Optimal Distribution Transformer Placement by Exploiting Graph Theory and Clustering Techniques

In the expansion of power distribution networks, the periodic task of determining the location, number, and capacity of the distribution transformers is still an open issue that needs to be systematically coped with. In this paper, a comprehensive approach for solving in practice the mentioned task is presented. The proposed methodology is based on an improved clustering technique, which considers not only the actual distances between consumers but also their electrical demand. Graph theory is exploited to represent the feasible paths of the complete system, so that, the distances and the obtained locations are accurate, and feasible in practice, respectively. The proposed objective function minimizes the total annual costs of the system, by considering investments, transformer losses, and operational costs. An approximate expression to calculate the maximum distance between each transformer and its furthest customer to accomplish voltage regulation has been obtained. Consequently, the outputs of the proposed model are the correct number of distribution transformers to be installed, their optimal locations and capacities, and the best consumer grouping with acceptable voltage drops. In order to validate the proposal, this methodology is applied to an urban system with 106 consumers, 23 vertexes, and 31 streets with promising results.