Sensor Fusion for Power Line Sensitive Monitoring and Load State Estimation
Abstract
:1. Introduction
1.1. Fault Detection
1.2. Contribution
- The original principle of a specifically adapted EKF as observer that estimates the fault condition of the power line of electrical health device management (fluctuation of the mains voltage of the power line in Europe is in the tolerance of at a mains frequency of ; see DIN IEC 60038 [28].
- The original principle of another EKF for a state estimation of the secondary galvanic decoupled side of a two-winding transformer and the electrical load resistance .
2. Problem Formulation
2.1. Mutual Inductor and Transformer
2.2. Transformer System
3. EKF Methods
3.1. State Observer for the Mutual Inductance and Load–EKF1
3.2. State Observer for the Power Line Condition– EKF2
3.3. Observability Analysis
4. Experiment Setup
5. Results and Discussion
6. Conclusions and Future Work
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations and Nomenclature
The following abbreviations are used in this manuscript: | |
ARX | Autoregressive model with exogenous input |
DC | Direct current |
DIN | Designation of standards; German Institute for Standardization |
EKF | Extended Kalman filter |
FDD | Fault detection and diagnosis |
IEC | Designation of standards; International Electrotechnical Commission |
ISO | Designation of standards; International Organization for Standardization |
KF | Kalman filter |
PMSG | Permanent magnet synchronous generator |
UKF | Unscented Kalman filter |
The following nomenclature is used in this manuscript: | |
A | Amplitude |
Matrix of the system dynamics | |
State-input feedback matrix | |
Nonlinear state function | |
, | Electrical voltages across the primary and secondary winding, respectively |
, | Electrical currents of the primary and secondary winding, respectively |
, , M | Primary, secondary, and mutual inductances of transformer, respectively |
Lie derivatives | |
White noise variable | |
Pre-compensation matrix | |
Scalar output measurement function | |
Output Jacobian measurement matrix, respectively | |
J | Assessment criteria |
Jacobian matrix | |
K | Inductive coupling coefficient |
Kalman gain | |
Nonlinear observability matrix | |
Natural numbers | |
Number of possible determinants | |
Numbers of columns and rows of observability matrix, respectively | |
Posterior and a priori estimation error covariance matrix | |
Covariance matrices of process noise, respectively | |
Variance matrices of soft sensors | |
Primary and secondary winding and electrical load resistances, respectively | |
Continuous time, start time, and stop time, respectively | |
Sampling period | |
System state | |
A posteriori estimation of system state | |
A priori estimation of system state | |
Angular frequency | |
Angular phase | |
Primary stray flux and core flux of transformer, respectively | |
Phase noises |
Appendix A
Listing A1. Observability test for EKF1. |
Listing A2. Observability test for EKF2. |
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Schimmack, M.; Belda, K.; Mercorelli, P. Sensor Fusion for Power Line Sensitive Monitoring and Load State Estimation. Sensors 2023, 23, 7173. https://doi.org/10.3390/s23167173
Schimmack M, Belda K, Mercorelli P. Sensor Fusion for Power Line Sensitive Monitoring and Load State Estimation. Sensors. 2023; 23(16):7173. https://doi.org/10.3390/s23167173
Chicago/Turabian StyleSchimmack, Manuel, Květoslav Belda, and Paolo Mercorelli. 2023. "Sensor Fusion for Power Line Sensitive Monitoring and Load State Estimation" Sensors 23, no. 16: 7173. https://doi.org/10.3390/s23167173
APA StyleSchimmack, M., Belda, K., & Mercorelli, P. (2023). Sensor Fusion for Power Line Sensitive Monitoring and Load State Estimation. Sensors, 23(16), 7173. https://doi.org/10.3390/s23167173