Overhead Line Models
Introduction
This article describes the most common overhead line (OHL) models used in power systems analysis. By line models, we mean equivalent circuits composed of elementary series and shunt impedances (i.e. resistances, inductances, capacitances and conductances). The calculation of these impedances (i.e. based on geometrical and material considerations) is covered elsewhere in the section on Overhead Line Constants.
So why even bother with having a range line models  isn't one enough? The problem is that there are several characteristics of transmission lines that complicates the modelling of lines, for instance:
 The line impedances are not lumped, but distributed continuously over the length of the line. The interaction of inductances and capacitances is therefore different when considering a line as having lumped parameters versus distributed parameters.
 The geometry of overhead line conductors / subbundles (phase and earth) are not always symmetrical and therefore, a singlephase, single conductor equivalent circuit is not always appropriate. In such cases, multiconductor models may be required.
 For transient studies (especially those covering higher frequencies), the line parameters can have significant frequency dependencies (in particular the series resistance and inductance). For example, the skin effect leads to increased resistances at higher AC frequencies. This necessitates the use of frequencydependent line models.
The factors listed above imply that the most accurate line model would have distributed parameters, be fully multiconductor to allow for asymmetrical geometries and imperfect line transpositions, and capture the frequency dependencies of the line. Such line models exist, but they are relatively complicated and often, much simpler alternatives can be used depending on the application.
Taxonomy of Overhead Line Models
Line Model  Applications  Properties  Remarks  

SteadyState (Frequency Domain) Models  SinglePhase Models  Lossless (L) Line 



Lossless (LC) Line 



RL Line 


 
Nominal Line 


 
Distributed Parameter Line 


 
MultiConductor Models  Nominal Line 


 
Cascaded Nominal Line 


 
Distributed Parameter Line 


 
Travelling Wave (Time Domain) Models  SinglePhase Models  Bergeron Line Model 



Frequency Dependent Line Model 


 
MultiConductor Models  Bergeron Line Model 


 
Frequency Dependent Line Model 


Selecting an Appropriate Line Model
Key considerations for selecting a suitable line model:
 Application: what kind of analysis is being done? e.g. power flow, stability, EMT, etc. For static studies such as power flows, simple fault studies, etc, then steadystate (frequency domain) models are appropriate. Steadystate models are also suitable for dynamic simulations that are only concerned with electromechanical transients (e.g. transient stability and motor starting) rather than electromagnetic transients (e.g. switching and lightning studies).
 Line Length: simpler models can be used for shorter lines
 Load unbalance and Transpositions: multiconductor line models should be used for longer untransposed lines and systems with significant imbalances
 Level of detail: is it a preliminary or a detailed study?
 Accuracy of input data: what kind of input data is available?