Electro-Thermal Transient Characteristics of Photovoltaic–Thermal (PV/T)–Heat Pump System

Abstract

This study investigates the electro-thermal transient response of a photovoltaic–thermal (PV/T)–heat pump system under dynamic disturbances to optimize operational stability. A dynamic model integrating a PV/T collector and a heat pump was developed by the transient heat current method, enabling high-fidelity simulations of step perturbations: solar irradiance reduction, compressor operation, condenser water flow rate variations, and thermal storage tank volume changes. This study highlights the thermal storage tank’s critical role. For V_tank = 2 m³, water tank volume significantly suppresses the water tank and PV/T collector temperature fluctuations caused by solar irradiance reduction. PV/T collector temperature fluctuation suppression improved by 46.7%. For the PV/T heat pump system in this study, the water tank volume was selected between 1 and 1.5 m³ to optimize the balance of thermal inertia and cost. Despite PV cell electrical efficiency gains from PV cell temperature reductions caused by solar irradiance reduction, power recovery remains limited. Compressor dynamic performance exhibits asymmetry: the hot water temperature drop caused by speed reduction exceeds the rise from speed increase. Load fluctuations reveal heightened risk: load reduction triggers a hot water 7.6 °C decline versus a 2.2 °C gain under equivalent load increases. Meanwhile, water flow rate variation in condenser identifies electro-thermal time lags (100 s thermal and 50 s electrical stabilization), necessitating predictive compressor control to prevent temperature and compressor operation oscillations caused by system condition changes. These findings advance hybrid renewable systems by resolving transient coupling mechanisms and enhancing operational resilience, offering actionable strategies for PV/T–heat pump deployment in building energy applications.

1. Introduction

The International Energy Agency (IEA) recently emphasized the critical need to promote heat pump implementation in multifamily buildings, given their significant potential to reduce greenhouse gas (GHG) emissions [1]. However, in China, most existing heating and domestic hot water (DHW) systems rely on combustion of fossil fuel, which results in low energy efficiency and substantial GHG emissions [2]. Apart from the heat pump technology, solar energy also holds promising prospects for decarbonizing building operations as a green and renewable energy source. However, conventional solar thermal systems face limitations in daily hot water output due to their dependence on solar irradiance input [3]. Heat pumps, which transfer thermal energy from low-temperature heat source to high-temperature heat sink by utilizing mechanical work, offer an efficient solution for DHW and space heating (SH) in residential settings. Synergistically integrating these technologies, the PV/T–heat pump system converts waste heat from PV/T collectors into high-temperature thermal energy for building services while partially powering the heat pump compressor through PV-generated electricity. This hybrid configuration demonstrates superior energy efficiency and annual cost effectiveness compared to that of standalone systems, presenting significant potential for concurrent electricity and thermal energy generation [4].

Solar photovoltaic–thermal (PV/T) collectors, like most solar energy technologies, exhibit inherently operational transient [5]. The equipment rarely achieves steady-state conditions due to dynamic environmental factors such as solar irradiance. Hence, reliable prediction of PV/T collector dynamics is paramount. This capability is fundamental for designing failure-resistant systems, circumventing operational breakdowns, and refining parameters to boost thermoelectric output efficiency [6].

For simulation research of PV/T collectors, researchers have developed various numerical models at different levels. Simulation methods employed in the dynamic modeling of photovoltaic–thermal (PV/T) systems encompass lumped-parameter and both two-dimensional (2D) and three-dimensional (3D) discretized numerical schemes. A novel PV/T collector model was proposed by Zarrella et al. [7]. The lumped parameter model adopts a one-dimensional discretized approach that incorporates the thermal capacitance of individual components. For analyzing internal temperature distribution, including the flat surface and the fluid flow path, researchers have widely adopted two-dimensional discretized approaches utilizing the finite volume method (FVM). To enhance simulation accuracy, some studies [8,9,10] have integrated FVM with computational fluid dynamics (CFD). While these models offer high physical fidelity, they demand substantial computational resources. This computational burden can impede system optimization efforts and the practical implementation of control strategies. In the research of Chen et al. [11], thermal resistance in steady-state heat exchangers is redefined, incorporating considerations of heat transfer irreversibility and employing a heat current model based on the electrical analogy principle. Extending this work, He et al. [12] derived transient thermal resistance and capacitance parameters to reconstruct a dynamic heat exchanger model. While the prevailing PV/T research predominantly relies on thermoelectric analogies to construct simplified equivalent circuit models, the present study introduces the heat flow method. This approach enables the formulation of linearized heat transfer equations without traditional simplifications and facilitates establishing topological network relationships for multiple PV/T collectors under various interconnection configurations.

Direct greenhouse gas (GHG) emissions are absent during the residential use of electrically powered heat pumps. Coupled with renewable sources like photovoltaic (PV) systems to meet most of their power requirements, these units constitute a fundamentally low-carbon heating technology, even when accounting for upstream energy generation impacts [13]. This synergy has driven increasing scholarly attention toward integrating PV/T and heat pump technology to simultaneously address electrical and thermal energy demands while minimizing carbon footprints. Recent research on PV/T–heat pump systems has predominantly focused on two configurations: direct expansion (DEPVT/HP) and indirect expansion (IEPVT/HP). Several studies [14,15,16] have developed and experimentally validated DEPVT/HP models, evaluating heat pump energy efficiency and conducting theoretical thermodynamic analyses. Abbas et al. [17] researched a novel series-coupled PV/T and a solar thermal collector (TC) with a solar direct expansion heat pump system. The PV/T-TC’s annual average COP was 5.68. Prakash et al. [3] developed a PV/T direct expansion heat pump system with PCM. The result suggest that the system heating and cooling COPs were 5.73 and 4.62, respectively. Qu et al. [4] performed an integrated energy, exergy, economic, and environmental (4E) assessment of a PV/T-WSHP water-heating system. Energy performance was comparatively evaluated against a hybrid setup consisting of independent PV modules coupled with an air-source heat pump water heater. Experimental work by Besgani et al. [18] on an IEPVT/HP system reported an average coefficient of performance (COP) which reached 3. Li et al. [19] established and experimentally validated an indirect expansion–solar-assisted heat pump by combining PV/T and a dual-source heat pump. The power generation by the PV cell could meet the water pump’s consumption, and the annual CO₂ emission reduction was 13,486.5 kg. In the research of David et al. [20], accounting for evaporator, condenser and refrigerant thermal inertia, the researchers formulated a heat pump model. Based on the dynamic model, the author utilized Model Predictive Control (MPC) to analyze the impact of various control strategies and boundary conditions on system performance. Further, in the study of Obalanlege et al. [21], a combined heat and power system based on a hybrid PV/T heat pump was investigated, analyzing the influence of key parameters, including solar irradiance, thermal storage tank size, and PV/T loop water flow rate, on overall system performance.

Compared to studies on standalone PV/T collectors or heat pumps, research on PV/T–heat pump systems remains limited. Existing investigations primarily focus on mid-to-long-term performance under various system configurations. Researchers pay scant attention to dynamic responses under transient operational perturbations, such as the dynamic response process of the outlet temperature in the heat source side to compressor load fluctuations and variations in heating water flow rates when there is a step change. Research on the impact of different thermal storage water tank capacities on the dynamic response process of PV/T–heat pump systems remains limited, too. Furthermore, the short-term impacts of solar intermittency on heat pump performance remain underexplored in the literature. This study establishes a PV/T–heat pump system using a transient heat current model with thermal inertia. Through dynamic simulations and parametric analysis, this study conducts research on the transient response of a PV/T–heat pump system under changes in solar radiation, compressor operation, and hot water flow rate. The focus was on exploring the impact of intermittent solar energy on a PV/T–heat pump system’s electrical and thermal performance. The influence of compressor operating parameters and hot water flow rate on the operation of other equipment in the system was investigated. At the same time, the regulation mechanism of the anti-interference ability of the system by the capacity of the hot water storage tank was clarified. This work provides actionable insights for optimizing transient operation and control strategies in hybrid solar energy systems.

2. PV/T–Heat Pump System Description and Physical Modeling

The PV/T–heat pump system includes an array of PV/T collectors and a water–water heat pump unit, connected by a thermal storage water tank. Figure 1a shows the physical model of the PV/T collector studied in this paper.

Table A1. Main parameters of PV/T collector.

Parameter	Value
Glass spacing (m)	0.025
Collector area (m2)	2 (2 m × 1 m)
Normal efficiency of PV module (%)	15
Temperature coefficient of PV module (1/ ℃)	−0.0045
Absorber thickness (m)	0.0003
Tube diameter (m)	0.01
Tube spacing (m)	0.1
Insulation thickness (m)	0.035

of Appendix A details the physical parameters of the PV/T collector. PV/T collectors are connected by a hybrid series–parallel combination. To investigate transient response performance with different step disturbances, a simulation PV/T–heat pump system model including 20 PV/T collectors is established. Figure 1b shows the system schematic diagram. The thermal storage water tank is 1.5 m³. The mass flow rate is 0.03 kg/(m²·s) per collector row. Referring to the author’s previous research [22], two PV/T collectors are connected in a series to form a row.

Between thermal storage water tank and heat load, the heat pump unit transfers heat by R-134a. The system components include an evaporator/condenser (shell-and-tube heat exchangers), a compressor and an expansion valve.

Table A2. Main parameters of component in heat pump.

Component	Parameters	Value
Condenser/Evaporator	Number of tube passes	2
	Number of shell passes	1
	Inner tube diameter (m)	0.00822
	Outside tube diameter (m)	0.00952
	Tube layout (°)	90
	The wall conductivity (W/m K)	111
	The ratio of length to diameter	8
Compressor	Number of cylinders	2
	Piston diameter (m)	0.085
	Stroke (m)	0.06
	Displaced volume (cm3)	681

of Appendix A details the equipment parameters of the heat pump unit.

3. Mathematical Model of PV/T–Heat Pump System

3.1. Transient Model of PV/T Collector

In the author’s previous study [22], a novel dynamic model for PV/T collectors was developed for numerical simulation and performance evaluation. The researchers integrated the transient heat current method with the PV/T collector model accounting for effective heat capacity. In the study of He et al. [12], the transient heat current model’s heat exchange expressions are provided by Equations (1) and (2),

$$C_{wall}{\displaystyle \frac{{dT}_{wall}}{dt}}={\displaystyle \frac{T_{hot,inlet}\left(t\right)-T_{wall}\left(t\right)}{R_{hot}}}-{\displaystyle \frac{T_{wall}\left(t\right)-T_{cold,inlet}\left(t\right)}{R_{cold}}}$$

(1)

$$T_{cold}\left(x,t\right)=T_{wall}\left(x,t\right)+\left[T_{cold,inlet}\left(t\right)-T_{wall}\left(t\right)\right]e^{-{\displaystyle \frac{h_{c}A}{G_{c}L}}x}$$

(2)

Within the PV/T collector’s heat transfer process, solar radiation functions analogous to the high temperature fluid in the heat exchanger, and it is the PV/T collector’s primary heat source.

Photovoltaic modules concurrently produce electricity while facilitating thermal exchange with both ambient surroundings and refrigerant medium. Expanding on Zou et al.’s [22,23] established parameters for effective heat capacity and thermal resistance in PV/T collectors, we derive the linearized heat transfer formulation in Equation (3), based on the heat current model.

$${\left(mc\right)}_{pv/t}{\displaystyle \frac{{dT}_p}{dt}}=A_p\left(G-E_{ele}\right)-{\displaystyle \frac{\left(T_p-T_{amb}\right)}{R_{amb}}}-{\displaystyle \frac{\left(T_p-T_{f,i}\right)}{R_{fluid}}}$$

(3)

$$T_{f,o}=T_p+\left(T_{f,i}-T_p\right)e^{-a_{fluid}}$$

(4)

$$E_{ele}={\tau }_{g}G{\mathrm{\eta }}_{ref}\left[1-\beta \left(T_p-T_{ref}\right)\right]$$

(5)

In the authors’ previous study [23], the PV/T collector heat transfer coefficients are expressed.

$T_{f,i}$ and $T_{f,o}$ denote PV/T collector inlet and outlet temperatures in Equation (4), respectively. The primary state variables requiring solution are the PV cell temperature, $T_p$, and fluid outlet temperature, $T_{f,o}$. Applying the thermoelectric analogy principle simplifies the heat transfer process to the equivalent circuit, as is shown in Figure 2. Here, electrical potential corresponds to temperature, and electrical current corresponds to heat transfer rate. The characteristic temperatures $T_{f,i}$, $T_{f,o}$, $T_p$ and ${\epsilon }_{pv}$ (representing the PV cell’s output electricity) reflecting the dynamic behavior of the PV/T collector. Their interrelationships are governed by thermal resistances and thermal capacitance. Consequently, this circuit-based model describes the PV/T collector’s heat transfer process, enabling direct application of electrical circuit principles to realize the character analysis of its operational performance.

3.2. Model of Thermal Storage Water Tank

In this paper, the thermal storage water tank model is simplified as follows: uniform water temperature with well-insulated, no water withdrawal, and negligible heat losses between the tank and the environment. The energy balance expression about thermal water tank is provided in Equation (6) [24],

$$m_w{C}_w{\displaystyle \frac{{dT}_w}{dt}}={\displaystyle \frac{\pi D_w^2}{4}}{\mathrm{\nu }}_w\left({\rho }_f{C}_f{T}_2-{\rho }_w{C}_w{T}_w\right)+{\displaystyle \frac{\pi D_{eva}^2}{4}}{\mathrm{\nu }}_{eva}\left({\rho }_w{C}_w{T}_{o,eva}-{\rho }_w{C}_w{T}_{in,eva}\right)$$

(6)

where $T_{\mathrm{w}}$ is the average water temperature and $T_2$ is the inlet water temperature in the thermal storage water tank. $T_{\mathrm{o},\mathrm{e}\mathrm{v}\mathrm{a}}$ and $T_{\mathrm{i}\mathrm{n},\mathrm{e}\mathrm{v}\mathrm{a}}$ are the evaporator’s outlet and inlet water temperatures.

Within serial PV/T modules branches, the upstream PV/T module’s outlet water temperature directly serves as the subsequent unit’s inlet temperature, while the second PV/T module’s outlet fluid temperature defines the thermal storage water tank’s inlet fluid temperature.

3.3. Model of Heat Pump Unit

In Figure 1b, the thermal storage water tank serves as a low-temperature heat source and the high-temperature water side in the condenser serves as a heat sink, the heat of which is delivered to the household and the end-user. For the evaporator and condenser model, we establish the heat current model considering thermal inertia. The energy balance equations are written as in Equations (7)–(10) [12,25].

The evaporator water-side heat input is written as follows:

$${\left(mc\right)}_{w,eva}{\displaystyle \frac{{dT}_{w,eva}}{dt}}={\displaystyle \frac{\left(T_{ref}-T_{w,eva}\right)}{R_{eva}}}+{\dot{m}}_{w,eva}·c_p·\left(T_{w,in}-T_{w,out}\right)$$

(7)

The energy balance equation on the refrigerant side is written as follows:

$${\left(mc\right)}_{eva}{\displaystyle \frac{{dT}_{ref}}{dt}}={\displaystyle \frac{\left(T_{w,eva}-T_{ref}\right)}{R_{eva}}}+{\dot{m}}_{ref}·\left(h_{ref,in}-h_{ref,out}\right)$$

(8)

where all the thermal inertia of the refrigerant and the evaporator are summarized into ${\left(mc\right)}_{eva}$. The thermal resistance of the evaporator refers to Kavian et al.’s [26] study.

Similarly, the condenser water-side heat transfer is written as follows:

$${\left(mc\right)}_{w,con}{\displaystyle \frac{{dT}_{w,con}}{dt}}={\displaystyle \frac{\left(T_{ref}-T_{w,con}\right)}{R_{eva}}}+{\dot{m}}_{w,con}·c_p·\left(T_{w,in}-T_{w,out}\right)$$

(9)

The energy balance equation on the refrigerant side is written as follows:

$${\left(mc\right)}_{con}{\displaystyle \frac{{dT}_{ref}}{dt}}={\displaystyle \frac{\left(T_{w,con}-T_{con}\right)}{R_{con}}}+{\dot{m}}_{ref}·\left(h_{ref,in}-h_{ref,out}\right)$$

(10)

Table A3. Correlations of heat transfer inside the shell and tube.

Reference	Location and State	Correlation Formula
McAdams et al. [27]	Inside the shell	$h_{out}=0.36{\left({\displaystyle \frac{D_e{G}_s}{\mu }}\right)}^{0.55}{\left({\displaystyle \frac{C_p\mu }{k}}\right)}^{{\displaystyle \frac{1}{3}}}{\left({\displaystyle \frac{{\mu }_b}{{\mu }_w}}\right)}^{0.14}({\displaystyle \frac{k}{D_e}})$
Gnielinski [27]	The single-phase inside the tube	$Nu={\displaystyle \frac{(f/2)(Re-1000)Pr}{1.07+12.7(f/2{)}^{\frac{1}{2}}({Pr}^{\frac{2}{3}}-1)}}$ $f=(1.58\mathrm{l}\mathrm{n}Re-3.28{)}^{-2}$
Gungor and Winterton [27]	The boiling flow inside the tube	$h=E{h}_l$ $h_l={\displaystyle \frac{0.023{Re}_l^{0.8}{Pr}_l^{0.4}{k}_l}{d_{in}}}$ ${Re}_l={\displaystyle \frac{G\left(1-x\right)d_{in}}{{\mu }_l}}$ $E=1+3000{Bo}^{0.86}+1.12({\displaystyle \frac{x}{1-x}}{)}^{0.75}({\displaystyle \frac{{\rho }_l}{{\rho }_g}}{)}^{0.41}$
Zecchin and Cavallini [27]	The condensation two-phase flow in the tube	$h_{TP}={\displaystyle \frac{0.05{Re}_{eq}^{0.8}{Pr}_l^{0.33}{k}_l}{d_{in}}}$ ${Re}_{eq}={Re}_v({\displaystyle \frac{{\mu }_v}{{\mu }_l}})({\displaystyle \frac{{\rho }_l}{{\rho }_v}}{)}^{0.5}+{Re}_l$

of Appendix A details the heat transfer coefficient correlations required by the above equation [27].

The refrigerant mass flux is written as follows [28,29,30]:

$${\dot{m}}_{ref}={\eta }_v·{\rho }_{in}·V_G·\omega$$

(11)

$${\eta }_v=0.9207-0.0756\left({\displaystyle \frac{P_{con}}{P_{eva}}}\right)+0.0018{\left({\displaystyle \frac{P_{con}}{P_{eva}}}\right)}^2$$

(12)

Under the isentropic compressor assumption, power consumption is formulated as follows [31]:

$$W_{com}={\displaystyle \frac{\frac{n}{n-1}{\eta }_v{V}_G\omega P_{eva}\left[{\left(\frac{P_{con}}{P_{eva}}\right)}^{\frac{n-1}{n}}-1\right]}{{\eta }_{com}}}$$

(13)

where ${\eta }_{com}$ is the total efficiency of compressor.

The heat pump COP is written as follows:

$$COP={\displaystyle \frac{Q_{con}}{W_{com}}}$$

(14)

This study adopts the primary energy conservation standard for holistic performance assessment. The system coefficient of performance, ${COP}_{system}$, quantifies overall PV/T–heat pump efficiency as useful thermal output versus net electrical input [31]:

$${COP}_{system}={\displaystyle \frac{Q_{con}+E_{elc}/{\eta }_{power}}{W_{com}}}$$

(15)

where $E_{elc}$ is the PV cell’s power output. ${\eta }_{power}$ is the reference efficiency (0.38) for conventional power generation efficiency in power plants.

3.4. Numerical Simulation

The simulation numerical solution of the transient models requires initial temperature distributions for photovoltaic cells, the thermal storage water tank, and heat exchangers, along with time-dependent boundary conditions: solar irradiance, ambient temperature, fluid inlet temperature, and mass flow rate.

Following discretization of the energy conservation equations, simulations were executed in MATLAB2021b referring to the authors’ previous study [23]. System parameters were initialized at simulation start, with dynamic inputs (irradiance, ambient temperature, fluid properties) driving the time-stepping procedure. Fourth-order Runge–Kutta integration resolved the energy balance equations, while the thermodynamic properties of water and refrigerant were determined via REFPROP 9.0 interfacing. The calculations iterated until the specified simulation duration was reached. The simulation flowchart is shown in Figure 3.

4. Model Validation

The PV/T collector model proposed in this paper has been validated in the authors’ previous work [23].

This study validates the proposed heat current model against a quasi-steady-state heat pump reference. Experimental validation employed a water-to-water heat pump utilizing R134a refrigerant, equipped with shell-and-tube heat exchangers and a variable-speed compressor. Equipment parameters and operating conditions are shown in

Table 1. The equipment parameters and experimental conditions in reference.

Parameters	Evaporator	Condenser
Tube length (m)	0.8182	0.8
Total number of tubes	76	20
Number of tube passes	2	2
Inner tube diameter (m)	0.00822	0.013
Outside tube diameter (m)	0.00952	0.016
Evaporator inlet temperature (K)	302	302
Volumetric flow (m3/h)	1.14	1.25
Compressor speed (rpm)	575	575

[32].

Figure 4 shows the comparison between simulated and experimental COP results across varying condenser inlet temperatures. The maximum relative error (RE) between simulated and experimental COP results remained approximately 8.3%, an acceptable deviation given negligible heat losses in piping.

5. Results and Discussion

During operation of the PV/T collector and heat pump, the system is subject to disturbances from fluctuating weather conditions and variable electrical/thermal load demands. Additionally, water tank capacity significantly influences the system’s ability to reject these disturbances. This section investigates the transient response of the system to perturbations in solar irradiance, compressor speed and load adjustments, and variations in the mass flow rate of hot water supply in the condenser. Additionally, the anti-disturbance performance under different thermal storage water tank volumes is analyzed. The equipment parameters of the PV/T–heat pump system established in this study are listed in

Table A4. Thermal and optical properties of different layers in PV/T collector.

Layer	Parameters	Value	Units
Glass cover	Density, ${\rho }_g$	2200	kg/m3
	Specific heat capacity, $c_g$	790	J/kg K
	Thermal conductivity, $k_g$	1.1	W/m K
	Absorptivity, ${\mathsf{\alpha }}_{\mathrm{g}}$	0.01	-
	Transmittance, ${\mathsf{\tau }}_{\mathrm{g}}$	0.90	-
PV module	Density, ${\rho }_{pv}$	2330	kg/m3
	Specific heat capacity, $c_{pv}$	677	J/kg K
	Thermal conductivity, $k_{pv}$	148	W/m K
	Absorptivity, ${\mathsf{\alpha }}_{pv}$	0.9	-
	Emissivity, ${\epsilon }_{pv}$	0.88	-
Absorber plate	Density, ${\rho }_{abs}$	2702	kg/m3
	Specific heat capacity, $c_{abs}$	880	J/kg K
	Thermal conductivity, $k_{abs}$	310	W/m K
	Absorptivity, ${\mathsf{\alpha }}_{abs}$	0.95	-
	Emissivity, ${\epsilon }_{abs}$	0.05	-
Tube	Density, ${\rho }_{tube}$	8920	kg/m3
	Specific heat capacity, $c_{tube}$	386	J/kg K
	Thermal conductivity, $k_{tube}$	377	W/m K
	Tube number	10	-
Insulation	Density, ${\rho }_{ins}$	230	kg/m3
	Specific heat capacity, $c_{ins}$	1670	J/kg K
	Thermal conductivity, $k_{ins}$	0.025	W/m K

and

Table A5. Equipment parameters in heat pump.

Component	Evaporator	Condenser
Volumetric flow (m3/h)	1.14	1.25
Total number of tubes	76	20
Number of tube passes	2	2
Tube length (m)	0.8182	0.8
Inner tube diameter (m)	0.00822	0.013
Outside tube diameter (m)	0.00952	0.016

of Appendix A.

5.1. Solar Irradiation Disturbance

Figure 5 shows the dynamic temperature response of the system when solar irradiance undergoes a step change from 750 W/m² to 350 W/m² at 100 s of simulation. As a primary factor affecting PV/T collector operation, the reduced solar irradiance directly causes the decrease in photovoltaic (PV) cell temperature. The supply of low-temperature heat sources is diminished and indirectly influences the heat pump’s heating capacity. Following irradiance reduction, the temperatures of the two serially connected PV/T collectors decrease first. The PV cell temperatures drop from 39.56 °C and 36.09 °C to 28.68 °C and 30.67 °C, respectively, due to reduced solar-to-thermal conversion. Consequently, the outlet water temperature of the PV/T collector array decreases from 35.67 °C to 28.39 °C. The coolant fluid’s inlet–outlet temperature difference across the PV/T collector array narrows from 7.37 °C to 4.23 °C. Despite these significant temperature variations in the collectors, the thermal storage water tank, with its high thermal capacity, effectively buffers the disturbance. The cooling water temperature drops from 28.3 °C to 24.16 °C in the tank. The water supply temperature of the heat pump decreases from 55 °C to 53.47 °C. The buffering effect of the thermal storage water tank mitigates the impact on the heat pump’s operation.

Figure 6 shows the dynamic responses of the PV/T collector’s electrical/thermal output power and the heat pump’s COP under the solar irradiance step change. The PV power supply declines sharply from 3.56 kW to 1.61 kW due to reduced solar irradiance. Although the PV cell’s temperature decrease theoretically enhances electrical efficiency (as described in Equation (5)), Figure 6 shows only a minor recovery in power output. In Figure 6, the PV power supply increases from 1.618 kW to 1.633 kW. Although the electrical efficiency of PV cells has been improved, the variation in solar irradiance still plays a dominant role in PV power supply. Due to the decrease in temperature difference between the inlet and outlet in the PV/T collector array, the thermal output of the PV/T collector also decreases when the flow rate of the coolant fluid remains constant. Figure 6 shows that the thermal output of the PV/T collector has decreased from 25.17 kW to 23.6 kW. As shown in Figure 6, the heat pump COP and COP_system exhibit slight increases owing to the lowered thermal storage tank temperature, further confirming the water tank’s stabilizing role.

Solar irradiance disturbance directly or indirectly affects all temperature and efficiency parameters in the system. The thermal storage water tank, serving as both a low-temperature heat source and a high-capacity buffer, demonstrates critical buffering effects. Its coolant fluid temperature varies with the solar irradiance disturbance, while its thermal inertia minimizes fluctuations in heat pump COP. These findings validate the water tank’s coolant temperature as a reliable monitoring variable for the transient response of the system and assessing system stability during transient operations.

5.2. Compressor Operating Parameters

In the heat pump system, the compressor mainly affects the refrigerant by controlling the speed, which, in turn, affects the heating capacity of the heat pump. When the compressor speed changes, the temperature and compressor power consumption in the PV/T–heat pump system are shown in Figure 7a,b.

Figure 7a shows that a 50% reduction in compressor speed lowers the hot water temperature from 54 °C to 49.8 °C. Compressor power consumption decreases from 15 kW to 6.8 kW. This speed reduction reduces both energy use and heat pump heating capacity, leading to a gradual temperature rise in the thermal storage water tank. Since the water in the tank also serves as the PV/T collector’s coolant, PV/T component temperatures consequently increase. Conversely, Figure 7b shows that a 50% compressor speed increase elevates hot water temperature from 54 °C to 56.7 °C. Compressor power consumption increases from 15 kW to 23.4 kW. PV/T and water tank temperatures exhibit opposing trends. As shown in Figure 7, the degree to which the increase or decrease in compressor speed affects the temperature change of hot water in the heat pump varies. As mentioned in the previous section, the compressor speed directly affects the refrigerant flow rate. Therefore, as the compressor speed increases, the heat transfer time of the refrigerant in the condenser is significantly reduced compared to when the speed decreases. The temperature drop of water caused by the compressor deceleration is significantly greater than the temperature rise caused by acceleration. At the same time, the dynamic response time of the compressor power consumption and hot water temperature with changes in speed are also different. The compressor power consumption only takes about 50 s to reach stability, while the temperature of the hot water in the condenser takes about 110 s. This means that as relates to dynamic processes, the difference in response time between electricity and heat needs to be considered.

The PV/T collector provides thermal energy while its photovoltaic cells also supply electricity to drive the compressor in the heat pump. However, the electrical power output of the PV cells is unstable due to fluctuations in solar irradiance, leading to irregular compressor load variation and unstable compressor speed. Figure 8 and Figure 9, respectively, show the variation in compressor speed and hot water temperature in the heat pump when the compressor load increases or decreases by 10% to 50%. As shown in Figure 8, as the load on the compressor increases, the compressor speed also increases from 23 r/s to 25 r/s, 29 r/s, and 33 r/s. On the contrary, the compressor speed decreases from 23 r/s to 21 r/s, 16 r/s, and 12 r/s. As shown in Figure 9, as the compressor load increases, the hot water temperature also increases from 54.4 °C to 55 °C, 56 °C, and 56.6 °C. On the contrary, the hot water temperature decreases from 54.4 °C to 53.8 °C, 52.3 °C, and 50.3 °C. The decrease in hot water temperature caused by the decrease in compressor load is larger than the increase caused by the increase in load. As mentioned in the previous section, compressor load directly affects the compressor speed. Therefore, as the compressor load changes, the reason for the different changes in water temperature in the condenser is as mentioned above. Therefore, it is important to maintain a stable compressor load during heat pump operation.

5.3. Water Flow Rate in Condenser

This section analyzes the effects of hot water flow rate changes in the condenser on the performance of the PV/T–heat pump system. As shown in Figure 10a, with a 20% reduction in hot water flow rate, the heat exchange duration in the condenser increases. The heat pump’s hot water temperature rises from 54.4 °C to 57.43 °C. With constant compressor power, the heat source temperature in the thermal storage water tank gradually rises from 28.3 °C to 28.9 °C due to the increase in condenser temperature and evaporator temperature. Due to the water tank’s buffering effect, the PV/T collector temperature also exhibits a slight increase. Conversely, Figure 10b shows that, with a 20% increase in hot water flow rate, the heat exchange duration in the condenser decreases. The hot water temperature decreases from 54.4 °C to 52.25 °C and the water temperature in the thermal storage water tank decreases to 27.9 °C. Figure 10 shows that after a step change in hot water flow rate in the condenser, the hot water temperature requires about 100 s to stabilize, consistent with previous results. These findings highlight the necessity to account for differences in electrical and thermal response time during heat pump operation, preventing temperature oscillations caused by sudden changes in fluid flow rate.

5.4. Thermal Storage Water Tank Capacity

As analyzed in the previous section, solar irradiance significantly influences the operation of components in the PV/T–heat pump system. Among these factors, the thermal storage tank provides critical anti-disturbance capability to the system due to its large thermal capacity. The thermal storage water tank temperature is suitable as a monitoring variable to assess transient response and determine system stability. As shown in Figure 11, this section investigates the dynamic response of the tank water temperature under a step reduction in solar irradiance, from 750 W/m² to 350 W/m², for different tank volumes.

As shown in Figure 11, when solar irradiance decreases from 750 W/m² to 350 W/m², the temperature decline of the water temperature is significantly reduced as the tank volume increases from 0.5 m³ to 2 m³. For V_tank = 0.5 m³, the water temperature declines from 28.4 °C to 21.6 °C, with no signs of stabilization by the end of the simulation. For V_tank = 2 m³, the water temperature in the tank declines from 28.4 °C to 26 °C and gradually stabilizes. Larger tank volumes progressively suppress temperature fluctuations, with the PV/T collector temperature decreasing from 39.6 °C to 28.9 °C for 0.5 m³ and to 32 °C for 2 m³. By increasing the volume of the thermal storage tank, a 46.7% improvement in temperature fluctuation mitigation can be achieved. According to the authors’ previous work, when the volume of the thermal storage tank is small, the variation in water temperature and photovoltaic cell temperature with solar irradiance is about 15–20 °C. In this case, a larger water tank capacity has a positive effect on maintaining the stability of system operation. However, the buffering effect diminishes rapidly for volumes exceeding 1.5 m³, beyond which the increased tank capacity no longer provides significant resistance to solar-induced disturbances.

6. Conclusions

In this study, a dynamic response model of the PV/T–heat pump system was developed based on the transient heat current method with effective heat capacity. The system operational characteristics under step disturbances were investigated, focusing on the effects of solar irradiance, compressor parameters, condenser hot water flow rate and thermal storage water tank volume. The transient response mechanisms and anti-disturbance optimization strategies under multi-perturbation coupling were systematically revealed.

(1)

A step reduction in solar irradiance caused a maximum temperature drop of 10 °C in PV/T collector cells. The thermal storage water tank, owing to its high thermal capacity, limited the water temperature decline to 4.14 °C. This effectively mitigates fluctuations in the heat pump’s supply water temperature (COP and COP_system variations < 3%). The water tank temperature is recommended as a stability-monitoring indicator, with its dynamic response providing theoretical guidance for anti-disturbance optimization.

(2)

Reducing compressor speed by 50% resulted in a 4.2 °C hot water temperature drop, significantly larger than the 2.7 °C rise observed under a 50% speed increase. It demonstrates asymmetric thermal responses to compressor speed variations. Load fluctuation experiments further confirmed that a 50% load reduction caused a 7.6 °C hot water temperature decline, whereas a 50% load increase raised hot water temperatures by only 2.2 °C. This highlights the critical risk of sudden load drops. Thus, maintaining compressor load stability is essential, with adaptive speed regulation via PV power prediction proposed for implementation.

(3)

A 20% reduction in hot water flow rate increased the outlet temperature by 3.03 °C, with a thermal response time (100 s) double that of electrical parameters (50 s). This electro-thermal time lag necessitates system control strategies to prevent temperature and compressor operation oscillations caused by system changes.

(4)

Increasing the tank volume from 0.5 m³ to 2 m³ reduced the water temperature decline, under solar irradiance disturbance, from 6.8 °C to 2.4 °C. And PV/T collector temperature fluctuation suppression improved by 46.7%. However, the anti-disturbance gain diminished significantly for V_tank > 1.5 m³. A water tank volume of 1–1.5 m³ is recommended to balance thermal inertia enhancement and cost efficiency.

In summary, this study elucidates the transient response mechanisms of PV/T–heat pump systems under solar, compressor, and hydraulic disturbances, establishing the thermal storage tank’s critical role in anti-disturbance regulation. Future research should address multi-disturbance coupling scenarios, climate adaptability, and techno-economic optimization to advance the deployment of PV/T–heat pump systems in building energy applications.