A Necessary Condition for Power Flow Insolvability in Power Distribution Systems with Distributed Generators

TL;DR

This paper introduces a necessary condition for power flow insolvability in distribution systems with distributed generators, linking Jacobian singularity to voltage instability and providing an efficient, operation-dependent index for real-time stability monitoring.

Contribution

It presents a novel necessary condition for power flow insolvability that accounts for DG operation modes and offers a less conservative, real-time applicable index for voltage stability assessment.

Findings

The proposed condition accurately predicts voltage instability points.

The index effectively indicates the distance to the solvability boundary.

Validation shows the method's efficiency and accuracy across different DG levels.

Abstract

This paper proposes a necessary condition for power flow insolvability in power distribution systems with distributed generators (DGs). We show that the proposed necessary condition indicates the impending singularity of the Jacobian matrix and the onset of voltage instability. We consider different operation modes of DG inverters, e.g., constant-power and constant-current operations, in the proposed method. A new index based on the presented necessary condition is developed to indicate the distance between the current operating point and the power flow solvability boundary. Compared to existing methods, the operating condition-dependent critical loading factor provided by the proposed condition is less conservative and is closer to the actual power flow solution space boundary. The proposed method only requires the present snapshots of voltage phasors to monitor the power flow insolvability and voltage stability. Hence, it is computationally efficient and suitable to be applied to a power distribution system with volatile DG outputs. The accuracy of the proposed necessary condition and the index is validated by simulations on a distribution test system with different DG penetration levels.