Advanced Safety Filter for Smooth Transient Operation of a Battery Energy Storage System

TL;DR

This paper addresses safe current limiting for a grid-connected Battery Energy Storage System (BESS) while preserving grid-forming Direct Power Control (EDPC) during transients. It introduces an advanced safety filter that combines a Control Barrier Function (CBF) and a Control Lyapunov-Like Function (CLF) with Sum-of-Squares (SOS) optimization to generate polynomial candidates and a Quadratically Constrained Quadratic Program (QCQP) to enforce safety under quadratic input constraints. The method achieves forward invariance of a safe set $\mathcal{X}_s \subset \mathcal{X}_a$ and finite-time convergence to a nominal region $\mathcal{X}_n \subset \mathcal{X}_s$ where the EDPC input remains undisturbed, with the dynamics of the filtered PCC voltage accounted for in the model. The approach is demonstrated on a three-phase inverter BESS with load-step experiments at the PCC, showing smoother current limiting and reduced current dip compared to a standard vector current controller, thereby certifying safety and smooth operation under grid transients. The results suggest the framework can be extended to other power-electronics applications requiring safety guarantees and seamless transitions between competing control modes.

Abstract

In this paper, we implement an advanced safety filter to smoothly limit the current of an inverter-based Battery Energy Storage System. The task involves finding suitable Control Barrier Function and Control Lyapunov Function via Sum-of-Squares optimization to certify the system's safety during grid transients. In contrast to the conventional safety filter, the advanced safety filter not only provides a safety certificate but also achieves finite-time convergence to a nominal region. Within this region, the action of the nominal control, i.e. the Enhanced Direct Power Control, remains unaltered by the safety filter. The advanced safety filter is implemented using a Quadratically Constrained Quadratic Program, providing the capability to also encode quadratic input constraints. Finally, we showcase the effectiveness of the implementation through simulations involving a load step at the Point of Common Coupling, and we compare the outcomes with those obtained using a standard vector current controller.

Figures (7)

• Figure 1: The BESS is implemented as a three-phase power inverter system connected to the PCC via a transformer and a grid filter. The EDPC in series with a current limiting control ensures GFM behavior during islanded grid operation while limiting the current during grid transients.
• Figure 2: The Enhanced Direct Power Control (EDPC) directly generates a converter voltage reference $v_{c,n}$ from a power control loop, integrating frequency and amplitude droop characteristics.
• Figure 3: The advanced safety filter ensures safe operation with respect to the maximum allowed current limits \ref{['eq:allowable_current']}. Additionally, it guarantees finite-time convergence to the nominal region, where the nominal control input $u_n^\top = v_{c,n}^\top\alpha_n^\top$ is -- assuming simplified system and EDPC control dynamics -- not perturbed by the advanced safety filter. The dynamics of the filtered PCC voltage $v_{\mathrm{PCC},f}$ is also taken into account to ensure the existence of the nominal region.
• Figure 4: The polynomial CBF $B(x)$ and CLF $V(x)$, along with their corresponding safe set $\mathcal{X}_s$, which must be contained within the allowed set of states $\mathcal{X}_a$, and nominal region $\mathcal{X}_n$, are computed using SOS optimization. The vector field $\dot x = f(x) + G(x) u_{sos}(x)$, projected to $(i_{d}, i_q)$ coordinates setting $(i_{r,d}, i_{r,q}) = (0, 1)$, is depicted in blue. Here, the polynomial $u_{sos}(x)$ is utilized to ensure compatibility between the CBF and CLF.
• Figure 5: Simulations are conducted by switching a load to the PCC, necessitating the limitation of the BESS's current.

Theorems & Definitions (1)

• Remark 1