Dynamic Phasors

In the power systems community, dynamic phasors were initially introduced for power electronics analysis Sanders1991 as a more general approach than state-space averaging. They were used to construct efficient models for the dynamics of switching gate phenomena with a high level of detail as shown in Mattavelli1999. A few years later, dynamic phasors were also employed for power system simulation as described in Demiray2008. In Strunz2006 the authors combine the dynamic phasor approach with the Electromagnetic Transients Program (EMTP) simulator concept which includes Modified Nodal Analysis (MNA). Further research topics include fault and stability analysis under unbalanced conditions as presented in Stankovic2000 and also rotating machine models have been developed in dynamic phasors Zhang 2007.

Bandpass Signals and Baseband Representation

Although here, dynamic phasors are presented as a power system modelling tool, it should be noted that the concept is also known in other domains, for example, microwave and communications engineering Maas2003, Suarez2009, Haykin2009, Proakis2001. In these domains, the approach is often denoted as base band representation or complex envelope. Another common term coming from power electrical engineering is shifted frequency analysis (SFA). In the following, the general approach of dynamic phasors for power system simulation is explained starting from the idea of bandpass signals. This is because the 50 Hz or 60 Hz fundamental and small deviations from it can be seen as such a bandpass signal. Futhermore, higher frequencies, for example, generated by power electronics can be modelled in a similar way.