P-Section Equivalent Circuits

PSCAD Coupled P-Section Model

Long-Line Correction

Transmission systems considered to be electrically short (i.e. the propagation delays are negligible) can be represented with reasonable accuracy by a simple circuit consisting of a series-impedance and shunt-admittance.  If the total shunt-admittance is halved and placed at each end of the circuit with the series-impedance between the two ends, the resulting equivalent circuit is referred to as a p-section [16].

Figure 8-30 – Single-Phase P-Section Equivalent Circuit

Where,

and,

PSCAD Coupled P-Section Model

The Line Constants Program is not used by EMTDC for the calculation of p-section parameters.  This is due to the fact that p-sections are entirely passive, and can be represented directly as part of the EMTDC conductance matrix.  The PSCAD Master Library includes a 'coupled' p-section model, which equivalences a single, three-phase, mutually coupled circuit.  There is also a double circuit 'coupled' p-section component, where both circuits are three-phase and mutually coupled.

Figure 8-31 – Coupled P-Section Components in PSCAD

For more information on these components, please see the respective topics in the PSCAD On-Line Help.

Long-Line Correction

Long-line correction is required when attempting to accurately equivalence a long transmission line as a coupled p-section circuit.  A 'long' transmission line can be defined as any line exceeding approximately 200 to 250 km in length [16], although this is surely open to interpretation.  

Regardless of the actual defined length, p-section equivalent circuits will become less and less accurate as the line becomes longer.  This is mainly due to the fact that a p-section does not account for the uniform distribution of line parameters.  It is possible however, to derive a set of long-line corrected, lumped parameters so that the p-section equivalent circuit does indeed provide a better representation.

The Line Constants Program displays the long-line corrected data directly in the Output File (*.out).  This information is provided specifically for users who wish to develop their own, multi-circuit p-section equivalents, using the Line Constants program as a starting point.  The long-line correction is performed directly on the elements of the modal impedance ZM and modal admittance YM matrices as follows:

Where,

The long-line corrected modal parameters are then transformed back to the phase domain before being displayed in the output file.