System and method for predicting electrical arcs in an electrical circuit
A system and method for predicting electrical arcs in an electrical circuit is provided. A time series data of the electrical circuit is received by a prediction system which is configured to detect an electrical signature indicating an upcoming electrical arc. The prediction system constructs Hankel matrix using the time series data which is decomposed using SVD to obtain a singular vector in which delay coordinate embedding is performed to generate reconstructed singular vector which includes plurality of eigen time delay coordinates. Further, threshold coefficient ‘r’ is calculated from the reconstructed singular vector. A first set of eigen time delay coordinates is identified in the reconstructed singular vector based on ‘r’ which are r th eigen time delay coordinates. A rate of change in magnitude of r th eigen time delay coordinates is calculated to detect the electrical signature based on which the upcoming electrical arc is predicted.
1. A method for predicting electrical arcs in an electrical protection device connected in an electrical circuit, the method comprising:
receiving, by a processor, time series data of the electrical circuit;
detecting, by the processor, an electrical signature in the time series data indicating an upcoming electrical arc in the electrical circuit by performing the following steps:
constructing a Hankel matrix using the time series data;
performing a singular value decomposition on the Hankel matrix to obtain at least one singular vector,
performing delay coordinate embedding on the at least one singular vector to generate at least one reconstructed singular vector, wherein the at least one reconstructed singular vector comprises a plurality of eigen time delay coordinates,
calculating a threshold coefficient ‘r’ from the at least one reconstructed singular vector, wherein the threshold coefficient ‘r’ indicates an optimal location in the at least one reconstructed singular vector representing a change in state of the electrical circuit,
identifying a first set of eigen time delay coordinates among the plurality of eigen time delay coordinates in the at least one reconstructed singular vector based on the threshold coefficient ‘r’, wherein r th eigen time delay coordinates constitute the first set of eigen time delay coordinates, and
computing a rate of change in magnitude of the first set of eigen time delay coordinates to detect the electrical signature,
predicting, by the prediction system, the upcoming electrical arc in the electrical circuit based on the electrical signature; and
generating, by the processor, a control signal to operate an actuator of the electrical protection device based on the prediction for quenching the electrical arc.
2. The method of claim 1 , wherein the electrical signature is detected when the rate of change in the magnitude of the first set of coefficients deviates from a reference value.
3. The method of claim 2 , wherein the reference value is determined based, at least in part, on a rate of change in magnitude computed at one or more preceding timesteps.
4. The method of claim 3 , wherein eigen time delay coordinates preceding the r th eigen time delay coordinates constitute a second set of eigen time delay coordinates.
5. The method of claim 4 , further comprising:
performing hard thresholding on the at least one reconstructed singular vector based on an optimum singular value hard threshold coefficient; and
determining the first set of eigen time delay coordinates and the second set of time delay coordinates from the at least one reconstructed singular vector.
6. The method of claim 5 , wherein the second set of eigen time delay coordinates in the at least one reconstructed singular vector is advanced in time based on corresponding first set of coefficients.
7. The method of claim 6 , wherein the second set of eigen time delay coordinates represent a linear response of the electrical protection device and the first set of eigen time delay coordinates represent the electrical signature.
8. The method of claim 1 , wherein the time series data comprises at least one of the group consisting of: current values, voltage values, power values and energy values in the electrical circuit.
9. A prediction system for predicting electrical arcs in an electrical protection device connected in an electric circuit, the prediction system comprising:
a memory configured to store instructions; and
a processor configured to execute the instructions stored in the memory and thereby cause the event prediction system to:
receive time series data of the electrical circuit;
detect an electrical signature in the time series data indicating an upcoming electrical arc in the electrical circuit by performing the following steps:
constructing a Hankel matrix using the time series data;
performing a singular value decomposition on the Hankel matrix to obtain at least one singular vector,
performing delay coordinate embedding on the at least one singular vector to generate at least one reconstructed singular vector, wherein the at least one reconstructed singular vector comprises a plurality of eigen time delay coordinates,
calculating a threshold coefficient ‘r’ from the at least one reconstructed singular vector, wherein the threshold coefficient ‘r’ indicates an optimal location in the at least one reconstructed singular vector representing a change in state of the electrical circuit,
identifying a first set of eigen time delay coordinates among the plurality of eigen time delay coordinates in the at least one reconstructed singular vector based on the threshold coefficient ‘r’, wherein r th eigen time delay coordinates constitute the first set of eigen time delay coordinates, and
computing a rate of change in magnitude of the first set of eigen time delay coordinates to detect the electrical signature,
predict the upcoming electrical arc in the electrical circuit based on the electrical signature; and
generate a control signal to operate an actuator based on the prediction for quenching the electrical arc.
10. The prediction system of claim 9 , wherein the electrical signature is detected when the rate of change in the magnitude of the first set of coefficients deviates from a reference value.
11. The prediction system of claim 10 , wherein the reference value is determined based, at least in part, on a rate of change in magnitude computed at one or more preceding timesteps.
12. The prediction system of claim 11 , wherein eigen time delay coordinates preceding the r th eigen time delay coordinates constitute a second set of eigen time delay coordinates.
13. The prediction system of claim 12 , wherein the prediction system is further configured to:
perform hard thresholding on the at least one reconstructed singular vector based on an optimum singular value hard threshold coefficient; and
determine the first set of eigen time delay coordinates and the second set of time delay coordinates from the at least one reconstructed singular vector.
14. The prediction system of claim 13 , wherein the second set of eigen time delay coordinates in the at least one reconstructed singular vector is advancing in time based on corresponding first set of coefficients.
15. The prediction system of claim 14 , wherein the second set of eigen time delay coordinates represent a linear response of the electrical protection device and the first set of eigen time delay coordinates represent the electrical signature.
16. The prediction system of claim 9 , wherein the time series data comprises at least one of: current values, voltage values, power values and energy values in the electrical circuit.
17. A non-transitory computer-readable medium storing instructions for predicting electrical arcs in an electrical protection device connected in an electrical circuit, the instructions when executed by a processor cause a prediction system to perform a method comprising:
receiving time series data of the electrical circuit;
detecting an electrical signature in the time series data indicating an upcoming electrical arc in the electrical circuit by performing the following steps:
constructing a Hankel matrix using the time series data;
performing a singular value decomposition on the Hankel matrix to obtain at least one singular vector,
performing delay coordinate embedding on the at least one singular vector to generate at least one reconstructed singular vector, wherein the at least one reconstructed singular vector comprises a plurality of eigen time delay coordinates,
calculating a threshold coefficient ‘r’ from the at least one reconstructed singular vector, wherein the threshold coefficient ‘r’ indicates an optimal location in the at least one reconstructed singular vector representing a change in state of the electrical circuit,
identifying a first set of eigen time delay coordinates among the plurality of eigen time delay coordinates in the at least one reconstructed singular vector based on the threshold coefficient ‘r’, wherein r th eigen time delay coordinates constitute the first set of eigen time delay coordinates, and
computing a rate of change in magnitude of the first set of eigen time delay coordinates to detect the electrical signature,
predicting the upcoming electrical arc in the electrical circuit based on the electrical signature; and
generating, by the processor, a control signal to operate an actuator of the electrical protection device based on the prediction for quenching the electrical arc.