An improved dynamic real time optimization strategy for heat pump heating system

doi:10.11949/j.issn.0438-1157.20180629

Abstract

Abstract:

The dynamic optimization operation of heat pump heating based on economic goals is of great significance, but the uncertainty of the change of ambient temperature and model parameters in the operating interval will bring great challenges to the actual optimization and control. In this work, based on well-established model of heat pump heating system with more detailed consideration, an improved dynamic optimal control strategy was proposed to improve the practical energy cost saving of the system. Firstly, the nonlinear dynamic model of the heat pump heating system was established and a dynamic real time optimization (D-RTO) problem was formulated with a comprehensive objective function to be minimized, the frequencies of compressor and water pump were used as manipulating variables for the control purpose. Then, with initially predicted ambient temperature in the future 24 h, the optimal frequency trajectories of the compressor and water pump were obtained through solving the optimization problem, and the system was controlled based on the optimal trajectories of present time. And then, at the next time point, based on the update of ambient temperature prediction and on line model correction, the optimal control trajectories were updated by solving the optimization problem and were executed again. The operation was repeated until the 24th hour is reached. Computing results of case study show that the proposed method can further improve the practical cost saving for the heat pump heating system, and can realize the requirement of terminal state constraint at the same time. This study has practical significance for the dynamic real time optimization of chemical processes with periodic and uncertain operating parameters.

Key words: dynamic, real time optimization, optimal control, prediction, heat pump

摘要：

基于经济性目标的热泵供暖动态优化操作具有重要意义，但在操作区间内环境温度和模型参数变化的不确定性会对实际优化操控带来很大挑战。在完善热泵供暖系统模型的基础上，提出了一种改进的动态实时优化控制策略以改善系统的实际节能效果。该方法首先建立以压缩机和送水泵运行频率为控制变量的热泵供暖系统的非线性动态关系模型，并得到以24 h为周期、以综合性能指标最低为目标的动态实时优化命题。然后，在给定24 h环境温度预测情况下通过求解该优化命题得到热泵压缩机和送水泵的最优运行频率轨线，并以当前时间点的最优控制量对热泵供暖系统进行控制；接着，基于天气逐时预测和模型参数最新校验结果对环境温度轨线或者模型参数进行更新，不断地求解原优化命题以更新最优控制轨线，并不断地采用当前点的最优控制量对热泵供暖系统进行控制，直到当前时间点达到第24 h。实例计算结果表明：采用本文提出的方法可以进一步改善热泵供暖系统的动态优化操控效果，并能够很好地满足给定终端约束要求。本方法对于具有周期性和不确定参数的动态实时优化问题求解具有一定的借鉴意义。

关键词: 动态, 实时优化, 优化控制, 预测, 热泵

CLC Number:

TP 202.7

Aipeng JIANG, Quannan ZHANG, Haokun WANG, Qiang DING, Weifeng XU, Jian WANG. An improved dynamic real time optimization strategy for heat pump heating system[J]. CIESC Journal, 2019, 70(4): 1494-1504.

江爱朋, 张全南, 王浩坤, 丁强, 徐炜峰, 王剑. 一种改进的热泵供暖系统动态实时优化策略[J]. 化工学报, 2019, 70(4): 1494-1504.

Figures/Tables 28

Fig.1 Schematic diagram of heat pump heating system

Fig.2 Diagram of dynamic real time optimal of the system

Fig.3 Time-of-use (TOU) of electricity price

Fig.4 Predicted and final ambient temperature in 24 h

Table 1 Parameter values of the model

Item	Value	Item	Value
C_w,s /(J/K)	1.19×10⁶	$κ w f$ / (W/(m²·K))	19.16
C_w,r /(J/K)	5.36×10⁴	A_wz /m²	600
C_f /(J/K)	4.56×10⁵	$κ f z$ / (W/(m²·K))	408
C_b /(J/K)	2.26×10⁶	$κ b$ /(W/(m²·K))	0.62
$m . w$ /(kg/s)	2.6	A_fz /m²	1500
$κ w z$ /(W/(m²·K))	25	A_b /m²	2800

Table 1 Parameter values of the model

Item	Value	Item	Value
C_w,s /(J/K)	1.19×10⁶	$κ w f$ / (W/(m²·K))	19.16
C_w,r /(J/K)	5.36×10⁴	A_wz /m²	600
C_f /(J/K)	4.56×10⁵	$κ f z$ / (W/(m²·K))	408
C_b /(J/K)	2.26×10⁶	$κ b$ /(W/(m²·K))	0.62
$m . w$ /(kg/s)	2.6	A_fz /m²	1500
$κ w z$ /(W/(m²·K))	25	A_b /m²	2800

Table 2 Solution results with different cases

Case

Objective

Discomfort

Heat pump

cost /CNY

Water pump

cost/CNY

TT(0)=

TT(24)

Fig.5 Profile of heat pump power consumption in 24 h

Fig.6 Profile of water pump flowrate in 24 h

Fig.7 Profile of heat pump frequency in 24 h

Fig.8 Profile of Tws in 24 h

Fig.9 Profile of Twr in 24 h

Fig.10 Profile of Tf in 24 h

Fig.11 Profile of Tz in 24 h

Fig.12 Profile of heat pump power with COP change

Fig.13 Profile of heat pump frequency with COP change

Fig.14 Profile of water pump flowrate with COP change

Fig.15 Profile of water pump frequency with COP change

Table 3 Solution results with different COP

Case	Objective	Discomfort	Heat pump cost /CNY	Water pump cost/CNY	TT(0)=TT(24)
Case 2	141.85	1.929	255.060	26.707	yes
Case 4	155.97	2.351	281.604	27.988	yes

Fig.16 Profile of ambient temperature at different time

Table 4 Solution results at different time points

Time point	Objective	Discomfort	Heat pump cost /CNY	Water pump cost/CNY	TT(0)=TT(24)
0 h	141.85	1.929	255.060	26.707	yes
6 h	139.40	2.331	250.074	26.412	yes
12 h	134.81	2.462	241.19	25.974	yes
18 h	129.91	2.344	231.783	25.692	yes
24 h	125.99	2.430	223.923	25.641	yes

Fig.17 Profile of heat pump power at different time

Fig.18 Profile of water pump flowrate at different time

Fig.19 Profile of heat pump frequency at different time

Fig.20 Profile of water pump frequency at different time

Fig.21 Profile of Tws at different time

Fig.22 Profile of Tz at different time

Fig.23 Profile of optimal water pump flowrate at the 20th hour

Fig.24 Profile of optimal heat pump power at the 20th hour

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