# Reduced and Aggregated Distribution Grid Representations Approximated by Polyhedral Sets

## TL;DR

This paper introduces a new method to create simplified, polyhedral representations of distribution grid capabilities, enhancing TSO-DSO interactions with reduced computational effort and acceptable accuracy.

## Contribution

The paper presents a novel, tractable approach to approximate distribution grid capabilities using polyhedral sets based on a linear power flow model, improving computational efficiency.

## Key findings

- Polyhedral sets effectively approximate grid capabilities.
- Method reduces computational complexity compared to full OPF solutions.
- Approximation errors are acceptable, especially for low voltage grids.

## Abstract

In this paper we present a novel tractable method to compute reduced and aggregated distribution grid representations that provide an interface in the form of active and reactive power (PQ) capability areas for improving transmission service operator - distribution service operator (TSO-DSO) interactions. Based on a lossless linear power flow approximation we derive polyhedral sets to determine a reduced PQ operating region capturing all voltage magnitude and branch power flow constraints of the entire distribution grid. To demonstrate the usefulness of our method, we compare the capability area obtained from the polyhedral approximation with an area generated by multiple optimal power flow (OPF) solutions for different distribution grids. While the approximation errors are reasonable, especially for low voltage (LV) grids, the computational complexity to compute the PQ capability area can be significantly reduced with our proposed method.