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Passivity
When
a model is to be included in a time domain simulation, it is important
that the model does not result in an unstable simulation. This requires
the model to satisfy two criteria:
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All
poles are stable
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The
model is passive
The
stable pole requirement is enforced by vector fitting. The passivity
requirement means that the model cannot generate energy when connected
to an external network. A model is passive provided that
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(1)
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model admittance matrix are positive for all frequencies. Most
approaches for passivity enforcement rely on a postprocessing step of
the model, assuming that only a small correction is needed. One method
described in [1.3] achieves this by solving the constrained equation
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(2a)
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(2b)
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First order perturbation leads to the constrained linear least
squares problem (3), which is solved by Quadratic Programming.
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(3a) |
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(3b) |
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This
passivity enforcement approach is available in package QPpassive.zip, see the
Downloads
page.
(Requires Matlab Optimization Toolbox). |
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