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238 CHAPTER 7 Strategies for Fault Detection and Diagnosis

energy over a given period of time, the daily or monthly evaluation [26e28]. For this
purpose, it is necessary to measure the energy produced by the PV system or the cor-
responding yield, Y a or Y f . The values of these yields can be calculated using Eqs.
(7.2) and (7.3) respectively, once the energy produced by the PV system has been
monitored and taking into account the nominal power of the PV array, P o . The ex-
pected value of the daily array yield, Y aE , can be obtained from the following
equation:
PSH Nsm Npm Im Vm
Y aE ¼ (7.8)
Po
where N sm and N pm are the number of PV modules in series per string and strings
forming part of the PV array, respectively, and Im and Vm are the current
and voltage corresponding to the maximum power point of the PV modules at
real operating temperature, given by the manufacturer, respectively. It is consid-
ered in the equation that the inverter includes maximum power point tracking
(MPPT).
The parameter PSH (Peak Sun-Hours) in Eq. (7.8) refers to the solar daily irra-
diation that a particular location would receive under STC irradiance,
2
G ref ¼ 1000 W/m (AM1.5), for a number of PSH hours. This parameter is equiva-
lent to the reference yield, Yr, given by Eq. (7.1) evaluated for a day and it is usually
used in sizing PV systems:
24
R
GðtÞdðtÞ
0
PSH ¼ (7.9)
G ref
where G(t) is the real profile of the irradiance along the 24 h of the day at the location
of the PV array.
On the other hand, the expected daily value of the field yield, Y fE , is given by the
following equation:
PSH Nsm Npm Im Vm h
Y fE ¼ (7.10)
Po
where h is the inverter efficiency.
The supervision system can estimate some kind of faults present in the PV sys-
tem when relevant differences between the expected and the measured yields are
observed. Small deviations between expected and measured yields could be associ-
ated with mismatch effects or ohmic losses present in the system [29]. Fig. 7.3 shows
the evolution of the expected and monitored array yields in a GCPVS sited in the
south of Spain along 15 days of July. As it can be seen in the figure, no relevant dis-
crepancies are observed between both yields. Therefore, the PV system is working
free of faults.
The supervision system can also be based on the analysis of the PR [30,31], pre-
viously defined in Section 2, that can be evaluated from Eq. (7.2) using Y r and Y f .