In recent years, the integration of concentrated solar power (CSP) with advanced thermodynamic cycles has garnered significant attention for enhancing energy conversion efficiency. This paper focuses on a novel solar power system that combines a tower-type CSP setup with an integrated energy storage mechanism, utilizing supercritical carbon dioxide (S-CO₂) and quartzite as storage media. The core of this solar power system is a recompressed S-CO₂ Brayton cycle, which replaces conventional Rankine cycles to achieve higher efficiency at elevated temperatures. The motivation stems from the intermittent nature of solar radiation, which necessitates reliable storage solutions to ensure continuous operation. Traditional CSP plants often employ molten salt dual-tank storage systems, but these face challenges such as high costs, material degradation, and potential solidification issues. In contrast, the proposed solar power system leverages S-CO₂ as both the working fluid and storage medium, coupled with a thermocline storage tank filled with low-cost solid materials like quartzite. This integration simplifies the system layout, reduces capital expenditure, and improves overall performance. The primary objective is to analyze the thermodynamic and economic characteristics of this solar power system, emphasizing dynamic storage behavior, collector efficiency, and cost-effectiveness compared to conventional configurations.
The solar power system described here comprises three main components: the power cycle, solar collector system, and thermocline storage tank. The recompressed S-CO₂ Brayton cycle operates with a turbine inlet temperature of 600°C and pressure of 30 MPa, achieving a net power output of 50 MW. The solar collector system, based on a heliostat field, captures and concentrates solar energy, with key parameters including a total optical efficiency of 0.75 and a design direct normal irradiance (DNI) of 0.85 kW/m². The thermocline storage tank, with a height of 24 m and diameter of 30 m, uses S-CO₂ and quartzite (with a porosity of 0.22) to store thermal energy for up to 9 hours. This solar power system eliminates the need for intermediate heat exchangers, such as molten salt-to-S-CO₂ units, thereby reducing exergy losses and enhancing temperature compatibility. The following sections detail the mathematical modeling, performance evaluation under typical daily conditions, and economic assessment, highlighting the advantages of this integrated approach for sustainable energy generation.
The mathematical models for the solar power system are developed using the Gensystem platform, ensuring accuracy through validation with experimental data and literature. The recompressed S-CO₂ Brayton cycle is modeled with energy balance equations for each component. The turbine work output is given by:
$$W_t = q_m (h_1 – h_2)$$
where \( W_t \) is the turbine work (kW), \( q_m \) is the mass flow rate (kg/s), and \( h \) represents specific enthalpy (kJ/kg) at state points. The compressor consumptions are calculated as:
$$W_{mc} = q_m (1 – x) (h_6 – h_5)$$
$$W_{rc} = x q_m (h_8 – h_4)$$
Here, \( x \) is the split ratio, and subscripts denote state points in the cycle. The net power output of the solar power system is:
$$W_{net} = W_t – W_{mc} – W_{rc}$$
The high-temperature and low-temperature recuperators adhere to thermal balance equations:
$$h_2 – h_3 = h_{10} – h_9$$
$$h_3 – h_4 = (1 – x)(h_7 – h_6)$$
Validation against reference data shows a maximum relative error of 1.35%, confirming model reliability. For the solar collector system, the energy received by the heliostat field is:
$$Q_{solar} = \delta_{DNI} A_{Heliostat} \eta_{hf} = Q_{rec} / \eta_{hf}$$
where \( \delta_{DNI} \) is the DNI (kW/m²), \( A_{Heliostat} \) is the total reflector area (m²), and \( \eta_{hf} \) is the optical efficiency. The collector efficiency \( \eta_{rec} \) is derived from:
$$\eta_{rec} = \frac{Q_0}{Q_{rec}} = \frac{Q_{rec} – Q_{ref} – Q_{conv} – Q_{rad}}{Q_{rec}}$$
Reflective, convective, and radiative losses are quantified using surface properties and environmental conditions. The thermocline storage tank model discretizes the tank into axial segments, with energy balances for the fluid and solid phases. The fluid phase equation is:
$$\varepsilon \rho_f (A_c \Delta x) c_{p,f} \frac{dT_f}{d\tau} + \varepsilon u_f \rho_f (A_c \Delta x) c_{p,f} \frac{\partial T_f}{\partial x} = \varepsilon \lambda_f (A_c \Delta x) \frac{\partial^2 T_f}{\partial x^2} – h_{fs} A_{fs} (T_f – T_s)$$
and the solid phase equation is:
$$(1 – \varepsilon) \rho_s (A_c \Delta x) c_{p,s} \frac{dT_s}{d\tau} = (1 – \varepsilon) \lambda_s (A_c \Delta x) \frac{\partial^2 T_s}{\partial x^2} + h_{fs} A_{fs} (T_f – T_s)$$
Parameters such as density (\( \rho \)), specific heat (\( c_p \)), and thermal conductivity (\( \lambda \)) are temperature-dependent for S-CO₂ and quartzite. The heat transfer coefficient \( h_{fs} \) is computed via Nusselt number correlation:
$$Nu = \frac{h_{fs} d_p}{\lambda_f} = 2 + 1.1 Pr^{1/3} Re^{0.6}$$
This model is validated against experimental results, showing good agreement in thermocline evolution.
| Component | Parameter | Value |
|---|---|---|
| Power Cycle | Rated Power | 50 MW |
| Turbine Inlet Temperature | 600°C | |
| Turbine Inlet Pressure | 30 MPa | |
| Compressor Efficiency | 0.89 | |
| Solar Collector | Heliostat Field Optical Efficiency | 0.75 |
| Design DNI | 0.85 kW/m² | |
| Collector Surface Area | 560 m² | |
| Thermocline Tank | Height | 24 m |
| Diameter | 30 m | |
| Porosity | 0.22 | |
| Storage Duration | 9 hours |
The performance of the solar power system is evaluated under typical daily conditions, such as summer and winter solstices, to assess efficiency and dynamic behavior. The collector efficiency varies with DNI; for instance, on the summer solstice, it remains stable at approximately 0.84, while on the winter solstice, it fluctuates more significantly due to lower radiation intensity. The thermocline storage tank exhibits dynamic characteristics during cyclic charging and discharging. After 13 cycles, the outlet temperatures stabilize, with a temperature drop of 63 K at the end of discharge and a rise of 46 K at the end of charge. The instantaneous energy storage in the tank decreases by 26% during charging, with the solid phase dominating storage capacity due to higher density and lower porosity.
For the solar power system on a summer solstice day, the net power output maintains 50 MW during charging, and the cycle efficiency averages 46.7%. During discharge, the power output slightly decreases to 49.8 MW due to temperature stratification in the tank. The mass flow rate varies to maintain constant power, increasing by 162 t/h by the end of discharge. On the winter solstice, the storage and discharge durations reduce to 7 hours, and the net power fluctuates with DNI. The integrated solar power system demonstrates superior performance compared to a dual-tank CSP system, with higher daily average generation efficiency—29.5% vs. 27.7% in summer and 26.0% vs. 24.3% in winter. This improvement stems from the elimination of intermediate heat exchangers, allowing higher turbine inlet temperatures.
| Parameter | Integrated System (Summer) | Dual-Tank System (Summer) | Integrated System (Winter) | Dual-Tank System (Winter) |
|---|---|---|---|---|
| Heliostat Field Area (m²) | 486,740 | 510,310 | 486,740 | 510,310 |
| Daily Solar Energy Received (MWh) | 3,043.7 | 3,253.7 | 2,374.3 | 2,489.3 |
| Daily Electricity Output (MWh) | 900.0 | 900.0 | 617.3 | 605.8 |
| Average Generation Efficiency (%) | 29.5 | 27.7 | 26.0 | 24.3 |
The economic analysis of the solar power system considers total investment costs, including equipment, operation and maintenance (O&M), and land costs. The equipment cost for key components is calculated using empirical equations adjusted to 2022 values via the Chemical Engineering Plant Cost Index (CEPCI). For example, turbine cost is given by:
$$Z_t = 479.34 \cdot q_{m,t} \cdot \left( \frac{1}{0.93 – \eta_t} \right) \cdot \ln \left( \frac{p_{in,t}}{p_{out,t}} \right) \cdot (1 + e^{0.036 \cdot T_{in} – 54.4})$$
where \( Z_t \) is in USD. Similarly, compressor cost is:
$$Z_c = 71.1 \cdot q_{m,c} \cdot \left( \frac{1}{0.92 – \eta_c} \right) \cdot \left( \frac{p_{out,t}}{p_{in,t}} \right) \cdot \ln \left( \frac{p_{out,t}}{p_{in,t}} \right)$$
Heliostat field cost is \( Z_h = 120 \cdot A_{Heliostat} \), and storage tank cost is derived from:
$$Z_s = 1.218 \cdot F_M \cdot \exp \left\{ 11.66 – 0.61 \cdot \ln(264.17 \cdot V) + 0.045 \cdot [\ln(264.17 \cdot V)]^2 \right\}$$
Here, \( F_M \) is the material factor (2.4 for dual-tank, 7.2 for thermocline), and \( V \) is the volume (m³). The total investment cost for the integrated solar power system is USD 152.051 million, compared to USD 167.936 million for the dual-tank system. O&M costs are assumed at 0.8% of equipment cost in the first year, escalating at 2.5% annually, and land cost is 3% of equipment cost. The levelized cost of electricity (LCOE) is computed as:
$$Z_{LCOE} = \frac{Z_{Equip} + Z_{Land} + \sum_{t=1}^{L} \frac{Z_{OM,t}}{(1 + i)^t}}{\sum_{t=1}^{L} \frac{\Delta E_t}{(1 + i)^t}}$$
where \( L = 30 \) years is the system lifetime, \( \Delta E_t \) is annual electricity generation (kWh), and \( i = 8\% \) is the discount rate. The dynamic payback period \( P_t \) satisfies:
$$\sum_{t=0}^{P_t} (PCI – PCO)_t (1 + i)^{-t} = 0$$
The integrated solar power system achieves an LCOE of USD 0.1112 per kWh, 9.45% lower than the dual-tank system (USD 0.1228 per kWh), and a payback period of 9.9 years, reduced by 1.8 years. This cost reduction is attributed to lower storage expenses, as S-CO₂ and quartzite replace expensive molten salt, and simplified components.
| Indicator | Integrated System | Dual-Tank System |
|---|---|---|
| Total Investment Cost (USD million) | 152.051 | 167.936 |
| LCOE (USD/kWh) | 0.1112 | 0.1228 |
| Dynamic Payback Period (years) | 9.9 | 11.7 |
| Storage Tank Volume (m³) | 16,956 | 6,916 (hot) / 6,428 (cold) |
In conclusion, the integrated solar power system with S-CO₂ Brayton cycle and thermocline storage demonstrates significant advantages in thermodynamic and economic performance. The dynamic analysis reveals stable operation after 13 charge-discharge cycles, with manageable temperature variations. The solar power system achieves higher efficiency and lower costs due to the direct use of S-CO₂, eliminating intermediate heat transfer losses. This approach not only enhances the reliability of solar energy utilization but also contributes to the decarbonization of power generation. Future work could explore optimization of component sizes and hybridization with other renewable sources to further improve this solar power system.
The robustness of this solar power system is underscored by its ability to maintain high performance across seasonal variations, making it a viable solution for large-scale renewable energy deployment. The integration of thermal energy storage directly into the power cycle exemplifies innovation in solar power system design, paving the way for more sustainable and economically feasible energy solutions. As the demand for clean energy grows, such advanced solar power systems will play a crucial role in meeting global energy needs while minimizing environmental impact.