Research on the influence of the VREs’ penetration on the capacity of transmission lines

Under the trend of global carbon emission reduction and energy transformation, variable renewable energies (VREs mainly wind power and solar) will develop rapidly. Many countries have put forward ambitious VREs development plans, and a high penetration of VREs will have a significant impact on the grid. This paper focuses on the analysis of the influence of the VREs’ penetration on the capacity of transmission lines, establishes an analysis model based on mixed integer optimization and power transfer distribution factors (FTDFs), and uses this model to carry out a quantitative study on a typical system. Through the analysis of the research results, as the penetration rate of VREs increases, the transmission power of the transmission lines and the investment cost of the transmission lines will increase, and the line utilization rate will decrease. Utility companies should pay attention to the impact of future development of VREs on grid investment costs and recovery.

Inverse modeling of zonal transmission network

Presently, many ideas have been proposed for constructing zonal models of the European transmission network. Most of them are based on transmission network reduction and bus clustering, which requires the ex-ante knowledge on the details (impedance, interconnections, etc.) of the network’s elements. Generally, the information is not publicly disclosed. This paper describes a method for serving the purpose, which only requires the ex-post (i.e., published) inter-zonal power flow data as input. It performs inverse modeling on the ex-post data to reveal the virtual reactance of the interconnectors in the zonal model. The reactance values are then used for computing the zonal Power Transfer Distribution Factors (PTDFs) of the model, which is the best representation of the loop flows. A large number of such zonal PTDFs could exist in one zonal model because of its dependency on the Generation Shift Keys (GSKs). Theoretically, the GSKs could exist as an infinite set of unique combinations but only a finite number of them applied in real system operations. As a solution, the authors propose a heuristic approach for grouping the ex-post power flow cases into clusters, and find the zonal PTDF for each of them; in order to effectively reduce the domain of the zonal PTDFs and enhance the tractability of the solution. The identified zonal PTDFs meaningfully represent the zonal model. Additionally, they can also be used for studying the best and worst case scenarios of cross-border security-constrained economic dispatch.

Extended Flow-Based Security Assessment for Real-Sized Transmission Network Planning

The evolution of electric power systems involves several aspects, dealing with policy and economics as well as security issues. Moreover, due to the high variability of operating conditions, evolution scenarios have to be carefully defined. The aim of this paper is to propose a flow-based procedure for the preliminary security analysis of yearly network evolution scenarios at the real scale level. This procedure is based on hourly load and generation conditions given by market solutions, and exploits Power Transfer Distribution Factors and Line Outage Distribution Factors to determine N and N−1 conditions, properly accounting for possible islanding in the latter case. The analysis of overloads is carried out by dealing with big data analysis through statistic indicators, based on power system background, to draw out critical operating conditions and outages. The procedure is applied to a provisional model of a European high voltage network.

Analysis between graph-based and Power Transfer Distribution Factors (PTDF)-based model reduction methods in Electric Power Systems

This article presents a comparison between two different methods to perform model reduction of an Electrical Power System (EPS). The first is the well-known Kron Reduction Method (KRM) that is used to remove the interior nodes (also known as internal, passive, or load nodes) of an EPS. This method computes the Schur complement of the primitive admittance matrix of an EPS to obtain a reduced model that preserves the information of the system as seen from to the generation nodes. Since the primitive admittance matrix is equivalent to the Laplacian of a graph that represents the interconnections between the nodes of an EPS, this procedure is also significant from the perspective of graph theory. On the other hand, the second procedure based on Power Transfer Distribution Factors (PTDF) uses approximations of DC power flows to define regions to be reduced within the system. In this study, both techniques were applied to obtain reduced-order models of two test beds: a 14-node IEEE system and the Colombian power system (1116 buses), in order to test scalability. In analyzing the reduction of the test beds, the characteristics of each method were classified and compiled in order to know its advantages depending on the type of application. Finally, it was found that the PTDF technique is more robust in terms of the definition of power transfer in congestion zones, while the KRM method may be more accurate.

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.