Using extremal conditions @P=@RL1 ¼ 0 and @P=@RL2 ¼ 0, one
can obtain variations of the maximum power output of the PV–
TEG hybrid system and the corresponding optimal value of RL2;opt
versus solar irradiance G with c ¼ 5; 9 and 13 m, as shown in
Figs. 10 and 11. Figs. 10 and 11 indicate that both the maximum
power output and the corresponding optimal load are of monotonically
increasing functions of G. Nonetheless, a large structure
parameter will result in a large maximum power output and a
small RL2;opt. These mean that one needs to make a compromise
between the maximum power and the external loading.
Fig. 12 presents the curves of the maximum efficiency of the
hybrid system gmax varying with the solar irradiance G. Result
shows that gmax first increases and then decreases as the solar irradiance
G increases. gmax can attain its maximum ðgmaxÞmax at an
optimum value of G. For a practical power generation system,
one always hopes to obtain a power output as large as possible,
indicating that a real PV–TEG hybrid system should be operated
in the following region:
G P Gm: ð30Þ
Fig. 11. The curves of the optimal load resistance of the TEG varying with the solar
irradiance. The values of parameters TC ; U1A1; U2A2; ZTC , and c are the same as
those used in Fig. 10.
Fig. 12. The curves of the maximum efficiency of the hybrid system varying with
the solar irradiance. The values of the parameters TC ; U1A1; U2A2; ZTC , and c are
the same as those used in Fig. 10.
Fig. 13. The maximum power output density of the hybrid system versus the solar
irradiance.
898 J. Lin et al. / Energy Conversion and Management 105 (2015) 891–899
The above results clearly show that gmax; Pmax; Iopt;ðRL1Þopt;
ðRL2Þopt;ðgmaxÞmax, and Gm are important parameters for the hybrid
system. The PV–TEG hybrid system can provide not only more
electrical power but also higher efficiency than a single PV cell.
Compared with the results of the PV–TEG hybrid system in Ref.
[15], it is clearly seen from Fig. 13 that the maximum power output
density of the present PV–TEG hybrid system is also a monotonically
increasing function of the solar irradiance and it is the same
as result of Ref. [15], but the maximum power output density of
the system is small than that of Ref. [15]. The reason is that in
the present paper, the finite-rate heat transfer between the TEG
and the heat reservoir is considered. Thus, the results obtained in
this paper are more general and can reveal better the general performance
characteristics of real PV–TEG hybrid systems.