Robustness Against Disturbances in Power Systems Under Frequency Constraints

Abstract

The wide deployment of renewable generation and the gradual decrease in the overall system inertia make modern power grids more vulnerable to transient instabilities and unacceptable frequency fluctuations. Time-domain simulationbased assessment of the system robustness against uncertain and stochastic disturbances is extremely time-consuming. In this paper, we develop an alternative approach, which has its roots in the input-output stability analysis for Lur'e systems. Our approach consists of a mathematically rigorous characterization of the external disturbances that the power system is transiently stable and the frequency constraints are not violated. The derived certificate is efficiently constructed via convex optimization and is shown to be non-conservative for different IEEE test cases.Index Terms-Input-output stability, small-gain analysis, constrained input constrained output stability, sector-bound nonlinearity, transient stability, frequency constraints.

A Robustness Measure of Transient Stability Under Operational Constraints in Power Systems

“…From a practical perspective, large angle differences are strongly undesired, and it is common practice to consider angle differences which do not greatly exceed π/2. In the following lemma, we show how the nonlinearity can be bounded as in (5) in two sets of practical interest.…”

“…This allows the direct extension of our methodology and results to more general power system models, which can be written in a Lur'e form with the nonlinearity composed by the same elements. For example, in [5] we consider a structure-preserving model with first order turbine governor dynamics.…”

“…Indeed, the high penetration of renewable generation can significantly unbalance the power supply and demand, leading to large frequency deviation, e.g., more than 0. 5 frequency deviation in turn will activate frequency protective relays on the power system network to shed loads/generators or trip interconnection lines [4]. Since the widespread protective relays are still poorly coordinated due to the large scale of the grid, load/generator shedding and line tripping, in the worst case, may result in further cascading failures and even power blackout.…”

“…A similar problem was considered in [5], where the same authors proposed an input-output stability framework to quantify the robustness against disturbances of the system operating at an equilibrium point. Differently, in this paper, the robustness against disturbances of the post-fault trajectory is considered, where the fault-dependent scenario is included in the assessment.…”

Double-layered distributed transient frequency control with regional coordination

“…Literature review: Literature [3], [4] proposes several sufficient conditions on power network synchronization; however, as they do not consider bus transient frequency limit as a constraint, the ideal synchronization condition may not hold due to possible violation in frequency transients. Work [5] studies the relation between power injection disturbance and frequency overshoot of individual bus without active control to regulate frequency transients. On the other hand, to actively control power network transients, several strategies have been investigated, including inertial placement [6], power system stabilizer [7], and power supply re-allocation [8].…”