Hybrid Energy Harvesting System - Energy Harvesting Autonomous Sensor Systems - page 139

5.1 Solar Energy Harvesting (SEH) System
Several mathematical models exist in the literature [130-132] that describe the
operation of photovoltaic (PV) cells, from simple to more complex models that
account for different reverse saturation currents. In this chapter, an electrical
circuit with a single diode (single exponential) is considered as the equivalent
PV model, which consists of n s number of PV cells in series, as shown in
Figure 5.1 .
Assuming that the shunt resistance R sh ,asshown in Figure 5.1 , is infinite,
the current-voltage (I-V) characteristic of the PV module can be described
with a single diode as the four-parameter model given by Equation 5.1 [130],

I o exp V pv 1

+

I pv R s
n s V t

= − −

I pv I L (5.1)

where I L is the light-generated current (A) and I o is the dark/reverse satura-
tion current of the p-n diodes (1 10 − 9 A). R s is the series resistance of the

PV module, and V t is the junction terminal thermal voltage (V) depending on
the cell absolute temperature, which is defined as

×

kT c
q

V t = (5.2)

where T c is the cell absolute temperature (K), k is the Boltzmann constant
(1.3807

10 − 19 C).
The ultimate goal is to determine whether the power harvested by the PV
module is able to power the wireless sensor node; hence, it is crucial to es-
timate the electrical power throughput of the PV module by leveraging on
the relationship between the current and voltage of the PV module expressed
by Equation 5.1 . Referring to Equation 5.1 , it can be deduced that the voltage
drop across the series resistance, V Rs

10 − 23 JK − 1 ), and q is the charge of the electron (1.6022

× ×

I pv R s ,iscomparably much lower than
the output PV voltage V pv due to the very low PV current I pv on the order of
microamperes flowing through the small series resistance R s of a few ohms;
thus the I pv R s term in Equation 5.1 can be neglected during the formulation

=

I pv

R s

I L I D I sh

V pv

R sh

FIGURE 5.1
Equivalent electrical circuit for a photovoltaic module.