arXiv subjects

Bohang Fang

Publications and source records attributed to Bohang Fang.

3 recordsLinked to original sources

arXiv2026

A Scalable Bundle Method for Exact Reformulation of SDP in Three-Phase Power Flow Feasibility

Power flow feasibility assessment is computationally challenging for unbalanced three-phase distribution networks. This paper develops a vectorized semidefinite program (SDP) based on the bus injection model (BIM) and reformulates its dual as an exact-penalty problem, enabling us to develop a scalable three-cut proximal bundle method for feasibility assessment. The proposed bundle method is numerically over 400 times faster than MOSEK with less than 1/2000 of its memory; on the decomposed BIM-SDP, approximately 2 times faster with 75% less memory.

math.OC↗

arXiv2026

Risk-Aware Allocation of Transmission Capacity for AI Data Centers

Rapid growth in AI-driven data center loads is creating significant challenges for transmission grid interconnection. This paper proposes robust and risk-aware frameworks to quantify transmission capacity as firm and flexible capacities. We efficiently solve the robust optimization problem to determine firm capacity when minimizing unserved data center demand. Building upon this, we introduce a risk-aware allocation for flexible capacity, showing that tolerating a minimal probability of service interruption and blackout can unlock substantial flexible capacity of transmission networks and accelerate data center interconnection. To efficiently allocate scarce transmission capacities among competing data centers, we adopt the simultaneous ascending auction, characterizing products by capacity, risk level, and location. Under additive or symmetric concave valuation functions, the auction converges to a competitive equilibrium and achieves efficient allocation.

eess.SY↗

arXiv2025

Approximating Dispatchable Regions in Three-Phase Radial Networks with Conditions for Exact SDP Relaxation

The concept of dispatchable region plays a pivotal role in quantifying the capacity of power systems to accommodate renewable generation. In this paper, we extend the previous approximations of the dispatchable regions on direct current (DC), linearized, and nonlinear single-phase alternating current (AC) models to unbalanced three-phase radial (tree) networks and provide improved outer and inner approximations of dispatchable regions. Based on the nonlinear bus injection model (BIM), we relax the non-convex problem that defines the dispatchable region to a solvable semidefinite program (SDP) and derive its strong dual problem (which is also an SDP). Utilizing the special mathematical structure of the dual problem, an SDP-based projection algorithm is developed to construct a convex polytopic outer approximation to the SDP-relaxed dispatchable region. Moreover, we provide sufficient conditions to guarantee the exact SDP relaxation by adding the power loss as a penalty term, thereby providing a theoretical guarantee for determining an inner approximation of the dispatchable region. Through numerical simulations, we validate the accuracy of our approximation of the dispatchable region and verify the conditions for exact SDP relaxation.

math.OC↗