Real-time update of a frequency dependant admittance matrix [power systems]

Network components are nonlinear devices and their impedance values vary with frequency, voltage and power variations. Tracking of these parameters and subsequent update tasks are mainly CPU intensive. Accuracy expected from modern digital simulators imposes frequent updates of the various admittance values. Real-time digital simulators impose the new challenge of performing these updates on large matrix at best in HRT (hard real-time) (every step) and at worst in near real-time (every few steps). HRT is achieved when the computations are performed as fast as the phenomena unfolds, in this case 60 Hz. The authors have focused on this problem and more specifically on the frequency dependency. They have examined various algorithms and developed an implementation strategy that allows real-time frequency compensation of large network admittance matrices. Their algorithm consists in representing each circuit element by its frequency dependent quadrupole model and the corresponding q-matrix. These q-matrices are combined to produce the network elements equivalent c-matrices. Finally, the c-matrices are used to compute the updated admittance matrix elements and update the network nodal matrix. Their strategy consists in isolating the q-matrix and c-matrix formation from the admittance matrix update. In this fashion, the algorithm can be easily implemented on a parallel architecture and thus achieve HRT. The algorithm, the models and the strategy have been implemented on a two serial and one parallel computers using the C programming language. In this paper, the authors present their results as applied to a single-phase balanced power network