String Test Application Note


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:

  1. Impedance curve measured at V_{OC}
  2. Low-frequency impedance at V_{OC}
  3. Low-frequency impedance close to V_{OC}
  4. PV string resistance R_{S}
  5. Open circuit voltage V_{OC}
  6. Short circuit current I_{SC}
  7. PV system isolation resistance R_{iso}
  8. The estimated position of R_{iso} faults
  9. 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 V_{PV+}>V_{G}> V_{PV-}.

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 (R_{iso}<1 M\Omega). This fault is given lower priority than the ‘internal disconnect’ due to the fact that accurate estimation of R_{iso} 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 3 k\Omega, when it is measured under the following conditions:

  • Irradiation > 100 \quad \frac{W}{m^2}
  • System size > 100 \quad \frac{W}{m^2}
  • Short circuit current I_{SC,0} > 1A, 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 V_{AC} on the PV system. The analyzer will meanwhile measure the alternating current flow I_{AC}, that is established by the voltage V_{AC}. The impedance Z is then found by dividing the AC voltage with the AC current, according to Ohm’s law:

Z = \frac{V_{AC}}{I_{AC}}


The analyzer will send out test signals V_{AC} in a frequency interval from 10 \, Hz to about 100 \, kHz. 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 R, and reactance X i.e. capacitance and inductance.

Z = \frac{V_{AC}}{I_{AC}}


Z = R + jX

j is the imaginary identity \sqrt{-1}. 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 Z i.e. the “norm”. This done by using the Pythagorean theorem on the impedance as follows:

Z^2 = R^2 + jX^2


|Z| = \sqrt{R^2 + X^2}

Note that whenever the reactance X \approx 0 or small enough to be omitted in practical testing, the value of |Z| is simply R. Indeed the impedance curve in Figure 2 has no X component below 9 kHz – it just shows plain resistance.

Figure 1: A graphical representation of the complex impedance plane. On the x-axis, we see the real part of the impedance which is the usual electrical resistance R. On the y-axis, we have the complex part of the impedance, which can be either capacitance or inductance.

Just before 10 kHz 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.

Figure 2: This plot shows the Z200 PV Analyzer module string impedance curve plot. The data is shown as the impedance norm |Z| against the logarithm of the frequency. This curve shows a healthy PV panel string with no obvious issues in the main conductor path.

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 RP the shunting (or parallel) resistance, RS the series resistance, and Cd the diffusion capacitance. The remaining components in the model are the light current generator ILIGHT and shunt diode with current ID. 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.

Figure 3: This plot shows the Z200 PV Analyzer module string impedance curve plot. The data is shown as the impedance norm |Z| against the logarithm of the frequency. In this measurement, the impedance is high in the open-circuit state but drops when a load is connected. The likely cause could be a diode in series with the PV panels or a fault internal to a panel.
Figure 4: Solar panel and panel string – equivalent circuit. This model is roughly equivalent to the solar panel string, and a basis for understanding the impedance measurement.

Series resistance

Rs 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 \frac{W}{m^2}) will in the simple model only have an impedance represented by RS. In the case of daylight illumination the diode (see Figure 4) is fully turned ON by the PV voltage, and thus effectively shorting Cd and Rp.

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 Rs 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. Rs should be estimated in the frequency range f = 100 Hz to f = 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 Rs on ISC0 (short- circuit current at 1000 \frac{W}{m^2} irradiation) and VOC (open-circuit voltage) to be:

R_S < 30 \Omega A \cdot \frac{V_{OC}}{100 V} \cdot \frac{1000 \frac {W}{m^2}}{Irr.} / I_{SC0}


The variables are VOC and irradiation. Let us take a look at an example of PV panels having ISC0 = 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

Figure 5: Series resistance in a PV panel string vs. irradiation. The rapid fall in resistance sets in as the voltage grows fast from 10 to 100 \frac {W}{m^2}. Above this value, the series resistance should be low for almost type of PV panel.

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 \frac{W}{m^2} 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 RS 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 RS 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\Omega at f = 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 k\Omega 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 RS value. In the case of a fault internal to a module Low-frequency norm and series resistance, RS may be raised by several hundred \Omega, while Low-frequency norm with load is just a few \Omega. 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 RS are all below 50 \Omega 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 V_{OC} and short circuit current I_{SC} 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 (\frac{W}{m^2}) 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 V_{OC} and I_{SC} 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 R_{iso} 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 R_{iso} is less than 3M\Omega 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 . We encourage the reader to study this also.


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.