[Paper Review] Evaluating Feasibility within Power Flow

Marko Jereminov, David M. Bromberg+3 more|arXiv (Cornell University)|Sep 5, 2018

Power System Optimization and Stability30 references4 citations

TL;DR

This paper proposes a circuit-theoretic method using adjoint networks to detect and quantify infeasibility in power flow studies, particularly beyond the nose curve. By modeling infeasibility as current sources injected into each bus and analyzing their response in the adjoint network, the method identifies locations of real and reactive power deficiency and computes optimally minimized corrective currents to restore feasibility.

ABSTRACT

Recent development of techniques that improve the convergence properties of power flow simulation have been demonstrated to facilitate scaling to large system sizes (80k+ buses). However, the problem remains to reliably identify cases that are infeasible, system configurations that have no solution. In this paper, we use the circuit theoretic approach based on adjoint networks to evaluate the feasibility of a power flow test case and further locate and quantify the source of infeasibility in the cases operating beyond the tip of the nose curve. By creating infeasibility current source models that are added to each node of the system model and further coupling each source to its corresponding node of the adjoint network, any locations of insufficient real or reactive power are captured by a non-zero response of the adjoint network. Furthermore, it is shown that the proposed joint simulation of power flow and its adjoint network models provide the optimally minimized currents that can be later utilized to inform corrective actions to restore the feasibility of power flow problems.

Motivation & Objective

• To address the challenge of reliably detecting infeasible power flow cases in large-scale systems.
• To identify the specific buses and types of power deficiency (real or reactive) causing infeasibility.
• To quantify the minimal corrective currents needed to restore feasibility in infeasible power flow cases.
• To provide actionable insights for system operators by localizing the root causes of infeasibility.

Proposed method

• Formulate an adjoint network model dual to the original power system network.
• Introduce infeasibility current sources at each bus, representing real and reactive power deficits.
• Couple each current source to its corresponding node in the adjoint network to capture system-wide responses.
• Use the adjoint network's voltage responses to detect and localize sources of infeasibility.
• Compute the optimally minimized corrective currents via joint simulation of power flow and adjoint network.
• Utilize the resulting current magnitudes and locations to guide corrective actions.

Experimental results

Research questions

• RQ1 Where in the system are real power deficiencies most critical for causing infeasibility?
• RQ2 Where in the system are reactive power deficiencies most critical for causing infeasibility?
• RQ3 Can the proposed method quantify the minimal corrective current needed to restore feasibility?
• RQ4 How accurately can the adjoint network localize the source of infeasibility in systems operating beyond the nose curve?

Key findings

• The method successfully identifies buses with insufficient real and reactive power support through non-zero adjoint network responses.
• The joint simulation of power flow and adjoint network enables precise localization of infeasibility sources.
• The computed corrective currents are optimally minimized, reducing the required corrective effort.
• The approach provides actionable, location-specific insights for system operators to restore feasibility.