Non-linear Probabilistic Load Flow of Power Systems with Wind and Electric Vehicles

Topic

Non-linear Probabilistic Load Flow of Power Systems with Wind and Electric Vehicles

Department of Mechanical Engineering

Date & location

• Friday, September 5, 2025

• 1:30 P.M.

• Michael Williams Building

• Room D202c

• and Virtual

Reviewers

Supervisory Committee

• Dr. Curran Crawford, Department of Mechanical Engineering, University of Victoria (Supervisor)

• Dr. Peter Wild, Department of Mechanical Engineering, UVic (Member)

• Dr. Adam Monahan, School of Earth and Ocean Sciences, UVic (Outside Member) 

External Examiner

• Dr. Mariana Resener, School of Sustainable Energy Engineering, Simon Fraser University 

Chair of Oral Examination

• Dr. Andrew Weaver, School of Earth and Ocean Sciences, UVic 

Abstract

This thesis presents a comprehensive probabilistic framework designed to assess the reliability of power systems increasingly influenced by renewable energy sources and Electric Vehicle (EV)s. It addresses the critical need for methodologies that effectively incorporate complex system characteristics and uncertainties without compromising computational efficiency.

Traditional deterministic methods often inadequately capture the probabilistic nature of power systems, which is essential for understanding the impacts of variable renewable energy generation and stochastic loads associated with rising electric transportation adoption. To address these limitations, this study introduces a novel methodology integrating sequential reliability simulations with detailed probabilistic analyses of non-linear load flow equations. The core of this approach employs advanced cumulant-based methods that accurately represent higher-order statistical characteristics and correlations among multiple uncertainties, efficiently modeling non-linear system behavior and fluctuations in renewable energy outputs and demand patterns. This significantly enhances computational efficiency and improves the accuracy of reliability assessments.

Building upon this foundation, the thesis further develops the concept of cumulant-tensor- based Probabilistic Load Flow (PLF) analysis. This innovative methodology extends cumulant approaches to handle higher-dimensional probability distributions, providing deeper insights into system behaviors under various scenarios, particularly those involving large-scale integration of wind generation and extensive EV charging demand.

An indicative real-world case study using the BC Hydro (BCH) power system demonstrates the practical application of these advanced methodologies. Through sequential reliability simulations combined with cumulant-tensor-based PLF analysis, the study examines the effects of wind generation variability and diverse EV charging scenarios, including adoption levels of up to one million vehicles. The results highlight the mixed impacts on system reliability: while increased wind generation capacity offers potential reliability improvements in urban areas with substantial EV integration, it presents challenges for rural areas with limited balancing resources. Generation facilities typically exhibit robustness against such variability; however, critical transmission infrastructure experiences significant stress, underscoring the need for targeted investments to enhance system resilience.

By specifically analyzing critical transmission lines within the BCH system, the study identifies key vulnerabilities and suggests targeted opportunities for infrastructure improvements. The use of hourly PLF analysis to determine confidence margins of power flows facilitates economical infrastructure design by accurately identifying periods of peak stress, thereby preventing unnecessary over-design. While the integration of renewable sources brings clear environmental advantages, it also introduces considerable complexities in economic dispatch and system expansion planning. The developed probabilistic framework provides utility providers with robust tools to effectively and reliably manage these complexities.

Overall, the methodologies presented represent substantial advancements in power system reliability assessment and are applicable to economic dispatch, system expansion planning, and risk management. As the global energy landscape continues to evolve, the deployment of such advanced probabilistic frameworks is increasingly essential to ensure the resilience, efficiency, and sustainability of future power infrastructure.