基於Gordon-Ng熱力學模型之冰水機組操作最佳化解析解

An Analytical Solution to the Optimal Chillers Operation Problem Based on Gordon-Ng Thermodynamic Model

許芙瑄(Fu-Hsuan Hsu)

指導教授 ： 劉佩玲

國立臺灣大學/工學院/應用力學研究所/碩士(2022年)

https://doi.org/10.6342/NTU202203356

摘要

台灣缺少自產能源，高度仰賴能源進口，因此提高能源效率為重要議題。而根據統計，辦公大樓空調耗電約占整體耗電的51%，其中又以冰水機耗電占空調耗電之大宗，因此找出冰水機的最佳操作方法可有效減少冰水機的耗電。冰水機的操作優化可以由開機排序與負載分配著手，本研究之目的即在建立一個同時考慮開機排序與負載分配之冰水機最佳操作方法。
冰水機操作最佳化問題之目標函數為冰水機總耗電量，冰水機之負載總和需等於該時段之冷卻負載，且冰水機之負載不得超出其上、下限，冰水機的開關還受到最短運行時間與最短停機時間的限制。本研究以Gordon-Ng熱力學模型預測各冰水機之能耗，從此模型各冰水機之耗能為其冷卻負載之二次函數且與冷卻水進水溫度與冰水出水溫度相關。本研究先將時間分段，將動態最佳化問題分解成多個靜態問題，再對每個靜態問題進行最佳負載求解。
在靜態最佳化問題中，冰水機負載上、下限限制形成一多維長方體，冰水機負載總和限制形成一多維平面，兩者之交集為一凸多邊形，即為最佳化問題之解空間。總耗電量的等高面可藉由正規化由楕球轉變為圓球，再計算等高圓球與解空間之切點，若切點落在解空間中則為最佳解，反之則最佳解必須落在解空間的邊界上。在邊界上，有某個冰水機負載取上限或下限值，故在邊界上的變數維度降一維，再以前述的求解過程在降維空間中求解。此降維求解程序可一直重複，一直到找到最佳解。若排序也同時要最佳化，須將可能之排序逐一列出，依照上述方法分別求出各別排序的最佳負載，經比較後找出耗電最小者，即可找出最佳排序與最佳負載，與傳統迭代不同，此方法可快速找到最佳化解析解。
本研究以臺北市政府大樓與A科技公司之歷史數據建立各冰水機之耗能模型，發現本研究之Gordon-Ng熱力學模型確實優於Gordon-Ng簡單模型及二次迴歸模型，對能耗預測之誤差較低。最佳化之結果顯示本研究之最佳化方法能有效降低冰水機群耗電量，即使增加冰水機組之停啟時間，仍有顯著的節能率，此外，提高冰水出水溫度也可增加節能率。

關鍵字

Gordon-Ng熱力學模型 ； 最佳排序 ； 最佳負載 ； 節能率 ； HVAC ； 冰水機群

並列摘要

Taiwan has insufficient primary energy and relies on imported sources; therefore, improving energy efficiency is crucial. According to statistics, power consumption of heating, ventilation, and air conditioning (HVAC) systems totals up to approximately 51% within office buildings, among which chillers consume the most significant fraction of power. Therefore, optimizing chiller operation can help reduce HVAC power consumption. As such, this study develops to establish a method for optimizing chiller operation, including chiller load distribution and sequencing.
In this study, a constrained optimization problem is constructed with the total power consumption of chillers as the objective function. Every chiller load ratio contains lower and upper bounds, the summation of the cooling loads must equate to cooling demand, and each chiller must run according to minimal uptime (MUT) and downtime (MDT) limitations. The Gordon-Ng thermodynamic model is adopted to estimate chiller efficiency. Based on Gordon-Ng thermodynamic model, the power consumption is a quadratic function of the cooling loads and is related to condenser water inlet and evaporator water outlet temperatures.
In this study, the dynamic optimal chiller loading problem is firstly decomposed into a sequence of static problems. In the static optimization problem, the upper and lower bounds of chiller loadings form a hyperrectangle, and the cooling demand constraint constructs a hyperplane in the chiller loading space. Their intersection constitutes the solution, which is a convex polytope. The chiller loadings can be normalized so that the total power consumption contours become spheres. If the tangent point between the contour spheres and the hyperplane falls in the solution space, it is the optimal solution. Otherwise, the optimal solution must fall on the boundary of the solution space, i.e., the facets of the polytope. On each facet of the polytope, one chiller loading takes its upper or lower limit value. Thus, the number of variables is reduced by one to find the optimal solution for each facet. One can repeat the solution procedure above in the reduced-dimension space for each facet. Further dimensionality reduction and optimization may be needed until one finds the optimal solution.
If the chiller sequence also needed to be optimized, one could determine the optimal load distributions for all admissible active chiller combinations and compare their respective power consumptions. Notice that the active chiller combinations must satisfy MDT and MUT constraints. The combination requiring minimal energy consumption gives the optimal chiller sequence. The optimal chiller sequence and the optimal load distribution together yield the optimal chiller operation. Unlike conventional methods, which require iterative solutions, the method developed in this research could quickly attain an analytical solution.
This study used historical data from Taipei City Hall's HVAC system and a technology company's HVAC system to verify the proposed solution. The Gordon-Ng thermodynamic model surpasses the Gordon-Ng simple model or the quadratic regression model in terms of the prediction error of energy consumption. The results showed that the proposed method was influential in reducing power consumption. Even with increased MDT and MUT, energy saving was still significant. In addition, increasing the temperature of the chilled water discharge could also increase the energy saving rate.

並列關鍵字

Gordon-Ng model ； optimal chiller loading ； optimal chiller sequencing ； HVAC ； energy saving ； multiple chillers

參考文獻

[1] 經濟部能源局, 2021, 能源統計手冊.

[2] 台灣綠色生產力基金會, 2019, "2019非生產性質行業能源查核年報."

[3] Gordon, J. M., Ng, K. C., and Chua, H. T., 1995, "Centrifugal Chillers - Thermodynamic Modeling and a Diagnostic Case-Study," Int J Refrig, 18(4), pp. 253-257.

[4] ASHRAE Guideline 14, 2014, "Measurement of Energy, Demand, and Water Savings."

[5] Hackner, R. J., 1984, "HVAC system dynamics and energy use in existing buildings,"Master Thesis, University of Wisconsin–Madison.