Jacobian singularities in optimal power flow problems caused by intertemporal constraints

In multi-timestep Optimal Power Flow (OPF) formulations, constraints that are time-dependent such as generator ramp limits and specifically energy storage constraints may cause the Jacobian matrix to become singular as the problem iterates towards the optimal solution. The particular case of this singularity happens when the gradients of the binding intertemporal constraints are linearly dependent. Methods such as using a Moore-Penrose pseudoinverse or modifying the models used in the optimization are discussed along with novel methods developed in this paper that avoid the singular Jacobian by exploiting the specific structure of the problem and constraints.