arXiv subjects

Kibaek Kim

Publications and source records attributed to Kibaek Kim.

58 records · Page 4Linked to original sources

arXiv2021

Data-driven two-stage conic optimization with zero-one uncertainties

We address high-dimensional zero-one random parameters in two-stage convex conic optimization problems. Such parameters typically represent failures of network elements and constitute rare, high-impact random events in several applications. Given a sparse training dataset of the parameters, we motivate and study a distributionally robust formulation of the problem using a Wasserstein ambiguity set centered at the empirical distribution. We present a simple, tractable, and conservative approximation of this problem that can be efficiently computed and iteratively improved. Our method relies on a reformulation that optimizes over the convex hull of a mixed-integer conic programming representable set, followed by an approximation of this convex hull using lift-and-project techniques. We illustrate the practical viability and strong out-of-sample performance of our method on nonlinear optimal power flow and multi-commodity network design problems that are affected by random contingencies, and we report improvements of up to 20\% over existing sample average approximation and two-stage robust optimization methods.

math.OC↗

arXiv2021

Leveraging GPU batching for scalable nonlinear programming through massive Lagrangian decomposition

We present the implementation of a trust-region Newton algorithm ExaTron for bound-constrained nonlinear programming problems, fully running on multiple GPUs. Without data transfers between CPU and GPU, our implementation has achieved the elimination of a major performance bottleneck under a memory-bound situation, particularly when solving many small problems in batch. We discuss the design principles and implementation details for our kernel function and core operations. Different design choices are justified by numerical experiments. By using the application of distributed control of alternating current optimal power flow, where a large problem is decomposed into many smaller nonlinear programs using a Lagrangian approach, we demonstrate computational performance of ExaTron on the Summit supercomputer at Oak RidgeNational Laboratory. Our numerical results show the linear scaling with respect to the batch size and the number of GPUs and more than 35 times speedup on 6 GPUs than on 40 CPUs available on a single node.

math.OC↗

arXiv2016

Data Centers as Dispatchable Loads to Harness Stranded Power

We analyze how both traditional data center integration and dispatchable load integration affect power grid efficiency. We use detailed network models, parallel optimization solvers, and thousands of renewable generation scenarios to perform our analysis. Our analysis reveals that significant spillage and stranded power will be observed in power grids as wind power levels are increased. A counter-intuitive finding is that collocating data centers with inflexible loads next to wind farms has limited impacts on renewable portfolio standard (RPS) goals because it provides limited system-level flexibility and can in fact increase stranded power and fossil-fueled generation. In contrast, optimally placing data centers that are dispatchable (with flexible loads) provides system-wide flexibility, reduces stranded power, and improves efficiency. In short, optimally placed dispatchable computing loads can enable better scaling to high RPS. We show that these dispatchable computing loads are powered to 60~80\% of their requested capacity, indicating that there are significant economic incentives provided by stranded power.

math.OC↗

arXiv2015

A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties

We argue that deterministic market clearing formulations introduce arbitrary distortions between day-ahead and expected real-time prices that bias economic incentives and block diversification. We extend and analyze the stochastic clearing formulation proposed by Pritchard et al. (2010) in which the social surplus function induces penalties between day-ahead and real-time quantities. We prove that the formulation yields price distortions that are bounded by the bid prices, and we show that adding a similar penalty term to transmission flows and phase angles ensures boundedness throughout the network. We prove that when the price distortions are zero, day-ahead quantities converge to the quantile of real-time counterparts. The undesired effects of price distortions suggest that stochastic settings provide significant benefits over deterministic ones that go beyond social surplus improvements. We propose additional metrics to evaluate these benefits.

econ.GN↗