# Data-driven p-norms for estimating transmission loss coefficients in power systems

## TL;DR

This paper presents a new data-driven method to estimate transmission loss coefficients in power systems, improving accuracy and reliability using convex optimization.

## Contribution

A novel convex methodology using p-norms and semi-definite programming for estimating B-coefficients in power systems.

## Key findings

- The proposed model achieves average estimation errors between −6% and 5% across various test systems.
- The method is robust and effective under diverse operating conditions with random variations in power injections and demand.
- Numerical evaluations on IEEE bus systems confirm the reliability of the approach.

## Abstract

This research introduces a novel convex methodology for estimating transmission loss coefficients (B-coefficients) in power systems using a data-driven approach based on power system measurements. To enhance estimation accuracy and practical relevance, the model is evaluated across a wide spectrum of operating conditions, incorporating random variations in active power injections and demand profiles modeled via uniform and Gaussian distributions. A semi-definite programming (SDP) model leveraging p-norm formulations is proposed to derive the B-coefficients efficiently. Numerical evaluations on IEEE 14-, 39-, 57-, and 118-bus test feeders demonstrate the effectiveness and robustness of the approach, yielding average estimation errors between −6% and 5% across diverse scenarios. These results confirm the reliability of the proposed methodology, contributing to improved accuracy in transmission loss modeling and supporting more efficient power system operations.