Experimental investigation and feasibility analysis of a thermophotovoltaic cogeneration system in high-temperature production processes

Abstract

The experimental I-V characteristics of a Si cell module in a thermophotovoltaic (TPV) system were investigated using SiC or Yb₂O₃ radiator. The results demonstrate that the short-circuit current increases while the open-circuit voltage, along with the fill factor, decreases with the cell temperature when the radiator temperature increases from 1273 to 1573 K, leading to a suppressed increase of the output power of the system. The maximum output power density of the cell module is 0.05 W/cm² when the temperature of the SiC radiator is 1573 K, while the electrical efficiency of the system is only 0.22%. The efficiency is 1.3% with a Yb₂O₃ radiator at the same temperature, however, the maximum output power density drops to 0.03 W/cm². The values of the open-circuit voltage and the maximum output power obtained from the theoretical model conform to the experimental ones. But the theoretical short-circuit current is higher because of the existence of the contact resistance inside the cell module. In addition, the performance and cost of TPV cogeneration systems with the SiC or Yb₂O₃ radiator using industrial high-temperature waste heat were analyzed. The system electrical efficiency could reach 3.1% with a Yb₂O₃ radiator at 1573 K. The system cost and investment recovery period are 6732 EUR/kWel and 14 years, respectively.

Keywords

thermophotovoltaic (TPV) / industrial waste heat / ytterbium oxide / system efficiency

Introduction

Thermophotovoltaic (TPV) systems offer interesting ways to convert heat into electricity with photocells and have potential applications in the fields of commerce and industry due to the diversity of heat sources and potential high efficiency [1-8]. Modern high-temperature production processes, such as metallurgy and ironmaking, are usually accompanied by the generation of a large quantity of high-temperature waste heat (1000-1800 K). In 2003, Bauer et al. analyzed the application prospect of the TPV technology using waste heat in the glass production [9]. The results indicated that the large-scale use of the TPV heat recovery in the UK glass industry could provide approximately 21% of the site electricity on average and reduce energy related CO₂ emissions by approximately 6%. Therefore, it is worthwhile to investigate the TPV cogeneration system using the high-temperature waste heat. TPV cells are the core component to realize the thermoelectric conversion process. At present, TPV cells are generally classified into two categories: commercial solar cells represented by Si (E_g = 1.12 eV) and low bandgap cells represented by GaSb (E_g = 0.72 eV) and InGaAsSb (E_g = 0.53 eV) [10]. Because Si ells are inexpensive and non toxic, it is attractive to develop the commercial TPV cogeneration system with Si cells. However, few related experiments have been reported, up to the present. In this paper, a TPV experimental system was established using an electric furnace to simulate the high-temperature pipeline. The output performances of a Si cell module at different radiator temperatures were obtained and a novel mathematical physical model was established. Besides, the performances of the TPV systems with SiC or Yb₂O₃ radiator using industrial high-temperature waste heat were predicted.

Experimental system

As shown in Fig. 1, the experimental system is made up of a high-temperature electric furnace, a radiator, a Si cell module, a cooling device, and a monitor and testing system, etc. The outer surface of the radiator was heated by 12 Si-Mo bars, and the Si cell module generated electric power using the radiant energy from the high-temperature radiator, as illustrated in Fig. 2(a). To ensure the uniformity of the radiator temperature, an effective length of 150 mm was set as the radiation zone, and the two ends of the radiator are blocked with insulation asbestos.

The radiator is of vital importance since the surface spectral emissivity determines the radiant energy at a specific wavelength. Two radiators, SiC and Yb₂O₃, with different spectral characteristics were adopted, as presented in Fig. 2(b) and (c). A vacuum plasma-spray coating technique was used to deposit the 100 μm thick Yb₂O₃ on SiC substrate. To facilitate the spray, the SiC tube was cut into two parts. The spectral emissivity of SiC and Yb₂O₃ were measured by the AvaSpec-NIR256 near-infrared optical spectroscopy at 1073 K, as demonstrated in Fig. 3. As can be seen from Fig. 3, the maximum spectral emissivity of Yb₂O₃ is 0.76 at approximately 980 nm. The spectral emissivity is less than 0.5 beyond 1100 nm. The spectra match with the spectral sensitivity of silicon photocells. However, the spectral emissivity of SiC in the whole wavelength rarely changes because SiC is a typical gray body material.

Water cooling was used to prevent the cell temperature from being too high to influence the performance. Mullite, 60 mm in length, was used to support the aluminum cooler. The outer surface of the radiator exposed to the environment was wrapped with insulation asbestos to reduce energy loss. The Si cells were pasted to the cooler with the 0.1 mm thick silicone. The dimension and active area of one cell were 1.7 cm × 1.3 cm and 1.99 cm², respectively. The cooler had 14-cell circuits mounted on the top and bottom faces, as depicted in Fig. 2(d), with highly reflective aluminum foil plated side walls, each circuit having two rows of 7 cells mounted in parallel. Then two circuits formed a module in series, which was connected to variable loads to obtain I-V characteristics by four-probe method under different experimental conditions.

The central temperatures of the inner and outer surfaces of the radiator were measure by B-type thermocouples with an accuracy of±1.0°C. The T and K-type thermocouples with an accuracy of±1.0°C were adopted to measure the inlet and outlet temperatures of the cooling water and the temperature of the cell, respectively. An Agilent 34970A data logger was used to collect data at an interval of 2 s. An electromagnetic flow meter (accuracy±0.5% F. S.) along with a pump was used to adjust the mass flow of the cooling water.

Theoretical model

The equivalent circuit of a single TPV cell is a multi-parameter active circuit. In practice, several cells usually compose a cell module in the form of series parallel, which will make the cell module more complex and difficult to describe using a similar equivalent circuit model. In this paper, each I-V characteristic of 28 Si cells was obtained using the equivalent circuit of a single TPV cell at first. Then, equations were established according to the Kirchhoff’s law through the connection relationship between the cells. Finally, the characteristic parameters of the entire module were obtained by adjusting the external load resistance.

I-V characteristic of a single cell

Although Shockley equation gives the I-V relationship of an ideal single cell, the influences of some factors, such as the surface effect, the generation and recombination of carriers in barrier region, the resistance effect, etc., will make the I-V characteristic of a practical TPV cell very different from the theoretical results [11]. So the equivalent circuit model of a practical P-N junction for a single TPV cell is given by [12]

(1)I=I_{\mathrm{ph}}-{\displaystyle \frac{V+I{R}_s}{R_{\mathrm{sh}}}}-I_{\mathrm{0}}\left[\exp {\displaystyle \frac{q(V+I{R}_s)}{nk{T}_c}}-\mathrm{1}\right].

The term on the left of Eq. (1) is the load current. The first term on the right of Eq. (1) is the photo-generated current I_ph. Referring to Ref [13], I_ph could be obtained.

(2)I_{\mathrm{ph}}=A_c{\displaystyle \frac{q}{hc}}{\displaystyle {\int }_{\mathrm{0}}^{\lambda g}(\mathrm{1}-R_c)\lambda {\eta }_Q(\lambda ,Tc)q_i(\lambda )d\lambda },

where A_c is the cell active area; q, the electron charge; R_c, the reflectance of the cell surface; h and c, the Planck Constant and light velocity, respectively; λ_g, the bandgap wavelength; η_Q(λ,T_c), the internal quantum efficiency of the cell; T_c, the cell temperature; and q_i(λ), the spectral irradiation density projected onto the cell surface. The second term is the current loss caused by the parallel resistance R_sh at the sum of the load voltage V and the series resistance voltage

I{R}_s

. R_sh is mainly created by the electric leakage on the cell edge and the recombination current in depletion region. R_s includes three parts: the contact resistance between the front metal electrode and the semiconductor material, the body resistance of the semiconductor material and the electrode resistance. R_s and R_sh can be expressed as

(3)R_s=\left|{\left({\displaystyle \frac{dI}{dV}}\right)}_{V=V_{\mathrm{oc}}}^{-\mathrm{1}}\right|=\left|{\left({\displaystyle \frac{dV}{dI}}\right)}_{I=\mathrm{0}}\right|,

(4)R_{\mathrm{sh}}=\left|{\left({\displaystyle \frac{dI}{dV}}\right)}_{V=\mathrm{0}}^{-\mathrm{1}}\right|=\left|{\left({\displaystyle \frac{dV}{dI}}\right)}_{I=I_{\mathrm{sc}}}\right|.

Therefore, R_s and R_sh could be obtained if the I-V curve slopes at V = V_oc and V = 0 were measured in the experiment. The third term is the current attenuation due to the diode effect of the PV cells. The reverse saturation current I₀ is given as [14]

(5)I_{\mathrm{0}}=\mathrm{17.2}\times {\mathrm{10}}^{-\mathrm{3}}{A}_c{T}_c^3\exp \left(-{\displaystyle \frac{E_g}{k{T}_c}}\right).

The bandgap energy E_g of the Si cell at any temperature is given by [15]

(6){\displaystyle \frac{E_g}{E_{g,Tref}}}=\mathrm{1}-\mathrm{0.0002677}(T_c-T_{\mathrm{ref}}),

where the reference temperature of the cell T_ref is 298 K and the reference bandgap energy E_g,Tref is 1.121 eV. The quality factor n could be obtained by Lambert W-function [16]

(7)I=n{\displaystyle \frac{kT}{q{R}_s}}\mathrm{Lambert}W\left[{\displaystyle \frac{q{R}_s{R}_{\mathrm{sh}}{I}_{\mathrm{0}}}{nkT(R_s+R_{\mathrm{sh}})}}\exp \left({\displaystyle \frac{q{R}_{\mathrm{sh}}(V+I_{\mathrm{0}}{R}_s+I_{\mathrm{ph}}{R}_s)}{nkT(R_s+R_{\mathrm{sh}})}}\right)\right]+{\displaystyle \frac{V-(I_{\mathrm{0}}+I_{\mathrm{ph}})R_{\mathrm{sh}}}{R_s+R_{\mathrm{sh}}}}.

Assuming I = 0, the quality factor n could be obtained with measured values of R_s, R_sh, T_c and V_oc.

The above analysis shows that it is easy to determine some parameters, such as I₀, R_s, R_sh, T_c and n. Therefore, I_ph could be determined if q_i(λ) is calculated and a theoretical I-V curve of a single cell could be obtained.

Spectral irradiation density

To accurately simulate the spectral irradiation density on each cell surface, Monte Carlo ray trace method was used. The radiant energy emitted by the radiator was divided into N energy beams. If an energy beam at a specific wavelength λ reached the cell surface through random movement, the tracking was stopped and another one was tracked. In this way, the spectral irradiation density at different wavelengths was obtained.

By repeating the above calculation processes, the I-V curves of 28 Si cells were obtained. Then the circuit network was constructed according to the corresponding cell position in the experiment. After substituting the performance parameters of each cell, the I-V characteristics of the cell module were obtained according to Kirchhoff’s law.

Results and discussions

SiC radiator

The I-V characteristics of the cell module at different SiC radiator temperatures were obtained by changing the heating power of the furnace. Due to the large number of cells, it was difficult to measure the performance parameters of each cell. Because the circuit was arrayed in the form of row-column of 2 × 7, the performance parameters of a single cell in the middle of the circuit on the top surface of the cooler, i.e., the fourth column, were measured and adopted to calculate the I-V characteristics of all cells. Experimental performance parameters of the single cell are listed in Table 1. The cell temperature increased from 323.1 to 344.7 K during the heating process. The quality factor of the cell deviated from the ideal state (R_s→0, R_sh→∞, n→1), resulting in the decrease of the fill factor (FF). The FF is only 0.34 when the radiator temperature was 1273 K.

Figure 4 illustrates the influence of the radiator temperature on the cell module performance when the radiator temperature is between 1273 and 1573 K including experimental and theoretical results. As the radiator temperature increases, the short circuit current and the output power increase, but the open circuit voltage drops slightly. When the radiator temperature is 1273 K, the short circuit current is 0.63 A. The maximum output power and the open circuit voltage are 0.79 W and 1.89 V, respectively. The FF is 0.66 and the maximum output power density p_el is 0.013 W/cm². When the radiator temperature increases to 1573 K, the short circuit current and the output power increase 7.2 and 3.9 times, respectively. But the open circuit voltage and the FF decrease to 1.68 V and 0.33, falling 10.6% and 50%, respectively. According to the Stephen-Boltzmann law and Planck law, the radiation density is directly proportional to T⁴. As the radiator temperature increases, more radiant energy is received by the cell and the proportion of photons with an energy greater than 1.12 eV is becoming even greater. This leads to the increase of the photo-generated current and the short circuit current. Meanwhile, the reverse saturation current increases exponentially and the open circuit voltage decreases with the cell temperature. The series resistance and shunt resistance deviate more seriously from the ideal state. The FF also decreases seriously. The interaction of these parameters makes the growth rate of the output power less than that of the short circuit current. Therefore, the cell cooling technology is critical for the TPV system. Moreover, as can be seen from Fig. 4, the trends of the current, the output power with the voltage, obtained by theoretical model (model 1), are in good consistent with the experimental results. When the radiator temperature varies from 1273 to 1573 K, the theoretical short circuit current and output power increase 8 and 3.7 times, respectively. There is a decrease of 11.1% and 47.9% in open circuit voltage and the FF. The maximum output power points shift to the left.

Data comparisons of the theoretical and experimental values are listed in Table 2. The theoretical model is reliable when used to predict the open-circuit voltage and the maximum output power. But the error of short circuit current is large, which can be attributed to the inaccuracy of the internal quantum efficiency and the existence of connection resistance inside the cell module. The internal quantum efficiency of a Si cell from theoretical prediction [17] is different from the experimental ones provided by the manufacturer, as displayed in Table 3. The actual values of internal quantum efficiency under several wavelengths are less than the corresponding theoretical ones. This leads to a smaller experimental photo-generated current. Thus, the errors of short circuit current are greater as the radiation density (the radiator temperature) increases. On the other hand, there are connection resistances inside the cell module. Although the four-probe method is adopted, only the influence of the connection resistances between the cell module and the load could be eliminated. The internal connection resistances were not taken into account in the theoretical mode. This leads to a more evident decay of the experimental output power caused by connection resistances under high current. Thus, the experimental short circuit current is lower than the theoretical value. Figure 5 exhibits the schematic of the internal connection of the cell module. The connection resistance consists of the wire resistances and the contact resistances between the cell and the wire. Because it was not easy to measure the contact resistances, only the effect of the wire resistances were considered. The measured total wire resistance R was added as extra series resistance to the equivalent circuit model of a single cell (model 2).

(8)I=I_{\mathrm{ph}}-I_{\mathrm{0}}\left\{\exp {\displaystyle \frac{q[V+I(R_s+R)]}{nk{T}_c}}-\mathrm{1}\right\}-{\displaystyle \frac{V+I(R_s+R)}{R_{\mathrm{sh}}}}.

The modified short circuit current is significantly reduced as shown in Table 2. When the radiator temperature is 1273 K, the error of the short-circuit current declines from 17% to 11%. When the radiator temperature is 1573 K, the error declines from 32% to 17%. Although the maximum theoretical output power is slightly smaller because of the consumption of the wire resistances, the error is acceptable.

Yb₂O₃ radiator

When the Yb₂O₃ radiator was in use, the cell temperature was reduced approximately 20 K compared with the SiC radiator at the same condition, as shown in Table 1. The quality factor of the cell is greatly improved and the FF is 0.52 at least. These results indicate that the Yb₂O₃ radiator is propitious to decrease the cell temperature and improve the cell performance. Figure 6 illustrates the influence of the temperature of the Yb₂O₃ radiator on the cell module performance when the radiator temperature is 1273-1573 K. Because of the lowered cell temperature, the open circuit voltage slightly increases. When the radiator temperature is 1273 K, the open circuit voltage is 1.91 V, increasing 0.02 V compared with the result for the SiC radiator. The difference increases to 0.04 V at the radiator temperature of 1573 K. However, the short circuit current and the maximum output power significantly decrease because the radiant energy (\le1.12 eV) decreases due to the spectral selectivity of the Yb₂O₃. The short circuit current and the maximum output power are only 0.46 A and 0.57 W at the radiator temperature of 1273 K. When the radiator temperature increases to 1573 K, the short circuit current and the maximum output power increase 6.5 and 3.6 times, respectively. In addition, the trends of the results from model 2 are similar to the condition of using the SiC radiator, as shown in Fig. 6.

System efficiency

There are two kinds of system efficiency for the TPV cogeneration system, i.e., the system electrical efficiency η_sys,el and the total system efficiency η_sys:

(9){\eta }_{sys,el}=P_{\mathrm{el}}/(P_{\mathrm{rad}}\times F_{r-c})=P_{\mathrm{el}}/P_a,

(10){\eta }_{\mathrm{sys}}=(P_{\mathrm{el}}+P_w)/P_a,

where P_el is the maximum output electric power; P_rad, the radiant energy; P_a, the energy arriving at the cell module surface; F_r-c, the view factor of the cell module toward the radiator; and P_w, the cooling power.

Table 4 tabulates the system efficiencies of the TPV cogeneration systems with the SiC or Yb₂O₃ radiator when the radiator temperature is 1573 K. The system electrical efficiency of the system with the SiC radiator is only 0.22%, six times less than that of the system with the Yb₂O₃ radiator. However, the maximum output electric power of the former system is 3.08 W, 1.5 times larger than that of the latter system. This shows that the selective radiator can effectively improve the system electrical efficiency but decrease the electrical power. Besides, the addition of the selective radiator makes it easier to keep cells at a low temperature.

TPV cogeneration system

In the ferrous metallurgy, ceramics and other modern industrial processes, there are a lot of high-temperature waste heat resources, where high-temperature waste heat mainly exists in high-temperature flue gas, high-temperature slag and high-temperature products. At present, the recovery of waste heat from high-temperature flue gas relies mainly on the traditional technology represented by the steam turbine whose power generation efficiency is approximately 25% and the equipment price of electric power per kilowatt is 2900 EUR [18]. However it is difficult to recycle waste heat from the high-temperature slag and the high-temperature products. Only a small portion of waste heat is recycled from products by the traditional technology. The technical advantage of the TPV could provide an alternative. The TPV systems can recycle the waste heat not only from flue gas, but also from slag and product.

A TPV cogeneration system is constituted of several basic units, each of which is made up of a radiator, Si cells, a cooling device, etc. sketched in Fig. 7. The high-temperature slag or products are made to get through the radiant pipe by a transmission device. The radiant energy emitted by the heated radiator is absorbed by the cells to generate electricity. The cooling system has eight water-cooled plates, each of which has a PV circuit with 8 cells mounted in series. The hot water, after cooling, can be used for production and living. Assuming the radiator diameter and length are 30 cm and 100 cm respectively, the distance between cells and radiator is 1.5 cm. Two kinds of radiators, the SiC and the Yb₂O₃, are used at 1573 K. The cell temperature adopts the experimental value of 344.7 K using the SiC radiator and 323.5 K using the Yb₂O₃ radiator. The revised model will be used to predict the feasibility of the TPV technology using high-temperature industrial waste heat.

Table 5 gives the system performances and costs of the two TPV systems. The output power of the system with the SiC radiator (TPV1) is 500 W, 2.6 times larger than that of the system with the Yb₂O₃ radiator (TPV2) at the same radiator temperature. However, in order to maintain the surface temperature of the radiator, the TPV1 system requires 103.1 kW of thermal power, which is 15.8 times higher than that of the TPV2 system. This means that the output power of the TPV1 system is only 16% of that of the TPV2 system for the same amount of waste heat. It is assumed that the rest of the energy is taken away by the cooling water, so the total system efficiency is 100%.

According to the experiments in this paper and the data from Ref. [14], the costs of the radiator and the cooling device are the key factors affecting the system cost (accounting for approximately 76%-84% of the total cost), since Si cell is highly commercialized. The cost of the TPV2 system is 6732 EUR/kWel. Although the cost of the TPV1 system is only 39% of that of the TPV2 system at the same radiator temperature, the TPV1 system will be more expensive for the same amount of waste heat. Viewed from the cost of per kilowatt electricity, the TPV system has no technical superiority over the steam turbine for recovery of the high-temperature flue gas. But it is believed that the cost gap will be greatly reduced after the TPV technology is commercialized. Besides, the operating conditions for the steam turbine are usually more complicated. To obtain a higher power generation efficiency, the high pressure or even ultra-high pressure steam may be required which limits the application range of steam turbine.

For a company with a daily output of 100 tons of glass, 1 kg of glass will consume 5800kJ of heat in which the slag temperature is 1200-1600°C, accounting for approximately 20% of the total energy consumption. Assuming the production time in a year is 8000 h, the generated energy is 0.31 MkW·h when the TPV system electric efficiency is 3.1%. If the system lifetime is 20 years, the payback period will be 14 years when the annual investment interest rate is 4%, the annual maintenance cost is 1% of the initial investment and the electricity price is 0.1 EUR/(kW·h).

Conclusions

An experimental TPV cogeneration system was set up to explore the influence of the radiator temperature on the I-V characteristics of the cell module. The technical feasibility and system cost were analyzed by numerical simulation. Both the experimental and theoretical results show that increasing the radiator surface temperature will improve the maximum output power and the short circuit current. However, there is a lower increase in the output power because of the decrease of the open circuit voltage and the FF. The open circuit voltage and the maximum output power obtained by the experiment are in consistent with those obtained from the theoretical model. Due to the existence of the connection resistances inside the module, the power loss is relatively serious under high current, which, in turn, makes the theoretical short circuit current greater than the experimental value. With the Yb₂O₃ radiator, the system electric efficiency of the TPV cogeneration system can be greatly increased, meanwhile, the radiation energy and the output power are both reduced. Considering the system electric efficiency, the power generation cost and the payback period, the TPV system discussed in this paper has no advantages over the steam turbine. However, the TPV technology still has potential in high-temperature industrial waste heat recovery because of its flexibility.

References

[1] Fraas L M, Minkin L. TPV history from 1990 to present & future trends. AIP Conference Proceedings, 2007, 890(1): 17–23

[2] Lange R G, Carroll W P. Review of recent advances of radioisotope power systems. Energy Conversion and Management, 2008, 49(3): 393–401

[3] Butcher T A, Hammonds J S, Horne E, Kamath B, Carpenter J, Woods D R. Heat transfer and thermophotovoltaic power generation in oil-fired heating systems. Applied Energy, 2011, 88(5): 1543–1548

[4] Xuan Y M, Chen X, Han Y G. Dsign and analysis of solar thermophotovoltaic systems. Renewable Energy, 2011, 36(1): 374–387

[5] Yang W, Chou S, Chua K, An H, Karthikeyan K, Zhao X. An advanced micro modular combustor-radiator with heat recuperation for micro-TPV system application. Applied Energy, 2012, 97: 749–753

[6] Saidov M S. Photothermoelectric cell for thermophotovoltaic systems and solar power plants with concentrators. Applied Solar Energy, 2012, 48(2): 67–70

[7] Mostafa S I, Rafat N H, El-Naggar S A. One-dimensional metallic-dielectric (Ag/SiO2) photonic crystals filter for thermophotovoltaic applications. Renewable Energy, 2012, 45: 245–250

[8] Conley B R, Naseem H, Sun G, Sharps P, Yu S Q. High efficiency MJ solar cells and TPV using SiGeSn materials. In: Proceedings of 2012 38th IEEE Photovoltaic Specialists Conference (PVSC). Austin, USA, 2012, 1189–1192

[9] Bauer T, Forbes I, Pearsall N. The potential of thermophotovoltaic heat recovery for the UK industry. International Journal of Ambient Energy, 2004, 25(1): 19–25

[10] Li Y H, Wu C Y, Lien Y S, Chao Y C. Development of a high-flame-luminosity thermophotovoltaic power system. Chemical Engineering Journal, 2010, 162(1): 307–313

[11] Singh P, Singh S N, Lal M, Husain M. Temperature dependence of I-V characteristics and performance parameters of silicon solar cell. Solar Energy Materials and Solar Cells, 2008, 92(12): 1611–1616

[12] Chakrabarty K, Singh S N. Depletion layer resistance and its effect on I-V characteristics of fully- and partially- illuminated siicon solar cells. Solid-State Electronics, 1996, 39(4): 577–581

[13] Chubb D L. Fundamentals of Thermophotovoltaic Energy Conversion. Netherlands: Elsevier Science, 2007

[14] Coutts T J. A review of progress in thermophotovoltaic generation of electricity. Renewable Sustainable Energy Reviews, 1999, 3(2,3): 77–184

[15] De Soto W, Klein S A, Beckman W A. Improvement and validation of a model for photovoltaic array performance. Solar Energy, 2006, 80(1): 78–88

[16] Jain A, Kapoor A. A new method to determine the diode ideality factor of real solar cell using Lambert W-function. Solar Energy Materials and Solar Cells, 2005, 85(3): 391–396

[17] Mao L, Ye H, Cheng Q. Numerical analysis of the thermal radiation-electricity module of TPV system. Chinese Journal of Computational Physics, 2008, 25(4): 450–457 (in Chinese)

[18] Palfinger G, Bitnar B, Durisch W, Mayor J C, Grützmacher D, Gobrecht J. Cost estimates of electricity from a TPV residential heating system. In: Proceedings of the 5th Conference on Thermophotovoltaic Generation of Electricity, Rome,Italy, 2003, 653: 29–37

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg