The non-convexities inherent in the AC load flow equations are major contributors to the computational complexity of the AC OPF problem that is essentially equivalent to the socially optimal market clearing problem

The socially optimal power market clearing problem with diverse, complex-utility-structure participants at the distribution level, poses computational challenges that are exacerbated by the associated non-convex load flow constraints. We investigate variations and extensions of Proximal Message Passing algorithms proposed in the literature and implemented on similar, though simpler, social welfare function instantiations. Numerical results demonstrate that (i) in comparison to solving a computationally demanding, yet exact, centralized market clearing problem, significant computational improvements are possible with the proposed PMP algorithm extensions, (ii) comparison to the benchmark results obtained by solving the centralized formulation reveals that excellent accuracy is attainable by the PMP algorithms and (iii) in comparison to the PMP algorithms existing in the literature, the proposed extension reduces significantly the communication requirements for sub-problem coordination and convergence verification and enables faster converging asynchronous sub-problem iterations.