EPIC 2019: Real-time Fault Localization in Power Grid

Real-time Fault Localization in Power Grid Through Submodular Deep Neural Networks Learning and Chance-constrained Optimization Masoud Barati Electrical and Computer Engineering Department University of Pittsburgh

What is the fault?

Fault Localizations in Power Grids

Fault Localizations in Power Grids

MXL4 Precision Locator - C. Scope Cable Location

RIDGID 56613 A-Frame Underground Cable Fault Locator and Receiver

Fault Localizations in Power Grids • Motivation: • Minimize the restoration time by fixing the faulty element(s).

• Traditional methods, test equipment.

• Limited number of measurement sensors in power grids, power distribution system!

• Bad location of sensors*, less observability and blind spot(s) *Sensor

= PMU, (CT + VT)

Fault Localizations in Power Grids • Traditional Methods: Traveling waves with testers & maintenance crews

Sensors

Faulted Feeder Model

Faulted Feeder Model

Network Changes for Faulted Feeder

Network Changes for Faulted Feeder

Feature Vector

Network Changes for Faulted Feeder

Feature Vector Off-Line Calculation: Step 01) Place different types of the fault (TP, LG, LLG, LL) in all nodes Step 02) Create feature vector

Classification • CNN classifier CNN classifier

Architecture Design Training Process

Classification: Architecture Design • AlexNet model • • • •

Convolutional Rectified Linear Unit (ReLU) Pooling, and fully connected operators; kernel matrices The size of the kernel matrices in these operators and the number of layers are hyper-parameters that are designed to fit the input.

Input

Output

Feature Vector

Labels

Classification: Architecture Design

Classification: Architecture Design Layer 1 Layer 2 Layer 3

Layer n

Last layer Last layer

Classification: Architecture Design

softmax

Cross Entropy Loss Function: Solution Methods _

^

Placement: Greedy Algorithm

Training + Placement: MIP

Sensor Placement Partial Observability: Greedy Algorithm _

Submodular set function

Solution Method: stochastic gradient descent (SGD)

Sensor Placement Partial Observability: 0-1 MIP

+

+

Sensor Placement Partial Observability: 0-1 MIP Bilinear term

+

Sensor Placement Partial Observability: 0-1 MIP, Chance Constraint Bilinear term

Uncertainty on the total number of sensors

Numerical Results • Four types of line faults, including three-phase short circuit (TP), line to ground(LG), double line to ground (DLG) and line to line (LL) faults are simulated through PST. • The fault impedance changes in the range of 0.0001 to 0.1 per unit (p.u.), and the fault is cleared after 0.2 seconds. The fault location performance is evaluated by the location accuracy rate (LAR):

Numerical Results • The structural parameters of the CNN for the 68-bus power system

Numerical Results

Most faults has located with more than 90% accuracy.

The maximal variation of the LARs, due to different ratios of measured buses, is less than 10%.

• The location accuracy rate (LAR) (%) of CNN in the 68-bus power system on the four types of faults under partial measurements:

• The location accuracy rate LAR (%) of CNN on the four types of faults with different fault impedance under different partial measurements

Numerical Results • The LARs of CNN (Greedy) classifier with different layer depths in terms of different percentage of measured buses The two-layer NN has better performance than other schemes.

Numerical Results • The LARs of the CNN-G (Greedy), CNN-MIP (0-1 MIP), CNN-MIPCC (0-1 MIP, Chance Constraint) on the four types of faults in terms of different percentage of measured buses

Takeaways • 1) a high location accuracy rate is reached even when the system has low observability; • 2) the true faulted line, even if not the highest, has a high output probability.

• 3) the location performance is further increased by using the design of the CNN classifier into a joint sensor placement algorithm, that is demonstrably superior to other random and topologybased methods.

• 4) testing the methodology on real-data (as opposed to synthetically generated data) is another direction for our future work.

Thank you!