  Joint operation of power, water, and heating networks is expected to improve
overall efficiency of infrastructure while also known as a challenging problem,
due to complex couplings of electric, hydraulic, and thermal models that are
nonlinear and nonconvex. We formulate an optimal power-water-heat flow (OPWHF)
problem and develop a computationally efficient and privacy preserving
heuristic to solve it. The proposed heuristic decomposes OPWHF into
subproblems, which are solved via convex relaxation and convex-concave
procedure while iteratively exchanging information to reach consensus on
coupling variables. Simulation results validate that the joint optimization can
improve operational flexibility and social welfare of the interconnected
system, wherein the water and heating networks respond to time-varying
electricity price and electric load as virtual energy storage. We also compare
two modes of heating network control: by flow rate and by temperature; case
studies reveal that the latter is more effective for most practical systems.
