A Data-Driven Sensor Placement Approach for Detecting Voltage Violations in Distribution Systems

TL;DR

This paper presents a novel bilevel optimization approach using conservative linear approximations to optimally place sensors in distribution systems for detecting voltage violations caused by DER fluctuations, improving detection accuracy and computational efficiency.

Contribution

It introduces a new linear approximation-based bilevel optimization framework for sensor placement that guarantees detection of voltage violations while reducing false alarms and computational complexity.

Findings

Effective detection of voltage violations in test cases.

Reduced number of sensors needed compared to baseline methods.

Enhanced computational tractability through reformulations.

Abstract

Stochastic fluctuations in power injections from distributed energy resources (DERs) combined with load variability can cause constraint violations (e.g., exceeded voltage limits) in electric distribution systems. To monitor grid operations, sensors are placed to measure important quantities such as the voltage magnitudes. In this paper, we consider a sensor placement problem which seeks to identify locations for installing sensors that can capture all possible violations of voltage magnitude limits. We formulate a bilevel optimization problem that minimizes the number of sensors and avoids false sensor alarms in the upper level while ensuring detection of any voltage violations in the lower level. This problem is challenging due to the nonlinearity of the power flow equations and the presence of binary variables. Accordingly, we employ recently developed conservative linear approximations of the power flow equations that overestimate or underestimate the voltage magnitudes. By replacing the nonlinear power flow equations with conservative linear approximations, we can ensure that the resulting sensor locations and thresholds are sufficient to identify any constraint violations. Additionally, we apply various problem reformulations to significantly improve computational tractability while simultaneously ensuring an appropriate placement of sensors. Lastly, we improve the quality of the results via an approximate gradient descent method that adjusts the sensor thresholds. We demonstrate the effectiveness of our proposed method for several test cases, including a system with multiple switching configurations.