Document Type

Dissertation - Open Access

Award Date


Degree Name

Doctor of Philosophy (PhD)

Department / School

Electrical Engineering and Computer Science

First Advisor

Reinaldo Tonkoski


The main objective of this dissertation is to develop a generalized simulation and modeling framework for extracting dynamics of power electronic converters (PECs) with grid support functions (GSFs) and validate model accuracy through experimental comparison with physical measurements. The dynamic models obtained from this modeling framework aim to facilitate accurate dynamic analysis of a highly integrated power system comprising inverter-based resources (IBRs), specifically for stability assessment. These dynamic models helped in reducing simulation time and computational complexity, thereby enhancing efficiency. Moreover, it provides valuable insights for utilities and grid operators involved in effective system planning, operation, and dispatch. The dynamics of the current power grid are poised to undergo substantial changes due to the replacement of traditional generators and the integration of distributed energy resources (DERs) based on PECs equipped with advanced GSFs. The utilization of these smart PECs is expected to increase in the future, primarily because they conform to the voltage and frequency support requirements outlined in the Institute of Electrical and Electronics Engineers (IEEE) 1547-2018 standard. However, the dynamic behavior of PECs, particularly when providing various ancillary services, is attributed to the adoption of modern control algorithms. Consequently, the system exhibits more stochastic and nonlinear dynamics, posing significant challenges to power system stability and control. Accurate modeling of these underlying nonlinear dynamics is required to ensure the stability and reliability of converter-dominated power system (CDPS). However, the proprietary nature and unknown parameters of the PECs control systems, coupled with the increasing system size, using a traditional modeling approach to obtain full dynamics becomes increasingly challenging and computationally expensive. Therefore, new modeling techniques are needed to accurately extract the PECs dynamics. This dissertation presents a data-driven modeling technique to obtain the dynamics of PECs as it does not require detail knowledge of PECs physical topology, the complex models of the various voltage/current control loops, the models of the phase-locked-loop (PLL), the protection-scheme employed, etc. Data-driven modeling is an approach that constructs models based on data rather than predefined equations or theoretical assumptions. The underlying theory behind data-driven modeling is rooted in the idea that the data itself contains valuable information about the system or process being modeled. It involves data collection (time domain input-output data) and dataset is then divided into training and testing datasets. The training dataset is passed into a system identification (SysId) algorithm which uses Instrument Variable (IV) method to process the training dataset such that least-square error is minimized for each data point and estimates the parameters. From the estimated parameters, a transfer function (TF) is obtained. The testing dataset is then used to validate the TF obtained. Finally, GoF based on normalized root-mean-square error (NRMSE) is calculated to check the accuracy of the TF. In data-driven modeling, it is essential to excite PECs with well-designed probing signals, as they serve as input data during SysId and allow a deeper understanding of system behavior. However, it is imperative to adhere to design constraints set by both power system requirements and SysId theory before using any signal as a probing signal, ensuring its alignment with the desired frequency band. Considering potential variations in system time constants, square and rectangle signals are highly suitable for accurate time constant estimation and effective emphasis on specific frequency ranges based on signal frequency. Square and rectangle signals are non-sinusoidal periodic waveforms characterized by alternating amplitudes between defined minimum and maximum values at a constant frequency. Based on this, four different probing signals (i.e., logarithmic square-chirp, square, sine, and logarithmic sine-chirp) are used and the results show that the logarithmic square-chirp probing signal adequately excites the PECs to fit a data-driven dynamic model, achieving a goodness-of-fit (GoF) exceeding 90%. Data-driven modeling techniques have also emerged as valuable tools for capturing the dynamic behavior of advanced control strategies for grid-forming inverters (GFM). This dissertation further investigates the application of a data-driven dynamic modeling technique for a GFM inverter using Power Hardware-in-the-Loop (PHIL) experiments to generate the data required. SysID is then used on collected data to obtain the dynamic model of GFM inverter. The effectiveness of the data-driven models is cross-validated with the model obtained from the analytical approach. GoF for analytical approach and data-driven approach are calculated to be 87.45% and 86.35%. Hence, both approaches are shown to accurately capture the dynamic response of GFM inverters under different loading conditions.

Library of Congress Subject Headings

Electric current converters.
Power electronics.
Electric inverters.
Distributed generation of electric power.
Smart power grids.


South Dakota State University



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