## Research ProjectsPlease note that this list of projects has not been update for a number of years. It is, however, indicative of the type research that I am undertaking. Inverse Problems in Power System Dynamics Analysis of Uncertainties in Power System Simulation Power System Parameter Estimation Stability of Limit Cycles in Hybrid Systems Stability and Optimization of Transformer Tapping Optimal Load Shedding to Alleviate Voltage Instability Parameter Values that Induce Marginal Stability Last updated 25 April 2001 ## Inverse
Problems in Power System Dynamics
Analysis of power system dynamic behavior frequently
takes the form of ## Trajectory Sensitivity Analysis of Hybrid SystemsThe development of trajectory sensitivity analysis for hybrid systems, such as power systems, is the main focus of this research. Crucial to this analysis is the development of jump conditions describing the behavior of sensitivities at discrete events such as switching and impulse action. Trajectory sensitivities can be computed efficiently as a by-product of numerical simulation, and underlie gradient-based algorithms for solving inverse problems. The project is extending earlier analysis to systems that contain variable time delays. Following a large disturbance, trajectory
sensitivities tend to exhibit more pronounced transient behavior than the
underlying trajectory. The project is investigating ways of exploiting this
phenomenon as an indicator of impending instability. Of particular interest is
the role played by the ## Analysis of Uncertainties in Power System SimulationParameters of power system models can never be known exactly, yet dynamic security assessment relies upon simulations derived from those uncertain models. This project is exploring ways of quantifying the uncertainty in simulations of power system dynamic behavior. Trajectory sensitivities can be used to generate an accurate first order approximation of the trajectory corresponding to a perturbed parameter set. Therefore it is feasible to quickly generate many approximate trajectories from a single nominal case. Monte-Carlo techniques can be used to estimate the statistics describing the effects of parameter uncertainty. ## Power System Parameter EstimationThe nonlinear non-smooth nature of power system dynamics complicates the process of validating system models from disturbance measurements. This project is investigating algorithms for computing a set of model parameters that provide the best fit between measurements and model response. Trajectory sensitivities are used to identify parameters that can be reliably estimated from available measurements. ## Stability of Limit Cycles in Hybrid SystemsLimit cycles are common in hybrid systems. However the non-smooth dynamics of such systems makes stability analysis difficult. We have been using recent extensions of trajectory sensitivity analysis to obtain the characteristic multipliers of non-smooth limit cycles. The stability of a limit cycle is determined by its characteristic multipliers. Numerous applications have been explored, ranging from on/off control of coupled tanks, through power electronic circuits, to the walking motion of a biped robot. Period-doubling bifurcations have been explored in these latter cases. ## Multi-layer SystemsCommunications networks play a significant role in the multi-layer representation of power systems. The communications network model being proposed is based on a conceptual abstraction involving finite channel and node capacities that trigger changes in message transmission delays. Numerical integration of systems that incorporate such variable time delay models is not straightforward. This is especially so when considering the switched (hybrid) nature of system behavior. The project is investigating various techniques to handle variable time delays within numerical integration techniques. An important criterion is that algorithms must be capable of efficiently computing trajectory sensitivities. ## Stability and Optimization of Transformer TappingDiscrete events introduced by on-load tapping of transformers can have a significant affect on the load-end dynamic behavior of power systems. This project is taking a hybrid systems approach to quantifying that behavior. Of particular interest is the stability of systems that involve cascaded tapping transformers. Limit cycles have been observed in such systems. Stability theory for switched ODE systems is being adapted to switched DAE systems, which are more common in power system applications. The project aims to devise optimal switching control strategies for minimizing tap-changer hunting. ## Optimal Load Shedding to Alleviate Voltage InstabilityLoad shedding provides an effective (though drastic) control strategy for alleviating voltage instability. However the disruption to consumers caused by load shedding should be minimized. This project is developing optimal control techniques that are applicable in this hybrid system setting. The aim is to determine locations and shedding times that minimize the total shed load. ## Parameter Values that Induce Marginal StabilityStability
limits place restrictions on power system operations. Calculation of these
limits is therefore very important, but is also quite difficult. This project is
exploring algorithms for determining parameter values that result in marginal
stability of a system. (A system is marginally stable for a particular
disturbance if the post-disturbance trajectory lies on the stability boundary.)
A nonlinear least-squares formulation has been developed to determine a In order to maintain marginal stability, perturbations in some parameters must be matched by compensating changes in other parameters. The project is developing sensitivity relationships between the two groups of parameters. These sensitivities form the predictor in a predictor-corrector continuation method for tracing the parameter space view of the stability boundary. ## Power Flow Solution SpaceKnowledge of the structure of the power flow solution space is important when analyzing the robustness of operating points. Unfortunately, that structure has not been clearly established. As part of this project, a predictor-corrector technique has been developed to assist in exploring the solution space boundary. Using that technique, it has been found that the solution space may contain holes, even for very simple systems. This project is characterizing the solution space structure for various sub-classes of systems. The ultimate aim is to see how far those results can be extended for general systems. |