Get Complex numbers to work without compromises

[Francesco Casella]

Complex numbers are increasingly used in Modelica, particularly for power system models. They are used by Modelica.Electrical.QuasiStationary, and also by other libraries being developed for electro-mechanical modelling of power systems.

OMC supports complex numbers, but there are still some issue that prevents their full, uncompromised use. This ticket collects all of them in the attempt of solving the pending problems soon.

In most, possibly all, cases, the best strategy to solve equations involving Complex variables is to turn them into scalar Real equations and then apply all possible symbolic simplifications. This is particularly important when Complex number that happen to be purely real or imaginary are used.

In simple cases, this already happens. If you compile this model

model TestComplex
  Complex z1, z2;
equation
  z1+z2 = Complex(0);
  z2 = Complex(1,2);
end TestComplex;

the record equations are turned into scalar equations and solved symbolically, so eventually z1 and z2 are evaluated at initialization, because they are constant.

Unfortunately, in some cases this does not happen, for reasons that need to be investigated. In #4354 and #4808 this issue leads to problems solving otherwise trivial equations, in #4157 it leads to problems with equations in when statements. #4611 is a slightly more involved case, where arrays of Complex constructors are involved.

The code generation for algorithms involving Complex numbers needs to be fixed, see #4055

Last, but not least, the sum of Complex numbers should be supported, see #4297.