In recent years, the global shift toward renewable energy has intensified, with solar power systems playing a pivotal role in this transition. Traditional solar energy utilization methods, such as photovoltaic (PV) and concentrated solar power (CSP) systems, face limitations in efficiency due to spectral mismatches and thermal losses. To address these challenges, we propose an innovative solar power system that integrates spectral beam splitting technology into a tower-type thermal-photovoltaic hybrid configuration. This approach aims to optimize the use of the solar spectrum by directing specific wavelengths to PV cells for electricity generation and reflecting the remainder to a thermal receiver for heat-based power production. By combining these elements, the solar power system achieves higher overall efficiency compared to conventional setups.
The core of this solar power system lies in its ability to split the solar spectrum efficiently. We designed a spectral beam splitting glass that transmits wavelengths between 500 nm and 900 nm—optimal for silicon-based PV cells—while reflecting other wavelengths to a central thermal receiver. This glass is incorporated into PV modules, replacing conventional heliostats in a tower-type CSP arrangement. The system’s layout includes a field of these modified heliostats, a central tower with a thermal receiver, and associated power generation components such as heat exchangers and turbines. This integration reduces optical path losses and enhances the solar power system’s performance by utilizing a broader range of the solar spectrum.
To optimize the heliostat field, we employed the MUUEN algorithm, which ensures minimal shading and blocking losses. This algorithm arranges heliostats in a radial staggered pattern around the central tower, with coordinates calculated to maximize cosine efficiency. The field consists of multiple concentric rings, where each heliostat’s position is determined based on solar geometry and receiver orientation. For instance, the coordinates of a heliostat are given by:
$$x_m = R_i \sin \psi_m$$
$$y_m = R_i \cos \psi_m$$
$$z_m = z_0$$
where \( R_i \) is the radius of the i-th ring, \( \psi_m \) is the angle from the north axis, and \( z_0 \) is the height of the heliostat. This arrangement results in an average annual cosine efficiency of approximately 75.18%, significantly higher than fixed-tilt PV systems, which typically achieve around 65.97%. The solar power system’s design thus leverages advanced optical modeling to improve energy capture.
The mathematical model for predicting electricity generation in this solar power system comprises PV and thermal components. For the PV part, the maximum power output under spectral beam splitting is calculated as:
$$P_{PV,BS} = V_{OC,BS} \cdot I_{SC,BS} \cdot FF$$
where \( V_{OC,BS} \) is the open-circuit voltage, \( I_{SC,BS} \) is the short-circuit current, and \( FF \) is the fill factor. These parameters are derived from the spectral properties of the beam splitter and the PV cells. Specifically, the short-circuit current is expressed as:
$$I_{SC,BS} = \int_0^{\infty} \tau(\lambda) \cdot E(\lambda) \cdot QE(\lambda) \cdot \frac{e \lambda}{hc} d\lambda$$
Here, \( \tau(\lambda) \) is the spectral transmittance of the beam splitting glass, \( E(\lambda) \) is the spectral irradiance under AM1.5D conditions, \( QE(\lambda) \) is the quantum efficiency of the PV cells, \( e \) is the electron charge, \( h \) is Planck’s constant, and \( c \) is the speed of light. The open-circuit voltage is adjusted for the spectral range:
$$V_{OC,BS} = \frac{hc}{\lambda_2} \cdot \frac{V_{OC}}{E_g}$$
where \( \lambda_2 = 900 \) nm is the upper cutoff wavelength, \( V_{OC} \) is the standard open-circuit voltage, and \( E_g = 1.4 \) eV is the bandgap energy of monocrystalline silicon. The fill factor is computed as:
$$FF = \frac{v_{OC} – \ln(v_{OC} + 0.72)}{1 + v_{OC}} (1 – R_S)$$
with \( v_{OC} = \frac{V_{OC,BS}}{V_{th}} \), where \( V_{th} = \frac{\eta_f k T}{e} \) is the thermal voltage, \( \eta_f \) is the diode ideality factor, \( k \) is Boltzmann’s constant, \( T \) is the cell temperature, and \( R_S \) is the series resistance. Typical values for these constants are summarized in Table 1.
| Parameter | Symbol | Value |
|---|---|---|
| Open-circuit voltage (standard) | \( V_{OC} \) | 0.7485 V |
| Fill factor | \( FF \) | 0.855 |
| Diode ideality factor | \( \eta_f \) | 1.28 |
| Series resistance | \( R_S \) | 0.012 Ω |
| Bandgap energy | \( E_g \) | 1.4 eV |
| Cell temperature | \( T \) | 30 °C |
For the thermal part of the solar power system, the power output is determined by the incident radiation on the thermal receiver and the efficiency of the heat-to-electricity conversion. The thermal power per unit area is given by:
$$P_{TH,BS} = Q_{TH,BS} \cdot \eta_{else}$$
where \( Q_{TH,BS} \) is the incident radiation on the receiver, calculated as:
$$Q_{TH,BS} = Q_{in} \int_0^{\infty} \rho(\lambda) d\lambda$$
Here, \( \rho(\lambda) \) is the spectral reflectance of the beam splitting glass, and \( Q_{in} \) is the total incident radiation on the heliostat field, accounting for cosine efficiency. The factor \( \eta_{else} = 0.237 \) represents losses due to factors like mirror reflectivity, cleanliness, and attenuation. The cosine efficiency for each heliostat is derived from solar geometry:
$$\eta_{\cos} = \cos \theta_i$$
with \( \cos 2\theta_i = \frac{(z_0 – z_1) \sin \alpha – e_1 \cos \alpha \sin A – n_1 \cos \alpha \cos A}{\sqrt{(z_0 – z_1)^2 + e_1^2 + n_1^2}} \), where \( \alpha \) is the solar altitude angle, \( A \) is the solar azimuth angle, and \( (z_1, e_1, n_1) \) are the coordinates of the heliostat relative to the receiver.
To evaluate the solar power system’s performance, we simulated it under AM1.5D solar spectrum conditions and used typical meteorological year data from Lhasa, China, which has high direct normal irradiance (DNI). The annual DNI distribution is relatively uniform, with seasonal variations shown in Table 2. The spectral beam splitting configuration was optimized by testing different wavelength ranges; the highest system efficiency was achieved with a transmission band of 500–900 nm, resulting in an average transmittance of 49.08% and reflectance of 50.92% for the incident radiation.
| Month | Direct Normal Irradiance (kWh/m²) | Cosine Efficiency (%) |
|---|---|---|
| January | 185.2 | 74.5 |
| February | 178.9 | 75.1 |
| March | 192.3 | 75.8 |
| April | 201.7 | 76.2 |
| May | 210.5 | 76.0 |
| June | 215.8 | 75.5 |
| July | 208.4 | 75.3 |
| August | 199.6 | 74.9 |
| September | 187.1 | 74.6 |
| October | 175.3 | 74.2 |
| November | 168.7 | 73.8 |
| December | 180.5 | 74.1 |
The annual electricity generation for the proposed solar power system was compared to conventional PV and CSP systems. For the PV part, the efficiency under spectral beam splitting reached 33.17%, compared to 25.06% for standard fixed-tilt PV systems. The thermal part achieved an efficiency of 17.83% after accounting for optical and system losses. The total system efficiency was calculated as:
$$\eta_{SYS} = \frac{P_{total}}{Q_Z}$$
where \( P_{total} = P_{PV,BS} + P_{TH,BS} \) is the combined power output, and \( Q_Z \) is the total solar radiation. The results, summarized in Table 3, show that the hybrid solar power system outperforms both conventional systems, with an overall efficiency of 21.32%, compared to 16.53% for PV-only and 17.83% for CSP-only systems.
| Parameter | Hybrid Solar Power System | Conventional PV System | Conventional CSP System |
|---|---|---|---|
| Total Incident Radiation, \( Q_Z \) (kWh/m²) | 7696.64 | 7696.64 | 7696.64 |
| PV Incident Radiation, \( Q_{PV} \) (kWh/m²) | 2839.81 | 5077.47 | — |
| Thermal Incident Radiation, \( Q_{TH} \) (kWh/m²) | 2946.53 | — | 5786.34 |
| PV Power Output, \( P_{PV} \) (kWh/m²) | 941.91 | 1272.41 | — |
| Thermal Power Output, \( P_{TH} \) (kWh/m²) | 698.91 | — | 1371.32 |
| Total Power Output, \( P_{total} \) (kWh/m²) | 1640.82 | 1272.41 | 1371.32 |
| PV Efficiency, \( \eta_{PV} \) (%) | 12.24 | 16.53 | — |
| Thermal Efficiency, \( \eta_{TH} \) (%) | 9.08 | — | 17.83 |
| Total System Efficiency, \( \eta_{SYS} \) (%) | 21.32 | 16.53 | 17.83 |
Further analysis involved simulating daily electricity generation throughout the year. The hybrid solar power system consistently produced higher output, with peaks during summer months due to longer daylight hours and higher irradiance. The daily power generation profile demonstrated the system’s reliability and superior performance across seasons. For instance, the average daily output in June was approximately 60 kWh/m², compared to 45 kWh/m² for conventional PV and 50 kWh/m² for CSP systems. This enhancement is attributed to the efficient spectral utilization and reduced thermal losses in the PV components.
The optical analysis under AM1.5D spectrum revealed that the spectral beam splitting glass effectively separates the solar spectrum, with the PV cells receiving radiation primarily in the 500–900 nm range, where silicon cells have high quantum efficiency. The reflected radiation, covering ultraviolet and infrared regions, is directed to the thermal receiver, minimizing energy waste. The quantum efficiency of monocrystalline silicon cells and the transmittance curve of the beam splitter are aligned to maximize photon conversion. The annual energy yield for the solar power system was computed by integrating the power output over time, considering the varying solar angles and weather conditions in Lhasa.
In discussion, the proposed solar power system offers significant advantages over traditional approaches. By decoupling the spectral bands for PV and thermal conversion, it reduces the thermal stress on PV cells, thereby maintaining higher efficiency. Moreover, the integration of beam splitting into heliostats simplifies the system architecture and reduces optical losses compared to intermediate beam splitter setups. However, challenges such as the cost of spectral beam splitting glass and the complexity of field maintenance need to be addressed in future implementations. The use of the MUUEN algorithm for heliostat field design ensures scalability, making this solar power system suitable for large-scale applications.
In conclusion, the novel tower-type spectral beam splitting hybrid solar power system demonstrates a substantial improvement in electricity generation efficiency. Through detailed optical and thermodynamic modeling, we have shown that this system achieves an annual efficiency of 21.32%, outperforming conventional PV and CSP systems by 4.79% and 3.49%, respectively. The integration of advanced spectral management and optimized field design makes this solar power system a promising solution for enhancing solar energy utilization. Future work will focus on experimental validation and cost-benefit analysis to facilitate commercial adoption of this innovative solar power system.