Electronic Thesis and Dissertation Repository

Thesis Format



Doctor of Philosophy


Electrical and Computer Engineering


Badrkhani Ajaei, Firouz

2nd Supervisor

Dounavis, Anestis

Joint Supervisor


In recent years, the application of DC power systems has attracted much attention. As an integral part of any DC power system, accurate and computationally efficient modeling of DC transmission lines consisting of cables and overhead lines is essential for the transient analysis. Developing a line model that takes into account the frequency dependency of the Per-Unit-Length (PUL) parameters and is valid over a wide frequency range is typically challenging.

This thesis initially focuses on the representation of the DC transmission line with a lumped model. In this regard, a Passive Lumped Frequency-Dependent Parameter (PLFDP) model is proposed for accurate representation of DC transmission lines consisting of a pair of single-conductor lines. To extend the application of the PLFDP model to DC cable systems with sheaths and/or armours, the PLFDP model is enhanced to take into account the electromagnetic coupling between the conducting layers of the multiconductor DC cable system. Furthermore, when the sheaths and/or armours of the cable system are solidly grounded, a procedure based on the Kron Reduction technique is introduced to develop a more simplified passive model. The proposed PLFDP models (i) include the frequency dependency of the PUL parameters, (ii) are scalable, i.e., once the model is developed for the unity length of the cable system, it can be simply scaled to represent other lengths, (iii) and have guaranteed passivity as they consist of passive circuit elements. Consequently, this thesis proposes passive lumped models that provide almost the same level of accuracy as compared to the most accurate line model available in PSCAD/EMTDC, while they significantly decrease the simulation time for electrically short lines (up to 11.3 times in a specific simulation study conducted).

Also, when the sheaths and/or armours of an electrically short cable system are resistively grounded, a novel approach is proposed to reduce the dimension of the original PUL parameters. The proposed method for the extraction of the reduced-dimension PUL parameters significantly decreases the simulation time (up to about 300 times in a conducted simulation study conducted) when compared to the application of the original PUL parameters, while it provides the same level of accuracy as compared to the application of the original PUL parameters.

Summary for Lay Audience

DC power systems have been developing at a fast pace in recent years. DC buried cables and overhead lines are indispensable parts of any DC power system. To investigate the behavior of the DC power system under different incidents such as electrical faults, the DC line models require to be accurate in a wider range of frequency. Also, the model should be computationally efficient so that it does not cause a prolonged simulation time.

For modeling of DC buried cables and overhead lines that their physical lengths are short, and the incident nature does not change very fast in respect to time, existing distributed parameter models impose overwhelmingly prolonged time for the simulation of the system. On the other hand, the other approach for transmission line modeling. i.e., lumped models, have serious limitations in terms of accuracy or requiring the user to repeat the process of line modeling from beginning for each line length (i.e., they are not scalable).

As a result, this thesis focuses on proposing models for DC lines that should be accurate and decrease the simulation time compared to existing line models. The proposed models are developed for single-conductor DC overhead lines and cables, multiconductor DC cables, and multiconductor DC cables with solidly grounded sheaths and/or armours. In addition, a novel method is introduced to reduce the dimension of the electrical parameters representing the frequency behavior of DC cables with resistance grounded sheaths and/or armours. It is demonstrated through the conducted simulations on different DC systems that the proposed methods drastically decrease the simulation time while accuracy is completely maintained.

Available for download on Wednesday, January 01, 2025