Data-driven Modeling of Grid-following Control in Grid-connected Converters

TL;DR

The paper addresses the challenge of modeling grid-following converter dynamics in modern grids using data-driven approaches. It compares Sparse Identification of Nonlinear Dynamics (SINDy) and Deep Symbolic Regression (DSR) on synthetic data generated from a converter-based resource replacing a traditional generator on a lossless line to an infinite bus, under grid-following control. The findings show that DS R provides more accurate and interpretable dynamics across the LCL filter, PLL, and inner/outer control loops, albeit with significantly higher computational cost than SINDy. This highlights a trade-off between modeling fidelity and real-time applicability, with DS R offering a valuable tool for designing and validating control strategies in high-renewables grids, and SINDy offering faster, compact representations for rapid analysis.

Abstract

As power systems evolve with the integration of renewable energy sources and the implementation of smart grid technologies, there is an increasing need for flexible and scalable modeling approaches capable of accurately capturing the complex dynamics of modern grids. To meet this need, various methods, such as the sparse identification of nonlinear dynamics and deep symbolic regression, have been developed to identify dynamical systems directly from data. In this study, we examine the application of a converter-based resource as a replacement for a traditional generator within a lossless transmission line linked to an infinite bus system. This setup is used to generate synthetic data in grid-following control mode, enabling the evaluation of these methods in effectively capturing system dynamics.

Figures (5)

• Figure 1: Schematic of the grid-following control of the stable grid-connected converter.
• Figure 2: Comparison of the identified dynamics of the LCL filter for the grid-connected converter in grid-following control mode, using the SINDy and DSR methods. Each subplot illustrates the time derivative of state variables under two distinct disturbances: a change in active power reference ($p^{ref} = 0.7$) at $t=0.3$s and a change in reactive power reference ($q^{ref} = 0.2$) at $t=0.6$s. The subplots correspond to each part are as follow; (a)$\frac{d}{dt}{i}_{r}^{\textnormal{cv}}$, (b)$\frac{d}{dt}{i}_{i}^{\textnormal{cv}}$, (c)$\frac{d}{dt}{v}_{r}^{\textnormal{filt}}$, (d)$\frac{d}{dt}{v}_{i}^{\textnormal{filt}}$, (e)$\frac{d}{dt}{i}_{r}^{\textnormal{filt}}$, and (f)$\frac{d}{dt}{i}_{i}^{\textnormal{filt}}$.
• Figure 3: Comparison of the identified dynamics of the PLL in the grid-connected converter under grid-following control mode, using the SINDy and DSR methods. Each subplot illustrates the time derivative of state variables under two distinct disturbances: a change in active power reference ($p^{ref} = 0.7$) at $t=0.3$s and a change in reactive power reference ($q^{ref} = 0.2$) at $t=0.6$s. The subplots correspond to each part are as follow; (a)$\frac{d}{dt}{v}_{q}^{\textnormal{pll}}$, (b)$\frac{d}{dt}{\epsilon}^{\textnormal{pll}}$, and (c)$\frac{d}{dt}{\theta}^{\textnormal{pll}}$
• Figure 4: Comparison of the identified dynamics of the outer control in the grid-connected converter under grid-following control mode, using the SINDy and DSR methods. Each subplot illustrates the time derivative of state variables under two distinct disturbances: a change in active power reference ($p^{ref} = 0.7$) at $t=0.3$s and a change in reactive power reference ($q^{ref} = 0.2$) at $t=0.6$s. The subplots correspond to each part are as follow; (a)$\frac{d}{dt}{\sigma}_{p}$, (b)$\frac{d}{dt}{p}_{m}$, (c)$\frac{d}{dt}{\sigma}_{q}$, and (d)$\frac{d}{dt}{q}_{m}$
• Figure 5: Comparison of the identified dynamics of the inner control in the grid-connected converter under grid-following control mode, using the SINDy and DSR methods. Each subplot illustrates the time derivative of state variables under two distinct disturbances: a change in active power reference ($p^{ref} = 0.7$) at $t=0.3$s and a change in reactive power reference ($q^{ref} = 0.2$) at $t=0.6$s. The subplots correspond to each part are as follow; (a)$\frac{d}{dt}{\gamma}_{d}$, and (b)$\frac{d}{dt}{\gamma}_{q}$.