H. Sharifzadeh - Department of Electrical and Computer Engineering, Hakim Sabzevari University, Sabzevar, Iran

Recently, some researchers have employed the McCormick envelopes method to convexify some NP-hard optimization problems with bilinear terms. However, few publications concentrate on its variants to derive a more tight convex relaxation for practical applications. This paper proposes a new viewpoint on Kron’s loss formula, also known as the B-matrix formula, as an equation having bilinear terms. Relying on the perspective, we transform the loss equation to some linear constraints using an enhanced McCormick relaxation. In the technique, the domain of bilinear variables is divided into some smaller parts to improve the relaxation tightness. Some case studies with different nonconvex terms are considered to verify the effectiveness of the enhanced envelopes for capturing Kron’s loss formula. The findings from the numerical simulations suggest that the proposed approach can represent Kron’s loss equation precisely. Moreover, the method performs more effectively than the other methods available in the literature as it usually converges to more optimal solutions.

Kron's loss formula, McCormick envelopes, Tight relaxations