[Paper Review] Engineering Inertial and Primary-frequency Response for Distributed Energy Resources

Swaroop S. Guggilam, Changhong Zhao+3 more|arXiv (Cornell University)|Jun 7, 2017

Microgrid Control and Optimization14 references4 citations

TL;DR

This paper proposes a second-order lumped-parameter model to systematically design synthetic-inertia and droop-control parameters for distributed energy resources (DERs) in power systems with synchronous generators. By relating reduced-model parameters to the original system, it enables precise tuning of DER controllers to meet transient and steady-state frequency response specifications using classical second-order system theory, validated via simulations showing accurate tracking of desired frequency dynamics and proportional power sharing.

ABSTRACT

We propose a framework to engineer synthetic-inertia and droop-control parameters for distributed energy resources (DERs) so that the system frequency in a network composed of DERs and synchronous generators conforms to prescribed transient and steady-state performance specifications. Our approach is grounded in a second-order lumped-parameter model that captures the dynamics of synchronous generators and frequency-responsive DERs endowed with inertial and droop control. A key feature of this reduced-order model is that its parameters can be related to those of the originating higher-order dynamical model. This allows one to systematically design the DER inertial and droop-control coefficients leveraging classical frequency-domain response characteristics of second-order systems. Time-domain simulations validate the accuracy of the model-reduction method and demonstrate how DER controllers can be designed to meet steady-state-regulation and transient-performance specifications.

Motivation & Objective

• To address the challenge of maintaining system frequency stability in power systems with high penetration of distributed energy resources (DERs) and reduced mechanical inertia.
• To develop a systematic method for designing DER synthetic-inertia and droop-control parameters that meet prescribed transient and steady-state frequency performance specifications.
• To create a reduced-order lumped-parameter model that preserves key dynamics of the original high-order system while enabling analytical design of DER control parameters.
• To decouple the model reduction process from controller parameter tuning by identifying a time constant for aggregated turbine-governor dynamics that depends only on synchronous generator parameters.
• To validate the model accuracy and demonstrate effective power sharing and frequency regulation through time-domain simulations on a test system.

Proposed method

• Formulate a second-order lumped-parameter model that captures system frequency and aggregated mechanical power output as states, incorporating synthetic inertia and droop control from DERs and real inertia and droop from synchronous generators.
• Derive the effective inertia $ M_{\text{eff}} $ and effective damping $ D_{\text{eff}} $ as the sum of generator mechanical inertia, DER synthetic inertia, generator droop, load damping, and DER droop coefficients.
• Determine the time constant $ \overline{\tau} $ for the aggregated turbine-governor dynamics by solving an optimization problem based on spectral properties of the system matrix, independent of DER parameters.
• Use classical second-order system theory to relate frequency response characteristics—such as damping ratio $ \zeta $ and regulation $ R_{\text{reg}} $—to the design of $ M_{\text{eff}} $ and $ D_{\text{eff}} $.
• Apply the design to assign individual DER synthetic-inertia and droop coefficients based on their power ratings, ensuring proportional sharing of frequency support.
• Validate the reduced model and controller design through time-domain simulations using the Pypower-based Simulator Tool (PST), comparing results with a detailed electromagnetic transients model.

Experimental results

Research questions

• RQ1 How can a reduced second-order model be constructed to accurately represent the frequency dynamics of a mixed system of DERs and synchronous generators, while preserving the physical meaning of control parameters?
• RQ2 What is the optimal time constant for the aggregated turbine-governor dynamics in the reduced model, and how can it be determined independently of DER control parameters?
• RQ3 How can synthetic-inertia and droop-control coefficients for DERs be systematically tuned to meet specific transient performance (e.g., damping ratio $ \zeta $) and steady-state regulation (e.g., $ R_{\text{reg}} $) specifications?
• RQ4 To what extent does the reduced-order model accurately predict the frequency response and power sharing behavior of the full system under large disturbances?
• RQ5 Can the proposed method ensure proportional active power sharing among DERs based on their ratings during inertial and primary-frequency response?

Key findings

• The reduced second-order model accurately captures the transient and steady-state frequency dynamics of the full system, with poles and zeros closely matching those of the original high-order model when $ \overline{\tau} $ is properly chosen.
• The optimal time constant $ \overline{\tau} $ for the aggregated turbine-governor dynamics depends only on synchronous generator droop and turbine-governor time constants, not on DER parameters, enabling decoupled model reduction and controller design.
• With $ R_{\text{reg}} = 0.4644 $ and $ \zeta = 0.7 $, the designed system achieves a damped frequency response with a lower frequency nadir and significantly reduced steady-state frequency deviation compared to the base case without DER participation.
• The steady-state frequency deviation is reduced to within analytical bounds, with computed and simulated values matching closely across all scenarios.
• DERs share the load increase in proportion to their power ratings ($ P^\text{rated}_3 / P^\text{rated}_4 = 1/3 $), confirming effective and proportional power sharing during frequency events.
• Simulations using the detailed PST model show excellent agreement with the reduced-order model, validating its accuracy despite the omission of line losses, voltage dynamics, and detailed machine models.