Quadratic power system modeling and simulation with application to voltage recovery and optimal allocation of VAR support

The main objectives of this research are to simulate voltage-recovery phenomena (using improved, realistic system models and accurate solution techniques) and to develop methods for the mitigation of problems related to slow voltage recovery. Therefore, this work concentrates on the areas of voltage-recovery analysis in electric power systems, dynamic load modeling with emphasis on induction-motor models, dynamic simulation with emphasis on the numerical integration methods, and optimal allocation and operation of static and dynamic VAr resources.;Power-system modeling and power-system simulation, both steady-state and dynamic, are fundamental for any type of power-system analysis, and thus for the study of voltage-recovery phenomena. In the first part of this work, a general framework for power-system analysis is presented the main characteristics of which are (a) the utilization of full three-phase models, which provide a more realistic and high-fidelity type of analysis that can capture system asymmetries and imbalances, and (b) the use of a "quadratized" mathematical formulation, which models the system under study as a set of mathematical equations of order no more than two. The modeling approach is essentially the same for steady-state, quasi-steady-state, and dynamic analysis. Models are constructed for each system component and then the model of the entire system is constructed by applying the connectivity constraints between all the components. The solution methodology is based on Newton's method for nonlinear equations. For the analysis of voltage recovery the quasi-steady-state model is introduced and primarily used in this work.;Furthermore, a new approach for time-domain transient simulation of electric power systems and dynamical systems, in general, is introduced in this research. The new methodology has been named quadratic integration method. The method is based on a numerical integration scheme that assumes that the system states vary "quadraticaly" within an integration time step. The approach demonstrates superior behavior compared to traditionally used methods in power system simulation (such as the trapezoidal integration rule) in terms of accuracy without sacrificing the essential numerical stability properties.;Accurate modeling and simulation of voltage-recovery phenomena allows the development of ways for the mitigation of such problems via the optimal allocation and operation of static and dynamic VAr resources, which is the topic of the second part of this work. First the topic is approached using static and dynamic (trajectory) sensitivity analysis. The static and dynamic sensitivity analysis are utilized for the optimal selection of candidate locations for VAr additions based on steady-state and dynamic performance criteria, respectively. Furthermore, the trajectory sensitivities can provide information about the optimal operation of existing VAr sources during transients. Then an approach based on dynamic programming is proposed for the optimal allocation of static and dynamic reactive support. The optimal operation of installed dynamic VAr sources is also addressed utilizing concepts from the theory of applied optimal control and trajectory optimization.