Probabilistic Voltage Stability Analysis of Renewable-Rich Power Systems

Abstract

The integration of intermittent renewable energy sources (RESs) and the variability of system loads have increased uncertainties in power networks, affecting voltage stability. Traditional deterministic stability analysis methods, by considering worst-case scenarios, often result in overly pessimistic solutions. Therefore, probabilistic stability analysis techniques are essential to model uncertainties accurately and assess their impact on voltage stability, allowing for more realistic system boundary determination. Thus, developing a probabilistic framework is vital for voltage studies in large-scale power systems to address the challenges posed by system uncertainties and maintain stable operation. The challenge lies in the implementation of the probabilistic techniques to identify the most suitable probability density function for power system input parameters such as wind speeds (research question 1). Probabilistic modelling approaches are generally inefficient as it needs to perform thousands of simulations, and hence the second challenge is to identify efficient yet accurate probabilistic modelling techniques (research question 2). The underlying theory of the probabilistic simulation with respect to the voltage stability indices has not been investigated yet (research question 3). Also, it is necessary to understand how voltage stability is affected by the consideration of the correlation of power system input parameters (research question 4). Firstly, this research critically investigates the impact of probabilistic modeling of wind speed uncertainties, considering their characteristics on voltage profiles and stability analysis. Thus, identifying an appropriate probability density function (PDF) capable of representing the uncertain input parameters of the probabilistic analysis is crucial for a valid assessment. The study includes a comprehensive analysis of fitting PDFs with different characteristics to power networks in order to capture the natural fluctuations in wind speed. Following power flow and system voltage profile analyses, a verification approach is presented to select a suitable PDF for probabilistic modeling of wind speed uncertainties. The simulation results verify that the best-suited PDFs are the Gamma distribution for low wind speeds, while the Weibull distribution is more suitable for high wind speeds. In the second stage of this research, various sampling techniques are implemented to identify an efficient and accurate approach for voltage stability assessment in large-scale systems. The Monte Carlo (MC) simulation method, a commonly used benchmark for probabilistic simulation, demands extensive simulations and computational time, making it less efficient for large-scale systems with numerous uncertainties, especially for high-resolution dynamic studies. Thus, six different sampling techniques are compared for their accuracy and efficiency in voltage stability analysis within large-scale systems. Power flow analysis is conducted to validate the suitability of the most efficient and accurate techniques based on RMSE and R2 criteria. The results demonstrate that the three variants of QMC prove to be the most efficient and accurate methods, requiring fewer random number samples to represent the reference data effectively. The third stage of this research explores the underlying theory that governs the effect of uncertain system parameters on probabilistic short-term voltage stability. This is the first work to establish a mathematical relationship between the uncertain parameters (wind speed, system load, and wind power penetration levels) and probabilistic voltage stability. The mathematical analysis of the probabilistic voltage stability analyses is essential to secure stable power system operation, especially with the increased use of RESs and the new types of system loads. It has been mathematically confirmed that the uncertain parameters (wind speed, system load, and wind generation level) significantly impact the system voltage. Specifically, an increase in wind speed, a reduction in system load, or an increase in wind power leads to higher voltage levels. This research concludes by introducing a probabilistic stability approach for modeling potential correlations among uncertain system input parameters, particularly those related to system loads and wind speeds. Neglecting these potential correlations can lead to significant errors in system responses. The proposed approach is then applied to examine various aspects of probabilistic voltage stability studies within a large-scale uncertain power network, encompassing voltage profile analysis, static voltage stability, and short-term voltage stability analysis. Various alternative sampling generation techniques are utilised to assess both independent and correlated techniques. The MVG and MVSt accurately followed the results of the real system data with accuracy rates of 98%, 97%, and 93% for voltage profiles, static voltage stability, and dynamic voltage stability, respectively. The outcomes of this thesis provide valuable insights for network operators, policymakers, and the power industry, enhancing their understanding of system behaviour under uncertainty, particularly with the growing presence of RESs. Academic researchers can also benefit by gaining insights into modern networks' challenges. Accounting for uncertainties helps establish realistic system boundaries and assess the complexity of modern networks to ensure stable static and dynamic operation.