Flow Allocation in Meshed AC-DC Electricity Grids

In power systems, flow allocation (FA) methods allow to allocate usage and costs of the transmission grid to each single market participant. Based on predefined assumptions, the power flow is split into isolated generator specific or producer specific sub-flows. Two prominent FA methods, Marginal Participation (MP) and Equivalent Bilateral Exchanges (EBE), build upon the linearized power flow and thus on the Power Transfer Distribution Factors (PTDF). Despite their intuitive and computationally efficient concept, they are restricted to networks with \emph{passive} transmission elements only. As soon as a significant number of \emph{controllable} transmission elements, such as High-voltage direct current (HVDC) lines, operate in the system, they loose their applicability. This work reformulates the two methods in terms of Virtual Injection Patters (VIP) which allows to efficiently introduce a shift parameter $q$, tuning contributions of net sources and net sinks in the network. Major properties and differences of the methods are pointed out. Finally, it is shown how the MA and EBE algorithm can be applied to generic meshed AC-DC electricity grids: Introducing a \emph{pseudo-impedance} which reflects the operational state of controllable elements, allows to extend the PTDF matrix under the assumption of knowing the current system's flow. Basic properties from graph theory are used for solving the pseudo-impedance dependent on the position in the network. This directly enables \emph{e.g.} HVDC lines to be considered in the MP and EBE algorithm. The extended methods are applied to a low-carbon European network model (PyPSA-EUR) with a spatial resolution of N=181 and an 18\% transmission expansion. The allocations of VIP and MP, show that countries with high wind potentials profit most from the transmission grid expansion. Based on the average usage of transmission system expansion a method of distributing operational and capital expenditures is proposed. Further it is shown, how injections from renewable resources strongly drive country-to-country allocations and thus cross-border electricity flows.