What resistor network topology to use when measuring thermistors in a battery pack

Question

Some EV competitions require that 20% of the cells in a battery pack be monitored for temperature, and go on to strongly recommend that it be 100%. Considering that batteries can easily contain hundreds of cells, having an equal number of wires which have all to be connected to a board is somewhat burdensome. Not to mention having to have hundreds of ADC channels as well.

However, a resistor network could be used to greatly reduce the number of connections. Imagine a simple "square" network such as the below:

(Assume for the sake of argument that at least one of the resistors is a calibrated resistance so that the precise resistance can be determined, instead of just the relative resistance.)

The switches would be controlled by a microcontroller so that they open and close appropriately to allow for measurements. For instance, in the above picture, the first measurement is identically 0V, because that leg is shorted to ground, but the other two measurements are functions of the individual resistance (as well as which input legs are turned on). So through all the permutations of the switches, a series of measurements can be made which would allow the system of simultaneous equations to be solved for the resistances, and thus the temperatures.

In a matrix approach such as the one above, the number of leg resistances which can be solved for is (INPUT! -1 ) * (OUTPUT! - 2), where ! is the factorial operator. In the above case, it's (3! - 1)*(3! - 2) = 5*4 = 20.

However, there are many interesting resistor networks, such as 2D triangles and 3D cube. Is there a straightforward way to determine the pros/cons of each topology? I don't have the mathematics worked out to validate this, but my hunch is that some topologies will be more sensitive to noise/failed sensors then others. I could also see optimizations which might be driven by which specific nodes in the circuit the ADCs are measuring. Furthermore, some topologies might be easier to solve for unknown resistances than others.

Simple simulation of the above square circuit.

Answer 1

A straightforward n*m matrix gives you nm resistors, with n+m leads, and the ability to measure the temperature of every thermistor uniquely, without interaction, without simultaneous equation mathematics in the MCU. It requires n voltage drives switchable between 0 V and some finite voltage, and m current sense channels.

Consider the following 3x4 matrix

^{simulate this circuit – Schematic created using CircuitLab}

BUF1 drives 5 V, the others drive 0 V. Because of the virtual ground amplifiers, resistors R5 to R12 have no voltage across them, so conduct no current. Only R1 to R4 supply current to the virtual ground amplifiers, which produce a voltage proportional to the current and hence 1/resistance.

Temperature in a battery pack changes fairly slowly, seconds to 10s of seconds, so multiplexing all those thermistors into a normal MCU should present no timing problem.

Obviously buffer outputs are cheaper than ADC inputs, so it might make sense to have a non-square array with perhaps twice as many buffers as virtual ground channels.

I would strongly advise against wiring up a huge battery pack in one go. Break the monitoring down into modules. Consider a small PCB with 2xHC595, two quad packs of opamps, and an 8:1 analogue multiplexer. That would connect back to your MCU/ADC by power, ground, SPI clock, SPI data line, one analogue output, these shared by all your other modules, and one dedicated board enable to write to that particular one. The 595s give you 16 outputs, 3 for analogue channel, one for analogue output enable, and 12 to drive the thermistor buffers, giving you a 12x8 = 96 thermistor module. That feels to me to be about the right size for modularity, or you could add a couple more 595s or delete some of the opamps, play with the dimensions, there is no right size. Replicate the board as often as required to equip all your battery modules.

Answer 2

Another approach would be to use digital output temperature sensors that can be daisy-chained, for example the TI TMP144

www.ti.com/product/TMP144

these are less than $1 each and have +/-1C accuracy, and all the conversions done for you. This one lets you chain 16 along one serial wire, significantly reducing the number of connections, you may find some that you can daisy-chain further.

No fun of a clever analog design, but probably pretty effective.

Update

A way to achieve Neil's idea with less wiring is to implement his method in a daisy-chain fashion:,

simply cascade D flip flops - something like the SN74LVC1G80 (available in something you can see - SOT23), make a long shift register, and simply clock a single pulse along it, sequentially selecting the thermistors. You need to take care with the clock line to ensure that the edges remain clean and the slew rate adequate, but within a battery pack this should be possible.

Answer 3

I helped students in FAE formula races since 2009 and I have seen them struggling with the same issue that you are encountering today. Therefore, rather that addressing your proposed solution (see X-Y problem) which is the proximate problem, please let me state that the ultimate problem is that the rules of the SAE Formula races pose excessive restriction on the students. In the real world, traction batteries, even those that use multiple cells in parallel, use just a handful of temperature sensors, not one sensor per cell. In formula races, when you use multiple cells you need to a) add a fuse to each cell, and b) add a thermistor to most if not all cells.

Let me share a solution that circumvents the need for so many thermistors in the first place, a solution that we reached in collaboration with Formula teams who raced in the past decade. The solution to the ultimate problem is to use single cells of the desired capacity (image a), not multiple cells in parallel (image b). When you do that, you only need N thermistors for N cells in series, and you don't need a fuse for every cell.