Nonconvex Nonlinear Constraints Research Articles

A Low-Order Steady-State Model of Electric Springs for Conservation Voltage Reduction in Active Distribution Networks With Renewables

Electric spring (ES), as a new type of power electronic device, can flexibly regulate the voltage of noncritical load (NL) and improve the voltage quality of critical load (CL). It can further increase the energy savings of conservation voltage reduction (CVR) in active distribution networks (ADNs). However, the high-order nonlinearity of ESs steady-state model brings the difficulty of solving the CVR optimization problem Therefore, this paper proposes a low-order steady-state model of ESs for CVR in ADNs. The operation modes of ESs are extended based on analysis of voltage regulation characteristics, firstly. The equivalent circuit of the bus with an ES is also derived, and a steady-state model with low-order nonlinearity is further proposed. Then, considering significant difference in response speeds among ESs, distributed generation (DGs) and discrete control devices (DCDs), a two-stage coordinated operation model of ESs, DGs and DCDs is established. By means of convex envelope and linearization, the nonconvex nonlinear constraints are transformed into linear constraints, which can improve the convergence and solving efficiency of the optimization model. Finally, the case studies demonstrate that ESs can increase the CVR energy savings, and the proposed low-order steady-state model can improve the solving efficiency of this CVR optimization problem.

Two-stage stochastic programming for interdisciplinary pain management

The goal of this research is to find an optimal adaptive treatment strategy to assist physicians in prescribing treatments for patients with chronic pain. This research proposes a two-stage stochastic programming (2SP) method to optimize a treatment procedure for interdisciplinary pain management. The 2SP model incorporates non-convex nonlinear mixed integer constraints, which are constructed based on data from a real pain management program. We derive a piecewise linear approximation method to approximate the non-convex nonlinear constraints in the 2SP model. Consequently, we formulate an equivalent mixed integer linear programming (MILP) model and then solve it using a commercial mixed-integer programming solver. A comparison of the policies generated by the MILP model with the policies generated by the original nonlinear 2SP model shows that, given limited CPU time, the policies generated by the MILP model outperform those of the original nonlinear 2SP model.

Multi-objective economic-resource-production optimization of sustainable organic mixed farming systems with nutrient recycling

Abstract This paper addresses the optimal design of mixed crop-livestock farming systems for resource efficiency, economic profitability, and environmental sustainability. The trade-offs among profit, water productivity, and organic matter accumulation are considered. We propose a novel optimization model that accounts for economics, crop cultivation, livestock production, water requirement, soil organic matter, and nitrogen cycling, among other important elements of organic farming systems. The resulting problem is a multi-objective mixed-integer nonlinear fractional programming (MINLFP) problem, which consists of fractional objective function and nonconvex nonlinear constraints. After reformulating the nonconvex constraints into convex ones, we propose a tailored global optimization algorithm to solve the resulting MINLFP problem. We further present a case study on a 100 ha organic mixed crop-livestock farm with 19 types of crops, 22 types of crop products, 3 type of livestock, and 2 types of animal products to illustrate the applicability of the proposed model and solution methods. Computational results suggest that it is more profitable to produce more high value cash crops and milk; it is more water efficient to grow cash crops than fodder; and it generates more soil organic matter accumulation by growing more crops with larger amount of root stubble and enlarging the heard size.