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Power System Applications

The underlying impetuous for our research is to improve the performance of electrical power system applications to provide real-time power system control and real-time support for proactive decision making. Our research has focused on load-flow and transient stability applications [1,10]. Sparse linear solvers are employed in both of these applications and linear solvers are responsible for the majority of the floating point operations. Scalability is desired in these applications because they have the potential to be utilized across different sized geographical areas, from single electrical power utilities to regional power authorities.

Load-flow analysis examines steady-state equations based on the network admittance matrix that represents the power system distribution network. Load-flow analysis is used for identifying potential network problems in contingency analyses, for examining steady-state operations in network planning and optimization, and also for determining initial system state in transient stability calculations [10]. Load flow analysis entails the solution of non-linear systems of simultaneous equations, which are performed by repeatedly solving sparse linear equations. Load flow is calculated using the network admittance matrices, which are symmetric positive definite and have sparsity defined by the power system network. The size of these matrices is limited because there are generally less than 2,000 sparse complex equations in the network matrices for individual power systems, while regional power authorities would be limited to less than 10,000 sparse complex equations in the network matrices.

Transient stability analysis is a detailed simulation of the power system, that models the dynamic behavior of the electrical distribution networks, electrical loads, and the electro-mechanical equations of motion of the interconnected generators [1]. Transient stability analysis can be used to perform selective detailed analyses of generator commitment stability, and to support crisis decision making during network recovery. The transient stability problem is modeled by differential algebraic equations (DAEs) with differential equations representing the generators and non-linear algebraic equations representing the power system network that interconnects the generators. The DAEs are in natural non-symmetric block-diagonal-bordered form, with diagonal blocks of generator equations coupled by the power system distribution network. In this representation, there are as many coupling equations as the entire sparse admittance matrix. However, it it possible to order the admittance matrix to block-diagonal-bordered form to order to increase available parallelism. The size of the sparse matrices representing the DAEs have as many as 10,000 complex equations for an individual power system, while regional power authorities could have as many as 50,000 sparse complex equations in the matrix formed from the DAEs.



next up previous
Next: Block-Diagonal-Bordered Sparse Linear Up: Parallel Block-Diagonal-Bordered Sparse Previous: Introduction



David P. Koester
Sun Oct 22 17:45:03 EDT 1995