The power transformer is a critical device in power systems. This paper addresses one of the major problems which hopes to enhance the accuracy of estimation of parameters, which is critical in power transformer modeling, maintenance, and operating efficiency. In that context, this work estimates the parameters of single- and three-phase power transformers by a new optimizer called Arctic Puffin Optimization Algorithm (APO). The algorithm is intended to improve estimation of transformer parameters with the goal of reducing the error incurred between the estimated and actual values of the parameters. To verify the accuracy of the APO, experimental measurements were conducted on single- and three-phase transformers. The assessment of the algorithm's effectiveness was performed against the effectiveness of other commonly used estimating methods. The results have shown that APO increases the accuracy of estimation of the parameters of both single- and three-phase transformers to considerable levels. Dependability of the APO was established by experimental verification, which disclosed an ultimate connection between the resultant quantities and actual measurements. The study also confirmed APO can be useful for transformer parameter estimation because APO converges more rapidly and more precisely compared with traditional methods of the literature.