State freeze is used by converter controllers during fault transients to fix a variable at the pre-fault values. The concept of state freeze is applicable to both state or algebraic variables. For example, in the renewable energy electric control model (REECA), the proportional-integral controllers for reactive power error and voltage error are subject to state freeze when voltage dip is observed. The internal and output states should be frozen when the freeze signal turns one and freed when the signal turns back to zero.
Freezing a state variable can be easily implemented by multiplying the freeze signal with the right-hand side (RHS) of the differential equation:
where \(f(x)\) is the original RHS of the differential equation, and \(z_f\) is the freeze signal. When \(z_f\) becomes zero the differential equation will evaluate to zero, making the increment zero.
Freezing an algebraic variable is more complicate to implement. One might consider a similar solution to freezing a differential variable by constructing a piecewise equation, for example,
where \(g(y)\) is the original RHS of the algebraic equation.
One might also need to add a small value to the diagonals of
associated with the algebraic variable to avoid singularity.
The rationale behind this implementation is to zero out the algebraic
equation mismatch and thus stop incremental correction:
in the frozen state, since \(z_f\) switches to zero,
the algebraic increment should be forced to zero.
This method, however, would not work when a dishonest Newton method is
If the Jacobian matrix is not updated after \(z_f\) switches to one, in the row associated with the equation, the derivatives will remain the same. For the algebraic equation of the PI controller given by
where \(K_p\) is the proportional gain, \(u\) is the input, \(x_I\) is the integrator output, and \(y\) is the PI controller output, the derivatives w.r.t \(u\), \(x_i\) and \(y\) are nonzero in the pre-frozen state. These derivative corrects \(y\) following the changes of \(u\) and \(x\). Although \(x\) has been frozen, if the Jacobian is not rebuilt, correction will still be made due to the change of \(u\). Since this equation is linear, only one iteration is needed to let \(y\) track the changes of \(u\). For nonlinear algebraic variables, this approach will likely give wrong results, since the residual is pegged at zero.
To correctly freeze an algebraic variable, the freezing signal needs to
be passed to an
EventFlag, which will set an
if any input changes.
EventFlag is a
VarService that will be evaluated at each
iteration after discrete components and before equations.
To speed up the command-line program, import profiling is used to breakdown the program loading time.
andes can be profiled with
profimp "import andes" --html > andes_import.htm. The
report can be viewed in any web browser.