Concentrated Solar Power - Efficiency

Efficiency

For thermodynamic solar systems, the maximum solar-to-work (ex: electricity) efficiency can be deduced by considering both thermal radiation properties and Carnot's principle. Indeed, solar irradiation must first be converted into heat via a solar receiver with an efficiency ; then this heat is converted into work with Carnot efficiency . Hence, for a solar receiver providing a heat source at temperature T_H and a heat sink at temperature T° (e.g.: atmosphere at T° = 300 K) :

with

and

where, are respectively the incoming solar flux and the fluxes absorbed and lost by the system solar receiver.

For a solar flux I (e.g. I = 1000 W/m2) concentrated C times with an efficiency on the system solar receiver with a collecting area A and an absorptivity :

,

,

For simplicity's sake, one can assume that the losses are only radiative ones (a fair assumption for high temperatures), thus for a reradiating area A and an emissivity applying the Stefan-Boltzmann law yields:

Simplifying these equations by considering perfect optics ( = 1), collecting and reradiating areas equal and maximum absorptivity and emissivity ( = 1, = 1) then substituting in the first equation gives

One sees that efficiency does not simply increase monotonically with the receiver temperature. Indeed, the higher the temperature, the higher the Carnot efficiency, but also the lower the receiver efficiency. Hence, the maximum reachable temperature (i.e.: when the receiver efficiency is null, blue curve on the figure below) is:

There is a temperature T_opt for which the efficiency is maximum, i.e. when the efficiency derivative relative to the receiver temperature is null:

Consequently, this leads us to the following equation:

Solving this equation numerically allows us to obtain the optimum process temperature according to the solar concentration ratio C (red curve on the figure below)