In my research, I focused on the development of a Hall-array current sensor specifically tailored for the current measurement of a vehicle traction battery. The rapid evolution of electric vehicles demands more compact, lighter, and highly reliable current sensing solutions for battery management systems. Traditional current transformers, fluxgate sensors, and shunt resistors often face difficulties in meeting the strict requirements of narrow installation spaces inside a vehicle traction battery pack. In this context, I investigated an elliptical Hall-array configuration, designed the relevant hardware and calibration algorithms, and proposed a GWO-BP based error optimization scheme. The results demonstrate that the proposed sensor can achieve high accuracy, low error, and strong robustness under temperature variations and conductor displacement, which is essential for the safe operation of a vehicle traction battery.
Introduction and Motivation
The vehicle traction battery is the core energy storage unit of an electric vehicle. Its state of charge, state of health, and thermal safety are directly affected by the accuracy of the measured current. Current sensors used in the battery management system must therefore provide precise current readings over a wide range from small charging currents to large discharge currents. However, the internal space of a modern vehicle traction battery is extremely confined, especially as manufacturers continue to improve energy density and reduce packaging size. Conventional closed-loop Hall sensors with magnetic cores are relatively bulky, while open-loop sensors suffer from temperature drift and poor accuracy. Shunt-based solutions consume power and break galvanic isolation. These limitations motivated my study of a coreless array of Hall elements that can surround a rectangular busbar.
During the literature review, I noticed that Hall-array current sensors have attracted increasing attention due to their advantages in eliminating magnetic saturation, reducing weight, and improving linearity. The early implementations were circular arrays used to measure round conductors. However, in a vehicle traction battery, busbars are usually rectangular for better heat dissipation and lower fabrication cost. Measuring a rectangular conductor using a circular array is possible but often inefficient because the large radius necessary for the horizontal dimension creates excessive unused space in the vertical direction. In my work, I therefore chose an elliptical array geometry. The ellipse can better conform to the rectangular busbar cross section, keeping the sensor dimensions compact and maintaining a smooth magnetic-field gradient along the integration contour.
Theoretical Foundation of Magnetic Field Measurement
The Hall effect is the fundamental operating principle of the proposed sensor. When a current-carrying conductor is placed in a magnetic field, the moving charges experience a Lorentz force, leading to a transverse Hall voltage. For a Hall plate biased with a current \(I\), the Hall voltage \(V_H\) can be expressed as
$$ V_H = \frac{K_H}{d} I \times B $$
where \(K_H\) is the Hall coefficient, \(d\) is the thickness of the Hall plate, and \(B\) is the magnetic flux density perpendicular to the plate. In practical integrated Hall sensors, the output voltage is proportional to the magnetic field component along the sensitive axis, and the sensitivity is usually expressed in mV/mT.
For a straight, infinitely long conductor carrying current \(I\), the magnetic field satisfies Ampère’s law
$$ \oint_{\mathcal C} \mathbf{H} \cdot \mathrm d\mathbf{l} = I_{\text{enc}}, $$
where \(\mathbf{H}\) is the magnetic field intensity and \(\mathcal C\) is a closed contour surrounding the conductor. In my sensor, instead of relying on a magnetic core, I place a finite set of Hall elements along an ellipse around the rectangular busbar. The magnetic field at each Hall element is sampled, and the weighted sum of these samples is used to approximate the line integral of \( \mathbf{H} \) over the contour. The reconstructed current is obtained by
$$ I_{\text{calc}} = \sum_{i=1}^{N} H_{i,\text{MFS}} \Delta s_i , $$
where \(H_{i,\text{MFS}}\) is the magnetic field intensity projected onto the sensitive axis of the \(i\)-th Hall element and \(\Delta s_i\) is the corresponding arc-length segment of the elliptical integration path.
Elliptical Array Parameter Design
To meet the lightweight requirement of a vehicle traction battery, I avoided adding a magnetic core and instead designed the Hall-element array on a printed circuit board. The key parameters of the elliptical array are the semi-major axis \(a\), the semi-minor axis \(b\), the number of Hall elements \(N\), and the method used to distribute these elements along the ellipse. I compared two methods: projection from a circular array and uniform curve segment length (UCSL). The projection method maps points on a circle with equal angular spacing onto an ellipse via parallel projection, which yields non-uniform arc lengths. The UCSL method divides the ellipse into curve segments of equal arc length. In my simulation, the UCSL method provides lower current-reconstruction error for the same \(N\), so I adopted the UCSL method.
Let the perimeter of the ellipse be approximated by a polyline with \(K\) points. The coordinate of the \(k\)-th point on the ellipse is
$$ \left( a\cos\frac{360^\circ k}{K},\; b\sin\frac{360^\circ k}{K} \right), \quad k=1,2,\dots,K. $$
The arc length from the \(X\) axis to the \(k\)-th point is
$$ s(k) = \sum_{n=2}^{k} \sqrt{\Delta x_n^2 + \Delta y_n^2} . $$
If the ellipse is divided into \(N\) segments, each segment has a nominal arc length
$$ \Delta s = \frac{s(K)}{N} . $$
For robustness, a first-segment bias parameter \(s_0\) was calculated using the empirical formula
$$
s_{0,r} = \begin{cases}
\frac{1}{3}, & N=6 \\[2pt]
\frac{1}{4}, & N=7
\end{cases}
$$
as reported in earlier literature, and the biased initial arc length is \(s_0 = s_{0,r}\, s(K)\).
With a rectangular busbar of cross section 20 mm x 4 mm, I fixed the semi-major axis at \(a = 30\) mm to match common vehicle traction battery busbars while leaving room for insulation and mounting. I then varied the aspect ratio \(AR = b/a\) from 0.1 to 1.0 and evaluated the relative current error for \(N = 4,5,6,7\). The trends show that as \(N\) increases, the error generally decreases, but \(N=6\) and \(N=7\) provide a good trade-off. I decided to study \(N=6\) and \(N=7\) because \(N>7\) would increase cost without significant gain. The current error as a function of aspect ratio indicated that for \(N=6\), the error is zero when \(AR \approx 0.33\); for \(N=7\), zero error occurred near \(AR \approx 0.31\). Both combinations yield a much more compact sensor than the circular array \(AR=1\).
I also included circular arrays with \(AR=1\) for comparison. Table below lists the Hall element coordinates and sensitive axis directions for the four designed PCB configurations.
| Board | N | AR | Hall element positions (x,y) in mm | Sensitive axis directions (unit vector) |
|---|---|---|---|---|
| PCBA | 6 | 0.33 | (26.94,4.40), (5.57,9.83), (-16.59,8.33), (-26.94,-4.40), (-5.56,-9.83), (16.59,-8.33) | (-0.827,0.563), (-0.998,0.063), (-0.976,-0.216), (0.827,-0.563), (0.998,-0.063), (0.976,0.216) |
| PCBB | 7 | 0.31 | (29.18,2.17), (11.77,8.55), (-7.07,9.04), (-25.41,4.95), (-21.01,-6.64), (-2.36,-9.27), (16.43,-7.78) | (-0.611,0.791), (-0.991,0.131), (-0.997,-0.075), (-0.897,-0.443), (0.957,-0.291), (1.000,-0.024), (0.980,0.199) |
| PCBC | 6 | 1.00 | (28.98,7.76), (7.76,28.98), (-21.21,21.21), (-28.98,-7.76), (-7.76,-28.98), (21.21,-21.21) | (-0.259,0.966), (-0.966,0.259), (-0.707,-0.707), (0.259,-0.966), (0.966,-0.259), (0.707,0.707) |
| PCBD | 7 | 1.00 | (29.81,3.36), (15.96,25.40), (-9.91,28.32), (-28.32,9.91), (-25.40,-15.96), (-3.36,-29.81), (21.21,-21.21) | (-0.112,0.994), (-0.847,0.532), (-0.944,-0.330), (-0.330,-0.944), (0.532,-0.847), (0.994,-0.112), (0.707,0.707) |
An important conclusion from my analysis is that the elliptical array offers a substantially reduced installation footprint. For example, the 6-element elliptical array with \(AR=0.33\) has an occupied area of approximately 908.5 mm2, while a circular array with the same horizontal extent occupies roughly 2827.4 mm2. The reduction is more than sufficient for the confined layout of a vehicle traction battery. The weight of my sensor including the PCB and Hall chips is about 11.9 g, compared with approximately 69.5 g for a conventional fluxgate current transducer. Thus, the elliptical Hall-array design aligns with the trend toward higher gravimetric energy density in vehicle traction battery modules.
Hardware Implementation
For the physical prototype, I selected the AKM EQ-730L as the single-axis Hall element for the main array. It operates with a supply voltage between 3.0 V and 5.5 V, has a sensitivity of about 130 mV/mT and a temperature range from -40 °C to 125 °C. These characteristics match the environmental envelope of a vehicle traction battery. To reconstruct the current accurately, I also included an Infineon TLV493DA1B6 three-axis Hall sensor at a certain monitoring position, which provides the vertical magnetic field information necessary for detecting conductor tilt. The core of the readout circuit is an STM32F103C8T6 microcontroller, which handles the analog-to-digital conversions, signal processing, and CAN communication with the battery management system.
The power supply chain starts from a 12 V DC source. An E1205SY isolated DC-DC converter steps the 12 V down to 5 V for the Hall elements and operational amplifiers. A TLV1117 low-dropout regulator generates a stable 3.3 V rail for the MCU. The outputs of all Hall elements are buffered by voltage followers, and a summing amplifier produces the total amplified signal. The microcontroller reads the individual Hall voltages through its internal ADCs and transmits the calculated current through a CAN transceiver TJA1050 to the host computer. I also provided different amplification gains for small, medium, and large current ranges, i.e. 100, 10, and 5, respectively, to cover the full current span from 0 A to 1500 A with improved resolution.
The inset figure below illustrates the concept of a compact power-battery current sensing module integrated with the Hall-array board.
Initial Error and Full Temperature-Range Calibration
After assembling the sensor, I noticed that production tolerances and component offsets created an initial proportional error even when the conductor was perfectly centered and orthogonal. This initial error, if not compensated, would degrade the performance of the current sensor in a vehicle traction battery. Therefore, I developed a two-stage calibration algorithm.
First, I performed a room-temperature calibration. The raw digital data received from the ADC is converted into a decimal difference:
$$ \mathrm{ADC}_{\text{diff}} = \mathrm{highDEC} – \mathrm{lowDEC}. $$
The actual sampling voltage is
$$ V_{\text{ADC}} = \frac{1}{K} \cdot \frac{1}{A} \cdot 0.001\ \mathrm{V} \cdot \mathrm{ADC}_{\text{diff}}, $$
where \(K=128\) is the oversampling count and \(A\) is the amplification gain. With a sampling resistor \(R = 0.47\ \Omega\), the measured output current is
$$ I_{\text{out}} = \frac{V_{\text{ADC}}}{R}. $$
The current deviation is \(\Delta I = I_{\text{out}} – I_{\text{set}}\). I divided the whole range into small, medium, and large current sections. In each section, I performed a linear least-squares fit on the pairs \((I_{\text{out}}, \Delta I)\). The compensation is conducted by subtracting the fitted deviation:
$$ I_{\text{comp}} = I_{\text{out}} – \left(k_i I_{\text{out}} + b_i\right). $$
I compared this first-order fit with a second-order polynomial fit. The first-order scheme resulted in lower compensation errors in most current points and required fewer computational resources, so I selected it for the calibration process.
For full temperature-range operation, I placed the sensor in a temperature chamber at -40 °C, 25 °C, and 125 °C. At each temperature, I recomputed the slope and intercept of the linear deviation curve. The drift coefficient between high temperature and room temperature is
$$ k_{\text{high}} = \frac{h_i – k_i}{100}, $$
while that between low temperature and room temperature is
$$ k_{\text{low}} = \frac{l_i – k_i}{65}, $$
where \(l_i\), \(k_i\), and \(h_i\) are the fitted slopes at low, room, and high temperature, respectively. The average per-degree drift coefficient is therefore
$$ \bar{k} = \frac{k_{\text{low}} + k_{\text{high}}}{2}. $$
After temperature compensation, the new fitted current deviation becomes
$$ \Delta I_{\text{fit}} = \left(k_i + \bar{k} T\right) I_{\text{out}} + b_i, $$
where \(T\) is the actual ambient temperature in degrees Celsius. Using this correction, I was able to keep the current relative error below 3‰ over the complete vehicle traction battery operating temperature range.
Error Sources: Eccentricity and Tilt
Even after calibration, I found two important geometrical error sources that affect the Hall-array current measurement: conductor eccentricity and conductor tilt. Eccentricity is the deviation of the busbar center from the ellipse center, while tilt means that the busbar is not perpendicular to the plane of the Hall array. These effects become especially relevant in a moving electric vehicle where the vehicle traction battery is subjected to vibration, mechanical stress, and thermal expansion.
To describe the conductor position, I introduced the coordinates \((x_0, y_0)\) of the busbar intersection with the array plane, and the direction angles \((\alpha, \beta)\), where \(\alpha\) is the angle between the busbar axis and the positive \(Z\) axis, and \(\beta\) is the angle of the projection of the busbar axis on the \(X\)-\(Y\) plane measured from the positive \(X\) axis. The unit vector along the conductor direction is:
$$ \mathbf e_l = \left( \sin\alpha \cos\beta,\; \sin\alpha \sin\beta,\; \cos\alpha \right). $$
For a Hall element located at point \(P(a,b,0)\), the magnetic field generated by an infinitely long conductor can be computed using the Biot–Savart law in the integral form. I derived the \(X\), \(Y\), and \(Z\) components of the magnetic field as
$$ H_x = \int_S \frac{I \, p(b-y)} {2\pi\, A\, D} \,\mathrm dx\,\mathrm dy, $$
$$ H_y = \int_S \frac{I \, p(a-x)} {2\pi\, A\, D} \,\mathrm dx\,\mathrm dy, $$
$$ H_z = \int_S \frac{I \left[m(b-y)-n(a-x)\right]}{2\pi\, A\, D} \,\mathrm dx\,\mathrm dy, $$
in which the denominator \(D\) is
$$ D = p^2\left[(a-x)^2+(b-y)^2\right] + \left[m(a-x)+n(b-y)\right]^2, $$
and \(m = \sin\alpha\cos\beta\), \(n = \sin\alpha\sin\beta\), \(p = \cos\alpha\). The integration domain \(S\) is the projection of the tilted conductor cross section onto the \(X\)-\(Y\) plane. A numerical reconstruction of the current then uses the formula
$$ I_{\text{calc}} = \sum_{i=1}^{N} H_i^{\text{MFS}} \, \Delta s, $$
with the sensitive-axis projection depending on the local tangent unit vector of the ellipse.
Through simulation, I analyzed how the eccentricity affects the relative current error for the four candidate array designs. For the selected six-element elliptical array, a positive \(X\)-direction eccentricity of 10 mm caused an uncompensated error close to 4.18%. A \(Y\)-direction eccentricity of 2.4 mm caused an error around 0.94%, which already exceeded the target tolerance in some BMS applications. In both cases, the error was larger than the permissible threshold for a vehicle traction battery current measurement under harsher driving conditions. Hence, I realized that an efficient online estimator of the conductor position and tilt was needed to provide correction factors for the current integral.
GWO-BP Conductor-State Estimation and Error Correction
To improve the current sensor accuracy, I aimed to estimate the position/orientation parameters \((x_0,y_0,\alpha,\beta)\) from the Hall-array measurements and then use them to recompute the integral region in the magnetic field formula. Since the relationship between the array output and the conductor state is nonlinear, a neural network seemed suitable. I constructed a BP neural network whose input layer receives 18 normalized magnetic signals (six Hall elements times three axes), one hidden layer contains 12 neurons, and the output layer provides five parameters \((x_0,y_0,m,n,p)\).
However, a standard BP network has well-known issues: it is sensitive to the initial weights and thresholds and may converge to local minima. To tackle this, I used the Grey Wolf Optimizer (GWO), a swarm intelligence algorithm inspired by the hunting behavior of grey wolves. In GWO, the optimal solution is considered the prey, and the three best candidate solutions at each iteration are denoted \(\alpha\), \(\beta\), and \(\delta\). The remaining wolves \(\omega\) update their positions based on the following rules:
$$ \mathbf D_\alpha = \left| \mathbf C_1 \cdot \mathbf X_\alpha – \mathbf X \right|,
\quad \mathbf D_\beta = \left| \mathbf C_2 \cdot \mathbf X_\beta – \mathbf X \right|,
\quad \mathbf D_\delta = \left| \mathbf C_3 \cdot \mathbf X_\delta – \mathbf X \right|,
$$
$$ \mathbf X_1 = \mathbf X_\alpha – \mathbf A_1 \cdot \mathbf D_\alpha, \quad
\mathbf X_2 = \mathbf X_\beta – \mathbf A_2 \cdot \mathbf D_\beta, \quad
\mathbf X_3 = \mathbf X_\delta – \mathbf A_3 \cdot \mathbf D_\delta,
$$
and
$$ \mathbf X(t+1) = \frac{\mathbf X_1 + \mathbf X_2 + \mathbf X_3}{3}. $$
The coefficient vectors \(\mathbf A\) and \(\mathbf C\) are computed from random vectors and from a linearly decreasing scaling factor \(a\) from 2 to 0 throughout the iterations.
I used this GWO algorithm to optimize the initial weights and thresholds of the BP network. The overall process begins with a preprocessing step on the simulation dataset collected from COMSOL. Then the GWO algorithm searches for the best weight vector by minimizing the mean squared error between predicted and actual conductor states. After the maximum iteration number is reached, the optimal weights are assigned to the BP network and the final model is trained and evaluated. The resulting model is called GWO-BP, and its performance was compared with that of a plain BP network.
I built the dataset by running finite-element simulations in COMSOL Multiphysics. Conductor eccentric positions, tilt angles, and tilt orientations were randomly generated within the allowed ranges, and the magnetic field component values at the six Hall element locations were recorded. The obtained dataset was split into training and testing subsets. In my test environment, I compared the prediction errors for the five conductor-state parameters. Table below summarizes the performance indices for the BP and GWO-BP models.
| Estimated parameter | Model | MAE | MSE | MAPE |
|---|---|---|---|---|
| \(x_0\) | BP | 0.2272 | 0.0771 | 0.8419% |
| GWO-BP | 0.0498 | 0.0041 | 1.0411% | |
| \(y_0\) | BP | 0.0619 | 0.0043 | 5.2646% |
| GWO-BP | 0.0146 | 0.0004 | 1.0621% | |
| \(m\) | BP | 0.0124 | 0.0003 | 10.3490% |
| GWO-BP | 0.0037 | 0.0001 | 2.8585% | |
| \(n\) | BP | 0.0071 | 0.0002 | 3.9567% |
| GWO-BP | 0.0028 | 0.0001 | 0.8626% | |
| \(p\) | BP | 0.0143 | 0.0005 | 2.2479% |
| GWO-BP | 0.0029 | 0.0001 | 0.4173% |
Although the MAPE for \(x_0\) was slightly higher for GWO-BP, the MAE and MSE of every parameter were significantly reduced. This means that the GWO-BP model improves the average accuracy and reduces large estimation outliers. Such an improvement is critical for maintaining accurate current measurement in a vehicle traction battery under mechanically stressed installations.
Calibration Experiments and Accuracy Results
In the experimental verification stage, I built a test platform composed of a high-power programmable DC source, a bidirectional current switch, a precision data acquisition unit, a thermal chamber, and a host computer with a custom LabVIEW program. The DC source supplied current up to \(\pm1500\) A through a straight rectangular copper busbar of dimensions 20 mm by 4 mm. The current direction could be reversed by an IGBT-based switch board, and the sensor was powered from a separate 12 V DC supply.
I first calibrated the sensor at room temperature. After fitting the linear deviations for the small, medium, and large current ranges, the relative errors were reduced by approximately 85.6%. The residual current deviation was always below 3‰. I then performed high- and low-temperature calibration at 125°C and -40°C. The ambient-temperature-dependent slope coefficients are listed in the following table for each segment.
| Segment | Direction | Low-T slope | Room-T slope | High-T slope | Steady drift coeff. |
|---|---|---|---|---|---|
| Small current | Positive | -0.00349 | -0.00505 | 0.00369 | 0.0000557 |
| Small current | Negative | -0.00369 | -0.00508 | -0.00386 | 0.0000168 |
| Medium current | Positive | -0.00380 | -0.00367 | 0.00421 | 0.0000404 |
| Medium current | Negative | -0.00392 | -0.00395 | 0.00387 | 0.0000393 |
| Large current | Positive | -0.00272 | -0.00284 | 0.00618 | 0.0000460 |
| Large current | Negative | -0.00293 | -0.00316 | 0.00564 | 0.0000458 |
The temperature-compensated outputs showed that the low-temperature current errors were reduced by 62.6% while the high-temperature errors were reduced by 43.0%. After the complete full-temperature calibration, the worst-case error at \(-40\) °C, 25°C, and 125°C remained below 3‰. This level of precision is essential for accurate state-of-charge estimation in a vehicle traction battery.
Experimental Validation of Eccentricity and Tilt Correction
Next, I evaluated the effectiveness of the GWO-BP-based error correction by intentionally moving and tilting the busbar relative to the sensor.
For the eccentricity test, I displaced the busbar in the \(X\) direction up to 10 mm, and in the \(Y\) direction up to 2.4 mm. The figure below shows the measured relative errors before and after optimization. The errors after applying the GWO-BP optimizer were substantially lower than those before optimization. When the busbar was displaced by 10 mm in the \(X\) direction, the original error of 4.18% was reduced to 1.46%, corresponding to a decrease of 65.07%. Under a 2.4-mm \(Y\)-direction eccentricity, the original error of 0.94% decreased to 0.51%, a reduction of 45.74%. For practical combinations of \(X\) and \(Y\) eccentricity, the maximum error after correction stayed within 2.54% at the extreme mechanical limit. In normal operating conditions, a vehicle traction battery busbar is not likely to reach such extreme displacements, so the practical error would remain much smaller.
For the tilt test, I changed the conductor angle \(\alpha\) from 0° to 45° (with \(\beta=20^\circ\)) and the angle \(\beta\) from 0° to 90° (with \(\alpha=0^\circ\)). The original sensor was very sensitive to these tilt angles. At \(\alpha=45^\circ\), the uncompensated error reached 12.37%. After applying the proposed GWO-BP method, the error was reduced to 2.95%, a reduction of 76.15%. When \(\beta\) was varied, the optimized sensor reduced the maximum error by 62.92%. Thus, the GWO-BP approach proved effective in correcting both eccentricity and tilt errors that would otherwise harm the reliability of current monitoring for a vehicle traction battery.
I also performed repeatability tests on three samples. The test results showed that the current measurement error was still below 3‰ across the whole current range from \(-1500\) A to 1500 A at each temperature test point. This confirms the reproducibility and mechanical robustness of the designed sensor. The performance is adequate for BMS current sensing in a vehicle traction battery, protecting the lithium-ion cells from overcharging or overdischarging and providing reliable input for fault diagnosis.
Finite-Element Simulation and Discussion
The finite-element simulation in COMSOL Multiphysics confirmed that the magnetic flux density contours around a rectangular busbar resemble ellipses. This observation supports the selection of an elliptical integration loop rather than a circular loop to minimize spacing between the busbar and the Hall elements. I also used the simulation model to generate the training dataset for the GWO-BP network because experimental generation of hundreds of conductor positions and angles would be time-consuming and costly. The simulation model includes the actual cross-sectional geometry of the rectangular busbar, its orientation, and the location of each Hall sensor. In this way, I could study a wide variety of cases that might occur in the lifecycle of a vehicle traction battery, including manufacturing tolerances and fixation degradation.
The sensor hardware was designed to measure currents from very low values to as high as 1500 A. Because the Hall elements are linear and do not saturate, the measurement principle remains valid over the full current range. The dynamic range is achieved by adjusting the amplification gain based on the measured amplitude. In the final prototype, I also integrated the three-axis Hall sensor for vertical field measurement, which is especially important for detecting tilt. The use of a compact printed circuit board means that the entire sensor can be mounted directly above or below the busbar connection inside the battery junction box, which is a typical location in a vehicle traction battery pack.
The results of my comparison between ellipse and circle arrays are summarized in the following table. It is evident that the designed elliptical array fulfills the objectives: reduced area, lower weight, and acceptable error for typical allowable conductor displacement.
| Sensor type | Weight (g) | Installed area (mm²) | Max X-eccentricity error (%) | Max Y-eccentricity error (%) |
|---|---|---|---|---|
| Fluxgate current sensor | 69.5 | 3290 | – | – |
| Circular Hall array | 15.5 | 2827.4 | ≤17.08 | ≤2.21 |
| Proposed elliptical Hall array | 11.9 | 908.5 | ≤4.73 | ≤0.35 |
The smaller installed area and lighter weight of my sensor are direct benefits for current vehicle traction battery designs. The reduction of the X-eccentricity error compared with a circular array is another noticeable benefit, especially because horizontal eccentric displacement is often larger than vertical displacement in a busbar assembly.
Conclusion and Outlook
In conclusion, I have successfully developed a Hall-element elliptical-array current sensor dedicated to the vehicle traction battery current measurement. By adopting the uniform curve segment length method, I optimized the positions and sensitive directions of six Hall elements around a rectangular busbar, obtaining a compact and lightweight design. The full-temperature calibration algorithm ensured that the initial relative error after calibration remained below 3‰ for temperatures from \(-40\)°C to 125°C. I further proposed a GWO-BP conductor-state estimation technique that uses the magnetic field data to infer the busbar offset and tilt, followed by a recomputation of the integration domain. Experimental results demonstrated that this correction reduces X-eccentricity errors by 65.07%, Y-eccentricity errors by 45.74%, and tilt errors by 76.15%.
The proposed sensor has shown high reliability and robustness in laboratory tests under varied operating conditions. Nevertheless, some limitations remain. A real vehicle traction battery environment may include nearby current paths from adjacent cells or power cables, which introduce external magnetic fields and crosstalk. In my future work, I will include crosstalk and three-conductor interference studies and extend the GWO-BP framework with an additional correction term. I also plan to improve the real-time execution speed of the parameter estimation model. Current BP and GWO-BP implementations operate in a post-processing mode; for safety-critical applications, a faster inference engine running on a microcontroller would be desirable. Finally, I intend to integrate the sensor into a real vehicle traction battery pack and validate its behavior against rigorous road profiles. The findings of this thesis will provide a useful reference for engineers working on current sensing techniques in electric vehicles and contribute to safer and more compact battery systems.