Bogus linear tearing in Buildings model

[Francesco Casella]

Please check ​Buildings.Electrical.AC.ThreePhasesUnbalanced.Validation.IEEETests.Test4NodesFeeder.BalancedStepDown.YD. The model fails during lambda0 initialization with

Failed to solve linear system of equations (no. 569) at time 0.000000, system is singular for U[2, 2].
Matrix U
        -0 
Output vector x
[ 1]                    0
The default linear solver fails, the fallback solver with total pivoting is started at time 0.000000. That might raise performance issues, for more information use -lv LOG_LS.

The debugger shows that system 569 is torn in this way:

linear (torn), unknowns: 3, iteration variables: 1 (transformer.conv2.terminal_p.i[1])
(torn) transformer.conv3.terminal_p.i[1] := transformer.conv2.terminal_p.i[1] - line2.i3[1]
(torn) transformer.conv1.terminal_p.i[1] := transformer.conv2.terminal_p.i[1] + line2.i2[1]
(residual) line2.i1[1] + transformer.conv1.terminal_p.i[1] - transformer.conv3.terminal_p.i[1] = 0

It is immediate to see that the term transformer.conv2.terminal_p.i[1] appears both in transformer.conv3.terminal_p.i[1] and in transformer.conv1.terminal_p.i[1], so when those two are subtracted to compute the residual, its sensitivity w.r.t. its unknown is zero.

I don't know what criterion is used to perform linear tearing, but it's obviously not a good one. Linear systems should be solved with proper pivoting; solving some equations according only to structural information but disregarding the coefficient values can be very dangerous.

Until this issue is solved, I would recommend to disable linear tearing by default. This will sure enough solve a lot of problems in the testsuite. BTW, now that we have sparse solvers to deal with large linear systems, the usefulness of linear tearing is probably quite limited.