Preceding chapters have concentrated on two objectives. The earliest chapters explained and quantified the performance of the major components of a TPV system. Later chapters developed the analysis to calculate the performance of a TPV system. Therefore, the major objective of this chapter is to describe the radiation transfer method for determining the performance of a TPV system.
The performance is a function of the thermal power input, the geometry of the optical cavity, and the optical properties of the various components. In Chapter 6 radiation transfer theory was applied to obtain the radiation fluxes leaving the surfaces of the optical cavity. These results are used to calculate TPV system performance. The two major assumptions of the radiation transfer analysis are the following. First, the surfaces behave in a diffuse manner so that the radiation intensity is the same in all directions. Second, it is assumed that the fluxes incident and leaving a surface are constant over the area of that surface.
A surface area, cm2
Ao ideality factor
co vacuum speed of light, 2.9979 x 1010 cm/sec
e electron charge, 1.602 x 10-19, Coul
eb blackbody emissive power, watts/cm2 nm
Eg bandgap energy, eV
Fab view-factor for radiation leaving area a and impinging on area b
FF fill factor
h Planck’s constant, 6.62 x 10-34, J-sec
I current, Amps
J current density, Amps/cm2
k Boltzmann constant, 1.38 x 10-23 J/K
PEL electrical power output, watts
q radiative energy flux, watts/cm2 nm
Q radiative power at wavelength, X, watts/nm
Q total radiative power, watts
R resistance, ohms or reflectivity
T temperature, K
ug Eg/kTE, dimensionless bandgap energy
V voltage, volts
X wavelength, nm
b denotes reflector of optical cavity
C denotes PV array in optical cavity
E denotes emitter in optical cavity
Illustrated in Figure 8.1 is the planar geometry optical cavity model that is to be considered. A planar emitter that can be either circular or rectangular in shape is separated a distance, h, from a plane that is divided into three areas: AC1, AC2, and AC3. At this plane are located the PV arrays and filters. If a filter is used, it is assumed that the filter and PV array are together so that the view-factor between the filter and PV array is 1. It is assumed that a vacuum exists between the emitter and PV array so that no convective heat transfer occurs between the emitter and PV array. The vacuum condition would occur naturally in a TPV system for a space application.
The reflector surface, b, is attached to the emitter so that Tb = TE. Attaching the reflector to the emitter eliminates the leakage of radiation from the cavity that would exist if a gap existed between the emitter and reflector.
Dividing the filter-PV array plane into three areas gives flexibility to the analysis. For example, AC1 and AC2 can be filter-PV arrays, and AC3 can be a reflecting surface such as gold. Or for another example, all three areas can be filter-PV arrays.
The total efficiency of the system is the following [equation (6.83)],
Q. QC PEL PEL
Лт = ЛлЛ Лто —m —C —L = -=L-
where pth is the thermal efficiency [equation (6.84)], pc is the cavity efficiency [equation (6.86)], and pPV is the photovoltaic efficiency [equation (6.88)]. Note that Qin = Qe + Qb has replaced QE in the definition of pc, since thermal energy is being supplied to the reflector, as well as, to the emitter. Only pc and pPV are calculated for the system in Figure 8.1. The thermal efficiency, pth, depends on the heat source, which is not being considered. In the next section, the radiation transfer equations are developed and solutions for the radiation power densities are given.