An Exact Algorithm for the Optimal Chiller Loading Problem and Its Application to the Optimal Chiller Sequencing Problem

The optimal management of multiple chiller systems calls for the solution of the so-called optimal chiller loading (OCL) problem. Due to the interplay of continuous and logical constraints, OCL is an NP-hard problem, so that a variety of heuristic algorithms have been proposed in the literature. Herein, an algorithm for its exact solution, named X-OCL, is developed under the assumption that the chillers' power consumption curves are quadratic. The proposed method hinges on a decomposition of the solution space so that the overall OCL problem is decomposed to a set of equality constrained quadratic programming problems that can be solved in closed form. By applying the new X-OCL solver to well known case studies, we assess and compare the performances of several literature algorithms, highlighting also some errors in the published results. Moreover, X-OCL is used to design a greedy optimal chiller sequencing (OCS) solver, called X-OCS. The X-OCS is tested on two literature benchmarks and on the model of the heating, ventilation and air-conditioning (HVAC) system of a semiconductor plant, over a two-year period. The performances of X-OCS are remarkably close to the theoretical optimal performance.