**Introduction**

This application note is based on the combined research and development efforts established by Dr. Ronni Basu, Dr. Daniel Hamkens, and Dr. Anders

Rand Andersen. The document is intended for supporting the application of the emazys Z200 PV Analyzer (Z200) – String Test mode. The String Test is a preprogrammed test sequence designed to assess the performance, safety, and health of PV panel strings. The strength of the “String Test” is that it can distinguish various fault modes and find the location of the electrical issues. This approach is very different when compared to the features of conventional PV testers. The String Test will conduct a series of measurements and calculations as follows:

- Impedance curve measured at
- Low-frequency impedance at
- Low-frequency impedance close to
- PV string resistance
- Open circuit voltage
- Short circuit current
- PV system isolation resistance
- The estimated position of faults
- State Machine – build in intelligence, that determines the most likely fault state of a PV panel string

Let us first take a look at the State Machine.

## State Machine – build in intelligence

The Z200 conducts a number of calculations based on the assembly of measured data. We call these calculations the State Machine. The State Machine is a systematic approach to the handling of potential PV system faults such as instrument connection problems and internal instrument hardware issues (instrument self-check). The State Machine was developed to provide a clear analysis of measurement data to the user. The assignment of priority to different types of faults has also been implemented. Fault priority depends on the severity of faults, and the effect the fault in itself can have on measurement quality and validity. We rank faults with the highest priority at the top is as follows:

**State 1 – voltage overload**

If the absolute terminal voltages either individually or the absolute voltage difference between pairs of terminal voltages exceed 1000V, then the instrument will alert the user of overload and disable further measurements. This is also the case if there is some HW problem preventing the measurement of the terminal voltages.

**State 2 – external disconnect**

If the low-frequency impedance of the PV string impedance measured with and without load is high, then typically there is a disconnect not masked by a PV

panel bypass diode. Such a system fault needs to be corrected before any other measurements have any real meaning. Symptoms of high impedance both with

and without load are also seen at night and if the user connected cables incorrectly.

**State 3 – voltage polarity**

This state is described by incorrect voltage polarity, or a PV system ground voltage not within intervals spanned by the positive and negative terminals of the PV string. The State Machine reports this condition whenever these conditions are not fulfilled .

**State 4 – internal disconnect**

The symptom here is a drop in the impedance at low frequencies with an applied load during the measurement. The cause could be the existence of a series fault internal to a module which is masked by the turn-on of an associated panel bypass diode. Another reason could be the presence of a rectifier diode in series with the PV panels. Such a diode is typically used in systems, employing parallel strings of PV panels connected to combiner boxes.

**State 5 – low isolation resistance**

Low isolation to ground (). This fault is given lower priority than the ‘internal disconnect’ due to the fact that accurate estimation of and the position of a possible leakage point will be influenced by internal disconnects and the user should be encouraged to first identify and correct such faults before the localization of ground faults.

**High string impedance**

By studying the Sandia PV panel data-base, we can conclude that a healthy string of PV panels will always have an impedance of less than , when it is measured under the following conditions:

- Irradiation
- System size
- Short circuit current , at Standard Testing Conditions (STC)

**The impedance curve of solar panels**

First of all, we only consider commercial silicon cells and common thin-film cells e.g. CIS and CIGS in the remainder of this application note.

The impedance curve is a way to assess the overall health condition of a string of PV panels. Often the impedance is what explains the origin of an issue when a PV system is not performing to its specifications.

A core technology in the emazys Z200 testing kit is a frequency generator, that will superimpose an alternating voltage test signal on the PV system. The analyzer will meanwhile measure the alternating current flow , that is established by the voltage . The impedance is then found by dividing the AC voltage with the AC current, according to Ohm’s law:

(1)

The analyzer will send out test signals in a frequency interval from to about . The impedance curve is therefore a “spectrum” showing the impedance value measured at each test frequency determined by the team at emazys, see Figure 2.

The impedance curve is shown as the “Impedance norm” plotted against a logarithmic frequency scale. This approach is a standard procedure in electrical

engineering, but less often seen in field testing of PV generators. To understand the impedance norm let us first express the impedance as a complex number. This makes it possible to accounts for both ordinary “Ohmic” resistance , and reactance i.e. capacitance and inductance.

is the imaginary identity . We use complex numbers, as this approach is the most visual and straightforward way to understand in-field measurements. The mathematical theory of impedance spectroscopy and complex numbers is not a prerequisite to work with the Z200. Let that be said! Here the point is simply, that impedance is made up of electrical resistance as we know it, and then some additional frequency-dependent reactance, see Figure 1. We will now express the size (length) of i.e. the “norm”. This done by using the Pythagorean theorem on the impedance as follows:

Note that whenever the reactance or small enough to be omitted in practical testing, the value of is simply . Indeed the impedance curve in Figure 2 has no component below 9 – it just shows plain resistance.

Just before 10 the curve goes up and we see the inductance from the DC cables kick in and dominate the high-frequency part of the curve. The curve in Figure 2 shows the impedance of a healthy string of PV panels in full daylight irradiation. Usually, this curve shape indicates a healthy PV system. In Figure 3 we see an example of a curve, where a series fault is indicated.

We can understand the impedance curve of the solar PV string, by studying the circuit model found below in Figure 4. The model contains the 3

components R_{P} the shunting (or parallel) resistance, R_{S} the series resistance, and C_{d} the diffusion capacitance. The remaining components in the model are the light current generator I_{LIGHT} and shunt diode with current I_{D}. The current source models the current delivered by the PV string, when illuminated. It is the diode and its electrical characteristics, that dictates the shape of IV curve.^{1} In this application note we will not go into details with IV curves. We do however recommend the reader to study the topic in e.g. “Handbook of Photovoltaic Science and Engineering” edited by Luque and Hegedus.

**Series resistance**

R_{s} is the string series resistance that should ideally be close to zero in order to minimize power loss. An illuminated healthy PV string (with irradiation

100 ) will in the simple model only have an impedance represented by R_{S}. In the case of daylight illumination the diode (see Figure 4) is fully turned ON by the PV voltage, and thus effectively shorting C_{d} and R_{p}.

Series resistance in a PV panel string is a very important topic to understand power loss mechanisms and fire hazards, and it is the sum of these main components:

- current transport through the emitter and base of the PV cells
- contact resistance between the metal contact and the PV cells
- resistance of the top and rear metal contacts at the PV cells
- resistance in bus bars
- resistance in DC cables exterior to the PV panels
- resistance in connectors (important)

Surely these resistance components can be divided into smaller complex contributions, but keep in mind that our aim is to assess the overall PV system health

score i.e. “OK” or “not OK”. Note, that the Z200 determines the R_{s} value by fitting the measured impedance data, to the equivalent circuit model shown in

Figure 4. Therefore a value of Rs is only returned when it is defined according to the solar cell model.

The main impact of series resistance in individual solar cells is to reduce the fill factor, although high values may also reduce the short-circuit current. Meanwhile, series resistance in a string of PV panels is an important parameter to assess safety and fire hazards.

This distinction is essential and showcases the difference in perspective when we 9 look at solar cell research and the actual operation of solar energy power plants. When it comes to PV assets operations and maintenance, a small deviation away from the specified performance is somewhat acceptable, but safety issues, fire incidents, and production stop is not.

A known method of measuring the series resistance in a solar cell is to calculate the slope of the IV curve at the open-circuit voltage point. This works

very well in the laboratory when the IV curve can be measured in a controlled environment under STC. But in a field test scenario, one is often far away from

STC and the IV curve become inaccurate for the assessment of conversion efficiency and series resistance.

By using a series of impedance measurements carried out at different frequencies, it is possible to deduce an accurate value of the series resistance. Furthermore, this testing methodology works well under non-STC e.g. in very low irradiation. R_{s} should be estimated in the frequency range = 100 Hz to = 10 kHz where the simple model is most accurate. At higher frequencies e.g. effects of cable inductance kick in and cause the impedance to increase. At emazys, a study on more than 500 commercial modules representing various PV cell technologies and sizes, has been conducted. We found a worst-case relationship concerning the dependence of R_{s} on I_{SC0} (short- circuit current at 1000 irradiation) and V_{OC} (open-circuit voltage) to be:

(2)

The variables are V_{OC} and irradiation. Let us take a look at an example of PV panels having I_{SC0} = 10A and string open circuit voltage is 500 V. If we enter

these values into equation 2 and plot the value of series resistance against the irradiance we get the curve seen in Figure 5

The takeaway from Figure 5 is two-fold. First of all, we see an inversely proportional relation between series resistance and irradiance, and secondly, we see that for irradiance values above 100 RS is very small. This estimate is generally applicable regardless of technology i.e. it applies to both crystalline and thin-film technologies. However, there is significant variation between technologies. For instance, PV modules based on mc-Si cells typically have an R_{S} value of half of the above estimate or less. Obviously, when there are many PV strings of similar construction in a test site it is possible to find potential outliers by comparison of measurement data.

If R_{S} is found to be too high, it is an indication of a problem e.g. with shading or bad cabling and connectors. If the impedance exceeds 10 k at = 100 Hz, there may be a disconnect in the string e.g. in the form of a bad internal junction, a broken cable, or faulty connector. Note that the Z200 was designed to easily locate such faults using the build-in tone generator and amplifier probe. Alternatively by measuring the position of the fault using impedance spectroscopy.

If RS is greater than expected, there could be also problems internal to one or more modules e.g. with broken bus bars or corrosion. In this case, the single PV panel testing functions of the Z200 come into play.

**Low frequency impedance with and without load**

The Z200 also returns values for low-frequency impedance with and without load. It means that the analyzer can insert loads in the size, and conduct the impedance measurement during a flow of current. This allows to determine, if a flow of DC current changes the electrical pathway in the PV panel string e.g. switching of bypass or rectifier diodes. Under normal operation without faults, the Low-frequency* norm* and the *Low-frequency norm with load* will be very close to the R_{S} value. In the case of a fault internal to a module *Low-frequency norm* and series resistance, R_{S} may be raised by several hundred , while *Low-frequency* norm with load is just a few . The flow of current establishes a new pathway across the PV panel string and reveals the nature of the issue in the system.

Ideally, *Low-frequency norm, with load* and series resistance R_{S} are all below 50 for most ordinary PV panels under full daylight. When we see big differences we know that “something” is at play. The natural step is to move on and try the Module Tester in the Z200, to pinpoint which areas are affected by the fault.

**Open circuit voltage and Short circuit current**

The Z200 also measures the values of open-circuit voltage and short circuit current as a reference to the impedance values recorded. This gives the user the option, to evaluate the overall energy output of the PV panel string. Currently, the Z200 is delivered without an irradiance meter, and we do not offer a formal output power evaluation. The user is, however, encouraged to use a 3rd party irradiance sensor and enter the measured value () in the report generator user interface of the Z200. The value is then stored with all other values, and may then be used for analysis later on e.g. in the form of a CSV file generated by the Z200. The values of and are used in the State Machine calculations, to make conclusions about the most likely fault scenarios.

**Isolation resistance and estimated position of faults**

The Z200 can within 60 seconds determine the string isolation resistance and the position of a ground fault. The unique feature is that the ground fault position is found using an impedance test circuitry, so a fault can in most cases be pinpointed when is less than i.e. well before the inverter shuts down production to avoid even larger leakage currents. We wrote an article on this topic, and it is published at https://emazys.com/isolation-resistance-faults-in-photovoltaics/ . We encourage the reader to study this also.

## Conclusion

The Z200 is based on advanced impedance testing technology, but we conclude that the user output can be condensed into simple coherent statements useful in

troubleshooting PV arrays. The Z200 combines a range of measurements and deduce the operational state of the PV array. This takes the burden of complex

analysis away from the instrument operator and makes field investigations more simple and conclusive.

The aim of the Z200 is to lower the overall cost of solar electricity. This is hence done by offering cost reductions in relation to field operations and maintenance work. In other words, we deliver a fault-finding unit, that does the difficult work without the need for tedious individual PV panel inspections. We would like to express our gratitude to the many customers and contributors, who have made this technology development possible.