Parameter Optimization of Heating System of Phase Change Energy Storage Tank Coupled with Solar Air Source Heat Pump

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To address the design challenges of key parameters in phase change energy storage systems integrated with solar-assisted air source heat pumps, this study proposes a numerical optimization framework based on TRNSYS simulations and the Hooke-Jeeves algorithm. The system configuration emphasizes energy storage efficiency and operational stability through multi-objective parameter tuning.

1. System Configuration and Mathematical Modeling

The hybrid energy storage system integrates three primary components:

  1. Flat-plate solar collectors
  2. Air-source heat pump (ASHP) unit
  3. Phase change material (PCM)-based thermal storage tank

Solar collector efficiency model:
$$ \eta = a_1 – a_2 \frac{T_{f,i} – T_a}{I_T} – a_3 \frac{(T_{f,i} – T_a)^2}{I_T} $$
where $a_1$, $a_2$, and $a_3$ are empirical coefficients.

PCM storage dynamics:
$$ \frac{dh_b}{dt} = \begin{cases}
c_s \frac{dT_b}{dt}, & T_b < T_{ml} \\
\frac{\Delta h_s}{T_{mh} – T_{ml}} \frac{dT_b}{dt}, & T_{ml} < T_b < T_{mh} \\
c_l \frac{dT_b}{dt}, & T_b > T_{mh}
\end{cases} $$

Table 1. Thermophysical Properties of PCM and System Components
Parameter Value
PCM latent heat 218 kJ/kg
Solid PCM conductivity 0.082 W/(m·K)
Collector area 187 m²
Storage tank volume 4 m³

2. Optimization Methodology

The Hooke-Jeeves algorithm minimizes annualized system costs through parametric tuning:

$$ \text{Minimize } Z = C_O + \frac{i(1+i)^n}{(1+i)^n-1}C_I $$

Key optimization variables include:

  • Collector tilt angle (20°–60°)
  • Storage tank volume factor (0.04–0.11)
  • ASHP capacity (30–80 kW)
Table 2. Optimization Constraints and Step Sizes
Variable Range Step
Collector area 125–200 m² 5 m²
PCM volume 2–8 m³ 0.5 m³

3. Performance Analysis

The optimized energy storage system demonstrates:

$$ \text{COP}_S = \frac{\int (Q_f + Q_{ASHP})dt}{\int (W_1 + W_2 + W_3 + W_4)dt} = 3.8 \text{ (21% improvement)} $$

Table 3. Thermal Performance Comparison
Metric Pre-optimization Post-optimization
Annual heat release (kWh/m³) 6,617 7,622
Storage efficiency (%) 64.2 75.1

4. Economic Evaluation

The optimized configuration reduces levelized costs by 21% through:

  1. 15% lower collector area requirements
  2. 36% reduction in ASHP capacity
  3. 20% improved storage utilization

$$ \text{Sensitivity index } S_i = \frac{\partial(f_i)/f_{i,opt}}{\partial(\pi_i)/\pi_{i,opt}} $$

Key sensitivity results:

  • Collector area: 0.231
  • ASHP capacity: 0.222
  • Storage volume: 0.0596

5. Conclusion

The proposed optimization framework enhances energy storage system performance through:

  1. Synergistic integration of solar thermal and ASHP resources
  2. Precise dimensional matching of storage capacity
  3. Climate-responsive collector orientation

Future work will investigate advanced PCM materials and predictive control strategies for grid-responsive operation.

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