153 Figure 6.17 Size error in estimated phasors of 14 A for (a) two sensors per phase at 7 mm and (b) three-phase CTs in triangular structure. 165 Figure 6.28 Size error in estimated phasors of 14 A for (a) two sensors per phase at 15 mm and (b) three-phase CTs in horizontal structure.
Introduction
- Research Background
- Traditional Current Measurement Device
- Alternative Technologies for Current Measurement
- Survey of Magnetoresistive Effect based Sensors: GMR, TMR Sensors
- Research Motivation
- Objectives of the Research
- Thesis Outline
The Hall voltage is proportional to the vector cross product of the current and the magnetic field [22-24]. Experimental results showed limitations due to crosstalk of magnetic fields and noise in the system.
Three-phase Current Estimation Technique using Magnetic Field Density
Measuring Magnetic Field
The study of magnetic fields generated by multiple sources can be carried out in detail for three-phase overhead lines with balanced three-phase voltages. The first objective of this research is to investigate the behavior of magnetic fields created by multiple alternating currents in a three-phase circuit.
Mathematical Model for Magnetic Field of Three-Phase, Three-Conductor System
In the above equation, d1, d2 and d3 are the distances of measurement points from each phase conductor as shown in figure 2.4(a) and (b). The resulting magnetic field obtained by equation (2.2.3) is a function of the distance of point P1 from each phase, and the current passing through each phase, A, B and C. The resulting magnetic field will then be an addition of the fields produced by three currents at several points placed together and will depend on the distance of these points from the conductor.
Calculation of Magnetic Field for Three-Phase Circuit
63] conducted a comparative study to find the accurate estimation of the surface magnetic field of overhead transmission line conductors. To calculate the magnetic field at the points described in Figure 2.6, a three-phase triangular structure of 12.47 kV is chosen, as explained earlier and shown in Figure 2.1.
Linear Regression Analysis to Estimate Three-Phase Currents
B XT ˆTX XT (2.4.6) By transposing on both sides of the above equation and rearranging we get. X XT T ˆ
Computer Simulation and Analysis for Three-Phase Triangular Arrangement
- Simulation Results for Group I: One Measurement Point per Phase
- Simulation Results for Group II: Two Measurement Points per Phase
- Simulation Results for Group III: Three Measurement Points per Phase
In this case, the measuring points of phase-A are located in the north, while all phases are far away from phase-B and phase-C. For case #c6, the first set of measurement points for phase-A is located in the north direction, while the measurement points of phase-B and phase-C are in the south direction.
Computer Simulation and Analysis for Three-Phase Horizontal Arrangement
- Simulation Results of Group I: One Measurement Point per Phase
- Simulation Results of Group II: Two Measurement Points per Phase
- Simulation Results of Group III: Three Measurement Points per Phase
The simulation is performed for three groups, the same as those of the previous section, in which there are single, two and three measurement points per phase. In this case, the measurement points for all phases are located in the north direction and therefore experience minimal interaction with the magnetic field of the adjacent phase. In this case there are two measurement points per phase and therefore show better results for the same combinations of directions as those of Group I.
Summary
It is North, East and West for the triangular structure; the north direction is for phase A, the east direction is for phase B and the west direction is for the phase C conductor. The second outcome is that if there are two measurement points, one at 2.5 cm and the other at 5 cm, they increase the current estimation accuracy. The analysis shows that the accuracy depends on the number of sensors and the distance from the sensor to the conductor.
Selection of Magnetic Sensors: Testing and Validation
- Contactless Sensors for Application in Current Measurement
- Measurement of Magnetic Field using Magnetic Sensors
- Experimental Setup for Sensor Testing
- Experimental Setup for Three-Axis Sensor
- Performance Evaluation
- Current Estimation from Magnetic Field
- Summary
The magnetic field generated by the current-carrying overhead conductors depends on the type of current generating the field. This can be achieved by rearranging Equation (3.2.1) as: 3.4.1) The values of magnetic field, B obtained for each case of injected input current, I and for respective distance, d are known. By inserting all known values into the right-hand side of Equation (3.4.1), the current is estimated for the respective case.
Calibration and Validation of Magnetic Sensors
Adopting Magnetic Sensors in Current Measurement Application
The experiment and analysis are performed on twelve sensors to calibrate and check their performance compared to each other and to verify their behavior in the presence of the same magnetic field. This approach will also help to calibrate the sensors to achieve maximum accuracy in current measurement. This chapter presents a detailed analysis of the calibration and comparative performance of the twelve sensors under the various factors mentioned above.
Multiple Sensors Arrangement
The purpose of this study is to investigate any manufacturing deficiencies or variation in the sensors and consequently finalize whether all sensors can be calibrated with the same calibration factor, or whether they would require individual calibration factors based on their quality. It has also been demonstrated that due to practical issues and manufacturing imperfections, the output of the sensors does not exactly follow the aforementioned theoretical equations. Therefore, it becomes important to calibrate and prepare the sensors to improve the accuracy of the current measurements.
Experimental Setup for Twelve TMR Sensors
The sampling rate was maintained at 7.2 kHz, and 10,000 samples were recorded for each injected current value. Completion of these sets marked the end of Stage 1 of the first part of the experiment. For part II, the combination of sensors and the possibility of their placement were changed, as shown in table 4.1.
Calibration of Sensors
- Using Direct Method: Biot-Savart Law
- Using Discrete Fourier Transform (DFT)
Before using the measured data for each case, the offset was removed from each to make it possible to determine the maximum value of the magnitude of the currents calculated using the above equation for these distances. The waveform represented by N samples can be decomposed using the orthogonality property of the complex sinusoid over the domain 0,N1and can. From the transformed waveform obtained above for each set of measured values corresponding to specific currents is then used to calculate the average value of the multiplication factor (MF).
Validation of Sensor Performance
- Sensor Quality
- Distance from Source
- Insulation
- Harmonics
According to equation (4.4.1), the strength of the magnetic field decreases as the distance from the source increases. The value of the MFs increases with the increase in distance from the source. The results of the DFT algorithm for the multiplication factors for both the WI and NI cases showed a variation of 110 to 120 for each sensor.
Performance of Sensors at High Currents
The %TVE values of S3 for all currents are shown with their mean, maximum and standard deviation in the last three columns of the table. The standard deviation is also shown in the same table for all input currents, and shows results below 0.30 with most results less than 0.1. The rated current of S1 for an input of 50 A is shown in Figure 4.28 which shows a clean sinusoid with an error of 0.21 A (refer to the results in Appendix C).
Conclusions and Summary
This is because the magnetic field intensity at 15 cm produced by 10 A current is weaker than that generated by higher currents. Moreover, after the successful calibration, these non-invasive TMR sensors can be deployed in the current measurement experiments for AC power systems. The standard deviation in the calculation of the %TVE for all sensors showed a consistently low value indicating that they can be deployed to measure currents in medium and high voltage AC power systems where currents are usually in the range of 300 A to 1500 A is.
Multiple Sensors and Fusion Technique for Improving Current Phasor
Introduction
A computer program based on the DFT technique and a current phasor estimation algorithm with stages as shown in the Figure 5.1 was developed in MATLAB software. Current phasors were estimated for each sensor as well as six combinations of sensor pairs for a set of four sensors. This chapter also introduces the current estimation technique by applying various combinations of sensor pairs using four sensors as well as the weighted fusion technique with inverse variance.
Study of Individual MFs and Average MF for Estimation of Current Phasor
The difference between the errors obtained using individual MFs and average MFs is within 0.2% to 0.3% for all distances and all currents after 10 A. The accuracy of all sensors was investigated for currents from 10 A to 25 A in 5 A steps and for all distances using individual and average MFs. Overall, for the 15 A current, it was observed that the difference between the errors using the individual MFs and the average MFs is negligible for all distances except for sensors S5, S8 and S9 and this difference is not very large for S8 and S9.
Estimation of Phase Angle Error and Total Vector Error
From the results obtained for all distances and currents for all sensors, it was observed that the error difference between using individual and average MF is much smaller. The phase representation of a single-frequency current signal can be represented as: where, Xm is the peak value of the sinusoidal signal, the subscripts r and i denote the real and imaginary parts of the rectangular complex value. The phase angle, of the phasor will advance when the phasor is calculated by advancing the data window by one sample and applying a non-recursive algorithm.
Sensor Performance at Various Low Frequencies
- Response to Low Frequencies
- Response to Harmonic Frequencies
The calculated %TVEs are plotted using Box and Whisker plots as shown in Figure 5.12. For comparison and analysis, the error results are shown in Figure 5.13 for sensor S2 and CT. Figure 5.13(b) shows that TVE increases for CT with increasing harmonic frequency and input current magnitude, while the errors are consistently below 1% for all harmonics for sensor S2, as shown in Figure 5.13. (a).
Duplicate Sensors and Sensor Fusion
TVE results obtained for a set of input currents of 1 Hz for two combinations of sensor pairs are shown in Table 5.3. The S1S4 sensor combination consistently gave the highest errors for all currents at 5 Hz as well as 10 Hz and can be seen in Table 5.4 and Table 5.5. Following a similar procedure, the TVEs were calculated for the CT output and are presented in Table 5.6.
Summary
Comparing the output of TMR sensors with that of conventional CT for low-frequency currents proved that these sensors can be very effective and accurate for measuring asymmetric fault currents that have inherent low-frequency components. Combining multiple sensors with weighting factors based on the variance of estimated 60 Hz current magnitudes improved the measurement accuracy of sensor pairs for all low frequencies. The sensor data fusion technique by selecting the best sensor combinations can yield improved sensor performance with improved accuracy with TVE % errors well below 2% compared to CT.
Estimation of Three-phase Current Phasors
Introduction
In type (a), phase-B is at the apex of the triangle and the other two phases are in a horizontal plane, equidistant from each other as well as in height, D1 = 98 cm from the top conductor and the distance between phase-A and phase-B is D2 = 113 cm as shown in figure 6.1(a). In the horizontal type of structure, all phases are in the horizontal plane with phase-B placed at an equal distance of D3 = 56.5 cm from phase-A and phase-C as shown in Figure 6.1(b). These distances are also called clearances and are followed using the USF standard applicable in the province of Ontario in Canada.
Experimental Setup for Three-Phase Current Measurement using TMR Sensors 137
- Results of One Sensor per Phase at Various Distances
- Lab Test Results of Two Sensors per Phase at Various Distances
- Test Results of Three Sensors per Phase at Various Distances
The angular errors of CTs are shown in Figure 6.9(b), which indicates smaller errors than all sensors. The magnitude errors in the estimated phasors for each current for all sensors and for all distances are shown in Figure 6.15. The size and angular errors for the same configuration are shown in Figure 6.25 and Figure 6.26.
Test Results and Performance Analysis of TMR Sensors for Three-Phase Horizontal
- Results of Two Sensors per-Phase at Various Distances
- Results of Three Sensors per Phase at Various Distances
Similar steps were followed for the remaining distance options and the entire procedure was repeated for the set of three sensors per phase. This test became the last phase of the experiment with three sensors per phase in the arrangement of the horizontal structure. The results for the random cases are presented in Appendix D which consists of the rectangular components of the estimated current phases of the sensor outputs for different cases, as well as the magnitude and angle errors for the same configuration of distances and sensors. per phase.
Field Experiment for Three-Phase High Currents Measurement
- Performance of Sensors in Measuring Three-Phase Currents
The results of sensor S2 for measuring phase A currents for all phases are given in Table 6.11. Similarly, the estimated output of the B-phase sensor S4 for an input current of 91.2 A is shown in Figure 6.33. The performance of sensor S4 is shown in terms of percentage errors for B-phase load currents between different stages and is shown in Table 6.12.
Summary
Detection of Unbalanced Three-Phase and Neutral Currents by using
Introduction
Experimental Setup
Computation of Current Phasors
Test Results
- Results for Symmetrical Three-phase Currents for Phase Sensors
- Results for Neutral Currents
Summary
Conclusions and Future Work
Thesis Conclusions
Future Work
Average Estimation Errors (A) for Group II: Two Measurement Points per Phase
Minimum Estimation Errors (A) for Group II: Two Measurement Points per Phase
Average Estimation Errors (A) for Group III: Three Measurement Point per Phase
Minimum Estimation Errors (A) for Group III: Three Measurement Points per
Experimental Setup
Combinations for Measuring Magnetic Field
Programming and Settings of Sensors
Orientation and Configuration of Sensors
Experiment Procedure
Interpretation of Data Stored in Bx, By and Bz Columns for Magnetic Fields
Experiment Results and Observations for Sensor 1 and Sensor 2 Combinations for
Results of Case: S1_1_10to15_AS_TBF_50.m
Performance Results of Sensor S 1 for High Currents
Performance Results of Sensor S 2 for High Currents
Performance Results of Sensor S 4 for High Currents
Performance Results of Sensor S 5 for High Currents