Fast Frequency Control Scheme through Adaptive Virtual Inertia Emulation

LQR-Based Adaptive Virtual Synchronous Machine for Power Systems With High Inverter Penetration

“…However, it was implemented on a simplified, single-inverter test case, and the adaptive damping was not taken into account. This paper extends the work in [13] in several directions by (i) deriving a uniform multimachine frequency model; (ii) including adaptive damping and proposing two novel control methods; (iii) providing a formulation for a decentralized multi-inverter control scheme; and (iv) incorporating the controllers into a detailed VSC model and verifying it through EMT simulations. To the best knowledge of the authors, such uniform approach has not been proposed in the literature thus far.…”

“…x T Qx + u T Ru dt (15) while simultaneously subjected to the system model constraints in (12) and the control input in (13). This problem formulation resembles the one of a Linear-Quadratic Regulator (LQR), which requires a linear system model and a state feedback control in order to compute the optimal control gains.…”

“…where V (ω,ω) represents the transient energy of the system in (ω,ω) coordinates after a step disturbance ∆P . Let us now consider the adaptive approach with M (ω,ω) and D(ω,ω) being functions of state variables through VSM feedback control described in (13). By analyzing the gradient ∇V of the proposed Lyapunov function we can determine its stationary points:…”

“…We have previously addressed this problem in [13], with an LQR-based adaptive virtual inertia controller that optimally adjusts the respective inertia gain to achieve a trade-off between the two objectives. However, it was implemented on a simplified, single-inverter test case, and the adaptive damping was not taken into account.…”

Interval-Based Adaptive Inertia and Damping Control of a Virtual Synchronous Machine

“…which is conservatively subsumed in ν M (t)+ν D (t) ≤ 0, ∀t ∈ [0, ∞). The non-smooth characteristic of ν M (t) and ν D (t) can be resolved by observing different segments of the response indicated in Table I, and subsequently approximating ∂M/∂t by its average value at the points of switching, i.e., ∆M * c /T , which implies the first condition in (9). Furthermore, it suggests that ensuringν D (t) ≤ 0 after the frequency nadir has been reached would guarantee stability, thus resulting in an inequality condition of the form:…”