Electricity Price Formation as a Complex Interacting System: Using Global Sensitivity Analysis, Polynomial Chaos Expansion and Sobol Sensitivity Indices to Analyze the Coupling of Day-Ahead and Balancing Markets Under the European Target Model

Modern electricity markets are complex socio-technical systems in which price formation results from interactions among physical, economic, operational, and institutional mechanisms. Under the European Target Model, the sequential coupling of Day-Ahead, Intraday, and Balancing Markets, together with renewable variability, cross-border exchanges, system imbalances, reserve activation, and settlement mechanisms, creates an interconnected nonlinear system. This study investigates the interaction structure underlying Market Clearing Price (MCP) formation in the Greek electricity market using variance-based Global Sensitivity Analysis. A Sparse Polynomial Chaos Expansion (PCE) surrogate represents MCP as a function of sixteen variables describing generation technologies, demand, cross-border exchanges, balancing-energy activation, system imbalances, reserves, and Uplift Accounts. Sobol sensitivity analysis decomposes MCP variance into individual, pairwise, and higher-order contributions. Natural-gas generation emerges as the dominant first-order driver, whereas hydropower constitutes the principal nonlinear interaction hub, linking domestic flexibility with renewable generation and cross-border exchanges. Individual effects account for approximately 74.5% of MCP variance, pairwise interactions for 19.1%, and higher-order effects for 6.4%. The strongest nonlinear interactions involve hydropower with exports, imports, and renewable generation, demonstrating that variables with moderate individual importance may nevertheless play structurally important roles through their interactions. These findings show that MCP variability cannot be explained solely by isolated market fundamentals but reflect the coupled operation of scheduling, flexibility, European market integration, renewable variability, and balancing mechanisms. The Sparse PCE–Sobol framework therefore provides an interpretable computational approach for revealing the interaction architecture of interconnected electricity markets as complex systems.