“…A set of binary variables x i,j,t and a sufficiently large positive value M were used to determine the direction of gas flow in pipes, and ensure only one of constraints ( 9) and ( 10) is active. Then, the bidirectional flow can be expressed by (11). Note that if x i,j,t = 1, f i,j,t = f + i,j,t , p i,t − p j,t ≥ 0, the direction of gas flow is positive (from i to j), on the contrary, if x i,j,t = 0, f i,j,t = −f − i,j,t , p i,t − p j,t ≤ 0, the direction of gas flow is negative (from j to i).…”