Compressor operation is determined by both indoor load and DC bus voltage. Fig. 2 shows a schematic diagram of the control logic of the compressor, Fig. 3 shows the speed adjustment of the compressor at the mode conversion and Table 1 shows the parameters of the compressor. During the normal operation stage, the compressor frequency was adjusted according to the indoor load to achieve the condition in which the cold generated by the compressor was level with the load. When the DC bus voltage fluctuated significantly in a short time, because the compressor stopped and restarted in a short time, the suction and exhaust pressure failed to immediately balance. The compressor withstood a large pressure difference to start. Improper control led to an overload or step loss, and the compressor could not be started. The frequency at start up was boosted by 2 Hz/s, and a wait period of at least 3 min allowed the compressor to heat up sufficiently while preventing lubricant in the compressor from flowing into the refrigeration system. During normal operation, frequency conversion was enabled according to the load change in the room. It was important to note the lower limit of frequency conversion. The fluctuation of speed in low frequency, which may increase vibration and stress in the piping, can shorten the compressor’s lifetime [22]. When the compressor received the shutdown command, it was necessary to first reduce the frequency at a rate of 2 Hz/s. When the voltage of the DC bus exceeded the safe working range, in order to avoid damage to the equipment and ensure safety in subsequent use, it was necessary to perform a rapid shutdown of the compressor.

The fan and compressor operating frequency is linked: when the indoor load is large, the compressor should increase the frequency to match the increased cooling capacity, while increasing the frequency of the fan; when the strong mode is turned on, the indoor air supply speed increases, and the frequency of fan and compressor also increases together. The specific control strategy is shown in Fig. 4. When the compressor frequency was low in normal working mode, the fan also maintained the minimum working frequency; when the user wanted to increase the air supply speed or cooling capacity, the compressor and fan frequency increased together until reaching the maximum working frequency.

The ice thermal storage system is used to transfer peak load and reduce cost in buildings, and its control strategy can greatly affect the economy of the system. Hajiah et al. [23,24] reported that the ice thermal storage (ITS) system can resolve both the peak-valley difference increasing and the mismatch problems due to the fact that the time of generation of cooling energy is separated from the time of its use. The ice thermal storage and control strategy is shown in Fig. 5. The ice storage period was 23:00 to 6:00. When the DC inverter heat pump set operated during the day, the ice storage system at night supplemented the load generated in the room during the period when the heat pump did not operate due to the DC bus voltage fluctuation, ensuring stability of the indoor temperature.

Liao et al. [25] summarized that traditional control strategies for heat pump system include: total cooling load-based sequencing control, return water temperature-based sequencing control, bypass flow-based sequencing control, and direct power-based sequencing control. The DC inverter heat pump control strategy in this paper was a load-based sequencing control, and the control flowchart is shown in Fig. 6. The input parameters include room temperature, bus voltage and air supply temperature. The corresponding compressor operation mode was selected after judging the bus voltage range. When the bus voltage was within 90%–105% of the rated voltage range, the equipment was able to operate normally according to its technical indicators and functions. When the DC bus voltage exceeded 90%–105% rated voltage range and was still within 80%–107% of the rated voltage range, the equipment could operate at reduced frequency. In other cases, the DC inverter heat pump set will stop the machine and the system will use the ice storage to supply cooling to the indoors. The heat pump set parameters used are shown in Table 2.

A dynamic model of a heat pump, which consisted of a compressor, a condenser, an electronic expansion valve and an evaporator, was built. The model assumed that the heat transfer process of each part of the heat pump was one-dimensional, stable and insulated. The four parts are as follows: 1)

Compressor

As the heart of the heat pump, the compressor provides power for the whole system. The relationship between refrigerant flow and the frequency of the compressor is obtained by fitting the relationship between refrigerant flow and compressor speed given by the manufacturer.

(1)m˙com=13.59fcom+53.52where f_com is the compressor frequency.

The input work of compressor can be calculated by [26]

(2)Wcom=mcom(hdis−hsuc)where h_suc is the specific enthalpy of the refrigerant at the compressor suction inlet; h_dis is the specific enthalpy of the refrigerant at the compressor discharge outlet, which can be obtained by

(3)hdis=hdis,is−hsucηis+hsucwhere h_dis is the ideal specific enthalpy of the refrigerant at the compressor discharge outlet under the isentropic compression condition; η_is is the isentropic efficiency of the compressor.

The refrigerating capacity of the DC variable frequency compressor used in the heat pump unit has a linear relationship with the speed; Eq. (4) shows that the power consumption also increases linearly. The refrigerating capacity of the compressor can be calculated by

(4)Q0=3.6[(hcom,suc−hcom,dis)/ν]Q1where h_suc is the specific enthalpy of the refrigerant at the compressor suction inlet; h_dis is the specific enthalpy of the refrigerant at the compressor discharge outlet; ν is the specific volume of gas at suction port of compressor; and Q₁ is the refrigerating capacity of compressor, which can be calculated by

(5)Q1=60ncomvcomwhere n_com is the speed of the compressor; and ν_com is the suction volume of the compressor. 2)

Condenser

The condenser is located at the high-temperature and high-pressure end of the heat pump system. In the condenser, the high-temperature and high-pressure refrigerant gas exchanges with the cooling water to release heat, and the gas refrigerant is condensed into liquid.

The heat exchange on the water side of the condenser can be written as

(6)Qw=cwmw(tcw,in−tcw,out)where c_w is the specific heat capacity of water at constant pressure; m_w is the mass flow of water, t_cw,in is the inlet temperature of cooling water; and t_cw,out is the outlet temperature of cooling water.

The heat exchange on the refrigerant side of the condenser can be calculated by

(7)Qrc=KcAcΔtc=mr(hcon,in−hcon,out)where K_c is the convective heat transfer coefficient at the condenser side; A_c is the total heat exchange area of the condenser; h_con,in is the specific enthalpy of refrigerant at condenser inlet; h_con,out is the specific enthalpy of the refrigerant at the condenser outlet; and Δt_c is the heat exchange temperature on the condenser side, which can be obtained by

(8)Δtc=tc−tcw,in+tcw,out2where t_c is the condensation temperature; t_cw,in is the inlet temperature of the cooling water; and t_cw,out is the outlet temperature of the cooling water.

The heat transfer balance on the condenser side can be written as

(9)Qw=Qrcwhere Q_w is the heat exchange on the water side of the condenser; and Q_rc is the heat exchange on the refrigerant side of the condenser. 3)

Expansion valve

The expansion process is considered to be isenthalpic, and thus the refrigerant mass flow rate across the expansion valve can be written as [27]

(10)mex=AexCex2ρex,in(Pex,in−Pex,out)where C_ev is the discharge coefficient of the expansion valve provided by the manufacturer; ρ_ev,in is the refrigerant density at the valve inlet, P_ev,in and P_ev,out are the inlet and outlet pressures of the expansion valve, respectively; and A_ev is the effective passage flow area of the expansion valve, which is [28]

(11)Aex=ϕexAex.nmwhere ϕ_ex is the opening degree of the expansion valve and ranges from 0% to 100%; and A_ex is the nominal orifice cross sectional area of the expansion valve. 4)

Evaporator

Modelling method involving the evaporator are similar to that of the condenser and therefore will not be described in detail in this paper.

The focus of the ice storage system was to address the insufficient cold supply of the heat pump unit caused by the voltage fluctuation of the DC bus with only two modes: the energy storage mode and the energy release mode. The model of the ice storage tank is

(12)Eis,t=Eis,t−1−Mis,t⋅Δt+ηis⋅Pis,t⋅Δtwhere E_is,t and M_is,t represent the ice storage capacity and melting volume of the ice storage system, respectively; η_is indicates the ice making efficiency of the ice storage system; and P_is,t is the output of ice maker at time.

According to the Law of Conservation of Energy, the total heat gain of indoor environment resulted from heat gain through building envelope, indoor occupants, and air-conditioning system can be calculated by Eq. (13).

(13)tout−tinr+Qhu−CaGs(tin−ts)−Mis,t=mFCadtindτwhere t_out is the outdoor temperature; t_in is the indoor temperature; C_a is the specific heat ratio of air; m_F is the air quality in the room; and Q_hu is heat brought by people. G_s is the air supply rate which can be calculated as

(14)Gs=π2D2⋅L⋅λ60ffan⋅(1−s)p⋅nwhere G_s is the air supply volume of the fan; D is the outer diameter of the impeller; L is the impeller length; λ is the area utilization of the fan; f_fan is the fan frequency; s is the speed difference; P means the number of motor poles and n expresses the speed of fan.

The control block diagram of the DC inverter heat pump with DC bus voltage as input is shown in Fig. 7. The control system adopted a dual-loop proportional-integral (PI) control structure, in which the outer loop controller was responsible for generating power reference values while the inner loop controller was responsible for generating inverter frequency commands. T_set represents the set temperature of the room, V_ref represents the nominal value of the DC bus voltage, V_m is the difference between the measured value of the DC bus voltage, and V_m and V_ref was input into the outer loop PI controller to generate the reference power value P_ref. The difference between the P_ref and the measured power P of the unit was input into the inner loop controller, and the frequency command was generated and input into the inverter, which outputs AC waves to change the power of the compressor.

As shown in Fig. 8, the DC inverter heat pump simulation model can be established by modelling the four parts described above.

In order to validate the simulation model of the DC inverter heat pump, experiments of a real heat pump system were carried out. The cooling capacity of the heat pump was set up as rated value and remained stable, while the DC bus voltage was varied at different stages as shown in Fig. 9. The simulation results and experimental data of effective current, outlet temperature of cooling water and chilling water were compared in Figs. 10 and 11. The average values of differences between the simulation results and the experimental data of effective current, outlet temperature of cooling water and chilling water were 4.4%, 0.2% and 0.02%, respectively, which indicated the models were justifiable.

Table 3 shows the simulation model operating conditions settings, including system refrigeration/heating conditions, simulation time, room control temperature input values, bus voltage range and corresponding compressor operating mode. According to the output of the simulation model of the DC inverter heat pump, the rationale of the control strategy could be explained by analysing the changes in compressor frequency and room temperature corresponding to the change in bus voltage.

Figs. 12 and 13 show the results of the simulation using condition 1 (refrigeration mode) and condition 2 (refrigeration mode). The settings are presented in Table 3. When the bus voltage was between 80% and 107%, the units functioned normally, in most cases allowing a small range of over the limit operation. However, if the bus voltage fluctuations were too severe, the ice storage module began cooling. As shown in Fig. 12a, the compressor using this control strategy worked normally and the frequency was generally constant when the bus voltage was in the range of 90%–105%. Fig. 13b shows that when the bus voltage was within the range of 80%–90% or 105%–107%, the compressor passively reduced the frequency due to the fluctuation of the bus voltage, the refrigeration capacity decreased, and the maximum frequency of the compressor decreased by 2.7%.

Fig. 14 shows the results of the simulation using condition 3 (refrigeration mode) using the settings in Table 3, when the bus voltage was less than 80% and more than 107%, and was no longer suitable for long term operation of the heat pump. The results show that the compressor stopped working because the bus voltage was much lower or higher than normal, and the required cooling capacity was provided through the energy storage system.

Fig. 15 shows the results of the simulation using the energy saving mode and operating condition 4 (refrigeration mode), using the settings shown in Table 3. In the energy saving mode, the bus voltage was 80%–90%, which was slightly lower than that of the normal working range of the system. With condition 4 (similar to with condition 2), the instantaneous cooling output of the compressor was reduced by 2.7%, the room temperature was stable, and the ice storage module of the system played its role in transferring the cooling power to the room.

Figs. 16 and 17 show the results of the simulation using condition 5 (heating mode) and condition 6. The settings are shown in Table 3. When the bus voltage was between 80% and 107%, the system took 30 min to reach the set temperature, after which the unit was able to ensure the stability of the indoor temperature. The maximum compressor frequency decreased by 3.3%. Fig. 17b shows results were the same using conditions 2 and 4.

The fluctuations in frequency and indoor temperature were within a reasonable range. This control strategy completed the indoor load control task under conditions with fluctuating bus voltage, offering stable and energy saving operations when the bus voltage supply was insufficient.