Abstract
In power systems, flow allocation (FA) methods enable to allocate the 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 (EBEs), build upon the linearized power flow and thus on the Power Transfer Distribution Factors (PTDFs). Despite their intuitive and computationally efficient concepts, they are restricted to networks with passive transmission elements only. As soon as a significant number of controllable transmission elements, such as high-voltage direct current (HVDC) lines, operate in the system, they lose their applicability. This work reformulates the two methods in terms of Virtual Injection Patterns (VIPs), which allows one to efficiently introduce a shift parameter q to tune contributions of net sources and net sinks in the network. In this work, major properties and differences in the methods are pointed out, and it is shown how the MP and EBE algorithms can be applied to generic meshed AC-DC electricity grids: by introducing a pseudo-impedance ω ¯ , which reflects the operational state of controllable elements and allows one to extend the PTDF matrix under the assumption of knowing the current flow in the system. Basic properties from graph theory are used to solve for the pseudo-impedance in dependence of the position within the network. This directly enables, e.g., HVDC lines to be considered in the MP and EBE algorithms. The extended methods are applied to a low-carbon European network model (PyPSA-EUR) with a spatial resolution of 181 nodes and an 18% transmission expansion compared to today’s total transmission capacity volume. The allocations of MP and EBE 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. In addition, it is shown how injections from renewable resources strongly drive country-to-country allocations and thus cross-border electricity flows.
Highlights
The shift from conventional to renewable power sources requires high investments in terms of the generation and in terms of the transmission and storage of a power system
It can the be concluded that the peer-to-peer relations for both Equivalent Bilateral Exchanges (EBEs) and Marginal Participation (MP) are the same, whereas the flow allocations and virtual injections patterns differ for mixed producer-consumer contributions
A mathematical consistent extension of the Power Transfer Distribution Factor (PTDF) matrix that incorporates the operational state of controllable elements as high-voltage direct current lines was presented
Summary
The shift from conventional to renewable power sources requires high investments in terms of the generation and in terms of the transmission and storage of a power system. Energies 2020, 13, 1233 flow into sub-flows driven by isolated power injections This opens the opportunity to distribute transmission costs based on the effective transmission usage of each single generator and consumer, as broadly reviewed by Jiuping et al [1]. Average Participation, referred to as Flow Tracing, firstly presented by Bialek [2] and used in various application cases such as by Hoersch et al [3] It follows the principle of proportional sharing when tracing a power flow from source to sink. Note that FA on a distribution network level is inappropriate for the MP and EBE algorithms, as the characteristics of high resistance-reactance ratios render the linear approximation of the power flow invalid This restricts the scope of application of the MP and EBE algorithms considerably.
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