We propose a GPU-accelerated distributed optimization algorithm for controlling multi-phase optimal power flow in active distribution systems with dynamically changing topologies. To handle varying network configurations and enable adaptable decomposition, we advocate a componentwise decomposition strategy. However, this approach can lead to a prolonged computation time mainly due to the excessive iterations required for achieving consensus among a large number of fine-grained components. To overcome this, we introduce a technique that segregates equality constraints from inequality constraints, enabling GPU parallelism to reduce per-iteration time by orders of magnitude, thereby significantly accelerating the overall computation. Numerical experiments on IEEE test systems ranging from 13 to 8500 buses demonstrate the superior scalability of the proposed approach compared to its CPU-based counterparts.

In a smart grid environment, communication network plays an important role as it must deliver data from the Phasor Measurement Units (PMUs) in the Substations (SSs) to the Control Center(s) (CCs) in real time. Accordingly, communication network design has received considerable attention from smart grid researchers in the last few years. In a recent paper, we studied this problem where all the substations were sending data to a single CC and formalized it as the Rooted Delay Constrained Minimum Spanning Tree problem. As the number of substations in a geographic area is often large, PMU data from the substations do not directly go to the Control Center (CC) and instead goes to multiple Local Controls Centers (LCC) within a specified delay threshold. The aggregated data from the LCCs is then sent to the CC. In this paper, we extend our earlier results by considering Multiple Local Control Centers (MLCCs) where the PMU data must arrive from the SSs to a LCC within a specified delay threshold. This gives rise to a new problem, where we need to create a Delay Constrained Spanning Forest instead of a Delay Constrained Spanning Tree as in earlier studies. We provide (i) an optimal solution for the problem using Integer Linear Programming, (ii) a Lagrangian Relaxation, and (iii) a Heuristic solution. Finally, we evaluate the performance of our solution techniques with real substation location data of Arizona.

Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications, such as pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel optimization problems in which the upper level problem features some integer variables and the lower level problem enjoys strong duality. We propose a dedicated Benders decomposition method for solving this class of bilevel problems, which decomposes the Benders subproblem into two more tractable, sequentially solvable problems that can be interpreted as the upper and lower level problems. We show that the Benders subproblem decomposition carries over to an interesting extension of bilevel problems, which connects the upper level solution with the lower level dual solution, and discuss some special cases of bilevel problems that allow sequence-independent subproblem decomposition. Several novel schemes for generating numerically stable cuts, finding a good incumbent solution, and accelerating the search tree are discussed. A computational study demonstrates the computational benefits of the proposed method over a state-of-the-art, bilevel-tailored, branch-and-cut method; a commercial solver; and the standard Benders method on standard test cases and the motivating applications in sequential energy markets.

Distributed generation and remotely controlled switches have emerged as important technologies to improve the resiliency of distribution grids against extreme weather-related disturbances. Therefore it becomes important to study how best to place them on the grid in order to meet a resiliency criteria, while minimizing costs and capturing their dependencies on the associated communication systems that sustain their distributed operations. This paper introduces the Optimal Resilient Design Problem for Distribution and Communication Systems (ORDPDC) to address this need. The ORDPDC is formulated as a two-stage stochastic mixed-integer program that captures the physical laws of distribution systems, the communication connectivity of the smart grid components, and a set of scenarios that specifies which components are affected by potential disasters. The paper proposes an exact branch-and-price algorithm for the ORDPDC that features a strong lower bound and a variety of acceleration schemes to address degeneracy. The ORDPDC model and branch-and-price algorithm were evaluated on a variety of test cases with varying disaster intensities and network topologies. The results demonstrate the significant impact of the network topologies on the expansion plans and costs, as well as the computational benefits of the proposed approach.