Tracing Power With Circuit Theory

Power tracing is the task of disaggregating the power injection of a generator (or a load) into a sum of constituent components that can unambiguously be attributed to loads (generators) and losses. Applications of power tracing range the broad spectrum of: transmission services pricing, loss allocation in distribution networks, fixed-cost allocation, modelling bilateral transactions, and financial storage rights. This paper develops an analytical approach to power tracing leveraging elementary circuit laws. The method is rigorous from a system-theoretic vantage point, and it yields unambiguous results that are consistent with constitutive principles that describe the steady-state behaviour of power networks. Moreover, it can be implemented with limited computational burden, applies to networks with arbitrary topologies, and preserves the coupling between active- and reactive-power injections. Numerical experiments indicate that given a solved power-flow solution, disaggregations can be computed for a test system with 2383 buses, 327 generators, and 2056 loads in 4.34 s on a personal computer, hence establishing computational scalability. Furthermore, applications are demonstrated in distribution and transmission networks with case studies focused on quantifying the impact of distributed generation on loss allocation and extracting nodal contributions to bilateral transactions, respectively.