Efficacious Models of Discrete Control Devices for Convex Optimization in Distribution Systems

Distribution system optimizations often lead to NP-hard programming problems. Although convex relaxations have proved effective for treating most of these problems, solution time increases drastically when discrete control devices (
dcd
s), e.g., tap-changers, and capacitor banks, are involved. The models of
dcd
s are categorized in two categories. The models of the first category rely on auxiliary binary variables to achieve a set of convex constraints. The first proposed model in this paper expedites the models of the first category by upgrading the coding of variables. The second category includes the models that elude the computational burden of handling the auxiliary binary variables by relaxing the equations of
dcd
s and restricting the relaxation region through a sequential bound tightening. Though this approach expedites solving large problems, the risk of encountering a suboptimal/infeasible solution is considerable. The second propounded model resolves such issues while being kept computationally competitive, by designing a parameter-free stopping criterion, a systematic mechanism to reduce the step-size in bound tightening, and an error-cognizant convex model selection function. A wide range of studies demonstrates that the proposed models resolve the issues of those available. The paper concludes with broad recommendations on the suitability of these models.