Estimating and Calibrating DER Model Parameters Using Levenberg–Marquardt Algorithm in Renewable Rich Power Grid

• Published in: Energies (Basel) Vol. 16; no. 8; p. 3512
• Main Authors: Foroutan, Armina, Basumallik, Sagnik, Srivastava, Anurag
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.04.2023; MDPI
• Subjects: Algorithms; Analysis; Calibration; Control algorithms; damped least-squares; DER_A; distributed energy resources; Electricity distribution; Energy & Fuels; ENERGY PLANNING, POLICY, AND ECONOMY; Jacobian; Laws, regulations and rules; model calibration; model parameter estimation; model validation; nonlinear least squares; OpenDSS; Parameter estimation; Simulation; United States
• ISSN: 1996-1073; 1996-1073
• DOI: 10.3390/en16083512

The proliferation of inverter-based distributed energy resources (IBDERs) has increased the number of control variables and dynamic interactions, leading to new grid control challenges. For stability analysis and designing appropriate protection controls, it is important that IBDER models are accurate. This paper focuses on the accurate estimation and parameter calibration of DER_A, a recently proposed aggregated IBDER model. In particular, we focus on the parameters of the reactive power–voltage regulation module. We formulate the problem of parameter tuning as a non-linear least square minimization problem and solve it using the Levenberg–Marquardt (LM) method. The LM method is primarily chosen due to its flexibility in adaptively selecting between the steepest descent and Gauss–Newton methods through a damping parameter. The LM approach is used to minimize the error between the actual measurements and the estimated response of the model. Further, the computational challenges posed by the numerical calculation of the Jacobian are tackled using a quasi-Newton root-finding approach. The proposed method is validated on a real feeder model in the northeastern part of the United States. The feeder is modeled in OpenDSS and the measurements thus obtained are fed to the DER_A model for calibration. The simulation results indicate that our approach is able to successfully calibrate the relevant model parameters quickly and with high accuracy, with a total sum of square error of 3.57×10−7.