High-speed extended-term time-domain simulation for online cascading analysis of power systemalysis of Power System

A high-speed extended-term (HSET) time domain simulator (TDS), intended to become a part of an energy management system (EMS), has been newly developed for use in online extended-term dynamic cascading analysis of power systems. HSET-TDS includes the following attributes for providing situational awareness of high-consequence events: i) online analysis, including n-1 and n-k events, ii) ability to simulate both fast and slow dynamics for 1-3 hours in advance, iii) inclusion of rigorous protection-system modeling, iv) intelligence for corrective action ID, storage, and fast retrieval, and v) high-speed execution. Very fast on-line computational capability is the most desired attribute of this simulator. Based on the process of solving algebraic differential equations describing the dynamics of power system, HSET-TDS seeks to develop computational efficiency at each of the following hierarchical levels, i) hardware, ii) strategies, iii) integration methods, iv) nonlinear solvers, and v) linear solver libraries. This thesis first describes the Hammer-Hollingsworth 4 (HH4) implicit integration method. Like the trapezoidal rule, HH4 is symmetrically A-Stable but it possesses greater high-order precision (h4) than the trapezoidal rule. Such precision enables larger integration steps and therefore improves simulation efficiency for variable step size implementations. This thesis provides the underlying theory on which we advocate use of HH4 over other numerical integration methods for power system time-domain simulation. Second, motivated by the need to perform high speed extended-term time domain simulation (HSET-TDS) for on-line purposes, this thesis presents principles for designing numerical solvers of differential algebraic systems associated with power system time-domain simulation, including DAE construction strategies (Direct Solution Method), integration methods(HH4), nonlinear solvers(Very Dishonest Newton), and linear solvers(SuperLU). We have implemented a design appropriate for HSET-TDS, and we compare it to various solvers, including the commercial grade PSS\E program, with respect to computational efficiency and accuracy, using as examples the New England 39 bus system, the expanded 8775 bus system, and PJM 13029 buses system. Third, we have explored a stiffness-decoupling method, intended to be part of parallel design of time domain simulation software for super computers. The stiffness-decoupling method is able to combine the advantages of implicit methods (A-stability) and explicit method(less computation). With the new stiffness detection method proposed herein, the stiffness can be captured. The expanded 975 buses system is used to test simulation efficiency. Finally, several parallel strategies for super computer deployment to simulate power system dynamics are proposed and compared. Design A partitions the task via scale with the stiffness decoupling method, waveform relaxation, and parallel linear solver. Design B partitions the task via the time axis using a highly precise integration method, the Kuntzmann-Butcher Method - order 8 (KB8). The strategy of partitioning events is designed to partition the whole simulation via the time axis through a simulated sequence of cascading events. For all strategies proposed, a strategy of partitioning cascading events is recommended, since the sub-tasks for each processor are totally independent, and therefore minimum communication time is needed

Cournot Competition Yields Spatial Avoiding Competition in Groups

This paper characterizes the properties of equilibrium location patterns in an Anderson-Neven-Pal model and uses these characteristics to comprehensively find the subgame perfect Nash equilibria, most of which are not yet found in the literature. Since the external competition effect may be exactly canceled out, or internal competition strictly dominates external competition, or the internal competition effect is consistent with the external competition effect, therefore without any externality and prior collusion, a competitive group structure may form endogenously in equilibrium and firms tend to avoid competition inside each group. The analyses of an Anderson-Neven-Pal model are instructive in studying the conditions for a capacity to implement a ``Nash combination."Cournot competition; Spatial competition; Nash equilibrium