How Many Grid-Forming Converters Do We Need? A Perspective From Small Signal Stability and Power Grid Strength

TL;DR

The paper addresses how many grid-forming converters are needed to improve small-signal stability in grids with grid-following converters. It develops a theoretical framework contrasting voltage-source behaviors via impedance/admittance modeling, introduces the 2D-VS vs 1D-VS concept, and links grid strength to stability through the generalized short-circuit ratio (gSCR). It derives a closed-form relation between gSCR and the GFM/GFL capacity ratio gamma, and validates the results with high-fidelity simulations across multiple bus voltages and control implementations. The findings indicate that a partial deployment of GFM converters—far from requiring all converters to be GFM—can significantly boost stability, guiding practical capacity allocation for future grids.

Abstract

Grid-forming (GFM) control has been considered a promising solution for accommodating large-scale power electronics converters into modern power grids thanks to its grid-friendly dynamics, in particular, voltage source behavior on the AC side. The voltage source behavior of GFM converters can provide voltage support for the power grid, and therefore enhance the power grid (voltage) strength. However, grid-following (GFL) converters can also perform constant AC voltage magnitude control by properly regulating their reactive current, which may also behave like a voltage source. Currently, it still remains unclear what are the essential differences between the voltage source behaviors of GFL and GFM converters, and which type of voltage source behavior can enhance the power grid strength. In this paper, we will demonstrate that only GFM converters can provide effective voltage source behavior and enhance the power grid strength in terms of small signal dynamics. Based on our analysis, we further study the problem of how to configure GFM converters in the grid and how many GFM converters we will need. We investigate how the capacity ratio between GFM and GFL converters affects the equivalent power grid strength and thus the small signal stability of the system. We give guidelines on how to choose this ratio to achieve a desired stability margin. We validate our analysis using high-fidelity simulations.

Figures (16)

• Figure 1: A grid-connected three-phase power converter. Control mode 1: GFL control (i.e., PLL-based control). Control mode 2: GFM control (applying VSM scheme). Here GFL control and GFM control share the same control objectives, i.e., regulating active power $P_E$ to its reference $P^{\rm ref}$, regulating the $q$-axis voltage $V_q$ to 0, and regulating the $d$-axis voltage $V_d$ to the voltage magnitude reference $V^{\rm ref}$; the only difference between GFL and GFM control is the way of connecting different control loops. For instance, in GFL mode, the frequency deviation $\Delta \omega$ comes from the $q$-axis voltage control loop (i.e., PLL), while in GFM mode, $\Delta \omega$ comes from the active power control loop.
• Figure 2: Impedance model of a grid-connected converter.
• Figure 3: The largest singular values of the impedance matrix in GFL mode (i.e., $\bar{\sigma}({\bf Z}_{\rm GFL}(s))$) and in GFM mode (i.e., $\bar{\sigma}({\bf Z}_{\rm GFM}(s))$ corresponds to VSMs without additional control methods where virtual inertia $J=20~{\rm pu}$ and virtual damping $D=500~{\rm pu}$; in addition, $\bar{\sigma}({\bf Z}_{\rm GFM-QD}(s))$, $\bar{\sigma}({\bf Z}_{\rm GFM-VI}(s))$, and $\bar{\sigma}({\bf Z}_{\rm GFM-damp}(s))$ correspond to VSMs with reactive power droop control, virtual impedance, and damping enhancement, respectively; $\bar{\sigma}({\bf Z}_{\rm droop}(s))$ and $\bar{\sigma}({\bf Z}_{\rm PI}(s))$ correspond to GFM converters under droop control and power synchronization control, respectively).
• Figure 4: A power grid integrated with multiple wind farms.
• Figure 5: Each wind farm in Fig. \ref{['Fig_wind_farms']} is equipped with a GFM converter. The GFM converter and the GFL converter are connected to one common 220 kV bus.

Theorems & Definitions (8)

• remark 1
• Definition 3.1: gSCR
• Proposition 3.2: gSCR and stability dong2018small
• Proposition 4.1: gSCR and capacity of GFM converters
• proof
• Example 1
• Example 2
• Example 3