Multiple solutions approach to tackle circular flows in real power tracing

Real power tracing algorithms were invented to find the network usage by various generators and loads. Two versions of real power tracing are popularly quoted: linear equations based and graph theoretic based. Both the methods make use of proportional sharing assumption. When the directed graph of power flow is cyclic, the graph theoretic approach is not able to proceed further, while the linear equations based approach may or may not fail depending on the distribution matrix structure. In this paper, we propose a new paradigm of real power tracing algorithms in which we show that the tracing problem can be formulated as a linear constrained multi-commodity network flow optimization problem. By exploiting multiplicity of solution space in real power tracing, it is shown that the proposed method converges to a solution even in the presence of circular flows by virtue of its constraint modeling. Results on practical data of Western Regional Grid of India demonstrate the usefulness of the method