懲罰函數法應用於空調系統之最佳化控制

Penalty Function Method for The Optimum Control of Air-Conditioning System

黃啟泰(Kai-Tai Wong)

指導教授 ： 陳希立

國立臺灣大學/工學院/機械工程學研究所/碩士(2006年)

https://doi.org/10.6342/NTU.2006.00745

摘要

本篇論文應用懲罰函數法(Penalty Function Method)對多台離心式冰水主機之負載作最佳化分配，根據各主機不同的性能，在滿足空調負荷的條件下，最佳化主機群組之負載分配，使系統所耗用的能源最小化。在多台主機的系統中，實際運轉時每台主機的效能都不一樣，利用懲罰函數法此種最佳化方法可將系統負載依個別主機之性能作最佳化的分配，使每台主機均處於最佳狀況下運轉，進而達到節省能源的目的。而且考慮到冰水主機有其特定之操作範圍限制，通過懲罰函數法控制主機在最佳的範圍下操作，超出操作範圍則設定為關機，保證上線運轉的每台冰水主機均處於最佳化之狀態下操作。此外，將懲罰函數法結果與平均負載法及拉氏乘數法之結果作比較，並透過各冰水主機之負載率、耗電量等參數之分析，探討各種最佳化方法之間的優缺點。計算結果顯示，在高負載區，以懲罰函數法之總耗電量最低，跟平均負載法之結果相比，最多可節省9.57%之總耗電量；而跟拉氏乘數法相比，亦可節省4.05%的耗電量。在系統低負載時，相比於平均負載法甚至能節省多達63.83%之耗電量。
一個全面的空調系統控制策略在考慮主機負載分配最佳化的同時，必須考慮到冷卻水塔性能對主機之影響，冷卻水之溫度及冷卻水塔之空氣流量均會影響主機之耗電量。本文利用由懲罰函數法所得之最佳主機負載分配，配合冷卻水塔的變頻控制，找出冷卻水之最佳水溫及冷卻水塔風扇之最佳轉速，以節省冰水主機及冷卻水塔之耗能。結果顯示，同樣使用懲罰函數法作為主機之負載分配法，搭配變頻式之冷卻水塔，跟定轉速之冷卻水塔之系統相比，可進一步節省約2%之總耗電量。

關鍵字

懲罰函數法 ； 空調系統 ； 冰水主機 ； 最佳化

並列摘要

This dissertation applied Penalty Function Method (PFM) to determine the optimal control of multiple centrifugal chillers. In multiple chiller system, chillers have different performance during the actual operation. According to each chiller performance, PFM is used to determine the optimal chiller load distribution to minimize the input power and satisfy the cooling demand. The applying of PFM controls the on-line chillers to operate at high efficiency and turn off the inefficient chillers to reduce the energy consumption. The optimal chiller load distribution by using PFM are compared with the equal load distribution (ELD) and Lagrange multiplier method (LGM) to show the feature of this method. The results show that the PFM can save 9.57% total power compared with ELD and also have 4.05% power save compared with LGM at high system cooling load. At the low system cooling load, PFM saved 63.83% total power consumption of multiple centrifugal chiller system.
In addition, a total solution of multiple chiller system control can be considered the influence of cooling tower. The power consumption of a chiller is sensitive to the condensing water temperature, which affected by the cooling tower air flow rates. This study using the optimal chiller load distribution by using PFM and the speed control of cooling tower fan, to optimize the condenser water temperature and tower air flow and reduced the power consumption of chillers and towers. The results shows the application of variable speed driven cooling tower can save about 2% total power compared with constant speed driven tower.

並列關鍵字

penalty function method ； Chiller ； optimum ； air conditioning ； optimum control

參考文獻

10. Edwin K.P. Chong, and Stanislaw H.Zak, 1996, An Introduction to Optimization, John Wiley & Sons, Inc.

11. Jasbir S. Arora, 1989, Introduction to Optimum Design, McGraw-Hill Book Company.

14. Karush, W., 1939. Minimum of Functions of Several Variables with Inequalities as Side Conditions, MS Thesis, Dept. of Mathematics, University of Chicago, Chicago, Illinois.

15. Kuhn, H. W., and Tucker, A. W., 1951. “Nonlinear Programming.” In Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (J. Neyman ed.). University of California Press, Berkeley, California.

1. Air-Conditioning and Refrigeration Institute, ARI, 1998, ARI Standard 550/590-1998.