SSN Switch Management in Real-Time Applications

The SSN method makes the complete state-space equations block-diagonal due to the decoupling induced by the approach. The decoupling is partial, however, as the nodal solution links all parts of the network equations. Using a single CPU approach, the computational gain can approach a factor of 2 if the state-space iteration becomes more important, in comparison to the same 3x3 matrix inversion.

Furthermore, the problem of memory storage of switch permutations is solved here: each group contains only the pre-calculated set of matrices for the switch contained within the groups. Taking again the specific example of Fig. 35, which is composed of two three-phase breakers, full pre-calculation of circuit modes in the standard state-space approach would require the storage of:

• 2^6=64 permutations of state-space equations of size x,u

In the SSN approach, two sets of 2^3=8 system matrices need to be stored (one for each group), that is:

• 2*(2^3)=16 permutations of state-space equations of size x/2,u/2

plus 3x3 admittance matrix.

The memory requirements are considerably reduced. As the SSN groups and switches are determined by the user, they, therefore, have full control over the memory requirements.

Separation of switches is always possible because they can be modeled as a separate group in the proposed method. In that case, only the D matrix subsystem is non-empty, and the group admittance is included directly in the global admittance matrix in a way similar to a standard nodal method.