  We present a pure linear cutting-plane relaxation approach for rapidly
proving tight and accurate lower bounds for the Alternating Current Optimal
Power Flow Problem (ACOPF) and its multi-period extension with ramping
constraints. Our method leverages outer-envelope linear cuts for well-known
second-order cone relaxations for ACOPF together with modern cut management
techniques and reformulations to attain numerical stability. These techniques
prove effective on a broad family of ACOPF instances, including the largest
ones publicly available, quickly and robustly yielding tight bounds.
Additionally, we consider the (frequent) case where an ACOPF instance is
handled following a small or moderate change in problem data, e.g., load
changes and generator or branch shut-offs. We provide significant computational
evidence, on single and multi-period ACOPF instances, that the cuts computed on
the prior instance provide very good lower bounds when warm-starting our
algorithm on the perturbed instance.
