Performance Optimization of Solar-Air Source Heat Pump Heating System for Rural Residences in Hot Summer and Cold Winter Zone

Abstract

Building energy consumption is a major source of carbon emissions, with the heating energy demand of rural buildings in the hot summer and cold winter (HSCW) zone having increased 575-fold over the past 15 years. This research investigated an optimized solar–air source heat pump (SASHP) system to meet the heating demand of rural residences in this region. First, a typical rural building model was developed using SketchUp, and its heating load was simulated using TRNSYS, revealing an average load of 3.38 kW and a peak load of 5.9 kW. Based on the latest technical standards, the SASHP system was designed and simulated using TRNSYS, achieving an overall coefficient of performance (COP) of 3.67 while maintaining indoor thermal comfort within ISO 7730 Category II. Subsequently, the system was optimized through GenOpt to minimize the annual equivalent cost, yielding key parameters: a 15 m² solar collector at a 40.75° tilt, a 0.35 m³ water tank, and a 10.16 kW air source heat pump. Compared with the initial design, the optimized configuration achieved reductions of 35.60% in initial investment and 32.68% in annual equivalent costs. By ensuring thermal comfort and overcoming the economic barrier, this study provides a viable pathway for adoption and promotion of renewable heating technology in rural areas.

1. Introduction

Currently, energy issues constitute a critical concern for society and economic development and command significant international attention. This prominence stems from challenges associated with fossil fuel dependence. In response, China announced ambitious targets at the 76th UN General Assembly (2021) to peak CO₂ emissions by 2030 and achieve carbon neutrality by 2060 [1], reaffirming its commitment to the green transition and the Paris Agreement at the 79th session (2024) [2]. Given the urgency of these goals, a transition to renewable energy is imperative. As a cornerstone of this transition, solar power is a pivotal option for addressing the core challenges [3]. Additionally, China has steadily amplified its support for renewable energy, with the government actively promoting the “Assessment Standard for Green Building” (GB/T 50378-2019) [4] and “Renewable Energy Law of the People’s Republic of China”. Furthermore, regional governments have rolled out energy-saving policies that encourage the utilization of solar energy not only for domestic hot water but also for space heating [3].

In China, rapid economic growth and evolving consumption patterns have escalated energy demand, making it a major carbon emitter [5]. The building operations sector is a crucial focus, accounting for 30% of total energy consumption [6]. Usage of renewable energy for heating systems in the HSCW zone is crucial to address dual carbon targets.

Heating strategies in China exhibit strong regional disparities due to the historical North–South Heating Divide policy of 1950, which limited centralized heating infrastructure largely to areas in the north of the Qinling–Huaihe line [5,7]. This policy aimed to conserve resources but resulted in lower winter thermal comfort, especially in the HSCW zone [8], which experiences harsh, humid winters with indoor temperatures notably 6 °C lower than in climatically similar regions such as the UK [7,9]. In recent years, frequent freezing rain and snowstorms in southern China have caused record-low temperatures, significantly disrupting daily life and economic activities. Consequently, the demand for winter heating in these areas has become increasingly urgent [10], surging by 575-fold in residential heating energy consumption over 15 years [11]. However, due to distinct climatic conditions, building typologies, and lifestyle patterns, the heating strategies used in northern rural areas settings cannot be directly applied to southern rural areas. In response, a growing number of households have turned to decentralized heating systems, encompassing individual household and small-scale district heating [12]. Currently, nearly 60% of heating in the zone relies on inefficient air conditioning units [13], triggering a sharp rise in electricity consumption which is primarily fossil-fuel-based, thereby straining the electricity grid’s supply–demand balance [14] and indirectly generating significant carbon emissions [6]. In addition, high operational costs also limit broader uptake [3]. While numerous studies have focused on heating systems in cold and severe cold zones [15], a significant research gap remains concerning the cost-effective and low-carbon heating solutions, especially for solar energy technology, for rural areas of the HSCW zone.

China’s solar energy resources are categorized into five zones according to solar radiation levels. Most cities in the HSCW zone belong to the medium-resource category (Zone III), with some falling into the low-resource tier (Zone IV) [16]. While solar resources in the HSCW zone are less abundant relative to other parts of China, solar radiation intensity in the HSCW zone remains higher than that in European nations such as Denmark, where solar heating is extensively utilized [17]. Consequently, despite comparative disadvantages, solar heating technologies can still fulfill winter heating requirements in the HSCW zone.

However, solar thermal systems often require auxiliary heat sources due to intermittency [18]. In the HSCW zone, electricity is commonly used for this purpose [16] via electric heaters, blankets, AC units, etc. However, this approach is inefficient due to the exergy degradation involved in converting high-exergy electricity to low-exergy heat, in addition to being costly and slow-responding [19]. Gas boilers offer an alternative auxiliary source [20] but still contribute to CO₂ emissions. Comparative research indicates that solar–air source heat pump (SASHP) systems achieve significantly higher exergy efficiency (two to three times) than solar–gas boiler systems [21]. By leveraging dual heat sources [22] and enabling multi-energy synergy [23], SASHP systems are especially suitable for the HSCW zone, where winter temperatures are moderate (0–10 °C). This configuration reduces frosting risks [24] and outperforms conventional air source heat pump (ASHP) systems. Notably, SASHP systems have been deployed across multiple global applications [25].

To address the inherent challenges of solar intermittency and the performance degradation of air-source heat pumps (ASHPs) at low temperatures, the integration of thermal energy storage (TES) offers a viable pathway to enhance system reliability, efficiency, and cost-effectiveness. Promising TES technologies include water storage tanks [18], phase-change materials, and sand-based floors [26]. As a predominant form of sensible heat storage, water storage tanks have been widely adopted and shown to significantly improve the system’s coefficient of performance (COP) [27]. Additionally, the capacity of the storage tank is a critical design parameter, as it substantially influences energy efficiency, solar fraction, and overall energy consumption [18].

While an SASHP system offers performance advantages, it requires a larger installation footprint than a conventional ASHP system. This makes rural areas, with their more abundant land availability, a more suitable environment for deploying SASHP systems. However, the paramount importance of affordability and maintainability leads households in rural areas to impose strict economic constraints on heating systems [26], and there is a notable scarcity of research on cost-effective SASHPs. Additionally, performance evaluation and cost-effectiveness studies of these integrated systems have yet to be conducted.

In economic analyses, operating costs [15,26,28,29] and the payback period [30,31] are commonly used as evaluation metrics. Specifically, operating costs have been applied to evaluate rural building heating systems [15,26]. Notably, affordability remains a primary constraint in rural areas. Meanwhile, the payback period serves as a measure of risk and liquidity, and operating costs directly reflect annual expenditures. Both metrics, despite their simplicity, fail to reveal the full life-cycle cost. Therefore, an economic indicator that not only clearly reflects the annual financial burden but also fully accounts for life-cycle costs is needed to better support decision-making in such contexts. Particularly well-suited, Annual Equivalent Cost (AEC) provides a more reliable basis for decision-making. It effectively balances the initial investment with long-term operational costs, thereby aligning with the core concerns of rural households: annual affordability and long-term financial predictability. Therefore, the design of future policy incentives should encourage economic evaluations grounded in life-cycle cost analysis.

Above all, this study aims to establish a theoretical foundation for improving the energy efficiency of solar heating systems in rural residential buildings within China’s HSCW zone. Its findings are expected to support the broader adoption of distributed solar heating technology, thereby contributing to energy conservation and economic feasibility. To this end, Section 2 details the development of the building model and its heating load. Upon this, Section 3 introduces the design scheme of the SASHP heating system with reference to the relevant standards in China. Subsequently, Section 4 presents an analysis and comparison of the performance of the optimized SASHP heating system against the initial design proposal. Finally, Section 5 concludes this study by summarizing the key findings and their implications.

2. Building Model and Heating Load

2.1. Building Parameters

This study investigates a residential building located in Hangzhou, Zhejiang Province. The building dimensions are 14 m (length) × 7 m (width) × 3.5 m (height), yielding a volume of 343 m³ and a total floor area of 98 m². It is occupied by three persons and features three south-facing, thermally broken aluminum windows, each measuring with an area of 3.2 m × 2.3 m. A three-dimensional model of the residence, developed in SketchUp, is presented in Figure 1. Additionally, the parameters of the building envelope and external windows are detailed in

Table 1. The enclosure structure and external window parameters.

Enclosure Type	Composition		Heat Transfer Coefficient W/(m2·K)	Limit Value of Heat Transfer Coefficient W/(m2·K)
	Construction Material	Thickness (mm)
External wall	Cement mortar	20	0.467	0.5
	Steel-reinforced concrete	165
	Extruded polystyrene foam board	55
	Cement mortar	20
Roof	Cement mortar	20	0.196	0.2
	Extruded polystyrene foam board	75
	Steel-reinforced concrete	80
	Extruded polystyrene foam board	70
	Cement mortar	20
External window	Broken bridge aluminum window		1.690	1.8
Floor	Cement mortar	20	0.755	-
	Aerated concrete	200
	Cement mortar	20

. It should be noted that the thermal resistance of the exterior wall coating is excluded from the analysis. This simplification is justified as the thermal resistance of such thin coatings is negligible [32], and their impact on overall heat loss is minimal at achievable thicknesses.

According to the local standard of China, “Energy Efficiency Design Standards for Residential Buildings in Zhejiang Province” (DB33/1015-2021) [33], the ventilation rate of the residence is one time per hour, and the indoor design temperature for residential spaces is maintained at 18 °C throughout the day during the heating period. Hangzhou city is located in the northern zone of the summer hot and winter cold zone. Its heating period is from 15 December to 20 February in the following year (a total of 68 days).

Regarding thermal comfort, according to the relevant provisions of the “Evaluation Standards for Indoor Thermal Environment of Civil Buildings” (GB/T50785-2012) [34], the thermal resistance of clothing is set to 1.3 clo, and the common activities in this building are seated activities with a metabolic rate of 69.78 W/m².

Indoor heat sources include persons, lighting, and equipment. According to the national standard of China, “General Code for Building Energy Efficiency and Renewable Energy Utilization”(GB55015-2021) [35], the lighting power of residential buildings is set as 5 W/m², including 3 W/m² for radiant heat dissipation and 2 W/m² for convective heat dissipation. The power of equipment in the residential building is 3.8 W/m², of which the radiation heat dissipation is 2.28 W/m², and the convection heat dissipation is 1.52 W/m². The heat dissipation of the human body is set to 100 kJ/h.

2.2. Climate Parameters

Hangzhou city is located in a subtropical monsoon climate zone. Weather data is exported from Meteonorm8 software and imported into TRNSYS 18 as an external weather file through the weather module. The annual dry-bulb temperature in Hangzhou is shown in Figure 2, from which it can be seen that the temperature in Hangzhou ranges from −5 °C to 40 °C. This temperate climate, characterized by a relatively high annual average temperature, thus presents a favorable environment with substantial ambient heat availability for ASHP operation.

Figure 3 shows the annual horizontal solar radiation distribution in Hangzhou. The annual average solar radiation is 494 kJ/(h·m²). During the heating season (15 December to 20 February of the following year), the solar radiation is roughly 300–2400 kJ/(h·m²). This substantial availability, particularly the significant radiation intensity even in winter, indicates that Hangzhou possesses abundant solar energy resources. Consequently, solar energy can be used as a viable and effective heating source for applications in this region.

2.3. Heating Load

The total heat load Q comprises three components:

$$Q=Q_{envelope}+Q_{infiltration}+Q_{instrusion}$$

(1)

where Q_envelope denotes the basic heat loss (W) through the building envelope structure, and it is satisfied as follows:

$$Q_{envelope}={\displaystyle \sum KA(t_{in}-t_{out})}\alpha$$

(2)

where K is the thermal transmittance of the envelope structure (W/(m²·°C)), A represents the surface area of the envelope structure (m²), t_in is the indoor design temperature (°C), t_out denotes the outdoor temperature of heating (°C), and α is the temperature difference correction factor.

In Equation (1), Q_infiltration denotes heat consumption for cold air infiltration, and it is satisfied as follows:

$$Q_{infiltration}=0.278V \rho c_P(t_{in}-t_{out})$$

(3)

where V refers to the air infiltration rate (m³/h), ρ is the air density (kg/m³), and c_p is the specific capacity of air (kJ/(kg·°C)).

In addition, in Equation (1), Q_intrusion denotes the heat loss (W) from cold air intrusion through external doors, and it is satisfied as follows:

$$Q_{intrusion}=N{Q}_{door}$$

(4)

where N is the additional coefficient of external door considering cold air intrusion, and Q_door is the basic heat loss of the external door (W).

The heat load simulation model is developed using TRNSYS as shown in Figure 4. To ensure calculation accuracy, a simulation time step of 0.125 h is adopted. Consequently, the TRNSYS model successfully outputs hourly heating loads, with the corresponding results presented in Figure 5. In TRNSYS, cooling loads are assigned positive values and heating loads are assigned negative ones. The negative sign is employed solely to distinguish between the two types of loads, rather than to imply a physically negative value. It is shown that the heating load profile of the single-unit small-scale building exhibits minimal variability during the heating season. All load values are negative, indicating consistent heating demand. The system achieves a peak heating load of 5.9 kW and an average load of 3.38 kW. The building’s heat consumption per unit area is 34.49 W/m², which is consistent with the estimated heating index within the range of 25~35 W/m² listed in reference [36]. Compared with reference [20], its heat consumption per unit area is 42.04 W/m²; thus, the building presented in this paper is more energy-efficient.

3. Design Scheme of the SASHP Heating System

3.1. SASHP System Model

Based on the integrated analysis, the building employs the SASHP system for heating applications. The dynamic simulation model of the SASHP system was developed in TRNSYS using a modular approach, with crucial components such as the flat plate solar collector (Type1b) and ASHP (Type941) explicitly defined. For reproduction, a list of TRNSYS modules is provided in

Table 2. TRNSYS module configuration table.

Module Name	Type	Quantity	Module Name	Type	Quantity
Meteorological data	Type15-2	1	Controller	Type2b	2
Flat plate solar collector	Type1b	1	Data reader	Type9e	1
ASHP	Type941	1	Calculator	Equation	6
Thermal storage tank	Type158	1	Integrator	Type24	2
Pump	Type114	3	Printer	Type65c	3
Converging tee	Type11h	1	Integral printer	Type28b	1
Diverging tee	Type11f	1	Scheduler	Type14h	2
Heating terminal	Type682	1	Optimizer	TRNOPT	1

. The full simulation architecture, which illustrates component interconnections, is detailed in Figure 6.

(1)

The model’s core operation revolves around the thermal storage tank (Type158), which acts as the central hub for heat collection, storage, and delivery. The system operates based on the following logic and interconnections:

(2)

Solar collection loop: Meteorological data (Type15-2) provides solar irradiance and ambient temperature inputs to the solar collector (Type1b). A pump (Type114) circulates the heat transfer fluid between the collector and the storage tank. This pump is activated by a differential controller (Type2b) that compares the temperature at the collector outlet with the temperature at the bottom of the storage tank. The pump operates when this temperature difference exceeds a set-point (T_solar − T_tank > 8 °C) and stops when it falls below a lower set-point (T_solar − T_tank < 2 °C).

(3)

ASHP loop: The air source heat pump (Type941) uses ambient air as its heat source. It is activated to charge the thermal storage tank based on the tank’s temperature. A controller (Type2b) monitors the temperature at the top of the storage tank. If the tank temperature drops below a set minimum (44 °C) during the heating period and solar energy is insufficient, the ASHP and its associated circulation pump are activated. The ASHP heats the water circulating through its internal condenser, which is then delivered to the storage tank. If the tank temperature increases up to a set minimum (45 °C), the ASHP and its associated circulation pump are deactivated.

(4)

Heating delivery loop: A third pump circulates hot water from the top of the storage tank to the heating terminal (Type682), which represents the building’s hydraulic heating system (e.g., floor heating or radiators). The heating demand calculated by the separate building model (see Section 2) is fed to this component. The return water from the heating terminal flows back to the bottom of the storage tank, completing the circuit.

3.2. Control Strategy for the SASHP System

The hybrid heating system employs a dual-condition control strategy consisting of time-based control and temperature difference control to optimize energy utilization. The daily operation period is governed by schedulers (Type14h). Mode switching between solar and air-source heat pump (ASHP) heating is managed by controllers (Type 2b) through a temperature-hierarchy logic that prioritizes solar energy. As detailed in Figure 7, solar collectors are scheduled to operate diurnally (06:00–18:00), with the ASHP providing auxiliary heat during periods of low solar radiation. The activation of the solar-side pump is triggered when the temperature difference (ΔT) between the collector outlet and the system inlet exceeds 8 °C. Conversely, the ASHP is activated if ΔT falls below 2 °C, ensuring efficient solar harvesting. Once the solar collector is off, the ASHP operates dynamically based on the storage tank temperature: it activates when the tank temperature drops below 44 °C and deactivates when it exceeds 45 °C, thereby balancing energy efficiency with thermal comfort.

3.3. Design Parameter Calculations for Equipment Selection

3.3.1. Solar Collector

As a core component of the heating system, the solar collector area directly impacts both energy collection efficiency and economic performance. The collector area A_c is calculated using the following formula:

$$A_c={\displaystyle \frac{86400Q_{a}f}{I_T{\eta }_{cd}(1-{\eta }_L)}}$$

(5)

where Q_a refers to the building heating demand, Q_a = 5900 W; I_T refers to the average solar irradiance on the tilted surface, I_T = 12,371,970 J/(m²·d) according to Section 2.2; f is the solar fraction, which was set to f = 45% according to the “Technical Standards for Solar Heating Engineering” (GB50495-2019) [37]; η_cd refers to the average collector efficiency during the heating period, which was set to η_cd = 40~60% for the flat plate collector (additionally, η_cd = 60% here); η_L is the heat loss coefficient of the thermal storage tank, which was set to η_L = 10~20% according to the “Technical Standards for Solar Heating Engineering” (GB50495-2019) [37] (additionally, η_L = 0.2 here).

According to “Technical Standards for Solar Heating and Heating Engineering” (GB50495-2019) [37], the tilt angle of the solar collector used throughout the year should be the local latitude (30°15′ in Hangzhou) plus 10°, resulting in 40°15′ (40.25°).

3.3.2. Nominal Heating Capacity of ASHP

The nominal heating capacity of the ASHP is adjusted according to outdoor design dry-bulb temperature, defrost frequency, and relative humidity as follows [38]:

$$Q_{norminal}={\displaystyle \frac{Q_{actual}}{k_t{k}_d{k}_h}}$$

(6)

where Q_actual refers to the actual heating capacity of the ASHP (kW); k_t is the temperature correction factor (0.9 for Hangzhou, interpolated from “Design Code for Heating Ventilation and Air Conditioning of Civil Buildings” (GB 50736-2012) [39]; k_d is the defrost correction factor (0.9 for once per hour; 0.8 for twice per hour) [38], adopted as 0.9; k_h is the humidity correction factor (0.9 for Hangzhou) [38]. Note that the correction curves for ASHP performance (Type941) under varying ambient temperatures and supply water temperatures are provided in Figure 8 and Figure 9. Lower ambient temperatures and higher outlet water temperatures significantly increase energy demand, highlighting the need for optimized control strategies in cold climates.

3.3.3. Thermal Storage Tank Volume

The volume of the thermal storage tank V is sized based on the principle of sensible thermal energy storage [38]. The thermal storage tank volume V is determined by balancing the peak heating demand and temperature differential, calculated as follows:

$$V={\displaystyle \frac{3600Q_{max}}{c\rho \Delta T}}$$

(7)

where Q_max is the daily peak heating load (5.9 kW in Section 2.3); ρ is the water density, adopted as 1000 kg/m³; c is the specific heat capacity of water, adopted as 4.18 kJ/(kg·K); and ΔT is the supply-return temperature difference, adopted as 10 °C.

3.3.4. Solar Collector-Side Pump Flow Rate

The flow rate for the solar collector loop is determined based on the recommended flow rate per unit aperture area specified in the Chinese national standard “Technical Standards for Solar Heating Engineering” (GB50495-2019) [37]. The recommended flow rate per unit collector area ranges from 0.024 to 0.036 m³/(h·m²). Following this specification, the pump flow rate of the solar collector side is calculated using the following equation:

$$G_{SOLAR}=36A_c$$

(8)

where the coefficient 36 derives from converting the maximum recommended flow rate of 0.036 m³/(h·m²) to units of kg/(h·m²).

3.3.5. ASHP-Side Pump Flow Rate

The ASHP-side pump flow rate G_ASHP (kg/h) is calculated based on the fundamental heat transfer equation [38], which is a standard method for sizing hydronic system pumps and ensures that the flow rate is sufficient to transfer the heat pump’s rated capacity given the design temperature difference:

$$G_{ASHP}={\displaystyle \frac{3600Q_{hp}}{c(T_{supply}-T_{return})}}$$

(9)

where Q_hp refers to ASHP rated heating capacity (kW); T_supply refers to the supply water temperature, where T_supply = 45 °C; T_return denotes the return water temperature, where T_return = 35 °C; and the coefficient 3600 is a unit conversion factor (from kW to kJ/h for consistency with the simulation.

3.3.6. Pump Power

The pump power P is calculated considering the total head and efficiency, calculated as follows:

$$P={\displaystyle \frac{GH}{367000\eta }}$$

(10)

where G is the water flow rate, measured in kg/h; η is the pump efficiency, assumed to be 70%; H refers to the total head, which includes the height of the building and hydraulic losses, and it is adopted as 6 m based on a building height of 3.5 m plus a 2.5 m safety margin according to engineering experience.

Above all, the key parameters of the equipment for the SASHP system are shown in

Table 3. Key design parameters for the SASHP system in Hangzhou.

Parameter	Value	Unit
Collector area (Ac)	38.63	m2
Tilt angle of collector	40°15′ (40.25°)	-
ASHP rated capacity (Qhp)	11	kW
ASHP rated power	2.72	kW
Thermal storage tank volume	1.16	m3
Solar collector pump flow rate	1391	kg/h
ASHP flow rate	945	kg/h

.

3.4. Design Scheme Results

Following the equipment selection and control strategy detailed above, the system’s performance was simulated. To assess the accuracy of the TRNSYS model, the COP results were compared against the theoretical COP. The mathematical model of COP for ASHP is as follows [20]:

$${\mathrm{COP}}_{theory}=0.002T_{amb}^2+0.0432T_{amb}+2.752$$

(11)

The comparison of COP_theory and COP of ASHP in this study is displayed in Figure 10, and the average error is calculated as 0.016. On this basis, it was confirmed that the accuracy of the simulated results is adequate.

3.4.1. Supply and Return Water Temperatures

The total heating duration is calculated as 1608 h (from 8352 h to 9960 h). To balance computational accuracy and efficiency, a time step of 0.125 h is adopted for this heating simulation. The temporal variations in supply and return temperatures are depicted in Figure 11. As illustrated in Figure 11, the system achieves stable hydraulic temperature profiles. The supply water temperature remains within 44~47 °C, and the return water temperature consistently exceeds 35 °C, fully complying with the design requirement of 45/35 °C supply–return water temperatures, thereby demonstrating the stabilized performance of the SASHP system model.

Compared with the supply water temperature reported in reference [5], the supply water temperature is higher in this paper, benefiting from the complementary thermal input provided by the solar collector in the SASHP system.

3.4.2. Energy Consumption Analysis

The cumulative energy distribution analysis is illustrated in Figure 12. During the heating season, the heating system consumed a cumulative total energy of 1356.03 kWh, with 1231.70 kWh from the ASHP, 19.43 kWh from the heating water pump, and 96.27 kWh from the circulating pump. In summary, the ASHP dominates the total consumption (90.8%), while the heating water pump accounts for only 1.4%. This underscores the importance of optimizing ASHP efficiency in hybrid heating systems.

The heating energy consumption per unit area in this work is 1356.03/14/7 = 13.84 kWh/m², which is significantly lower than the value (6278.2/120 = 52.32 kWh/m²) reported in reference [5]. As seen, renewable energy shows appealing benefits.

The actual COP of the ASHP is presented in Figure 13. It can be shown that the COP of the heat pump exhibits continuous variation due to multiple ambient factors, including outdoor temperature and humidity. Moreover, calculation results indicate an average COP of 2.43 for ASHP and 3.67 for the heating system summarized in Figure 14. This marked improvement in the system COP over that of the standalone ASHP unit demonstrates that the integrated system design effectively enhances overall energy efficiency.

The comparison about performances of building heating with solar-air source heat pump technology is shown in

Table 4. Comparison of results for building heating system integrated with solar-air source heat pump technology.

Location	System	Performance	Economic Analysis	Source
Shenyang	Solar-air source heat pump coupled heating system based on heat grid	COPsys = 6.274	The economic benefit analysis neglects to factor in the initial investment costs.	[28]
Chifeng	Solar-air source heat pump coupled with sand-base thermal storage	COPsys = 2.6	Optimizing the operational mode according to local electricity pricing policies can minimize the operating costs.	[26]
Hefei	Solar-air composite heat source heat pump system	COPsys = 2.87~3.8	/	[40]
Gobi Desert region	Solar air source heat pump technology with underground pipe systems	The average COPs during daytime and nighttime are 4.33 and 4.8, respectively.	The system can recover its costs within four years	[30]
Zhengzhou, Beijing, Shenyang, Wuhan,	Solar hybrid heat pump with integrated air-source compression cycle	COPsys = 3.45~4.24 in typical cities.	Annual operation cost and the life cycle cost are compared. The longer the life cycle, the better the economy of the system.	[29]
Zibo	PVT integrated heat pump systems and ice-tank	COPsys = 3.02	The payback period is 3.86 years.	[31]

. For system performance, it is found that the solar assisted system performance in this paper is consistent with that in Chifeng [26], Hefei [40], Gobi Desert region [30], Wuhan [29], and Zibo [31]. More importantly, COP_sys = 6.274 for solar-air source heat pump coupled heating system based on heat grid in Shenyang in Severe Cold (SC) Zone. Such a high system COP achieved in SC region provides strong inspiration for the potential application of solar-based centralized heating systems in HSCW zones in future. Subsequently, turning to the economic analysis, it is seen that most studies considered the payback period in economic analysis. But affordability holds the main limitation in rural region. Therefore, AEC—an economic metric that intuitively reflects the annual financial burden while fully accounting for life-cycle costs—is better suited to facilitate decision-making in these areas.

3.4.3. Thermal Comfort

Thermal comfort was evaluated according to the PMV-PPD indices specified in the ISO 7730 standard [41]. The PMV (predicted mean vote) is an index that predicts the mean response of a large group of people on a seven-point thermal sensation scale (from −3, cold, to +3, hot). A PMV of zero represents thermal neutrality. The PPD (predicted percentage of dissatisfied) is an index that predicts the percentage of people likely to feel thermally dissatisfied (feeling too hot or too cold).

The ISO 7730 standard defines three categories of thermal comfort:

• Category A (high comfort): PPD ≤ 6%, PMV between −0.2 and +0.2.
• Category B (medium comfort): PPD ≤ 10%, PMV between −0.5 and +0.5.
• Category C (moderate comfort): PPD ≤ 15%, PMV between −0.7 and +0.7.

The PMV-PPD results for the optimized SASHP system, measured at the room’s center point with coordinate parameter (x, y, z) = (18, 20.5, 1.7), are presented in Figure 15. It can be seen that the system maintained PMV values between −0.09 and −0.79, with corresponding PPD values ranging from 5% to 18%, and that the vast majority of data points fall within the ISO 7730 Category C comfort band (PPD ≤ 15%). This indicates that the thermal environment created by the SASHP system can be classified as providing a moderate level of thermal comfort, which is fully acceptable for residential buildings. The occasional slight drift of the PMV to just below −0.7 (indicating a “slightly cool” sensation) corresponds to the system’s lowest performance points but remains within the defined comfort limits for this category. Importantly, the PPD rarely exceeds 15%, demonstrating that the system successfully maintains a thermally acceptable environment for over 83% of the occupants throughout the heating season. This performance confirms that the optimization for cost-effectiveness did not compromise the fundamental requirement for occupant thermal comfort.

4. Optimization of the SASHP System

This study employs GenOpt, a Java-based optimization platform, coupled with TRNSYS to address optimization challenges in complex system simulations. The coupling is facilitated by the TRNOPT module from the TESS library.

The optimization aims to minimize AEC by tuning four key variables: the solar collector area, the rated heating capacity of the ASHP, the ratio of storage tank volume to collector area, and the collector tilt angle. Within the TRNOPT module, the following parameters are configured for each variable: the initial guess, lower and upper bounds, and the step size. And the AEC output is selected as the objective function for minimization.

4.1. Optimizing Configurations

AEC (CNY/year) is as follows:

$$AEC={\displaystyle \frac{i{(1+i)}^m}{{(1+i)}^m-1}}\times C_0+C$$

(12)

where C₀ indicates the initial investment (CNY);

i is the interest rate, which is assumed to be 5.66% here;

m is the service life, assumed to be 15 years here;

C is the annual operating cost (CNY/year), including penalty fees and power consumption fees such as ASHP.

The initial investment C₀ includes investments in equipment such as solar collectors, ASHP, thermal storage water tanks, and water pumps. The initial investment calculation formula is as follows:

$$C_0=A_c{C}_{sc}+R_{HP}{C}_{HP}+V_{ST}{C}_{ST}+C_{FJ}$$

(13)

where A_c is the area of the collector (m²);

C_SC indicates the cost per square meter of collector area (CNY/m²);

R_HP represents the customized heat for ASHP (kW);

C_HP denotes the ASHP equipment cost per power (CNY/kW);

V_ST is the capacity of the hot water storage tank (m³);

C_ST represents the cost per cubic meter of a hot water storage tank (CNY/m³);

C_FJ indicates the cost of the water pump (CNY).

The unit price of the system equipment in Equation (13) is listed in

Table 5. System equipment price list.

Equipment	Unit Price
ASHP	CHP = 1000 CNY/kW
Solar collector	CSC = 300 CNY/m2
Heat storage water tank	CST = 600 CNY/m3
Water pumps and other equipment	CFJ = 20% of the total price of the above three devices

.

The operating cost C is the cost generated by the electricity consumption of the equipment. To safeguard against sub-optimal heating performance during optimization, a penalty function is introduced. The logic stipulates that if the storage tank outlet temperature is below 43 °C for two hours during operation, a penalty of CNY 2500 is added to the annual operating cost. It functions as a hard constraint proxy within the economic optimization framework, ensuring that any solution resulting in a tank temperature below 43 °C is rendered economically non-viable and is effectively eliminated by the algorithm. This approach guides the optimization search towards the feasible region where thermal comfort constraints are satisfied through maintaining supply water temperature >43 °C. The significant magnitude of this penalty relative to normal costs ensures that the optimization process automatically avoids solutions where the tank temperature is lower than 43 °C.

Regarding the significant penalty value, three reasons were considered. On one hand, before the study, the operating cost for heating in a rural residence with three rooms was investigated and found to be within the range of CNY 300 (poor thermal comfort)~CNY 2500 (excellent thermal comfort) during the heating period. On the other hand, the maximum conceivable annual operating cost was calculated using the primary cost of running the ASHP at full power during peak electricity rates, estimated to be below 0.568 CNY/kWh × 2.72 kW × (9960 − 8352 h) ≈ CNY 2484. In addition, the hourly expense was 0.568 CNY/kWh × 2.72 kW × 1 h ≈ CNY 1.55. Finally, it was found that the heating in a vast majority of households demonstrate relatively low winter electricity consumption (around 500 kWh/year/household), but the electricity consumption is skewed upward to 2458 kWh/year/household by a small number of households with extremely high usage in the hot summer and cold winter zone [24]. When converted, 0.568 CNY/kWh × 500 kWh/year/household = 284 CNY/year/household, and 0.568 CNY/kWh × 2458 kWh/year/household = 1396.144 CNY/year/household. The penalty was set higher than the expenses above. Thus, CNY 2500 was adopted as the penalty value. Therefore, the operating cost C is as follows:

$$C=(W_{HP}+W_{HW}+W_{CP})\times M_D+2500\times if\left(T_{\mathrm{tank}}<43\right)\times if(time>2\mathrm{h})$$

(14)

where W_HP is the power consumption of the ASHP (kWh);

W_HW indicates the power consumption of the heating water pump (kWh);

W_CP represents the power consumption of the circulating pump (kWh);

M_D denotes the electricity price (detailed in

Table 6. Electricity price.

Period of Time	Electricity Price (CNY/kWh)
8:00–22:00	0.568
22:00–8:00 (the next day)	0.288

).

4.2. Optimized Results

After determining the optimization variables and objective function, the initial value, minimum value, maximum value, and iteration step of the optimization variables are configured in GenOpt as shown in

Table 7. GenOpt variable parameter settings.

Parameter	Collector Area (m2)	Tilt of Collector (°)	Rated Heat Capacity of ASHP (kW)	Water Tank Volume Per Unit Heat Collection Area (m3/m2)
Initial value	38.63	40.25	11.00	0.20
Minimum value	15.00	20.00	5.00	0.02
Maximum value	80.00	80.00	13.00	0.60
Iterative step	0.01	0.05	0.01	0.02

. In this study, the TRNSYS-GenOpt framework employs the Hooke–Jeeves algorithm (HJ), particle swarm optimization algorithm with inertial weight (PSO), and hybrid global optimization algorithm (HGO), respectively. The results are displayed in

Table 8. Results of different optimization algorithms.

Algorithms	HJ	PSO	HGO
AEC (CNY)	2033.89	2030.57	2029.53

. It can be seen that the global search algorithm HGO leads to the minimum AEC value, namely, CNY 2029.53.

The comparisons before and after optimization are shown in

Table 9. Comparison of heating system variables before and after optimization.

Parameter	Collector Area (m2)	Tilt Angle of Collector (°)	Rated Heat Capacity of ASHP (kW)	Water Tank Volume (m3)	C0	AEC (CNY/Year)	Average COP of ASHP	COP of System
Before optimization	38.63	40.25	11.00	1.16	24,245.00	3014.73	2.4263	3.6723
After optimization	15.00	40.75	10.16	0.35	15,613.00	2029.53	2.4298	2.9273
Changing ratio	−61.17%	1.24%	−7.64%	−69.82%	−35.60%	−32.68%	1.44%	−20.89%

and Figure 16 and Figure 17. It can be seen that the optimized collector area and heat pump rated heat output have significantly decreased. After optimization, the area of the collector was decreased by 23.63 m², with a decrease ratio of 61.17%. Furthermore, the tilt angle of the collector was increased by 0.5, with a decrease ratio of 1.24%, showing good compliance with the result (in Section 3.3.1) guided by the Chinese standard “Technical Standards for Solar Heating and Heating Engineering” (GB50495-2019) [37]. In addition, the rated heat capacity of the heat pump decreased by 0.84, with a decrease ratio of 7.64%; the volume of the thermal storage water tank was 0.35 m³, decreased by 69.82%. As a result, the initial investment decreased by CNY 8632, with a decrease ratio of 35.60%. AEC decreased by CNY 994.33, with a decrease ratio of 32.68%. The results reveal a complex trade-off between system performance and economic benefits, as evidenced by the following two aspects.

(1)

A noteworthy phenomenon observed post-optimization is that while the ASHP’s rated heating capacity decreased, its COP increased slightly. This can be attributed to two synergistic effects. On one hand, adjustments to the collector area resulted in increased ASHP operation during daytime hours in cold weather. Higher ambient temperatures improved its operating conditions, leading to occasional gains in COP. On the other hand, ASHPs with smaller capacity are compelled to operate at higher load ratios, reducing compressor start–stop cycles and inefficient low-load operation. Generally, higher part-load ratios contribute to improved average operational efficiency of the compressor.

(2)

In contrast to the improvement in component performance, the overall COP of the integrated heating system decreased significantly by 20.89%. This quantitative result clearly highlights the balance between economic improvement and energy efficiency. The fundamental reason for this is that the substantially reduced collector area limits the system’s ability to utilize free solar energy effectively, necessitating greater energy input from electrical equipment (primarily the ASHP), thereby reducing the system’s overall energy efficiency.

The above analysis demonstrates that the optimization framework employed in this study successfully shifts the system configuration from a purely technical performance-oriented approach to a techno-economically oriented one. Although the decline in the system’s overall COP indicates a compromise in energy utilization, the substantial reduction in AEC holds greater practical significance for cost-sensitive rural users. This result underscores that the optimal design of renewable energy systems must strike a balance between energy efficiency, initial investment, and operational costs.

5. Conclusions

This study demonstrated, through integrated modeling, simulation, and optimization, that the SASHP system is both technically viable and economically attractive for rural residential heating in China’s HSCW zone. The optimized system achieves this by significantly reducing both capital and operational expenditures, thereby establishing it as a competitive alternative to conventional heating solutions. The principal findings are summarized as follows:

(1)

The average building heat load during the heating season in Hangzhou is 3.38 kW, with a maximum of 5.9 kW.

(2)

In this design scheme, the supply and return water temperatures are generally within the range of 45/35 °C. The cumulative total energy consumption of all equipment is 1354.01 kWh. The COP of the air source heat pump is 2.43, while the COP of the system is 3.67. Furthermore, the thermal comfort calculation is based on the center point of the room, and the results show that the room is in a C-level thermal comfort state. This 51% improvement in overall system efficiency not only validates the integration methodology but also indicates reduced grid dependency during operation while ensuring consistent comfort.

(3)

After optimization, the 35.60% reduction in initial investment brings the system within reach of rural households, while the 32.68% reduction in AEC particularly enhances long-term affordability. These improvements directly address the primary barrier of economic accessibility, transforming the SASHP system from a technical possibility into a financially viable solution for rural households, providing a quantitative decision-making basis for such trade-offs, representing a crucial pathway in renewable heating technology adoption for rural areas.

(4)

This study demonstrates a clear return on investment through lower annual operating costs. Thus, the significant reduction in initial investment (35.60%) after optimization becomes a key driver for promotion. Accordingly, further uptake can be accelerated through targeted government subsidies or low-interest green loans aimed at covering the upfront capital cost of renewable heating systems for rural households.

This study in Hangzhou in an HSCW climate zone suggests strong reproducibility across similar climatic zones, potentially impacting regional energy strategies. Future research directions should explore scaling effects for community-level implementations and integration with other renewable sources. The optimization framework established herein provides a validated methodology for continuous improvement of hybrid energy systems, contributing to global efforts in sustainable building energy solutions.