[Paper Review] Method to Build Equivalent Models of Microgrids for RMS Dynamic Simulation of Power Systems

Rodrigo A. Ramos, Ahda P. Grilo+2 more|arXiv (Cornell University)|Oct 12, 2021

Microgrid Control and Optimization4 citations

TL;DR

This paper proposes a gray-box equivalent modeling method for grid-connected microgrids in RMS dynamic simulations, using trajectory sensitivity analysis to select key parameters before estimating them via Differential Evolution. The approach reduces parameter search space, enabling accurate, computationally efficient models that closely match full-model dynamics with MSE values below 1.04 for active and reactive power responses under disturbances.

ABSTRACT

The high penetration of distributed renewable energy resources in power systems has changed their dynamic behavior, not only at the distribution level but also at the transmission levels. For analyses performed in this new reality of interconnected systems, a suitable equivalent model is required to represent the active dynamics of distribution systems. In this context, this paper proposes the application of a gray-box method to obtain an appropriate equivalent model for active distribution networks. From data measured at the point of common coupling, a trajectory sensitivity analysis is carried out to select the most important parameters of this equivalent model, which are then estimated by an evolutionary algorithm. The results show that the application of the sensitivity analysis can improve the quality of the parameter estimation process (since it focuses only on relevant parameters), enabling an efficient tuning of an equivalent ADN model.

Motivation & Objective

• To address the challenge of modeling active distribution networks (ADNs) and microgrids (MGs) with high renewable penetration, where traditional lumped load models are inadequate.
• To develop a computationally feasible equivalent model for RMS dynamic simulation that captures the active dynamics of ADNs and MGs.
• To overcome limitations of black-box models by ensuring physical interpretability and compatibility with commercial dynamic simulation tools.
• To reduce the computational burden of parameter estimation by identifying only the most sensitive parameters for tuning.
• To validate the equivalent model’s accuracy through comparison with full-model responses under multiple disturbances.

Proposed method

• A gray-box equivalent model is constructed using a VSC, a synchronous generator, and a composite load model to represent the microgrid’s dynamic behavior.
• Trajectory sensitivity analysis is applied to measured PCC data to identify the most influential parameters, reducing the dimension of the parameter space.
• An initial parameter estimation stage uses Differential Evolution (DE) with 15 individuals, Fₛ = 0.8, and Cr = 0.3 to tune load-related parameters within defined bounds.
• A second estimation stage applies DE with 30 individuals, Fₛ = 0.8, and Cr = 0.7 to refine remaining parameters, using 80–120% of reference values as search limits.
• The model is validated using a three-phase fault at the PCC (11.0 s, 700 ms, 5.0 Ω resistance), comparing responses with the full model.
• Performance is quantified using Mean Squared Error (MSE) between equivalent and full-model outputs over defined time windows.

Experimental results

Research questions

• RQ1 Can trajectory sensitivity analysis effectively reduce the number of parameters requiring estimation in microgrid equivalent modeling?
• RQ2 Does the proposed gray-box equivalent model accurately replicate the dynamic response of a full microgrid model under disturbances?
• RQ3 Can the use of a reduced parameter set improve the convergence and efficiency of the parameter estimation process?
• RQ4 How well does the equivalent model perform in simulating active and reactive power dynamics during and after a fault?
• RQ5 Is the resulting equivalent model suitable for integration into commercial RMS dynamic simulation tools?

Key findings

• The trajectory sensitivity analysis successfully identified the most critical parameters, significantly reducing the search space and improving estimation efficiency.
• The equivalent model accurately replicates the active power dynamics of the full model, with an MSE of 0.729 under the first fault and 0.157 under the second.
• The reactive power response of the equivalent model closely matches the full model, with MSE values of 0.246 and 0.113, respectively.
• The combined active and reactive power MSE for the two fault scenarios was 1.038 and 0.270, confirming good overall dynamic fidelity.
• The model parameters were successfully estimated using Differential Evolution, with key values such as X'd = 0.282 pu, H = 3.108 s, and S_VSC = 3.027 MVA.
• The validation under a three-phase fault confirmed the model’s robustness and suitability for dynamic studies in RMS simulations.