# James Green's Research Pages

Magnetic Field 'Imaging'

## What are we doing?

We are attempting to reconstruct the moving charge distribution in batteries, super-capacitors and power systems composed of these two devices by measuring the magnetic field surrounding the device and, using some, assumptions and appropriate constraints estimating the likely current that caused the measured field. We then use some standard electromagnetic theory to calculate what magnetic field should arise from our estimate of the current distribution. The measured magnetic field result and the calculated field due to the estimate are then compared and a new - ideally improved - estimate of the current distribution is produced. We continue in this way until a acceptable tolerance of error is reached. This method is computationally intensive however it is widely believed that direct solution of the inverse problem is impossible because the problem is, except for some very simple cases, almost always ill-defined.

## Why are we interested in current distribution?

We believe that knowledge of the current distribution may inform our understanding of how batteries age and degrade due to continuously occurring processes and due to their duty, which in most of our work is traction or electric vehicle applications. We also believe that certain current distributions and aspect ratios of battery electrodes represent an optimum in terms of the energy storage potential per unit mass and per unit volume. Although both mass and volume may not necessarily be optimised together in all situations. Such optimisations are highly desirable in traction applications where the battery system often represents a significant component of the vehicle mass and consumes volume which otherwise would be available for other uses.

## Why is 'imaging' in quotes?

Imaging (in quotes), because what we're measuring is not an image in the same way that optical photography produces images of the objects which are illuminated by light sources. Consider a match struck in an otherwise dark empty space. From wherever one stands in the room the object appears the same - other than a square law intensity drop as a function of distance between the match and the observer. In the magnetic images however the distance to the object changes not only the magnitude of the field crossing the sensor plane but the direction of the field crossing the plan too. Taking a magnetic photo of the field around a long wire carrying a constant current yields different images as the distance between the wire and the imaging plane increases. The same is not true for the match and optical image.

## How does the measurement work?

We use an array of several hundred magnito-resistive sensors similar to those used in mobile telephones or marine navigation systems for compassing applications. The devices are arranged in a grid 32 sensors across and 8 sensors high. The sensors are accessed via I2C by a micro-controller which communicates with a PC over USB. The magnetic field data is saved in 3 orthogonal directions for each pixel. The vector magnetic field cutting the measurement plane is plotted using Matlab. Matlab is also used to sequentially plot every frame in turn, convert the graphs to JPGs which are then combined to become the frames of an MP4 video. generally we replay the video at about 5x real-time but it depends on the length of data and the speed at which interesting events occur. Full details of our measurement system will appear shortly in an upcoming publication.

## A Magnetic "Picture" Example

The composite photo below is a representation of the vector magnetic field cutting a measurement plane which is parallel to one side of a lead acid battery. The magnetic data and photograph are aligned and are in proportion to the relative size and position of the measurement array and the battery. The magnetic data is sliced across the battery at the midpoint so the first column of cones represents the field half way along the depth of the battery (into the screen). The vertical and depth (into the screen) axis of the magnetic data are measured inches. The horizontal axis of the magnetic data is arbitrary. The setup and the specifics of this experiment are discussed in a forthcoming publication. The extent of the active area is an estimate based on our knowledge of the general internal structure of this battery type and the indentations in the casing. In the simplest possible assumption the battery could be reduced to a single current carrying conductor which passes through the screen normal to the shown surface of the battery. Under this (extremely) simple Biot-Savart long wire assumption the dominant region of current flow should be where the cones change direction most between adjacent rows. We have shown that the dominant current is therefore near or at the top of the plates. Our forthcoming paper extends this somewhat and we have shown that the current distribution as a function of distance down the plate (vertical in the picture) is very likely to have a particular form, and that this form agrees well with our measurements.

## A "Video" Example

The video below is a representation of the vector magnetic field on one side of a super-capacitor bank and lead acid battery. The setup of the energy storage devices and measurement system is shown in the photograph below. The video and photograph are generally in vertical alignment. The field around the super-capacitors in the video is more or less lined up with the position of the super-capacitors in the photograph, similar arguments apply to the battery. The setup and the specifics of this experiment are discussed in a forthcoming publication. Because of the limitations of a paper based journal the video element is discussed here instead. The video is approximately 1 minute long and shows approximately 5 minutes of real time (it has been sped up to make the result more apparent). The battery and super-capacitor combination have been in quiescence for a 'long' time and are about to be discharged at approximately 12 Amps. The battery is a 8.5 Ah lead acid motorcycle battery (Yuasa YTZ10S 12 V AGM) and the super-capacitors are 6 x Maxwell Technologies Power Cache PC2500 connected in series yielding a capacitance of just over 400 F. The fixed cone (bottom left) represents a magnitude of 100 mG all cone sizes may by judged relative to this.

### Chronology

Time is measured according to the video transport (multiply by five for real times). At 18 seconds the discharge begins and the super-capacitor dominates the current contribution. By 25 seconds (so 7 seconds of video or 35 seconds of measurement) the super-capacitors and battery are contributing more or less equally to the current flow. After 28 seconds the battery begins to dominate the current flow and this situation is maintained until 44 seconds, when the discharge current is removed. Thereafter charge redistribution takes place between the battery and super-capacitors.