A controller is required for a VSC HVDC (Voltage Source Converter High Voltage Direct Current) terminal that provides good performance across a range of operating conditions. A nominal mixed sensitivity H∞ design is first presented. An LMI based robust H∞ design and two genetic algorithm based direct search methods methods are then applied to optimize the same H∞ norm across an operating range to provide robust performance. It is demonstrated that in this application the controllers designed by direct search using GA give better robust performance than the LMI based method. The principal reason for this is that unlike LMI based methods they do not guarantee quadratic stability across the operating range, even though stability across the operating range is demonstrated. © 2006 IEEE.

The design of a robust controller for a VSC HVDC terminal using LMI based robust H2 and multi-objective H₂- H∞ design methods is described. The operating range of the terminal is first characterised as an uncertainty region around a linear nominal model using the operating points of a non-linear model. The performance and robustness of controllers designed using the two methods and the effects of approximations in the uncertainty region definition are then described and compared. The best trade-off between robustness and performance on the non-linear model is demonstrated to be achieved using the robust H₂ method.

In this paper a genetic algorithm (GA) approach to designing controllers for a VSC HVDC terminal is described. The controller is required to have good time domain performance, actuator usage roll-off and robustness across a range of operating points. Suitable controllers are found by direct search for LQG controllers that fulfill the series of performance and robustness objectives at characteristic points within the operating range, as built into an objective function suitable for use with genetic algorithms. The idea is extended to include as extra variables the elements of the constant Youla parameter associated with the LQG controller. Different formulations of the objective function are discussed and compared and the results demonstrated on a non-linear model of the plant. © 2006 IEEE.

This paper presents an analytical non-linear model of the power controlling terminal of a VSC HVDC (Voltage Source Converter High Voltage Direct Current) transmission system attached to a weak (high impedance) AC network. In contrast to the standard 2 state model of a VSC, the proposed model explicitly includes the behaviour of the Phased Locked Loop and AC filter in the system. When linearised around particular operating points, the proposed model follows a rigorous PSCAD model more closely than the standard model. The proposed model is therefore more appropriate for use in control system design and analysis for VSC HVDC transmission systems attached to weak AC networks.

In this paper a robust controller for a Voltage Source Converter High Voltage Direct Current (VSC HVDC) transmission system is designed. The dynamic behaviour of the power controlling terminal of VSC HVDC transmission varies with the impedance of the attached AC system and the power flow across the DC link. A single controller is sought to provide the performance across a range of operating conditions. First, a linear fractional transformation (LFT) uncertainty model is constructed from a set of linearised models using a technique based on the singular value decomposition. The controller is then designed using a new iterative algorithm which has low conservatism. The controller is obtained by solving a linear matrix inequality (LMI) problem for which efficient solvers are available. The method produces a successful design: numerical simulation confirms the achievement of realistic control objectives for the nominal model, and an acceptable robust performance for all operating conditions.

The design of a controller for a VSC HVDC terminal which is robust over a range of operating points is described. The operating range is first characterized as an uncertainty region around a linear nominal model using the operating points of a non-linear model. An LMI based formulation is then used to synthesize a controller which maximizes the size of the uncertainty region within which closed loop stability is maintained, while achieving closed loop pole region constraints for the nominal model. Scaling matrices are used to take advantage of the structure of the uncertainty. The controller optimization including these matrices as variables is a bilinear problem and a D-K type iterative scheme is used to find their optimizing values. The performance of the resulting controllers over the range of operating points on the non-linear model is described and compared with that of a low order controller designed using classical methods. The conservatism of the approach and the use of the pole region constraint as a tuning parameter is analyzed.