scheme for harmonic and unbalance compensation of a three-phase uninterruptible power supply wherein the problems mentioned above are addressed. The control takes place in the fundamental positive-sequence reference frame using only a set of feedback and feed-forward compensators. The harmonic components are extracted by process of frame transformations and used as feed-forward compensation terms in the positive-sequence fundamental reference frame. This study uses a method wherein the measured signal itself is used for fundamental negative-sequence compensation. As the feed-forward compensator handles the high-bandwidth components, the feedback compensator can be a simple low-bandwidth one. This control algorithm is explained and validated experimentally.

A QUADRATIC C degrees INTERIOR PENALTY METHOD FOR LINEAR FOURTH ORDER BOUNDARY VALUE PROBLEMS WITH BOUNDARY CONDITIONS OF THE CAHN-HILLIARD TYPE

We develop a quadratic C degrees interior penalty method for linear fourth order boundary value problems with essential and natural boundary conditions of the Cahn-Hilliard type. Both a priori and a posteriori error estimates are derived. The performance of the method is illustrated by numerical experiments.

State estimation in power systems using linear model infinity norm-based trust region approach

State estimation is one of the most important functions in an energy control centre. An computationally efficient state estimator which is free from numerical instability/ill-conditioning is essential for security assessment of electric power grid. Whereas approaches to successfully overcome the numerical ill-conditioning issues have been proposed, an efficient algorithm for addressing the convergence issues in the presence of topological errors is yet to be evolved. Trust region (TR) methods have been successfully employed to overcome the divergence problem to certain extent. In this study, case studies are presented where the conventional algorithms including the existing TR methods would fail to converge. A linearised model-based TR method for successfully overcoming the convergence issues is proposed. On the computational front, unlike the existing TR methods for state estimation which employ quadratic models, the proposed linear model-based estimator is computationally efficient because the model minimiser can be computed in a single step. The model minimiser at each step is computed by minimising the linearised model in the presence of TR and measurement mismatch constraints. The infinity norm is used to define the geometry of the TR. Measurement mismatch constraints are employed to improve the accuracy. The proposed algorithm is compared with the quadratic model-based TR algorithm with case studies on the IEEE 30-bus system, 205-bus and 514-bus equivalent systems of part of Indian grid.

Optimal bounded control of first-passage failure of strongly non-linear oscillators under combined harmonic and white-noise excitations

A procedure for designing the optimal bounded control of strongly non-linear oscillators under combined harmonic and white-noise excitations for minimizing their first-passage failure is proposed. First, a stochastic averaging method for strongly non-linear oscillators under combined harmonic and white-noise excitations using generalized harmonic functions is introduced. Then, the dynamical programming equations and their boundary and final time conditions for the control problems of maximizing reliability and of maximizing mean first-passage time are formulated from the averaged Ito equations by using the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraint. Finally, the conditional reliability function, the conditional probability density and mean of the first-passage time of the optimally controlled system are obtained from solving the backward Kolmogorov equation and Pontryagin equation. An example is given to illustrate the proposed procedure and the results obtained are verified by using those from digital simulation. (C) 2003 Elsevier Ltd. All rights reserved.