This letter extends the complex-variable perturbed Gauss-Newton method to estimate the state of unbalanced power systems by exploiting the Fortescue transformation. It proposes a novel and efficient graph-based way to deal with singularities due to zero-sequence network parts bounded with delta transformer windings and isolated from the ground. The estimator can handle both phasor and complex power measurements. Compared with the standard complex-variable unbalanced state estimator, it achieves better numerical stability and a speed-up of around three times using a sequential implementation and five times using parallel execution.