Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical and Computer Engineering


Dr. R.T.H. Alden


This thesis presents a comprehensive approach for the steady state stability analysis of AC-DC power systems. A new method is presented for the evaluation of the system state matrix which is then used to determine system stability and develop new algorithms for the stability analysis and control of large power systems.

The method exploits the powerful features of the Component Connection Method for power system modelling and overcomes the disadvantages of the earlier methods. The state matrix is formulated from two separate sets of equations. One set models the component subsystems whereas the other defines the interconnection between the subsystems. The main advantage of this is the great flexibility provided in the modelling of the power system components. As long as the input-output quantities are fixed the modelling complexity of the subsystems may be changed without affecting the interconnection equation. A compact interconnection equation has been derived relating machine voltages and currents in the presence of a multiterminal HVDC network. The subsystems retain their physical identity in this formulation and allow the derivatives of the system state matrix to be easily obtained. The power system operating point is determined by a new sequential AC-DC loadflow scheme. Any AC loadflow method can be used. The DC network is solved using the Gauss-Siedel method and any HVDC network configuration and terminals control scheme can he accommodated. The DC network solution need not be repeated and the method ensures that a feasible HVDC system operating point is selected.

A new eigenvalue tracking algorithm has been developed based on the evaluation of the sensitivity of a matrix determinant. It iteratively updates the eigenvalues following any change in the system state matrix at one-third the cost of eigenvalue computation using the QR algorithm. Used together with the proposed state matrix formulation method, it is particularly useful for identifying the modes due to any particular subsystem.

Two new methods for decentralized placement have been developed. The first method assigns the given poles among the various subsystems and the elements of the feedback gain matrix are varied to cancel the effects of the system interconnection. The second method is based on the sensitivity of a matrix determinant and solves the decentralized pole placement problem as an inverse eigenvalue problem. Both methods are easy to implement and computationally efficient.

The methods presented in this thesis have all been verified by applying them to realistic power system models. These have included a single machine infinite bus system, a three-machine AC system with six buses and nine lines and a three-machine three-terminal AC-DC system. These applications include simulation, analysis and decentralized controller design.