Machine Learning-Based Power Flow Solver

1. Machine Learning-Based Power Flow Solver GridLAB-D TAC Meeting September 6, 2019

2. The Power Flow Problem

3. Standard Approach: Newton Raphson Iteration Newton Raphson method: Iterative root finding method Seed initial guess with last solver solution New approach: replace Newton-Raphson solver with data-driven approximation: Initial guess Evaluate function Update guess Linearize model

4. Literature on Data-Driven Power Flow Approximation Yu, Jiafan, Yang Weng, and Ram Rajagopal. "Robust mapping rule estimation for power flow analysis in distribution grids." 2017 North American Power Symposium (NAPS). IEEE, 2017. Development of SVM-based power flow approximation Forward and backward power flow mappings Comparison with regression-based methods

5. Challenges for Implementation in GridLAB-D Model formulation • 3-phase unbalanced power flow • Current injection method • ZIP load representation Scalability • Which modeling methods work well in high dimension? • How much training data is needed? Accuracy • How often should the model be re-trained? • Can model accuracy be predicted? Computation speed • Can the number of Newton Raphson iterations be predicted? • How does an ML-approach compare to existing methods for speeding up power flow simulations? ZIP load model

6. Cluster-based Linear Regression Model Linear regression model: Learn separate model for each bus Regularized least squares regression: • Cluster training data into different operating modes and train a different model for each • Clustering methods: • Gaussian mixture model • K-means clustering K-means clustering of residential load profiles

7. Error Checking and Solver Integration Voltage vector: Error metric: normalized vector error: Interaction with NR solver: • Error check • Distance check • Step change check

8. Test Case: IEEE 123 Bus Network IEEE 123 bus network IEEE 123 bus model • Replace spot loads with time-varying real and reactive power profiles for 344 residential homes • 4.2 kV nominal voltage • 4 voltage regulators GridLAB-D simulation • 7 day training • 21 day testing • 1-minute simulation timestep Training and testing data breakdown

9. Results: Cluster-Based Modeling Training error Testing error Base Case: no clustering Mean prediction error: 0.2% GMM test error K-Means test error Cluster-based models (k=7):

10. Results: Error checking Final model performance: • Parameters of error checks were tuned using sensitivity analysis • Best performance results from a combination of error checks • Significant reduction in number of Newton Raphson solves Final error distribution using error checks:

11. Results: Load Composition and Loading Level ZIP load model

12. Example: Voltage magnitude prediction Low loading level High loading level

13. Results: Effects of Training Set Size

14. Next steps: Comparison of SVM and other ML-based methods with linear regression Scalability – test accuracy on larger networks (IEEE 8500 node network) Optimal training set design Algorithm implementation with online interaction with GridLAB-D Newton Raphson solver

15. Questions?

16. Extra Slides