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Transient Stability Analysis

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 [4]. 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. It is also possible to order the admittance matrix to block-diagonal-bordered form in order to increase available parallelism. This is illustrated in figure gif. 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.

 
Figure: Ordering the Admittance Sub-Matrix in Transient Stability Differential-Algebraic Equations  

It is also possible to solve the above equations by decoupling the generator equations from the network equations. For decoupled transient stability analysis, the transient stability differential-algebraic equation matrix is partitioned into four sub-matrices. In figure gif, the generator equations are in the block-diagonal matrix labeled . The generator equations are solved independently of the network equations, then the sparse admittance matrix is modified by the matrix coefficients in the sparse borders, labeled B and C. The admittance matrix is labeled in this figure. Instead of the common practice of decoupling the generator and network calculations in a transient stability simulation, we hope to continue this research and eventually examine the use of more powerful differential-algebraic equation solvers for transient stability analysis that do not decouple the generator and network equations. The fully-coupled differential-algebraic equations will offer more potential for good parallel performance because

The amount of work available will be greater and the effects of load-balance overhead will be minimized, while the amount of communications overhead will remain nearly the same as solving for the decoupled transient stability equations.



next up previous
Next: Power System Network Up: Power System Applications Previous: Load-Flow Analysis



David P. Koester
Sun Oct 22 17:27:14 EDT 1995