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

Federica Acerbi,Giuseppe De Nicolao,Mirco Rampazzo

doi:10.3390/en13236372

Federica Acerbi, Giuseppe De Nicolao + Show 1 more

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https://doi.org/10.3390/en13236372

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Journal: Energies	Publication Date: Dec 2, 2020
Citations: 8	License type: CC BY 4.0

Affiliation: University of Pavia, University of Padua

Abstract

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.

Highlights

Heating, ventilation and air-conditioning (HVAC) systems typically utilize a large percentage of the total building energy consumption, amounting to approximately 25–30% for dwellings [1]and up to more than 50% in industries relying on clean-rooms [2]
The partition of the solution set in the 4n subsets S j, j = 1, . . . 4n allows one to divide the mixed-integer nonlinear program (MINLP)
The solution of the QP( j) problem is reduced to the solution of an equality-constrained quadratic problems (EQP)( j) problem that admits a unique critical point, computable in closed form

Summary

Introduction

Ventilation and air-conditioning (HVAC) systems typically utilize a large percentage of the total building energy consumption, amounting to approximately 25–30% for dwellings [1]and up to more than 50% in industries relying on clean-rooms [2]. Between 40% and 60% of this requirement is due to chillers, which are responsible for a significant fraction of total energy use. Such numbers indicate that the efficiency of HVAC systems is closely dependent on the efficiency of the chiller unit. Since a multiple chiller system typically employs machines, there are usually several combinations of chillers’ part loads that are able to satisfy the load demand. The problem of determining the load fraction that each chiller has to deliver in order to minimize the system power consumption is known as optimal chiller loading (OCL) problem. Chang et al [3] assume that the chillers’

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