Page 275 - Advances in Renewable Energies and Power Technologies

248 CHAPTER 7 Strategies for Fault Detection and Diagnosis

where Vm and Im are the voltage and current of the MPP at the DC output of the PV
generator, respectively, and Isc and Voc the short-circuit current and open-circuit
voltage of the PV array, respectively.
Most inverters incorporate, nowadays, inputs for sensors of irradiance and tem-
perature. Therefore, these indicators could be calculated by the inverter itself from
the MPP coordinates available at the inverter input, and the values of Isc and Voc,of
arbitrary series-parallel: Nsm Npm, connection of PV modules, obtained for
actual conditions of irradiance, G, and temperature, Tc, in real time [46]:
Iscmr dIscm

Isc ¼ Npm G þ ðTc Tref Þ (7.38)
1000 dT

dVocm Iscm
Voc ¼ Nsm Vocmr þ ðTc Tref Þþ V t ln (7.39)
dT Iscmr
where Vocm and Iscm are the open-circuit voltage and short-circuit current of a PV
module forming part of the array at STC.
The indicators, NRco and NRvo, the expected values of NRc and NRv, in normal
operation of the PV system (absence of faults) are given by:
I mo
NRco ¼ (7.40)
I sc
V mo
NRvo ¼ (7.41)
V oc
where the coordinates of the MPP of the PV array, I mo and V mo , are given by Eqs.
(7.20) and (7.21), respectively.
The definition of thresholds for current, TNRcfs, and voltage, TNRvbm, allows
detecting both short and open circuits in the PVarray. These thresholds were defined
by the following equations [42]:
TNRcfs ¼ 1:02 a NRco (7.42)
TNRvbm ¼ 1:02 b NRvo (7.43)

where a and b are the relationship between the ratios of current in the case of one
faulty string and fault-free operation and the ratio between the voltage ratios in
the case of one bypassed PV module and fault-free operation, respectively, given
by Eqs. (7.7) and (7.8). On the other hand, the constant included in Eqs. (7.42)
and (7.43) was fixed by means of statistical procedures to avoid false fault detections
as an offset of 2% with respect the NRco and NRvo values.
The parameters a and b depend only on the number of PV modules forming the
array and on the PV array configuration, Nsm x Npm [42,43]:
1
a ¼ 1 (7.44)
Npm
1
b ¼ 1 (7.45)
Nsm