The stability of a transmission line model can be ensured by verifying a property called passivity. The physical meaning of passivity, with regard to electrical circuits, is that passive networks always absorb real power and thus the total energy delivered to the network is positive. Although transmission lines are passive as a matter of physical reality, the transmission line model may be not passive due to the errors introduced during the various approximations (i.e. curve-fitting, etc.).
Figure 8-23 – Simple Three Single-Core Cable Configuration
The passivity can be guaranteed by verifying that the eigenvalues of the Hermitian matrix derived from transmission line parameters are positive for the frequency range of interest. The above graph shows the eigenvalues of H for particular cable configuration. The presence of negative eigenvalues at very low frequencies indicates the non-passive cable model which may lead to unstable simulation. In power system studies, the unstable simulation may be frequently observed, especially when simulating HVDC underground cables and overhead lines. The proper fitting parameter selection may help to obtain passive model and hence stable simulation. The following options can be used to verify passivity of the model.
Passivity checking is controlled from within the Frequency Dependent (Phase) Model component.