Multi-Port Resistance Networks and a Generalized Theory for Flow Preserving Clustered Equivalents for Market Analysis of Power Grids

The excessive computational burden encountered in power market analysis has necessitated the need for obtaining reduced equivalent networks that preserve flows along certain selected lines called tie lines in a larger power system. In this context, the concept of PTDF (Power Transfer Distribution Factors) matrix was introduced and studied using the DC flow model. On the other hand, the concept of modified circuit matrix of a multi-port resistance network was introduced by Thulasiraman and Murti. In this paper we draw attention to certain limitations of the approach by Cheng and Overbye to determine an equivalent that preserves a PTDF matrix. We then show the equivalence of the concept of modified circuit matrix of a multi-port resistance network and the concept of the PTDF matrix under the DC flow model. We then present a generalized theory of flow preserving equivalence that is not constrained by these limitations. We give a methodology to generate a flow preserving equivalent network and demonstrate its feasibility through simulations.