Periodic economic model predictive control with nonlinear-constraint relaxation for water distribution networks

In this paper, a periodic economic model predictive control (EMPC) strategy with nonlinear algebraic constraint relaxations for water distribution networks (WDNs) is presented. A WDN is usually modeled by a series of differential-algebraic equations. When the hydraulic pressure/head and flow relations in the interconnected pipes are considered, the nonlinear algebraic equations will appear in the control-oriented model of WDNs. Specifically, two types of nonlinear algebraic equations are studied in terms of unidirectional and bidirectional flows in pipes. These nonlinear algebraic constraints are iteratively relaxed by a series of linear constraints. Therefore, the proposed EMPC strategy can be implemented by solving an optimization problem using the linear programming technique. Finally, the EMPC strategy with nonlinear algebraic constraint relaxations is verified in the Richmond water network. The comparison results of applying nonlinear EMPC strategy are also provided. The proposed nonlinear-constraint relaxation technique turns out to be much faster than the one obtained by a standard nonlinear optimization solver.