Gerald Kunz, Andreas Wagner

University of Applied Sciences Dortmund
Postfach 10 50 18, 44047 Dortmund, Germany
wagner@fh-dortmund. de

1. Introduction

The principal task of photovoltaic measurement is to monitor the correct function of all components of a PV-system, to detect problems and to iniciate maintenance and repair where necessary, otherwise defects will result in losses in energy yield. As the energy yield decreases if the peak power decreases, the measurement of the peak power of the complete PV-generator is necessary on site under natural ambient conditions [1], [3]. If a decrease of the peak power is detected, an increase of the internal series resistance can be the cause for the decrease of the peak power.

For the determination of the internal series resistance out of one dark IV-curve several methods are known, e. g. [7]. The dark IV-curve can be easily measured for single cells or singele modules. For the measurement of the dark IV-curve an external DC-current source is necessary. Such strong external DC-current sources for large PV-generators (several kW) are very expensive and so hardly available.

For the measurement of the internal series resistance under illumination two IV-curves of different irradiance but of the same spectrum and at the same temperature are necessary according to IEC 60891 [6]. With a new method for the simulation of the second IV-curve, using the effective solar cell equation-method [2], now it is possible to obtain the internal series resistance out of only one IV-curve measured under illumination.

2. Effective Solar Cell Characteristic

The purpose of I-V-characteristic approximation by means of equivalent circuit diagrams lies in the explicit calculability of the I-V-curve. A calculation method for the internal series resistance Rs out of a measured I-V-curve demands the following options:

— Explicit calculation of current-voltage-characteristic equation V(I)

— Explicit calculation of the parameters of the characteristic equation from the measured parameters Isc, Voc, I

— Degree of accuracy of approximation within the range of degree of accuracy of measuring method (state-of-the-art: 1%)

— The unknown parameter Rs, which shall be the result of the calculation, must not be a parameter of the current-voltage-characteristic equation.

The "Effective Solar Cell Characteristic” [1], [2] meets all four demanded options, as it has the same approximation accuracy as the two-diodes-model [1] and does not include Rs.

-*ph I

R

Fig. 1. Equivalent circuit diagram for the effective solar cell characteristic

I

The equivalent circuit diagram contains a fictitious component which presents either a positive or a negative resistance. This parameter is called Rpv (photovoltaic resistance). Important: the true internal series resistance Rs must not be confused with the photovoltaic resistance Rpv. The determination of the actual Rs will be desribed later. Follows the effective solar cell characteristic:

V +1 Rpv

I = Iph — 1o(e V -1) (1)

Explicit version

V = V ln(-^———— -1 Rpv (2)

10

With the introduction of the photovoltaic resistance the explicit calculability of matching problems between solar generators and several loads is possible with an accuracy of 1%, related to the maximum power of the solar generator.

dV M =—(I = 0) dI then for the 4 equation parameters 5 equations are available. The following in general valid approximate function for the slope M could be derived [2].

(3)

V I V M = —Oc (k -2=-^ I 1 IV

-k>

Vc

(4.1)

For the determination of the 4 independent equation parameters Rpv, VT, I0, Iph there are also 4 independent measured parameters necessary. In the present case these measured parameters are Isc, Voc, Ipmax, Vpmax. If in addition the slope M at open-circuit voltage is to be considered

-K)

with the equation-constants

-5.411

(4.2)

6.450

k

3.417

-4.422

Important notice: these equation-constants are not empirical constants, they are, independent of material properties of the solar cell.

The equation parameters can be determined as follows [2]:

I V I -^

Rpv=-M+7=41 — J*4 VT=-(M +Rpv) Isc h=LerT Iph = Ic (5)

pmax p max pmax

Example 1: Monocrystalline PV-Module BP585F:

Check of approximation quality of the effective solar cell characteristic: Comparison with measured values.

4 = 1.015 A		Rpv = 0.43Ш
Voc = 20.508 A		VT = 1.12—	(6)
Ip max = 0.951 A	V M = -1.535— A	I0 = 1.142 10-8 A
Vp max = 17.002 V		Iph = 1.015 A

Voltage (V)

Fig.2. IV-curve approximation of a
crystalline PV-module

Example 2: Amorphous PV-module Solarex MSX 40:

Check of approximation quality of the effective solar cell characteristic: Comparison with measured values.

Isc = 2.874 A Rpv = 0.906 Q Voc = 22.662 A VT = 4.80 V I = 2.099 A M = -2.454 V I0 = 0.026 A p max A V = 14.653 V p max Iph = 2.974 A

Fig. 2 and Fig.3. show both the good accord of the measured I-V-curves with the effective solar cell characteristic.

(7)

Voltage [V]

Fig.3. IV-curve approximation of an
amorphous PV-module