The transition towards renewable energy has increased the importance of virtual power plants (VPPs) in integrating distributed energy resources (DERs). However, questions remain regarding the most appropriate auction mechanisms (pay-as-bid (PAB) versus pay-as-clear (PAC)) and imbalance penalty structures, which significantly influence VPP bidding strategies and market operations. This study employs a three-stage stochastic programming model to evaluate VPP bidding behaviors under these auction mechanisms while also considering the effects of imbalance penalty structures. By simulating various market scenarios, the results reveal that PAC markets offer higher VPP revenues due to settlement at the market-clearing price; they also exhibit greater volatility and elevated imbalance penalties. For instance, power deviations in PAC markets were 52.60% higher than in PAB markets under specific penalty structures, and imbalance penalty cost ranges differed by up to 82.32%. In contrast, PAB markets foster stable, stepwise bidding strategies that minimize imbalance penalties and improve renewable energy utilization, particularly during high- and moderate-generation periods. The findings emphasize the advantages of the PAB mechanism in electricity markets with substantial renewable energy integration, providing significant insights for the design of auction mechanisms that facilitate reliable and sustainable market operations.
