Interdependence of Transmission Branch Parameters on the Voltage Levels

Mir Hadi Athari Electrical and Computer Engineering Virginia Commonwealth University atharih@vcu.edu
Zhifang Wang Electrical and Computer Engineering Virginia Commonwealth University zfwang@vcu.edu

Abstract

Transformers and transmission lines are critical components of a grid network. This paper analyzes the statistical properties of the electrical parameters of transmission branches and especially examines their interdependence on the voltage levels. Some interesting findings include: (a) with appropriate conversion of MVA rating, a transformer’s per unit reactance exhibits consistent statistical pattern independent of voltage levels and capacity; (b) the distributed reactance (ohms/km) of transmission lines also has some consistent patterns regardless of voltage levels; (c) other parameters such as the branch resistance, the MVA ratings, the transmission line length, etc, manifest strong interdependence on the voltage levels which can be approximated by a power function with different power constants. The results will be useful in both creation of synthetic power grid test cases and validation of existing grid models.

Keywords: Transmission network, synthetic power grid, statistical analysis, interdependence on voltage

1. Introduction

Modern power systems use multiple voltage levels to decrease energy loss in the transmission network [1]. The voltage level is changed through the extensive use of transmission transformers to step up the voltage for long-distance transmission lines and then step down to lower voltages to go through the distribution network. This multi voltage-level structure causes different grid components to have voltage dependent parameters and features. Branches in power networks are among those components that can have a heavy dependence on voltage level. Generally, in power systems, the term “branches” refers to transmission lines or transformers between two buses in a network. The study of the interdependence of transmission branch parameters on voltage levels can provide useful insights as well as multiple validation metrics for synthetic power networks. Synthetic power networks are introduced as a potential solution for the restricted access to real-world power system test cases. Confidentiality requirements limit the access to real data in critical infrastructures like power systems. On the other hand, researchers in power industry need realistic test cases of varying sizes and complexities and appropriate properties in order to evaluate and verify their proposed solutions and novel approaches. For example, the algorithms introduced by authors in [2]–[4] need some verification in larger systems to identify the pros and cons of the solution. Another example is the concept of real-time optimal power flow in [5] that can be evaluated in numerous synthetic grids. Since Synthetic power networks are entirely fictitious but with the same characteristics as real networks, they can be freely published to the public to facilitate advancement of new technologies in power systems. One such characteristic is the interdependence of different branch parameters on voltage level. In the literature, many studies are dedicated for characterizing actual power networks and/or developing a synthetic one, mainly from topological perspectives such as ring-structured power grid developed in [6] and tree structured power grid model to address the power system robustness [7], [8]. Works of [9]–[11] used the small world approach described in [12] as a reference to generate some synthetic transmission network topologies. The RT-nestedSmallWorld random topology model proposed in [10] is based on comprehensive studies on the electrical topology of some real-world power grids. Authors in [13] studied the impacts of randomized and correlated siting of generation and loads in a grid on its vulnerability to cascading failures. [14]–[17] defined a topology measure called “bus type entropy” to characterize the correlated siting of generation and load in actual power grids, based on which an optimization algorithm was developed to determine appropriate bus type assignments in a synthetic grid modeling. [18] studied the statistics of generation size and load settings. [19] gave a comprehensive report about the scaling property of power grid in terms of selected topology measures and electric parameters. Authors in [20] reported some initial study results on the statistics of transmission line

parameters. The substation placement method and transmission lines assignment based on population and energy data in [21] uses the methodology introduced in [22], [23], where they employ a clustering technique to ensure that synthetic substations meet realistic proportions of load and generation. [24] addressed the need for synthetic l

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