Systems and methods for determining arc events using wavelet decomposition and support vector machines

1. A system for detecting arc events, the system comprising:

an arc fault detector configured to receive signals from a photovoltaic (PV) module via one or more wires; and

wherein the arc fault detector comprises a controller coupled to the one or more wires and trained with a classification model to distinguish between signals indicating arc events from the PV module and signals not indicating arc events from the PV module, the controller further configured to:

receive the signals;

extract a plurality of features from the received signals, wherein the plurality of extracted features include a current and a voltage;

classify the extracted features using the classification model;

determine an occurrence of the arc event based on the classification; and

provide an output signal indicating an arc event;

wherein the classification system is based on a separating hyperplane is according to the following equation:

ω T x+b =0,

wherein ω is an n-dimensional vector and b is the intercept term, and wherein ω and b determine the position of the separating hyperplane, and wherein a functional margin of the hyperplane is according to the following equation;

y i (ω T x i +b )≥1,

wherein y i are labels for the classification system, and wherein x i are n-dimensional inputs, wherein an optimum hyperplane can be found according to the following equation;

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wherein C is an error penalty, and wherein ξ i is a slack variable, and wherein a Lagrangian is according to the following equation;

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wherein α i and r i are Lagrange multipliers, and wherein a final weight equation to solve for the separating hyperplane is according to the following equation;

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2. The system of claim 1 , wherein the output signal is configured to shut-off the system based on the determination of the occurrence of the arc event.

3. The system of claim 1 , wherein the arc event includes an arc fault.

4. The system of claim 1 , wherein the arc event includes arc flash.

5. The system of claim 1 , wherein the controller is configured to extract the features at least in part by wavelet decomposition.

6. The system of claim 1 , wherein the classification model is a support vector machine (SVM) classification model.

7. The system of claim 1 , wherein the controller is further configured to rescale the received signals at least once before classifying the extracted features using the classification model.

8. The system of claim 1 , wherein the controller is configured to provide a time-stamp on the detected arc event.

9. A method for detecting arc events, the method comprising:

receiving signals from a photovoltaic (PV) module with an arc fault detector via one or more wires, wherein the one or more wires couple the PV module to a controller of the arc fault detector, wherein the controller is trained with a classification model to distinguish between signals indicating arc events from the PV module and signals not indicating arc events from the PV module;

acquiring, by the controller, data relating to the received signals;

extracting, by the controller, a plurality of features from the received signals, wherein the plurality of extracted features include a current and a voltage;

classifying, by the controller, the plurality of features using the classification model; and

determining, by the controller, an occurrence of an arc event based on the classification;

wherein the classification system is based on a separating hyperplane is according to the following equation:

ω T x+b= 0 ,

wherein ω is an n-dimensional vector and b is the intercept term, and wherein ω and b determine the position of the separating hyperplane, and wherein a functional margin of the hyperplane is according to the following equation;

y i (ω T x i +b )≥1,

wherein y i are labels for the classification system, and wherein x i are n-dimensional inputs, wherein an optimum hyperplane can be found according to the following equation;

min

ω

,

b

⁢

1

2

⁢



ω



2

+

C

⁢

∑

i

=

1

m

⁢

⁢

ξ

i

,

wherein C is an error penalty, and wherein ξ i is a slack variable, and wherein a Lagrangian is according to the following equation;

1

2

⁢

ω

T

⁢

ω

+

C

⁢

∑

i

=

1

m

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ξ

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=

1

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α

i

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i

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+

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-

1

+

ξ

i

]

-

∑

i

=

1

m

⁢

⁢

r

i

⁢

ξ

i

,

wherein α i and r i are Lagrange multipliers, and wherein a final weight equation to solve for the separating hyperplane is according to the following equation;

∑

i

=

1

m

⁢

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α

i

-

1

2

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y

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y

j

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α

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α

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x

i

,

x

j

〉

.

10. The method of claim 9 , wherein the extracting the plurality of features includes transforming the received signals.

11. The method of claim 10 , further comprising rescaling, by the controller, the received signals at least once to extract the plurality of features.

12. The method of claim 9 , wherein the classification model is a support vector machine (SVM) model.

13. The method of claim 9 , further comprising shutting off, by the controller, an electrical system based on the determination of the occurrence of the arc event.

14. A photovoltaic system, comprising:

an arc fault detector configured to receive signals from a photovoltaic (PV) module via one or more wires, wherein the arc fault detector comprises a controller coupled to one or more wires, wherein the controller is trained with a classification model to distinguish between signals indicating arc events from the PV module and signals not indicating arc events in the PV module, the controller further configured to:

receive the signals;

extract a plurality of features from the received signals, wherein the plurality of extracted signals include a current and a voltage;

classify the extracted features using the classification model;

determine an occurrence of the arc event based on the classification; and

provide an output signal indicating an arc event;

wherein the classification system is based on a separating hyperplane is according to the following equation:

ω T x+b =0,

wherein ω is an n-dimensional vector and b is the intercept term, and wherein ω and b determine the position of the separating hyperplane, and wherein a functional margin of the hyperplane is according to the following equation;

y i (ω T x i +b )≥1,

wherein y i are labels for the classification system, and wherein x i are n-dimensional inputs, wherein an optimum hyperplane can be found according to the following equation;

min

ω

,

b

⁢

1

2

⁢



ω



2

+

C

⁢

∑

i

=

1

m

⁢

⁢

ξ

i

,

wherein C is an error penalty, and wherein ξ i is a slack variable, and wherein a Lagrangian is according to the following equation;

1

2

⁢

ω

T

⁢

ω

+

C

⁢

∑

i

=

1

m

⁢

⁢

ξ

i

-

∑

i

=

1

m

⁢

⁢

α

i

⁡

[

y

i

⁡

(

x

T

⁢

ω

+

b

)

-

1

+

ξ

i

]

-

∑

i

=

1

m

⁢

⁢

r

i

⁢

ξ

i

,

wherein α i and r i are Lagrange multipliers, and wherein a final weight equation to solve for the separating hyperplane is according to the following equation;

∑

i

=

1

m

⁢

⁢

α

i

-

1

2

⁢

∑

⁢

y

i

⁢

y

j

⁢

α

i

⁢

α

j

⁢

〈

x

i

,

x

j

〉

.

15. The photovoltaic system of claim 14 , wherein the extracting the plurality of features includes transforming the received signals using wavelet decomposition.

16. The photovoltaic system of claim 14 , further comprises the controller rescaling the received signals at least once before classifying the plurality of features.

17. The photovoltaic system of claim 14 , wherein the classification model is a support vector machine (SVM) model.

18. The photovoltaic system of claim 14 , wherein the output signal is configured to shut-off the photovoltaic system based on the determination of the occurrence of the arc event.

19. The system of claim 14 , wherein the arc event includes an arc fault.

20. The system of claim 14 , wherein the arc event includes arc flash.