Approximate Scheduling of DERs with Discrete Complex Injections.

Rapid penetration of renewable energy based Distributed Energy Resources (DER) has the potential to exacerbate the challenges inherent in grid frequency and voltage regulation. However, their real time controllability can be leveraged to not only mitigate such challenges, but improve the economics and quality of grid operations. A plethora of DER scheduling algorithms have been developed for fast and efficient scheduling of these resources. These algorithms schedule the complex - real and reactive power injected into (or drawn from) the grid by the DERs under various cost objective functions and grid constraints. However, a vast majority of such algorithms assume the feasible range of power injections to be continuous. In reality, the control options available for several DERs form a discrete space. This implies that the feasible range of power injections also forms a discrete space. This makes DER scheduling an NP-hard problem. Integer/Mixed Integer program based algorithms, which guarantee optimality in the objective value, have been developed. But these are prohibitively expensive in terms of computational time requirements. On the other hand, fast heuristic based solutions have also been developed. But as they do not provide any guarantee on the optimality of the objective, or on satisfying the constraints, they are unreliable for grid operations. Recent works have developed approximation algorithms which offer the best of both the approaches above: (near) optimality and low computational complexity, both of which are governed by a user defined accuracy parameter.. In this work, we significantly improve upon such existing works by developing an approximation algorithm which schedules DERs with complex injections (as opposed to only real injection) and whose runtime is polynomial (as opposed to exponential) in 1/epsilon. We provide theoretical analysis and support them with experimental results to validate the guarantees provided by our approximation algorithm.