Power Electronics

Every inverter model here is averaged: the switching is not represented, and the converter is treated as a controllable voltage behind its filter. Averaging removes the switching frequency from the problem, which is what allows a step size set by the control bandwidth rather than by the carrier. It also means these models say nothing about switching losses, harmonic injection or any behaviour that depends on the modulation itself.

The control that sits on top of each is derived separately under converter control, because the same cascade appears in more than one of these models.

Choosing among them

The models differ along two axes: which domain they are written in, and whether the converter follows the grid or forms it.

EMT Ph3 averaged VSI is the reference formulation. All fourteen states are real, the three filter phases are represented individually, and there is no carrier, so nothing is assumed about the bandwidth of what it carries.

DP Ph1 averaged VSI is the same converter as a single positive-sequence envelope. Its six real filter states become two complex envelopes, which is the saving the envelope description buys, at the cost of being unable to represent an unbalance.

DP Ph3 averaged VSI restores per-phase representation in the envelope domain, with one complex envelope per phase and a controller that keeps a single positive-sequence frame. Because three independent phase envelopes admit a negative-sequence component, it carries negative-sequence current control that the single-phase model has no need for.

EMT Ph3 grid-forming VSI is the one that differs in kind rather than in representation. It carries its own frequency and angle as states instead of tracking the grid’s, so it can energise a network with no other source. Its control is nonlinear enough that the model is linearized numerically at each operating point rather than written in closed form.

What they share

All four are solved simultaneously with the network rather than through a delayed injection, using the state-space nodal method described under SSN components. All four are therefore re-formed as the operating point moves, and all four make the system matrix change at every step, which is the cost of the approach.