Distributed Transient Safety Verification via Robust Control Invariant Sets: A Microgrid Application

Abstract

Modern safety-critical energy infrastructures are increasingly operated in a hierarchical and modular control framework which allows for limited data exchange between the modules. In this context, it is important for each module to synthesize and communicate constraints on the values of exchanged information in order to assure system-wide safety. To ensure transient safety in inverter-based microgrids, we develop a set invariance-based distributed safety verification algorithm for each inverter module. Applying Nagumo's invariance condition, we construct a robust polynomial optimization problem to jointly search for safety-admissible set of control set-points and design parameters, under allowable disturbances from neighbors. We use sum-of-squares (SOS) programming to solve the verification problem and we perform numerical simulations using grid-forming inverters to illustrate the algorithm.

Safe and Stable Secondary Voltage Control of Microgrids Based on Explicit Neural Networks

“…where xaug (0) is an initial value, and φ denotes the solution of the closed-loop system (7) with secondary controller ũaug . When steady-state condition (9) holds, the safety constraint (10) and SSR (11) of the augmented system (7) are equivalent to (3) and ( 4) of the original system (1), respectively.…”

“…Therefore, state observers are needed to estimate the states by using input and output data only. For linear system (7), the separation property holds, so that the state observer and controller can be designed separately. Assume that the system is detectable, i.e., unobservable modes are stable, then it is simple to design a classical linear state observer to obtain the estimated states x, which is used in the following state feedback controller design.…”

“…The equilibrium xaug, * of system (7) with controller ũaug = U( xaug ) satisfies xaug, * = Ax aug * + BU(x aug, * ). To ensure that xaug, * = 0, the controller should satisfy U(0) = 0, which translates to a nonconvex constraint on (w i , b i ).…”

“…According to the time scales, stability and safety can be classified into steady-state and transient-state [7]. Transient stability problem has been widely investigated in MG control, which ensures that the trajectories of MG states (e.g., voltage, current, frequency, etc.)…”

“…Thus, in MPC-based secondary control, the order of the MG dynamic model is usually highly reduced, leading to the loss of faster dynamics and corresponding stability and safety guarantees. Moreover, nonlinearities of MG and information disparity due to communication overheads are also challenging to overcome in such a method [7]. Another method that can guarantee transient stability and safety in power systems is the control Lyapunov function (CLF) and control barrier function (CBF) based method.…”