Trouble understanding shunt resistance for short-circuit current measurement

You really need more than one cell to do what you are trying to do.

 

The Hall-effect sensor is probably your simplest current-measuring solution, but you need to explicitly define what you are trying to DO. Take a look at the Allegro ACS723 for a sensor more closely matching your anticipated current range. The most precise current measuring techniques use a four-wire Kelvin measurement. The so-called "shunt" or current measuring resistor has two heavy-gauge wires to carry the current to a precision low-resistance element and two small-gauge wires to measure the voltage drop across the resistance element. Depending on current rating, these devices have fairly low current-to-voltage sensitivities on the order of a few millivolts per ampere. Below is an image of a typical Kelvin current measurement using a precision measuring resistor:



The two inner terminals with the red and black test leads are precisely located at two points on the low-resistance "shunt" bar to allow measurement of the voltage drop across this element when current is present in the two blue test leads. Note the blue leads do not appear to be "heavy" enough to handle the maximum possible current the device is capable of supporting, but the measurement will nevertheless be accurate regardless of the resistance presented in series with the load by the blue test leads because very little of that measured current will be "burdened" by the high input impedance of the digital voltmeter.

The Arduino ADC is very limited in accuracy and resolution, but these are relative terms. You need to determine what accuracy and resolution you require before deciding an Arduino is the solution. For example, it is moderately easy to interface the digital ports of an Arduino to an external ADC that does meet your requirements, but you first have to define those requirements.

Calculating the resistance of the current-measuring shunt depends on how much of a burden this device will place on your solar cell. For example, if the solar cell can produce 5 A of current with 0.5 V output, then its internal resistance is R = V / I = 0.5 / 5 = 0.1 ohm or 100 mΩ. A shunt with a resistance of 0.01 or 0.001 ohms might be appropriate, and this will provide a "full scale" output of V = I x R = 50 mV (for 0.01 ohms) or 5 mV (for 0.001 ohms). Clearly some amplification is necessary to match this low range of voltage output to the chosen ADC input range.

Another problem might be how you choose to "short circuit" the solar cell array output. MOSFETs with low on-resistance are a possibility. A heavy-duty motor contactor is another. All depends on how much resistance you can tolerate in the "short circuit" path. Mercury-wetted relays might even be a possibility. In any case, you need to carefully measure the solar cell output voltage when it is "shorted" to determine if the "short" is good enough for your purposes (which you haven't told us).

Perhaps you are trying to compare the performance of a lot of solar cells. Have you considered how stable and uniform the solar cell illumination is? An integrating sphere and a radiometer are typically used for the most accurate measurements, but you may get by with a cloudless sky at high-noon, again depending on accuracy and resolution requirements... and the weather of course.

We can help you better if you describe what you are trying to DO.

 

Lead resistance should be taken into account.
Various load resistors could be used to extrapolate to zero resistance.
A mosfet, though good will have appeciable resistance.

 

Your approach seems very doable. But to obtain consistent results from day-to-day among a group of test cells you also need long-term accuracy, even when doing comparative measurements. Don't forget to record a date and time stamp along with data to identify specific solar cells in your SD module. I have never tried to use an SD module with Arduino and didn't realize it was easy to do so. Maybe a visit to one of the few remaining Radio Shack stores in my area is in order!

One problem I see is providing power to last for several days in an outdoor (perhaps remote) environment. Not a problem if you take along a motor-generator set (to the annoyance of everyone within ten miles of your site) but a PITA if you need to operate from batteries. What will be the logistics of that? Have you ever conducted a field operation in a remote location? Plan, plan,plan. You will still forget something. It's a character-building experience.

The most important aspect might be the series resistance presented by the Hall-Effect sensor, Another consideration is it's poor accuracy (typically ±2%) compared to a precision shunt resistor using a 4-wire Kelvin measurement, which can easily yield 0.01% accuracy after calibration and temperature compensation.

You haven't said how much maximum series resistance the solar cell current-sensing circuit may impose (burden) on the current measurement. Obviously lower is better. It is not difficult to make a high-current shunt with 0.001 Ω of resistance from Manganan wire, which has a very low temperature coefficient of resistance. You use two small OFHC (oxygen free high conductivity) copper bars or rods with slits to clamp onto a specific length of Manganan wire. You would fasten the copper to an insulating substrate such as Lexan (polycarbonate) plastic. Add two terminals to the ends of the copper for the current leads, and two more terminals located close to the Manganan wire entry into the copper for the Kelvin voltage measurement. Or ask to have a shunt custom made by this company.

You would also need a precision differential instrumentation amplifier (an off-the-shelf item) to convert the voltage across the current-measuring resistor to a voltage suitable for digitization by the Arduino ADC. If you need, say, 1 mΩ resistance then that will produce 12 mV of output with 12 A current. A gain of 500 in the instrumentation amplifier will provide a 6 V signal for the ADC at this current. You would, of course, make the gain adjustable for whatever full-scale voltage your ADC requires, or 5 V for the Arduino ADC.

You can, with some expense and design effort, incorporate an op-amp to provide a "virtual ground" at your short-circuited solar cell return lead. You would need a power op-amp capable of providing the 12 A or so of current and an appropriate feedback resistor. The solar cell return lead goes to the inverting input of the op-amp, an appropriate feedback resistor connects between inverting input and op-amp output, and the non-inverting input goes to measurement common. Any current supplied by the solar cell tries to drive the inverting input above ground, but the op-amp output provides an equal and opposite current to the inverting input to make the differential voltage between the inverting and non-inverting op-amp inputs essentially zero, thus establishing a virtual ground at the inverting input. A one ohm feedback resistor will yield 12 V output with 12 A input current and dissipate 144 watts, but you are free to use whatever value suits your purpose. It will be difficult (and expensive) to find a power op-amp capable of providing 144 watts of power, so this example is not very realistic, especially for field operation.

Smaller is better (less power dissipation and heating) at the sacrifice of output voltage, but you can make that up with another op-amp. A value of 0.1 Ω gives an output of 1.2 V and dissipates only 14.4 watts. Similarly, 0.01 Ω will provide 120 mV at 12 A and dissipate only 1.4 watts. Note that whatever value feedback resistor is employed, it has no effect on the resistance "seen" by the solar cell return lead. It serves only to scale the op-amp output voltage. You could of course use a commercial shunt as the feedback resistor, which is advisable since these are available calibrated and temperature compensated. Power op-amps with 15 A capability are available from this company, or you can add a "booster" stage to a conventional op-amp.

Unless you need the "virtual ground" provided by the op-amp solution, I would go with a temperature-compensated low-resistance current-measuring resistance and a 4-wire Kelvin measurement using a differential instrumentation amplifier.

You still haven't specified accuracy requirements or how you plan to temperature compensate your current measurements.

 

The resistance of 1,2 mΩ for the Allegro ACS711 has NO effect on its current measurement. It is only a consideration in limiting the true short-circuit current of the solar cell being tested. What accuracy do you require for the short-circuit current measurements?

The Allegro measures, with a linear bi-polar Hall-Effect sensor, the magnetic field produced by passing current through a copper conductor inside the Allegro package. The fact that this copper conductor presents an ohmic resistance of 1.2 mΩ is a simple consequence of the geometry of the conductor and its alloy composition. It has NOTHING to do with the measurement of actual current.

Ideally, if you truly want to measure the solar cell short-circuit current, the solar cell needs to drive a zero-resistance load, or in other words a true short-circuit. This is impossible without superconductors connecting the leads of the solar cell to a "virtual ground" as previously described. And it probably isn't necessary for comparative measurements of candidate solar cells, but you decide whether that is true or not. You have to decide how much resistance is "short-circuit" enough. The series resistance of your "short circuit" should certainly be as small as practical, but what, exactly, is that "small" value to be? Do some calculations on wire resistance and relay or contactor contact resistance or MOSFET on resistance... whatever device you choose to implement a momentary "short circuit". Compare these value with the resistance the Allegro current sensor adds to the complete circuit. Then you can decide if 1.2 mΩ plus the wire and "switch" resistance is "close enough" to being a true "short circuit" of the solar cell output for your purposes.

I don't think the ACS711 is a good choice. It "features" an over-current latch that will turn the device off when its rated current is reached. To reset it, and restore normal operation, requires that power be removed from the ACS711. Not a good plan for unattended data acquisition, but certainly you could configure the Arduino program to "automagically" perform the reset if the over-current "fault" condition occurs.

The ACS723 that I recommended is available in 0 to 10, ±10, 0 to 20, and ±20 ampere versions and has better temperature compensation. ALL of the Allegro devices are capable of conducting at least five times full-scale rated current without damage, although the output will saturate and no longer be representative of the input current when that occurs. It is also not necessary to accurately match the anticipated maximum solar cell short-circuit current to the rated Allegro full-scale current. Leaving some "headroom" in the Allegro full-scale rating will only slightly decrease the accuracy and resolution of your measurements.

The Allegro devices are NOT precision current measuring sensors. Their main purpose is to allow monitoring of currents while providing galvanic isolation between the current being measured and the instrumentation performing the monitoring function. Since your solar cells are already "galvanically isolated" devices, the Allegro is not necessary and will complicate obtaining accurate current measurements compared to 4-wire Kelvin measurements using a calibrated, temperature-compensated shunt and a differential-input instrumentation amplifier.

However, you have still not specified any accuracy or resolution requirements for your data logging, other than stating the 10-bit ADC in the Arduino will provide sufficient resolution. So perhaps the Allegro will be good enough.

What does "will not use lots of power" mean? How much power will the Arduino require while running during the day? What ampere-hour capacity battery will that require? What do you consider to be "large batteries" and why wire them in parallel? Since you are testing solar cells, why not dedicate a commercial solar cell panel charging a battery to power the Arduino? Do you intend for the Arduino to operate (for whatever reason) at night? Why would you do this? There is no data to collect at night.

That's a challenge all right. The entire endeavor is a challenge, but that's what makes life interesting.

 

Why do you want to measure the short-circuit current?
You don't buy solar cells for their short-circuit current capability.

 

He is probably using the open-circuit voltage versus short-circuit current as a criterion for comparing solar cell efficiency among four test solar cells. And its a good excuse to bivouac in the desert.

 

I went to get a slow puncture fixed yesterday and the mechanic said that he repaired valve televisions.

He showed me a device for measuring current without connection in automobile circuits. This would work on AC or DC. It was very sensitive to orientation presumably due to the earth's magnetic field. Not good for accuracy in a portable device.
A zero circuit would need to be used every time the detector is moved.

 

Oh, yeah, no one has mentioned how you establish the "zero current" output state of the Allegro current sensor. The bipolar sensor nominally places zero current at one half the sensor supply voltage. The unipoloar version places zero current at one tenth the sensor supply voltage. Since neither of these is an actual zero voltage level, the ADC should measure and record the open-circuit (zero current) output of the Allegro prior to each recorded measurement of the "short circuit" current. This is necessary to establish the zero current reference, a finite ADC number that is not numerically zero. A minor programming detail. Of course it is a good idea to check the "zero current" output no matter what current sensing method is used. It is also a good idea to perform a full-scale calibration prior to each measurement, using a precision constant-current source. So that's three measurements per data point: zero, full-scale, and actual data measurement. That's just good metrology practice.

 

A good experimental procedure is what it is. A poor experimental procedure, performed for the sake of expediency or lower cost, isn't worth the paper the final report is printed on.

Probably the point of interest in comparing the "efficiency" of solar cells is the maximum power point of a particular cell, Pmax. The figure below plots solar cell current against solar cell voltage with the maximum power point indicated. This curve cannot be obtained with just two measurements of open-circuit voltage and short-circuit current, nor is it easy to determine by inspection where the maximum power point occurs.



The second set of curves, shown below, plots the V-I characteristic curve for three different levels of illumination and also the power produced (dashed lines). Clearly the maximum power peak not only increases with increasing illumination, but the cell voltage where maximum power occurs also increases (slightly). A constant-voltage power supply capable of sinking the solar cell current is typically used to obtain the V-I characteristic curve, while differentiation of the the VI product will yield the maximum power point when the first derivative of the power curve is zero.



It seems reasonable to me that when comparing solar cells under identical uniform lighting conditions, temperature and known "fill factors" you would judge the cell with the greatest peak power output to be superior to cells with lesser output. And it may be possible to forego obtaining the complete V-I characteristic curve to do obtain a valid comparison if the cells are sufficiently similar, but I think that would be bad science. especially if there are substantial differences among the cell constructions. There is a short discussion found here, from which I copied the two graphs above.

The curves shown above apply only to a particular cell. To obtain a valid comparison among a group of cells, each cell in the group would need to have a V-I curve obtained and the maximum power point for that cell determined from the V-I data. Using an arbitrary fraction of the open-circuit cell voltage to "compute" the maximum power point is, IMHO, not a valid way to compute the maximum power point. Your mileage (or kilometers) may differ. And a two-point measurement of short-circuit current and open-circuit voltage may be "good enough" for sales advertising purposes.

IEC Standard 61215 is commonly used to test and evaluate solar cell performance. It covers a lot more than just a maximum power point determination, although that is important. Quoting from IEC 61215:

Getting the Pmax measurement correct would seem to be of paramount importance.

 

You said The idea is to compare 4 groups of cells, all 4 measurements being taken (almost) simultaneously and repeated on a regular basis (say, every 1 minute) during the whole day.

Am I correct in thinking you intend to take four sets of measurements each time?

This sounds like a lot of measurements. You will want to take these automatically, including switching among the different cells or groups.

So either you need four measurement circuits, or else switch one measurement circuit among the four batteries. ( Or possibly some combination of these approaches.)

It's not clear to me what you mean by a "group" of cells. Are you not measuring each cell individually? Does a group consist of more than one cell connected together? In series? In parallel? In either case you have a "battery".

As already pointed out, you may want to locate the maximum power point for each measurement and log that. Not hard to do with your controller.

For most cell types, it is not critical to provide a really low resistance "short" to get an accurate short circuit current measurement. The current is nearly constant from zero volts up to a large % of the open circuit voltage. See the curves in the above post by Hop. Obviously, you should confirm that the cells you are working with have similar E / I curves, but I think you will find that they do. This means that the wire resistance, resistance of solder joints, switch resistance and shunt resistance need not be extremely low. I expect that a standard 10A 50mV ( 0.005 ohm )shunt will be satisfactory.

Again, assuming that the cells have typical E/I curves, the short circuit current is little more than the normal operating current. There should be no problem with cells "burning down" while shorted.

This application does not call for a Hall effect measurement module. Use a simple shunt resistor and stable amplifier to scale the current to the voltage needed by your ADC input.

If you are logging four different cells or batteries, four power FETs can multiplex the current to a single current shunt. The FETs can also be used to control the load to locate the maximum power point, or even to take enough data points for a complete E/I curve.

Use an analog multiplexer IC to select one of the batteries for the voltage measurements. One of the SN74HCxx multiplexers can do this well. If you have decided to go beyond the open circuit voltage, short circuit current measurements, you might want to make this a differential measurement, with both positive and negative connections multiplexed.

It appears to me that the solar array itself should be able to power your measurement system. While not being measured, the juice from each cell could be used to keep your accumulator charged.

Be sure your data logging system saves the data in a flash card, or something, that will retain it when the computer crashes, the power cord is unplugged, etc!

Very likely you will want to log the ambient temperature each measurement cycle. It also might be good to include a reference measurement made using a standard cell. Possibly might snap and save a photo of the sky, as well. Use a wide angle lens so you can see the huge bird perched on your array during the measurement.

Ted