Probabilistic Modeling of Available Transfer Capability for Enhancing the Grid Integration of Renewable Energy Sources

The shift towards renewable energy sources (RES) is a key element in transitioning to sustainable power grids. However, the high penetration of RES, particularly wind and solar generation, introduces significant operational challenges due to the intermittent and stochastic nature of these energy sources. As the demand for clean energy grows, ensuring the grid's reliability and stability becomes critical. One of the most pressing challenges in modern grids is accurately determining the Available Transfer Capability (ATC), which quantifies the ability of an electrical power grid to transport electricity among regions while maintaining operational security. Traditional methods for calculating ATC and its key component, the Transmission Reliability Margin (TRM), are based on deterministic approaches that assume static, predictable grid conditions. These methods are increasingly inadequate as they do not account for the variability and uncertainty introduced by RES, leading to either overly conservative margins that curtail renewable energy export or insufficient margins that compromise system reliability. This thesis addresses these challenges by developing a dynamic TRM estimation framework and a probabilistic ATC assessment methodology for power systems with high penetration of RES. The research proposes a rolling-window statistical analysis approach to continuously adapt the confidence factor, K, in real time based on observed system volatility, replacing the traditional static confidence factor. Key uncertainties, including load demand and renewable generation variability, are modelled probabilistically using Latin Hypercube Sampling (LHS) with Iman-Conover rank-correlation control to capture their dynamic behaviours and interdependencies. The framework is further extended to incorporate demand-side management (DSM) through Direct Load Control (DLC), demonstrating that active demand participation can reduce TRM requirements and enhance ATC. The proposed methodologies are validated on standard IEEE test systems and the New Zealand inter-island HVDC corridor using operational data from the Electricity Market Information (EMI) database. The background and motivation for this thesis are presented in Chapter 1. It highlights the research questions, identifies the research gaps in existing TRM and ATC assessment methods, and outlines the specific contributions of the thesis. Chapter 2 provides a comprehensive review of existing TRM assessment methods, covering deterministic, probabilistic, statistical, and intelligent approaches. The review systematically identifies the limitations of current methods, particularly the universal reliance on static confidence factors, and establishes the research gaps that motivate the subsequent chapters. The research work in this thesis is organized under three main sections, presented in Chapters 3, 4, and 5. Chapter 3 presents the core methodological contribution: a dynamic TRM estimation framework based on rolling-window statistical analysis. The methodology introduces an adaptive confidence factor, K(t), that expands during periods of high system volatility and contracts during stable intervals, ensuring that TRM values reflect real-time grid conditions. The approach is validated on the IEEE 30-bus test system with integrated wind generation, demonstrating its superiority over static confidence factor methods in capturing time-varying load and wind uncertainty. Chapter 4 extends the dynamic TRM methodology into a comprehensive probabilistic ATC assessment framework. The framework employs LHS with Iman-Conover rank-correlation control for realistic uncertainty characterization, ensuring that correlations among uncertain inputs such as load demand and wind generation are preserved during scenario generation. The methodology is validated on the IEEE 39-bus New England test system and applied to the New Zealand inter-island HVDC corridor using one year of EMI operational data, including North Island load demand and South Island wind generation records. Scalability is demonstrated on the IEEE 118-bus system. The results confirm that the dynamic TRM approach improves the allocation of reliability margins while recovering additional transfer capability compared with conventional static methods, although the reported coverage remains below the nominal 95% one-sided reliability target in the principal validation cases. Chapter 5 extends the framework by incorporating demand-side management through Direct Load Control into the adaptive TRM-ATC assessment. The study demonstrates that DSM activation during high-volatility periods can relieve corridor loading and increase available transfer capability under the modeled conditions. However, the achieved 89.6% empirical fifth-percentile coverage remains below the nominal 95% one-sided reliability target, so uncompromised system security cannot be inferred from these results. The methodology is validated on the IEEE 24-bus Reliability Test System. In conclusion, this research contributes to enhancing the reliability, efficiency, and adaptability of power systems by providing dynamic and probabilistic tools for TRM and ATC assessment. The developed frameworks enable more accurate utilization of transmission capacity in renewable-rich grids, supporting the global transition towards sustainable energy systems.