Ensembles of realistic power distribution networks

Abstract

The power grid is going through significant changes with the introduction of renewable energy sources and the incorporation of smart grid technologies. These rapid advancements necessitate new models and analyses to keep up with the various emergent phenomena they induce. A major prerequisite of such work is the acquisition of well-constructed and accurate network datasets for the power grid infrastructure. In this paper, we propose a robust, scalable framework to synthesize power distribution networks that resemble their physical counterparts for a given region. We use openly available information about interdependent road and building infrastructures to construct the networks. In contrast to prior work based on network statistics, we incorporate engineering and economic constraints to create the networks. Additionally, we provide a framework to create ensembles of power distribution networks to generate multiple possible instances of the network for a given region. The comprehensive dataset consists of nodes with attributes, such as geocoordinates; type of node (residence, transformer, or substation); and edges with attributes, such as geometry, type of line (feeder lines, primary or secondary), and line parameters. For validation, we provide detailed comparisons of the generated networks with actual distribution networks. The generated datasets represent realistic test systems (as compared with standard test cases published by Institute of Electrical and Electronics Engineers (IEEE)) that can be used by network scientists to analyze complex events in power grids and to perform detailed sensitivity and statistical analyses over ensembles of networks.

Keywords: digital twin; ensemble of networks; mixed integer programming; power distribution networks; synthetic networks.

Fig. 1.

Proposed framework for constructing ensembles of realistic power distribution networks. The framework uses the input datasets and constructs an ensemble of networks using the steps detailed in Algorithm. The created networks are validated against actual power distribution networks.

Fig. 2.

Plots showing degree distribution (Left), hop distribution (Center), and reach distribution (Right) in rural and urban areas. Colors depict network attributes of urban vs. rural areas. The degree and hop distribution are similar for both rural and urban regions. The reach distribution of urban networks peaks at small value since the distribution network nodes are more closely placed to the substation than rural areas.

Fig. 3.

Plots showing the number of four-node paths (Left) and four-node star motifs (Right) as a function of network size (measured as the number of nodes in the network). Colors depict motif numbers in urban vs. rural areas. Urban distribution networks have a larger number of star motifs than rural networks. In contrast, the path motif count does not differ significantly across rural and urban areas. Urban networks are often larger than rural networks as measured by the number of nodes due to the larger population size.

Fig. 4.

Plots showing variation in degree distribution (Left), hop distribution (Center), and reach distribution (Right) for the ensemble of distribution networks created for Montgomery County of southwest Virginia. The error bars in the bar plots show the variation over the networks in the ensemble.

Fig. 5.

Plots showing variation in the number of four-node path motifs (Left) and the number of four-node star motifs (Right) for the ensembles of distribution networks created for Montgomery County of southwest Virginia. Results are shown for 19 ensembles of varying size in the county fed by different substations. Each ensemble consists of 20 networks. The error bars in the bar plots show the variation over the networks in each ensemble.

Fig. 6.

Plots comparing the residential node voltages (Left) and edge power flows (Right) for actual and synthetic networks. The majority of residence voltages in the synthetic network are within $\pm 0.4\%$ voltage regulation of the voltages in the actual network. The edge flows in both networks follow similar distributions, with a computed KL divergence of 0.15.

Fig. 7.

Plots comparing the degree distribution (Left), hop distribution (Center), and reach distribution (Right) of actual and synthetic distribution networks for the town of Blacksburg in southwest Virginia. The degree and hop distributions are fairly close to each other, which signifies their resemblance. The reach distribution differs between the networks because of the difference in the way each of them is created.

Fig. 8.

Plots showing Hausdorff distance–based geometry comparison of actual and synthetic networks for the town of Blacksburg in southwest Virginia. The geometry comparison is performed for grid cells with two different resolutions: low resolution of 5 × 5 grid cells (Left) and high resolution of 7 × 7 grid cells (Right). The color in each grid cell denotes the magnitude of deviation in meters. Grid cells with no available actual network data are shaded with black dots.

Fig. 9.

Plots showing the impact of PV penetration in rural and urban networks. Colors depict the percentages of nodes with various levels of overvoltages. Shaded and nonshaded bars denote MV- and LV-level penetration, respectively. LV-level penetration is less likely to cause severe overvoltages as compared with MV-level penetration. PV penetration in rural networks is more likely to cause overvoltage issues (greater than 1.05 pu).