The integration of phase change energy storage technology with solar air source heat pump (ASHP) systems presents a promising solution for enhancing energy efficiency and operational stability in heating applications. This study focuses on optimizing the critical parameters of an air energy storage system combined with solar ASHP to minimize annual costs while maximizing thermal performance. The methodology employs TRNSYS simulation software coupled with the Hooke-Jeeves optimization algorithm via GENOPT, targeting variables such as collector area, heat pump capacity, tilt angle, azimuth angle, storage tank volume, and volume factor.
System Overview and Mathematical Formulation
The hybrid system comprises vacuum tube solar collectors, an ASHP unit, a phase change energy storage tank (air energy storage system), and auxiliary components (Figure 1). Key equations governing the system’s thermal dynamics are outlined below:
1. Solar Collector Efficiency
The efficiency of the vacuum tube collector is modeled as:η=a1−a2Tf,i−TaIT−a3(Tf,i−Ta)2ITη=a1−a2ITTf,i−Ta−a3IT(Tf,i−Ta)2
where a1=0.73a1=0.73, a2=2.40a2=2.40, and a3=0a3=0 are empirical coefficients, Tf,iTf,i is the collector inlet temperature, TaTa is ambient temperature, and ITIT is solar irradiance.
2. ASHP Coefficient of Performance (COP)
The COP of the air source heat pump is defined as:COPa=QASHPPASHPCOPa=PASHPQASHP
where QASHPQASHP is the heat output (kW), and PASHPPASHP is the power consumption (kW).
3. Thermal Dynamics of the Air Energy Storage System
The phase change material (PCM) tank’s energy balance is governed by:Qhs=mhschs(Ths,o−Ths,i)=mbdhbdtQhs=mhschs(Ths,o−Ths,i)=mbdtdhb
where mhsmhs and chschs are the mass flow rate and specific heat of the heat transfer fluid, Ths,oThs,o and Ths,iThs,i are outlet/inlet temperatures, and dhb/dtdhb/dt represents the enthalpy change of the PCM.
The latent heat release/absorption during phase transition is modeled using a temperature-dependent liquid fraction (ϵbϵb):ϵb=ϵb=
where TmlTml and TmhTmh are the melting and solidification temperatures of the PCM (58–60°C for paraffin wax).
Optimization Framework
The Hooke-Jeeves algorithm minimizes the annualized cost function (ZZ), which combines capital expenditure (CI) and operational costs (CO):Z=CO+i(1+i)n(1+i)n−1CIZ=CO+(1+i)n−1i(1+i)nCI
where i=5.5%i=5.5% is the annual interest rate, and n=15n=15 years is the system lifespan.
Cost Components
- Capital Cost (CI):
CI=A×850+V1×600+QASHP×2400+V2×7600+18,000CI=A×850+V1×600+QASHP×2400+V2×7600+18,000
- AA: Collector area (m²)
- V1V1: Water tank volume (m³)
- QASHPQASHP: ASHP heating capacity (kW)
- V2V2: PCM tank volume (m³)
- Operational Cost (CO):
CO=(W1+W2+W3+W4)×0.51CO=(W1+W2+W3+W4)×0.51
- W1,W2,W3,W4W1,W2,W3,W4: Energy consumption of pumps and ASHP (kWh)
Key Optimization Variables and Constraints
The optimization variables and their bounds are summarized in Table 1.
Table 1: Optimization Parameters and Ranges
| Parameter | Range | Step Size |
|---|---|---|
| Collector area (m²) | 125–200 | 5 |
| ASHP capacity (kW) | 30–80 | 2 |
| Collector tilt (°) | 20–60 | 2 |
| Azimuth angle (°) | -10–10 | 1 |
| PCM tank volume (m³) | 2–8 | 0.5 |
| Volume factor | 0.04–0.11 | 0.01 |
Optimization Results
The optimized parameters (Table 2) reduced the annualized cost by 21%, from ¥56,100 to ¥43,750, while improving thermal performance.
Table 2: Pre- and Post-Optimization Parameters
| Parameter | Pre-Optimization | Post-Optimization |
|---|---|---|
| Collector area (m²) | 157 | 187 |
| ASHP capacity (kW) | 63.8 | 40.5 |
| Collector tilt (°) | 40 | 44.1 |
| Azimuth angle (°) | 0 | -1 |
| PCM tank volume (m³) | 5 | 4 |
| Volume factor | 0.07 | 0.1 |
Performance Improvements
- Thermal Storage Capacity:
- Annual heat storage per unit volume increased by 16.5% (6,651.5 → 7,754.4 kWh/m³).
- Annual heat release per unit volume increased by 15.1% (6,617.2 → 7,621.6 kWh/m³).
- Collector Efficiency:
Monthly average efficiency improved across all seasons, peaking at 50% in February (Figure 2). - System Stability:
The coefficient of performance (COPsCOPs) demonstrated reduced sensitivity to environmental fluctuations, indicating enhanced operational stability (Figure 3).
Sensitivity Analysis
The relative sensitivity (SiSi) of each parameter to the annual cost is quantified in Table 3.
Table 3: Relative Sensitivity of Optimization Variables
| Parameter | Sensitivity (SiSi) |
|---|---|
| Collector area | 0.231 |
| ASHP capacity | 0.222 |
| PCM tank volume | 0.0596 |
| Collector tilt | 0.00489 |
| Volume factor | -0.0083 |
Key findings:
- Collector area and ASHP capacity dominate cost sensitivity.
- Increasing solar collector contribution while reducing ASHP dependency lowers costs.
Conclusion
The air energy storage system integrated with solar ASHP achieves significant cost savings and performance enhancements through parameter optimization. By prioritizing solar energy utilization and optimizing PCM tank dimensions, the system attains higher thermal storage capacity, improved efficiency, and resilience against environmental variability. This work underscores the potential of hybrid air energy storage systems in sustainable heating applications, offering a roadmap for future designs in renewable energy integration.