Date of Award


Document Type

Open Access Dissertation


Electrical Engineering

First Advisor

Roger Dougal


This research presents an investigation of behavioral intricacies of the Quantized DEVS Latency Insertion Method (QDL) method and proposes resolutions to the previously unsolved and unexplained discrepancies between the reference solution and the QDL method. QDL method is a combination of two other methods namely the Latency Insertion Method (LIM) and Linear Implicit Quantized State (LIQSS)method. This technique is rigorously evaluated across a diverse array of systems and scenarios, with the aim of unearthing nuanced insights into its respective functionalities.

The research seeks to discern novel attributes of this method while gauging its comparative efficacy against conventional discrete-time methodologies, both for the transient and steady-state performance analysis of electric power networks. Although many of the primary objectives were successfully achieved, certain methodological behaviors manifested unanticipated characteristics.

Although Kofman originally formulated QSS methods and more recently LIQSS over two decades ago, their integration into electric system simulators has been limited. The field primarily relies on the resource-intensive 5th-order implicit Runge- Kutta method of the Radau IIA family. In 2020, Hood introduced the QDL method, which combines QSS principles with latency techniques to enhance its application to power systems. While the QDL method offers several advantages, such as efficient computation for high-stiff nonlinear power systems, reduced simulation run time in quasi-steady state conditions, improved accuracy and stability in the face of stiff and marginally stable systems, decreased computational burden, asynchronous variable updates, and suitability for high-stiff nonlinear systems, it still faced unresolved issues. One significant drawback pointed out by the QDL method’s creator but left unresolved was the presence of steady-state oscillations, which clearly diminished its computational efficiency and introduced large errors. We have addressed it in chapter 10 resulting in a reduction of the error by a factor of 100 for most of the states of the system and currently most of the errors instead of falling between 2 to 10 percent, fall within 0.1 percent. Furthermore, this method’s behavior concerning the impact of quantization sizes on QDL simulation resilience and its performance under system scaling and increased connectivity has been thoroughly explored in respective chapters. One essential misconception about the QDL method’s behavior has been addressed in Chapter 6. Many other aspects have been investigated and answered, with results dispersed throughout this work’s chapters. Importantly, some of the findings from this research have been shared in collaborative publications [1] [2], and further contributions are ongoing.

Of significance is that all systems examined contain components featuring nonlinear V-I characteristics and substantial variability in rate constants.

• Among the notable outcomes observed during the inquiry, it is found that at a quantization size of approximately 1% of a variable’s maximum value, the QDL method yielded results diverging by less than 1% from outcomes computed via established continuous-system state-space approaches. The computational efficiency of QDL demonstrated logarithmic augmentation with escalating quantization size, maintaining accuracy until a particular threshold beyond which errors escalated steeply. A "sweet spot" was identified, wherein a specific quantization size harmonized computational efficiency and accuracy.

• QDL method demonstrated heightened computational efficiency during steady-state operation in its current version. When not in a steady state, updates were selectively applied to states impacted by quantum-level changes in connected states. While anticipated benefits were largely realized, certain complexities emerged, including limit cycle oscillations in case of not judiciously setting up the system control parameters and the quantization sizes in states following disturbances that should have returned to stationary. We have shown these limit cycle oscillations in our work followed by the resolution of how to omit them.

• The QDL method, as currently formulated, may present limitations in fault analysis due to diminished computational efficiency when large disturbances induce significant excursions across numerous system states. The study outlines the strengths and weaknesses of this approach and proposes enhancements to overcome inherent deficiencies.

• While facing the scaling up of the system, the simulation time of the QDL method, although super linear, was far from being quadratic but showed that the simulation runtime factor is greater than the factor the states are getting multiplied.

• In terms of sparsity, as the system gets more connected, the computational efficiency degrades to a certain point but the cumulative updates of the fully connected network were still below the number of reference simulation time steps.

• The QDL method as currently formulated, may present limitations in fault analysis due to diminished computational efficiency when large disturbances induce significant excursions across numerous system states.

In conclusion, this research uncovers a spectrum of intriguing results across various chapters. Notable outcomes include the influence of quantization sizes on steady-state waveform shapes and oscillation amplitudes. Additionally, the selection of quantization sizes to mitigate minor system perturbations is elucidated, and the impact of an increasing state count on QDL simulation times is quantified. The study underscores the need for further investigation into certain anomalous behaviors and unanticipated outcomes encountered during the research. Ultimately, the comprehensive analysis conducted in this work enhances the understanding of these innovative simulation techniques within the domain of electrical engineering.


© 2023, Navid Gholizadeh