基于小负荷换热单元保护的松弛策略优化换热网络

doi:10.19596/j.cnki.1001-246x.8392

摘要/Abstract

摘要：

WCE算法优化换热网络时，固定投资费用的存在易造成小负荷换热单元难以产生和保留，使部分尚未完全进化的结构过早被淘汰。本文建立一种固定投资费用的松弛处理方法，将固定投资费用与换热单元热负荷进行因变处理，根据换热单元热负荷的大小实时调整优化过程中的松弛力度，引导并促进小负荷换热单元的顺利产生和进化，从而增强换热网络的结构进化能力。将松弛策略应用于9SP和15SP算例，验证松弛策略促进结构进化的有效性，提升优化质量，获得的最优结果(2 903 528 ＄ ·a^-1、5 115 061 ＄ ·a^-1)优于文献结果。

关键词: 换热网络, 固定投资费用, 松弛, 小负荷换热单元, 热负荷

Abstract:

As RWCE algorithm is used to optimize heat exchanger networks, the existence of fixed investment cost makes it difficult to produce and retain heat exchanger units with small loads. It makes structures that have not yet fully evolved be eliminated too early. We established a relaxation method of fixed investment cost. The fixed investment cost and the heat exchange of heat exchange unit are processed according to their variation. With heat exchange of heat exchange unit, relaxation strength in optimization process is adjusted in real time to guide and promote the smooth generation and evolution of small load heat exchange unit, so as to enhance structural evolution ability of heat exchange network. The relaxation strategy is applied to 9SP and 15SP examples to verify that the relaxation strategy promotes structural evolution effectively and improves optimization quality. The optimal results (2 903 528 ＄ ·a^-1, 5 115 061 ＄ ·a^-1) are better than those in literatures.

Key words: heat exchanger network, fixed investment cost, slack, small load heat exchanger unit, heat load

张璐, 崔国民, 刘薇薇, 肖媛, 徐玥, 张冠华. 基于小负荷换热单元保护的松弛策略优化换热网络[J]. 计算物理, 2022, 39(3): 352-360.

Lu ZHANG, Guomin CUI, Weiwei LIU, Yuan XIAO, Yue XU, Guanhua ZHANG. Optimization of Heat Exchanger Network Based on Relaxation Strategy of Small Heat Exchanger Protection[J]. Chinese Journal of Computational Physics, 2022, 39(3): 352-360.

图/表 13

图1 节点非结构模型示意图(a) 节点设置；(b) 换热网络结构

Fig.1 Schematic diagrams of node unstructured model (a) node setting; (b) heat exchange network structure

表1 15SP算例换热单元生成情况统计

Table 1 Statistics of heat exchange unit generation in 15SP example

固定投资费用	有效换热单元数	换热单元生成总数	有效生成概率/%
C_F	37 068	3 003 670	1.2
0	70 159	2 765 376	2.5

图2 小负荷换热单元产生障碍原理图

Fig.2 A schematic of obstacles in small load heat exchange unit

图3 固定投资费用松弛曲线

Fig.3 Fixed investment cost relaxation curve

图4 优化过程中年综合费用变化(a) 不同ω的年综合费用; (b) 不同Qm的年综合费用

Fig.4 Variation of comprehensive cost in optimization process (a) with different ω, (b) with different Qm

图5 算例1最优结构

Fig.5 Optimal structure of Example 1

表2 算例1的最优结果

Table 2 Optimal results in Example 1

	换热单元数	热公用工程/kW	冷公用工程/kW	年综合费用/(＄·a^-1)
Ref.[14]	13	25 310	33 030	2.960×10⁶
Ref.[15]	12	25 090	32 810	2.936×10⁶
Ref.[16]	10	25 610	33 330	2.945×10⁶
Ref.[17]	16	23 350	31 070	2.943×10⁶
Ref.[18]	11	23 880	31 600	2.936×10⁶
Ref.[10]	14	23 878	31 597	2 926 788
Ref.[19]	17	24 656	32 376	2 926 485
Ref.[20]	18	23 770	31 490	2 924 117
Ref.[21]	15	23 994	31 714	2 922 515
本文	21	23 957	31 677	2 903 528

图6 优化过程中年综合费用、换热单元数变化(a) 年综合费用；(b) 换热单元数目

Fig.6 Variation of (a) comprehensive cost and (b) number of heat exchange units in optimization process

图7 采用两种不同算法的TAC

Fig.7 TAC with two algorithms

表3 算例2的最优结果

Table 3 Optimal results of Example 2

	换热单元数目	热公用工程/kW	冷公用工程/kW	年综合费用/(＄·a^-1)
Ref.[13]	24	41 349	59 219	6 019 310
Ref.[22]	29	43 280	61 150	5 613 283
Ref.[23]	26	27 380	45 250	5 233 287
Ref.[24]	26	27 223	45 068	5 169 883
图 8	23	27 418	45 229	5 155 770
图 9	24	26 500	44 311	5 115 061

图8 RWCE算法的最优结构

Fig.8 Optimal structure by the RWCE algorithm

图9 RWCE-PR算法的最优结构

Fig.9 Optimal structure by the RWCE-PR algorithm

图10 算例2优化过程中(a) TAC、(b) 换热单元数目变化(有分流)

Fig.10 Variation of (a) TAC and (b) number of heat exchange units (with split flow) in optimization process in Example 2

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