Optimal L-Infinity Frequency Control in Microgrids Considering Actuator Saturation

Abstract

Inverter-connected resources can improve transient stability in low-inertia grids by injecting active power to minimize system frequency deviations following disturbances. In practice, most generation and load disturbances are step changes and the engineering figure-of-merit is often the peak overshoot in frequency resulting from these step disturbances. In addition, the inverter-connected resources tend to saturate much more easily than conventional synchronous machines. However, despite these challenges, standard controller designs must deal with averaged quantities through H2 or H∞ norms and must account for saturation in ad hoc manners. In this paper, we address these challenges by explicitly considering L∞ control with saturation using a linear matrix inequality-based approach. We show that this approach leads to significant improvements in stability performance.

Reinforcement Learning for Optimal Primary Frequency Control: A Lyapunov Approach

“…We consider two costs in the objective function of optimal frequency control problem: the cost on frequency deviations and the cost of controllers. Firstly, considering that the power system operators restrict the maximum frequency deviation, the cost on frequency deviation is represented by the infinity norm of ω i (t) over the time horizon from 0 to the total time length T defined by ||ω i || ∞ = sup 0≤t≤T |ω i (t)| [15]. Secondly, the cost on controller is the quadratic function of action defined by its two-norm [12]- [14].…”

Lyapunov-Regularized Reinforcement Learning for Power System Transient Stability

“…The objective is to minimize the cost on frequency deviations and the control effort. In this paper, we use frequency nadir, which is the infinite norm of ω i (t) over the time horizon from 0 to the time T defined as [19]. We use a quadratic cost for the control actions defined by…”