Sparse Control Synthesis for Uncertain Responsive Loads with Stochastic Stability Guarantees

TL;DR

This paper develops a stochastic control framework for uncertain responsive loads to ensure frequency stability, promoting sparsity and robustness in power system control under load variability.

Contribution

It introduces a novel LMI-based sparse control synthesis method that guarantees stochastic stability and handles load uncertainties with partial measurements.

Findings

Demonstrates effective frequency response under load uncertainties on IEEE 39-bus system.

Establishes a trade-off between allowable uncertainties and control effort.

Extends stability results to partial-state measurement scenarios.

Abstract

Recent studies have demonstrated the potential of flexible loads in providing frequency response services. However, uncertainty and variability in various weather-related and end-use behavioral factors often affect the demand-side control performance. This work addresses this problem with the design of a demand-side control to achieve frequency response under load uncertainties. Our approach involves modeling the load uncertainties via stochastic processes that appear as both multiplicative and additive to the system states in closed-loop power system dynamics. Extending the recently developed mean square exponential stability (MSES) results for stochastic systems, we formulate multi-objective linear matrix inequality (LMI)-based optimal control synthesis problems to not only guarantee stochastic stability, but also promote sparsity, enhance closed-loop transient performance, and maximize allowable uncertainties. The fundamental trade-off between the maximum allowable (\textit{critical}) uncertainty levels and the optimal stochastic stabilizing control efforts is established. Moreover, the sparse control synthesis problem is generalized to the realistic power systems scenario in which only partial-state measurements are available. Detailed numerical studies are carried out on IEEE 39-bus system to demonstrate the closed-loop stochastic stabilizing performance of the sparse controllers in enhancing frequency response under load uncertainties; as well as illustrate the fundamental trade-off between the allowable uncertainties and optimal control efforts.