Distributed flow network control with demand response via price adjustment

In this paper, we consider a flow network with demand response, namely, demand-side control by adjusting the price of commodities. First, a flow controller is proposed to reduce the imbalance between inflows and outflows on each vertex. This controller is distributed in the sense that the required information to flow managers is only the imbalances on the adjacent vertexes. We derive a necessary and sufficient condition such that the imbalances on all vertexes converge to zero. Next, a price controller is proposed to maintain the supply-demand balance. We reveal that there is a trade-off in the price controller between the stability of the demand system and the effect of the demand restraint. We derive a necessary and sufficient condition of the price controller to satisfy the trade-off. Furthermore, the minimum required supply capacity is derived, which is smaller than the supposed aggregate demand due to the effect of the price adjustment. Finally, the effectiveness of the proposed method is shown by a simulation.