Autonomous Grid-Forming Inverter Exponential Droop Control for Improved Frequency Stability

TL;DR

The paper tackles frequency stability in grids with high penetrations of grid-forming PECs by introducing Droop-e, an exponential, non-linear droop that uses available headroom to damp frequency deviations and reduce ROCOF. It presents a full mathematical formulation, including curve shaping, origin inversion, hard limits, and an autonomous power-sharing controller, along with analytic stability proofs and small-signal analysis. Time-domain EM simulations on a 3-bus system and the IEEE-39-bus system demonstrate improved nadir, damping, and faster transient support when using Droop-e compared to linear droop, with autonomous sharing activated after disturbances. The work demonstrates substantial potential for enhancing frequency resilience in future grids with high renewable and energy-storage penetration and outlines directions for larger-network analyses and parameter optimization.

Abstract

This paper introduces the novel Droop-e grid-forming power electronic converter control strategy, which establishes a non-linear, active power--frequency droop relationship based on an exponential function of the power output. A primary advantage of Droop-e is an increased utilization of available power headroom that directly mitigates system frequency excursions and reduces the rate of change of frequency. The motivation for Droop-e as compared to a linear grid-forming control is first established, and then the full controller is described, including the mirrored inversion at the origin, the linearization at a parameterized limit, and the auxiliary autonomous power sharing controller. The analytic stability of the controller, including synchronization criteria and a small signal stability analysis, is assessed. Electromagnetic transient time domain simulations of the Droop-e controller with full order power electronic converters and accompanying DC-side dynamics, connected in parallel with synchronous generators, are executed at a range of dispatches on a simple 3-bus system. Finally, IEEE 39-bus system simulations highlight the improved frequency stability of the system with multiple, Droop-e controlled grid-forming inverters.

Figures (11)

• Figure 1: The full Droop-e controller that receives the filter output power $p$, and calculates the output frequency $\omega_I$. The autonomous power sharing controller adds a frequency offset $\omega_{ps}$ to achieve power sharing within the primary frequency response period, only if this control objective is desired. The calculation of $p_l$ and $\omega_{set}$ are not explicitly shown.
• Figure 2: Droop-e frequency curve as a function of power output for the parameters specified in Table \ref{['tab: Droop-e parameters']}, compared to a 5% linear droop.
• Figure 3: Droop-e tangent droop value across the full range of power output $p$ with parameters from Table \ref{['tab: Droop-e parameters']}. Note the limits for $|p|>p_l$ and the continuous value across the range of outputs.
• Figure 4: Eigenvalue trajectories of the simple 3-bus system for those with GFM state participation. Note the varied x and y axis scales.
• Figure 5: The simple 3-bus system with a synchronous generator located at bus 1 and a Droop-e grid-forming PEC at bus 3.