Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical and Computer Engineering


Professor J.W. Bandler


Professor M.A. El-Kady


The material presented in this thesis is a logical extension of and addition to previous work on network sensitivities as applied to power system analysis and planning. The continuing tendency of supplementing the existing extra-high voltage a.c. transmission systems with high-voltage d.c.(HVDC) lines has been taken into consideration, and various relevant component models have been investigated using a new hybrid network formulation based on the methedology developed by Bandler and EI-Kady. The load buses, frequently modelled as PQ-buses at which both the real and reactive injected powers are known, and the generator buses characterized by a constant voltage magnitude and constant real injected power, have been dealt with by exploiting a special complex conjugate notation. In addition, the current, voltage and/or power relationships associated with the transmission network branches have been investigated. A hybrid formulation for generalized power system component models has been developed. This novel formulation not only encompasses the work established on the basis of one-port theory, but it is also capable of manipulating multiport, nonreciprocal, a.c. as well as integrated a.c.d.c. bulk transmission networks. The attractive features of adjoint modeling have been retained, and consequently, exact sensitivity formulas associated with various control variabies have been derived, tabulated and verified. Applications of the novel sensitivity formulation to both, the HVDC link and phase-shifting transformer modeling, are presented. In the first application, a two-port model of an HVDC link connecting two a.c. networks has been used. The terminal relations of the converters have been utilized ingeniously to develop an adjoint converter model. Both firing angle and commutation reactance have been considered as the control variables of interest, and their respective sensitivity formulas have been numerically verified on a test power system. In the second application, a cascaded phase-shifting transformer model comprising an ideal transformer in series with a transformer equivalent impedance has been considered. Exact sensitivity formulas for the control variables representing transformer turns ratio magnitude, phase angle, equivalent resistance and reactance have been derived elegantly and compactly.

The theoretical results achieved have been extensively verified using a 2-bus and a 6-bus sample power systems. The functions encountered in steady-state security assessment have been considered, and investigated in applications to two practical IEEE (30-bus and 118-bus) test systems.

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