Optimal Electricity Procurement Enabled by Privacy-Preserving Samples

Prior sample-based mechanisms rely predominately on empirical validations for their efficiency, with little attention to how finite samples theoretically impact decision-making. Additionally, differentially private noise injection before data publication further complicates the understanding of the samples' impact. To this end, taking electricity procurement as an example, we seek to theoretically quantify the impact of authentic and privacy-preserving samples on decision-making. Specifically, based on the customized sample average approximation procurement solution, we derive the minimum number of samples to guarantee near-optimal decisions. Numerical studies validate the theoretical bounds by comparing them to empirical observations. Our analysis offers practical insights into effective demand forecast mechanism design and efficient sample collection.