Systematically address convergence issues with direct and inverse models

[casella]

The convergence of several non-trivial test cases in Metroscopia_NPP is fragile with the currently provided default start attributes. This means that changing the tool or even the version of the tool may lead to success or failure, depending on the details of how the nonlinear equations are solved.

This issue should be approached systematically to avoid a long-term frustrating end-user experience.

The first step is to analyze the causes of the convergence failure using the method I developed with my colleague Bernhard Bachmann, see OpenModelica/OpenModelica#9603. The implementation is nearly complete, I hope it will be available anytime soon in the nightly build of OMC.

If we understand that the failures are due to a small subset of the start attributes, then we can figure out a way to manage them, e.g. via suitable parameters to set them, so that inputting a few extra parameters in the system model is enough to guarantee the convergence.

Otherwise, we should probably devise a strategy based on homotopy and on suitably simplified models, as we did successfully with ThermoPower many years ago. If you have a rough idea of what the solution should look like a-priori, that is sure doable.

Another tool that could be used if we manage to get reliable convergence for direct cases but not for inverse ones is to import the results obtained with the direct computation (which will be somewhat approximated but more or less in the ballpark) as start values for the inverse problems, using the feature described here.

[pierre-eliep-met]

As discussed with Francesco today, we will wait until this feature is implemented into modelica :)