  In light of the increasing coupling between electricity and gas networks,
this paper introduces two novel iterative methods for efficiently solving the
multiperiod optimal electricity and gas flow (MOEGF) problem. The first is an
iterative MILP-based method and the second is an iterative LP-based method with
an elaborate procedure for ensuring an integral solution. The convergence of
the two approaches is founded on two key features. The first is a penalty term
with a single, automatically tuned, parameter for controlling the step size of
the gas network iterates. The second is a sequence of supporting hyperplanes
together with an increasing number of carefully constructed halfspaces for
controlling the convergence of the electricity network iterates. Moreover, the
two proposed algorithms use as a warm start the solution from a novel
polyhedral relaxation of the MOEGF problem, for a noticeable improvement in
computation time as compared to a cold start. Unlike the first method, which
invokes a branch-and-bound algorithm to find an integral solution, the second
method implements an elaborate steering procedure that guides the continuous
variables to take integral values at the solution. Numerical evaluation
demonstrates that the two proposed methods can converge to high-quality
feasible solutions in computation times at least two orders of magnitude faster
than both a state-of-the-art nonlinear branch-and-bound (NLBB) MINLP solver and
a mixed-integer convex programming (MICP) relaxation of the MOEGF problem. The
experimental setup consists of five test cases, three of which involve the real
electricity and gas transmission networks of the state of Victoria with actual
linepack and demand profiles.
