# Statistical Modeling of Networked Solar Resources for Assessing and Mitigating Risk of Interdependent Inverter Tripping Events in Distribution Grids

## TL;DR

This paper introduces a probabilistic modeling approach using Chebyshev's inequality to assess and mitigate the risk of interdependent inverter tripping events in distribution grids with high PV penetration, addressing real-time observability limitations.

## Contribution

It develops a scalable probabilistic model based on PV/load statistics for predicting inverter tripping risks and integrates it into an optimization framework for mitigation strategies.

## Key findings

- Model accurately estimates tripping probabilities using only statistical data.
- The approach is scalable and suitable for systems with limited real-time observability.
- Numerical experiments validate the effectiveness of the proposed method.

## Abstract

It is speculated that higher penetration of inverter-based distributed photo-voltaic (PV) power generators can increase the risk of tripping events due to voltage fluctuations. To quantify this risk utilities need to solve the interactive equations of tripping events for networked PVs in real-time. However, these equations are non-differentiable, nonlinear, and exponentially complex, and thus, cannot be used as a tractable basis for solar curtailment prediction and mitigation. Furthermore, load/PV power values might not be available in real-time due to limited grid observability, which further complicates tripping event prediction. To address these challenges, we have employed Chebyshev's inequality to obtain an alternative probabilistic model for quantifying the risk of tripping for networked PVs. The proposed model enables operators to estimate the probability of interdependent inverter tripping events using only PV/load statistics and in a scalable manner. Furthermore, by integrating this probabilistic model into an optimization framework, countermeasures are designed to mitigate massive interdependent tripping events. Since the proposed model is parameterized using only the statistical characteristics of nodal active/reactive powers, it is especially beneficial in practical systems, which have limited real-time observability. Numerical experiments have been performed employing real data and feeder models to verify the performance of the proposed technique.