Model development and software implementation for predicting APF of multi-split air conditioning system

doi:10.11949/0438-1157.20241177

Abstract

Abstract:

The energy efficiency evaluation index of multi-split air conditioner (VRF) system has been converted into the annual performance factor (APF). To improve the APF performance of VRF system, it is necessary to improve the design efficiency through computer simulation. Based on the component models and solving method of VRF system, this article proposes a correction method for low-temperature heating under unsteady conditions, using factors such as compressor frequency and indoor and outdoor fan wind speed to correct system performance parameters, and obtain the average value of system performance during the defrosting cycle. Based on modular framework design, a multi-split air conditioner APF performance simulation software has been developed. The accuracy of the software has been verified through experimental data, and the prediction errors of the software for the system capacity and power of a single APF condition are within 7%, and the prediction errors for the overall APF of the system are within 5%. The results show that the multi-split air conditioning system APF performance simulation software developed in this article has good accuracy and can meet the needs of system optimization.

Key words: VRF-system, annual performance factor, steady-state, computer simulation

摘要：

多联机的能效评价指标已转换为全年性能系数（annual performance factor，APF）。实现多联机APF性能的提升，需要通过计算机仿真以提高设计效率。基于多联机的部件模型和求解方法，提出针对低温制热非稳态工况的修正方法，使用压缩机频率和室内外风机风速等因素对系统性能参数进行修正，获取除霜周期内系统性能的平均值，基于模块化的框架设计开发了多联机的APF性能仿真软件。通过实验数据对软件精度进行验证，软件对于APF单个工况的系统能力和功率的预测误差均在7%以内，对于系统总体APF的预测误差均在5%以内。结果表明，开发的多联机APF性能仿真软件具有良好的精度，能够满足系统优化的需要。

关键词: 多联机, APF, 稳态, 计算机模拟

CLC Number:

TB 657.2

Senqing ZHUO, Hua CHEN, Wei CHEN, Bin SHANG, Hengheng LIU, Tangtang GU, Wei BAI, Longyan WANG, Haomin CAO, Guoliang DING. Model development and software implementation for predicting APF of multi-split air conditioning system[J]. CIESC Journal, 2025, 76(S1): 370-376.

卓森庆, 陈华, 陈伟, 尚彬, 刘恒恒, 古汤汤, 白韡, 王龙炎, 曹昊敏, 丁国良. 多联式空调系统APF性能仿真的模型开发与软件实现[J]. 化工学报, 2025, 76(S1): 370-376.

Figures/Tables 9

Fig.1 Schematic diagram of multi-split air conditioning system

Table 1 Multi-split air conditioner component model

部件	模型类型	公式
变频压缩机	半经验模型^[17]	制冷剂流量： $m ˙ c o m p = V d i s p ρ s u c a 0 + a 1 F + a 2 P d i s P s u c + a 3 F P d i s P s u c$
变频压缩机	半经验模型^[17]	输入功率： $W ˙ c o m p = m ˙ c o m p P s u c ρ s u c × κ κ - 1 P d i s P s u c κ - 1 κ - 1 b 0 + b 1 P s u c + b 2 P d i s + b 3$
电子膨胀阀	半经验模型^[18]	制冷剂流量： $m ˙ E E V = C v A m a x 2 ρ i n Δ p c 0 + c 1 p l s p l s m a x + c 2 p l s p l s m a x 2$
换热器	分相模型^[19]	传热： $Q r = ∑ j = 1 N m ˙ r h r, j, i n - h r, j, o u t = ∑ j = 1 N α r, j A r, j T r, j - T w, j$ $Q a = m ˙ a h a, i n - h a, o u t = α a A a T a - T w$ $Q r = Q a$
		压降： $Δ P t o t = Δ P f + Δ P a c c$
		制冷剂质量： $M = ∫ ρ A t u b e d L$
连接管	关联式^[20]	单相流动： $Δ P = f L ρ u 2 / 2 D$
		两相流动： $Δ P = Φ f L ρ u 2 / 2 D$
		制冷剂质量： $M = ∫ ρ A t u b e d L$

Table 1 Multi-split air conditioner component model

部件	模型类型	公式
变频压缩机	半经验模型^[17]	制冷剂流量： $m ˙ c o m p = V d i s p ρ s u c a 0 + a 1 F + a 2 P d i s P s u c + a 3 F P d i s P s u c$
变频压缩机	半经验模型^[17]	输入功率： $W ˙ c o m p = m ˙ c o m p P s u c ρ s u c × κ κ - 1 P d i s P s u c κ - 1 κ - 1 b 0 + b 1 P s u c + b 2 P d i s + b 3$
电子膨胀阀	半经验模型^[18]	制冷剂流量： $m ˙ E E V = C v A m a x 2 ρ i n Δ p c 0 + c 1 p l s p l s m a x + c 2 p l s p l s m a x 2$
换热器	分相模型^[19]	传热： $Q r = ∑ j = 1 N m ˙ r h r, j, i n - h r, j, o u t = ∑ j = 1 N α r, j A r, j T r, j - T w, j$ $Q a = m ˙ a h a, i n - h a, o u t = α a A a T a - T w$ $Q r = Q a$
		压降： $Δ P t o t = Δ P f + Δ P a c c$
		制冷剂质量： $M = ∫ ρ A t u b e d L$
连接管	关联式^[20]	单相流动： $Δ P = f L ρ u 2 / 2 D$
		两相流动： $Δ P = Φ f L ρ u 2 / 2 D$
		制冷剂质量： $M = ∫ ρ A t u b e d L$

Fig.2 Schematic diagram of low temperature heating and defrosting cycle

Fig.3 Multi-split air conditioner system APF performance simulation software framework

Fig.4 Main interface of multi-split air conditioner system APF performance simulation software

Table 2 APF test control parameters for each operating condition

工况		额定制冷	中间制冷	最小制冷	额定制热	中间制热	最小制热	低温制热
室外侧控制参数	压缩机频率/Hz	68	25	15	77	41	22	92
	空气干球/湿球温度/℃	35/24	35/24	35/24	7/6	7/6	7/6	2/1
	风机转速/(r/mim)	900	705	495	900	645	600	900
	电子膨胀阀开度	480	480	480	155	90	75	142
室内侧控制参数	空气干球/湿球温度/℃	27/19	27/19	27/19	20/15	20/15	20/15	20/15
	风量/(m³/h)	4491	4443	3066	3613	3971	4038	2958
	电子膨胀阀#1开度	99	60	60	480	480	480	401
	电子膨胀阀#2开度	112	60	60	480	480	480	408
	电子膨胀阀#3开度	110	60	60	480	480	480	427
	电子膨胀阀#4开度	159	60	0	480	480	70	419

Table 3 Comparison of system performance for standard cooling and standard heating conditions

标准制冷工况	参数	额定制冷			中间制冷			最小制冷
	参数	实验值	仿真值	误差	实验值	仿真值	误差	实验值	仿真值	误差
	制冷量/W	15931	16160	1.44%	7637	7895	3.38%	5660	5793	2.34%
	功率/W	4493	4563	1.56%	1503	1597	6.25%	1222	1271	4.02%
标准制热工况	参数	额定制热			中间制热			最小制热
	参数	实验值	仿真值	误差	实验值	仿真值	误差	实验值	仿真值	误差
	制热量/W	17353	17669	1.82%	8925	8665	-2.91%	6081	6213	2.17%
	功率/W	4905	4834	-1.44%	2016	1909	-5.30%	1286	1237	-3.81%

Table 4 Comparison of system performance for low temperature heating conditions

参数	低温制热最大值		低温制热周期平均值
参数	实验值	仿真值	实验值	修正后	误差
制热量/W	19171	18688	13780	13433	-2.52%
功率/W	6557	6690	5384	5493	2.03%

Table 5 Comparison of system energy efficiency simulation results and experimental values

参数	标准制冷			标准制热			低温制热（周期平均）	APF
参数	额定制冷	中间制冷	最小制冷	额定制热	中间制热	最小制热	低温制热（周期平均）	APF
误差	-0.12%	-2.70%	-1.61%	3.31%	2.52%	6.22%	-4.46%	-1.64%
能效实验值	3.55	5.08	4.63	3.54	4.43	4.73	2.56	4.26
能效仿真值	3.54	4.94	4.56	3.66	4.54	5.02	2.45	4.19

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