Coordinated Control of Wind Turbine Generator and Energy Storage System for Frequency Regulation under Temporal Logic Specifications

Abstract

In this paper, we present a controller synthesis approach for wind turbine generators (WTG) and energy storage systems with metric temporal logic (MTL) specifications, with provable probabilistic guarantees in the stochastic environment of wind power generation. The MTL specifications are requirements for the grid frequency deviations, WTG rotor speed variations and the power flow constraints at different lines. We present the stochastic control bisimulation function, which bounds the divergence of the trajectories of a switched stochastic control system and the switched nominal control system in a probabilistic fashion. We first design a feedforward controller by solving an optimization problem for the nominal trajectory of the deterministic control system with robustness against initial state variations and stochastic uncertainties. Then we generate a feedback control law from the data of the simulated trajectories. We implement our control method on both a four-bus system and a nine-bus system, and test the effectiveness of the method with a generation loss disturbance. We also test the advantage of the feedback controller over the feedforward controller when unexpected disturbance occurs.Keywords-Controller synthesis, differential-algebraic equations, temporal logic, energy storage systems * 1 ∧ [2,Tend]p * 2 ∧ [2,Tend]p * 1 3 , p * 1 3 =(−0.25 + 0.0258e −0.01t ≤ P 28 ≤ 0.25 − 0.0258e −0.01t ).

Control strategies for COVID-19 epidemic with vaccination, shield immunity and quarantine: A metric temporal logic approach

“…The first category of approaches abstract the system as a transition system and transform the control syntheses problem into a series of constrained reachability problems [32][33][34]. The second category of approaches mainly focus on linear dynamical systems and they convert the control synthesis problem into a mixed-integer linear programming (MILP) problem [35][36][37][38][39][40] which can be solved efficiently by MILP solvers. The third category of approaches substitute the temporal logic constraint into the objective function of the optimization problem and apply a functional gradient descent algorithm on the resulting unconstrained problem [10,[41][42][43].…”

Robust Pandemic Control Synthesis with Formal Specifications: A Case Study on COVID-19 Pandemic

“…However, how to utilize such models in the optimal pandemic control synthesis is still an open problem. Formal control synthesis with temporal logic specifications: The control synthesis approaches with temporal logic specifications mainly convert the control synthesis problem into a mixed-integer linear programming (MILP) problem [26], [27], [28], [29], [30], [31] which can be solved efficiently by MILP solvers. Another set of approaches substitute the temporal logic constraint into the objective function of the optimization problem and apply a functional gradient descent algorithm on the resulting unconstrained problem [32], [33], [3], [34].…”

Controller Synthesis for Multi-Agent Systems With Intermittent Communication. A Metric Temporal Logic Approach

“…If there are such followers, we update the state estimates of those followers with their true state values (Line 7). Then we modify the MTL formula as in (25) and the updated m i (Line 8). The MILP is solved for time with the updated state values and the modified MTL formula [φ] 0 (Line 9).…”