Solar energy conversion with thermal cycles - Solar Energy Sciences and Engineering Applications - page 453

(in principle the storage can be designed to deliver up 12 hours of power at full
load).

When TES is employed to increase the number of operating hours of the plant,
the optimization parameter “solar multiple'' (SM) is introduced (see Equation 14.2.1).
Without TES, the SM is close to 1 (usually between 1 and 1.25) and all the collected
thermal power is immediately used. Values higher than 1 mean that the plant can
store the excess thermal energy (SM higher than 2.5 normally allows continuous oper-
ation throughout the day). From an economic perspective, the advantage of increasing
SM is to extend the working hours of the plant, which also operates at higher effi-
ciency thanks to higher load fraction values. On the other hand, the construction cost
of the plant increases proportionally to the capacity of the thermal storage system and
SM. For these opposing tendencies there is an optimal size for both TES and SM that
maximizes the revenues from sales of electricity or equivalently minimizes the levelized
cost of energy (LCOE). An optimum has to be found on a case-by-case basis by means
of economic analysis (for further details see Section 14.6).

14.4.2.1 Thermal energy storage materials

There are different TES technologies which are characterized by the type of storage
medium and its integration into the power plant. The TES medium can be different
from the solar field fluid, requiring a heat exchanger to transfer the stored heat to the
power plant and a separated loop for the solar field.
Commonly used TES exploit “sensible heat'' variations of a substance, which can
be measured by the change in its internal energy/temperature. This type of TES consists
of a storage medium, a container (usually a tank) and inlet/outlet devices. Tanks must
both contain the storage material and prevent losses of thermal energy. The amount of
energy input to TES by a sensible heat device is proportional to the difference between
the final and the initial storage temperature, the mass of the storage medium and its
heat capacity. The amount of stored heat can be expressed as:

Q = mc p T = ρVc p T (14.4.1)

where c p [kJ/kg K] is the specific heat at constant pressure of the storage material,
T [ ◦ C] is the temperature variation in the storage, V [m 3 ] is the material volume
and ρ [kg/m 3 ] is the density of the material. However, besides the density and the
specific heat of the storage material, other properties are significant for sensible heat
storage: namely, allowable operational temperatures; thermal conductivity and diffu-
sivity; vapour pressure; compatibility among materials; thermal stability; heat transfer
coefficients; and cost. Sensible heat storage media can be classified as solid or liquid
materials:

• Solid media (mainly high-temperature concrete and castable ceramics) are usually

used in packed beds, requiring a fluid to exchange heat with the solar field or the
power block. When the fluid is a liquid, heat capacity of the liquid in the packed
bed is not negligible, and the system is called dual-storage. Packed beds also favour
thermal stratification, which can be exploited in a profitable way. Another advan-
tage of the dual system is the potential use of inexpensive solids such as rock, sand