# A Metric-Based Validation Process to Assess the Realism of Synthetic Power Grids

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## Abstract

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## 1. Introduction

## 2. Proposed Validation Methodology

## 3. Metrics of System Proportions: Substations, Load, and Generation

**Number of buses per substation.**Substation aggregation of buses indicates how buses are related to a specific geographic location. While substation grouping and geographic location are not strictly necessary for power flow solutions, they are integral to an understanding of grid topology, since geography is a major driving factor in system design.

^{−4}threshold at about 27 buses.

**Substation voltage levels.**The synthetic networks will focus on transmission nominal voltage levels of 69+ kV. Table 1 shows the percentages of such substations with buses in the 69–200 kV range and the 200+ kV range, for each of the fourteen cases. The majority cluster of areas in Table 1 indicates synthetic networks should have a 69–200 kV bus at 85–100% of substations, and 7–25% of transmission substations should have a bus in the range 201+ kV. The two exceptions to this rule, areas 8 and 10, use 230 kV as a system-wide voltage, while the rest of the areas use a voltage below 200 kV for a system-wide network. Synthetic networks could be designed in this way, in which case substations with 230 kV would fall in the lower category rather than the upper one.

**Percentage of substations containing load.**Categorizing buses or substations as load, generating, or neither plays an important role in synthesis methods and relates to the core energy delivery purpose of power systems. Except for two cases, areas 5 and 9, all of those studied show 75–90% of substations containing load, as shown in Table 1. Load, of course, is an aggregation of sub-transmission, distribution, and customer-level circuits, which for these exceptions appears to be grouped at a higher level than for typical grid cases.

**Load at each bus.**The selected cases vary from about 6–18 MW of load per bus on average. This excludes a couple of cases, which, because of their large net import or export of power, are outliers. Synthetic networks are often designed as self-contained systems. This average metric is important because it indicates the relationship between the size of a network in buses and the amount of peak load it serves.

**Ratio of total generation capacity to total load.**The EI and WECC and their sub-regions generally have 20–60% more generation capacity than the peak load, as shown in the rightmost column of Table 1. There are two exceptions, one which imports lots of power and has 12% less generation capacity than total load, and one which has 104% more capacity as it exports a lot of power. The other cases fall within the realistic range of 20–60% capacity surplus. For any self-contained system, this metric should be almost inviolable.

**Percent of substations containing generation.**In the EI, 11% of substations contain generation, and in the WECC, the proportion is 17%. The values are shown in the sixth column of Table 1. Several of these cases tend to be outliers, since this metric is also related to the sort of generators that are used in a particular area and how many small generators are modeled. The defined metrics is that synthetic cases should contain generation in 5–25% of substations, which centers around the aggregate statistics from the full interconnects and includes most of the actual cases studied.

**Capacities of generators.**The selected cases consistently contain a wide variety of generator MW capacities, and it is important for synthetic cases to contain not only the correct total and average generation, but the spectrum of generator sizes real cases contain. Figure 3 shows these cases, with the range of 25 MW to 200 MW being the most common range for all cases, and most cases containing a few generators larger than 200 MW. Below 25 MW, the modeling varies. Some cases include a sizeable set of small generators, while at least a few areas largely ignore or aggregate them.

**Percent of generators committed.**The percent of generating units which are committed, that is, connected to the grid and generating power positive active power, is an important metric of the reserves and economics of the generation fleet. As shown in Figure 4, this value is 60–80% for most of the real cases considered.

**Generator dispatch percentage.**Most committed generators in peak planning cases are operated close to their maximum MW capacity. This is especially true in certain areas of the EI. Recognizing the wide variation of this parameter, as illustrated in Figure 5, the defined criterion is that at least 50% of generators should be dispatched above 80%. The EI and WECC are shown to have diverging distributions, nevertheless, they share the characteristics that the majority of generators are operated close to their MW limit. Parameters closely tied to operational considerations such as this one will change over time and show larger variance, but the focus is on the planning case values and capturing the salient characteristics.

**Generator reactive power limits.**Generators’ ratio between maximum reactive power limit and maximum active power limit, MaxQ/MaxP, shows the relationship between the size of a generator and how much voltage support it can give. This parameter also has a wide range of variety, since in actuality these are approximations for the capability curves, since reactive power limits are not the same at each active power operating point. As a basic qualification that seems to meet the data in real cases, for at least 70% of generators, that ratio of maximum reactive power to maximum active power should be between 0.40 and 0.55.

## 4. Metrics of System Network: Transformers and Transmission Lines

**Transformer per-unit reactance.**Transformer reactance X is evaluated on the transformer power base in MVA, ${S}_{B}^{Txf}$, which is related to the ${X}_{p.u.}$ value used in the power flow case by the formula:

**Transformer MVA limit and X/R ratio.**Transformer MVA limit and X/R ratio statistics include outliers for large cases, because R and MVA limits for transformers are not absolutely essential to power flow studies. Sometimes a default small R value is used, so that the X/R ratio appears to be 10000 or more, which is unlikely to be accurate. However, for many transformers the data is reliable.

**Transmission line reactance.**Transmission line parameters are organized by voltage level, since many aspects of transmission line design depend on the voltage level. The per-unit reactance depends heavily on the length of the transmission line, which, while not available exactly, can be approximated from the geographic distance between the two substations it connects. This distance will always be shorter than the actual right-of-way length, but serves as an approximation, especially for longer lines. Transmission line per-km impedances at a certain nominal voltage level typically have a unimodal distribution with heavy tails corresponding to outliers, as shown in Figure 7. Some of the outliers may be due to smaller transmission lines for which the per-distance metric is less accurate. Similar to the transformer parameters, the transmission line statistics used are the 10th percentile, the 50th percentile (median) and the 90th percentile. This encompasses most transmission lines. Table 3 shows these percentages. Data on the distribution of transmission line parameters is also significantly impacted by the number of conductors bundled together in a phase, with 2- and 3- conductor bundling reducing the 345 and 500 kV lines.

**Transmission line X/R ratio and MVA limit.**In the same way, the 10/50/90 percentiles were calculated for transmission line X/R ratio and MVA limit, for major voltage levels, as shown in Table 4. Reference [18] has also examined MVA limit for transmission lines. These statistics do not consider transmission lines whose R values or MVA limits are not given. It is noticeable how narrow the 10–90 window is in each statistic, indicating the relatively consistent range in which realistic line parameters fall. The rule-of-thumb for validation, allowing for some variability, is for at least 70% of lines to fall inside the 10–90 window. Synthetic transmission lines are also validated during construction if they are synthesized from actual conductors and tower configurations, as described in [12] and done for synthesized cases in this paper.

**Ratio of transmission lines to substations, at a single nominal voltage level.**The next set of metrics relate to the most-studied aspect of power grid synthesis: the transmission line topology. While the complex network literature has approximated the topology analysis with random models such as small-world [3,5,7,8], others have discussed the limitations of such a model because of its deviations from node distribution and its highly-designed, static topological nature [4,9,12].

**Percent of lines on the minimum spanning tree.**The Euclidian minimum spanning tree (MST) is the minimum distance graph which connects all substations at a voltage level. This statistic, along with the following Delaunay triangulation statistics, helps to capture the geographic constraints of transmission line networks. Using the spatial relationships between nodes as key to understanding the topology is central to the approaches of [9,11], and [13]. Reference [13] shows the fraction of actual lines which come from MST, Delaunay, and Delaunay neighbors in EI and WECC, with the MST percentage around 50%.

**Distance of transmission lines along the Delaunay triangulation.**The Delaunay triangulation is calculated from a set of coordinates, dividing the plane into triangles, in which no triangle’s circumcircle contains another point [20]. As shown in [12], which appears to be the first application of this technique to power grid synthesis, most transmission lines have a very short distance along it, and this is an excellent metric of the geographic constraints of transmission line topologies. This reference shows about 75% of lines are on their Delaunay triangulation, about 20% are second neighbors, and about 5% are third neighbors. The number of lines that are fourth neighbors and higher is consistently below 1%.

**Ratio of total length of all lines to the length of the minimum spanning tree.**This metric compares line length at a nominal voltage level to the minimum length needed to connect all the substations, i.e., the length of the minimum spanning tree. These values are shown in Table 5. For networks above 100 kV and larger than 50 substations, most have this ratio between 1.4 and 2.6. In addition to the relative consistency in this ratio, the driving intuition is that it measures the relationship between the actual size of a power grid and the theoretical geographic minimum required.

## 5. Validating Two Example Cases

## 6. Discussion and Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Power Flow Cases. Available online: http://electricgrids.engr.tamu.edu (accessed on 10 August 2017).
- Zhou, Q.; Bialek, J.W. Approximate model of European interconnected system as a benchmark system to study effects of cross-border trades. IEEE Trans. Power Syst.
**2005**, 20, 782–788. [Google Scholar] [CrossRef] - Watts, D.J.; Strogatz, S.H. Collective dynamics of ‘small-world’ networks. Nature
**1998**, 393, 440–442. [Google Scholar] [CrossRef] [PubMed] - Cotilla-Sanchez, E.; Hines, P.D.H.; Barrows, C.; Blumsack, S. Comparing the topological and electrical structure of the North American electric power infrastructure. IEEE Syst. J.
**2012**, 6, 616–626. [Google Scholar] [CrossRef] - Pagani, G.A.; Aiello, M. The power grid as a complex network: A survey. Phys. A Stat. Mech. Appl.
**2013**, 392, 2688–2700. [Google Scholar] [CrossRef] - Albert, R.; Albert, I.; Nakarado, G.L. Structural vulnerability of the North American power grid. Phys. Rev. E
**2004**, 69. [Google Scholar] [CrossRef] [PubMed] - Hines, P.; Blumsack, S.; Cotilla Sanchez, E.; Barrows, C. The topological and electrical structure of power grids. In Proceedings of the 2010 43rd Hawaii International Conference System Sciences, Koloa, HI, USA, 5–8 January 2010. [Google Scholar]
- Wang, Z.; Scaglione, A.; Thomas, R.J. Generating statistically correct random topologies for testing smart grid communication and control networks. IEEE Trans. Smart Grid
**2010**, 1, 28–39. [Google Scholar] [CrossRef] - Cloteaux, B. Limits in modeling power grid topology. In Proceedings of the 2013 IEEE 2nd Network Science Workshop (NSW), West Point, NY, USA, 29 April–1 May 2013. [Google Scholar]
- Hu, J.; Sankar, L.; Mir, D.J. Cluster-and-Connect: An algorithmic approach to generating synthetic electric power network graphs. In Proceedings of the 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton), Monticello, IL, USA, 29 September–2 October 2015. [Google Scholar]
- Gegner, K.M.; Birchfield, A.B.; Xu, T.; Shetye, K.S.; Overbye, T.J. A methodology for the creation of geographically realistic synthetic power flow models. In Proceedings of the 2016 IEEE Power and Energy Conference at Illinois, Champaign, IL, USA, 19–20 February 2016. [Google Scholar]
- Soltan, S.; Zussman, G. Generation of synthetic spatially embedded power grid networks. In Proceedings of the 2016 IEEE Power and Energy Society General Meeting (PESGM), Boston, MA, USA, 17–21 July 2016. [Google Scholar]
- Birchfield, A.B.; Gegner, K.M.; Xu, T.; Shetye, K.S.; Overbye, T.J. Statistical considerations in the creation of realistic synthetic power grids for geomagnetic disturbance studies. IEEE Trans. Power Syst.
**2017**, 32, 1502–1510. [Google Scholar] [CrossRef] - Birchfield, A.B.; Xu, T.; Gegner, K.M.; Shetye, K.S.; Overbye, T.J. Grid structural characteristics as validation criteria for synthetic networks. IEEE Trans. Power Syst.
**2017**, 32, 3258–3265. [Google Scholar] [CrossRef] - Xu, T.; Birchfield, A.B.; Gegner, K.M.; Shetye, K.S.; Overbye, T.J. Application of large-scale synthetic power system models for energy economic studies. In Proceedings of the 2017 50th Hawaii International Conference on System Sciences, Waikoloa, HI, USA, 4 January 2017. [Google Scholar]
- Elyas, S.H.; Wang, Z. A multi-objective optimization algorithm for bus type assignments in random topology power grid model. In Proceedings of the 2016 49th Hawaii International Conference on System Sciences (HICSS), Koloa, HI, USA, 5–8 January 2016; pp. 2446–2455. [Google Scholar]
- Elyas, S.H.; Wang, Z. Improved synthetic power grid modeling with correlated bus type assignments. IEEE Trans. Power Syst.
**2017**, 32, 3391–3402. [Google Scholar] [CrossRef] - Elyas, S.H.; Wang, Z. Statistical analysis of transmission line capacities in electric power grids. In Proceedings of the 2016 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT), Minneapolis, MN, USA, 6–9 September 2016. [Google Scholar]
- Federal Energy Regulatory Commission. Form No. 715—Annual Transmission Planning and Evaluation Report; Federal Energy Regulatory Commission (FERC): Washington, DC, USA, 2015.
- Preparata, F.M.; Shamos, M.I. Computational Geometry: An Introduction; Springer: New York, NY, USA, 1985. [Google Scholar]

**Figure 1.**Probability mass function of substations in a case which have a certain number of buses, for eastern interconnect (EI) (blue), western interconnect cases (WECC) (orange), and 12 subset cases (black).

**Figure 2.**Probability mass function of the amount of load at load buses, for EI (blue), WECC (orange), and 12 subset cases (black).

**Figure 3.**Probability density of generator capacity, with height representing area since it is a logarithmic plot, for EI (blue), WECC (orange), and 12 subset cases (black).

**Figure 5.**Cumulative fraction plot of generator dispatch percentage for EI (blue) and WECC (orange).

**Figure 6.**Probability density of transformer reactance, for EI (blue), WECC (orange), and envelope of 12 subset cases (black), and normal fit (red).

**Figure 7.**Discrete probability transmission line impedance characteristics, for 500 kV lines in the EI.

**Figure 8.**(

**a**) One-line diagram of the ACTIVSg200 test case, with 230 kV lines in blue and 115 kV lines in black. (

**b**) One-line diagram of the ACTIVSg500 test case, with 345 kV lines in red and 138 kV lines in black.

Case | No. Buses | Percent of Transmission Substations with Bus at 69–200 kV | Percent of Transmission Substations with Bus at 201+ kV | Percent of Substations with Load | Percent of Substations with Generation | Ratio of Generation Capacity to Load |
---|---|---|---|---|---|---|

EI | 62,605 | 93% | 15% | 87% | 11% | 1.35 |

WECC | 20,131 | 89% | 22% | 76% | 17% | 1.56 |

Area 1 | 4939 | 99% | 7% | 88% | 4% | 1.19 |

Area 2 | 1505 | 93% | 21% | 79% | 14% | 1.28 |

Area 3 | 3363 | 97% | 13% | 81% | 28% | 1.37 |

Area 4 | 693 | 97% | 8% | 90% | 8% | 1.54 |

Area 5 | 4013 | 94% | 15% | 79% | 10% | 2.04 |

Area 6 | 434 | 98% | 13% | 89% | 18% | 1.33 |

Area 7 | 2762 | 96% | 12% | 83% | 29% | 1.49 |

Area 8 | 768 | 56% | 67% | 88% | 15% | 0.87 |

Area 9 | 3266 | 87% | 21% | 67% | 22% | 1.45 |

Area 10 | 1453 | 73% | 38% | 59% | 39% | 1.28 |

Area 11 | 4322 | 90% | 19% | 90% | 4% | 1.33 |

Area 12 | 1885 | 98% | 7% | 90% | 9% | 1.25 |

High Voltage Level (kV) | MVA Limit | X/R Ratio | |||||
---|---|---|---|---|---|---|---|

10% | Median | 90% | 10% | Median | 90% | ||

EI | 69 | 10 | 42 | 115 | 10 | 20 | 50 |

115 | 22 | 53 | 140 | 16 | 25 | 48 | |

138 | 39 | 83 | 239 | 19 | 30 | 54 | |

161 | 48 | 100 | 276 | 18 | 32 | 68 | |

230 | 63 | 203 | 470 | 25 | 44 | 84 | |

345 | 200 | 444 | 702 | 35 | 60 | 157 | |

500 | 215 | 812 | 1383 | 44 | 70 | 119 | |

WECC | 69 | 7 | 26 | 83 | 10 | 20 | 37 |

115 | 17 | 37 | 118 | 15 | 25 | 50 | |

138 | 15 | 35 | 90 | 18 | 25 | 38 | |

161 | 30 | 63 | 125 | 19 | 27 | 46 | |

230 | 50 | 162 | 304 | 21 | 37 | 79 | |

345 | 160 | 336 | 672 | 33 | 59 | 139 | |

500 | 150 | 600 | 1233 | 32 | 70 | 140 |

Voltage Level (kV) | 90% | Median | 10% |
---|---|---|---|

500 | 0.000210 | 0.000155 | 0.000121 |

345 | 0.000518 | 0.000360 | 0.000198 |

230 | 0.001550 | 0.000945 | 0.000343 |

161 | 0.003780 | 0.001828 | 0.000517 |

138 | 0.006295 | 0.002471 | 0.000596 |

115 | 0.006387 | 0.003398 | 0.000796 |

Voltage Level (kV) | X/R Ratio | MVA Limit | ||||
---|---|---|---|---|---|---|

90% | Median | 10% | 90% | Median | 10% | |

500 | 26.0 | 17.0 | 11.0 | 3464 | 2598 | 1732 |

345 | 16.0 | 12.0 | 9.0 | 1494 | 1195 | 897 |

230 | 12.5 | 9.0 | 6.4 | 797 | 541 | 327 |

161 | 10.0 | 6.0 | 4.1 | 410 | 265 | 176 |

138 | 9.1 | 5.7 | 3.0 | 344 | 223 | 141 |

115 | 8.3 | 4.6 | 2.5 | 255 | 160 | 92 |

**Table 5.**Ratio of lines to substations and line length to minimum spanning tree (MST) at nominal voltage level.

Case | Largest Network 201+ kV | Largest Network 115–200 kV | ||
---|---|---|---|---|

Lines/Substations | Line Length/MST | Lines/Substations | Line Length/MST | |

Area 1 | 1.26 | 2.07 | 1.41 | 2.57 |

Area 2 | 1.29 | 2.49 | 1.25 | 1.84 |

Area 3 | 1.18 | 1.64 | 1.24 | 2.03 |

Area 4 | - | - | 1.21 | 1.95 |

Area 5 | 1.21 | 1.99 | 1.20 | 1.70 |

Area 6 | - | - | 1.15 | 1.43 |

Area 7 | 1.32 | 2.37 | 1.27 | 2.16 |

Area 8 | 1.16 | 1.69 | - | - |

Area 9 | 1.41 | 2.98 | 1.26 | 2.07 |

Area 10 | 1.36 | 2.12 | 1.3 | 1.84 |

Area 11 | 1.2 | 1.85 | 1.21 | 1.83 |

Area 12 | 1.2 | 1.81 | 1.28 | 2.17 |

# | Validation Metric | Criteria | ACTIVSg200 | ACTIVSg500 | ||
---|---|---|---|---|---|---|

1 | Buses per substation | Mean 1.7–3.5 | 1.8 | 2.4 | ||

Exponential decay | See Figure 9 | See Figure 10 | ||||

2 | Percent of substations containing buses in kV range | <200 kV, 85–100% | 100% | 100% | ||

>201 kV, 7–25% | 15.3% | 15% | ||||

3 | Substations with load | 75–90% | 90% | 90% | ||

4 | Load per bus | Mean 6–18 MW | 11 MW | 16 MW | ||

Exponential decay | See Figure 9 | See Figure 10 | ||||

5 | Generation capacity/load | 1.2–1.6 | 1.59 | 1.57 | ||

6 | Substations with generators | 5–25% | 15% | 15% | ||

7 | Generator Capacities | 25–200 MW, 40+% | 47% | 44% | ||

200+ MW, 5–20% | 6% | 16% | ||||

8 | Committed Generators | 60–80% | 78% | 62% | ||

9 | Generators dispatched >80% | 50+% | 63% | 93% | ||

10 | Generator MaxQ/MaxP | 0.40–0.55, >70% | 86% | 93% (incl. 0.38) | ||

11 | Transformer per-unit X, own base. | 80% within [0.05, 0.2] | 230 kV | 115 kV | 345 kV | 138 kV |

98% | 94% | 100% | 95% | |||

12 | Transformer X/R ratio and MVA limits, by kV level (Table 2) | 40% below median | 50/44 | 59/47 | 45/45 | 46/44 |

40% above median | 50/56 | 41/53 | 55/55 | 54/56 | ||

80% within 10–90 range | 90/84 | 85/88 | 100/100 | 97/87 | ||

13 | Line p.u., per-dist. reactance, by kV level (Table 3) | 70% within 10–90 range | 71 | 93 | 100 | 100 |

14 | Line X/R ratio and MVA limits, by kV level (Table 4) | 70% within 10–90 range | 100/100 | 100/100 | 100/100 | 100/100 |

15 | Lines/Substations, by kV level | 1.1–1.4 | 1.24 | 1.22 | 1.22 | 1.22 |

16 | Lines on min. spanning tree | 45–55% | 52% | 50% | 47% | 50% |

17 | Distance of line along Delaunay triangulation, by kV level | 1, 65–80% | 71% | 70% | 68% | 70% |

2, 15–25% | 24% | 25% | 26% | 25% | ||

3+, 3–10% | 5% | 5% | 5% | 5% | ||

18 | Total line length/MST | 1.2–2.2 | 1.49 | 1.80 | 1.74 | 1.83 |

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## Share and Cite

**MDPI and ACS Style**

Birchfield, A.B.; Schweitzer, E.; Athari, M.H.; Xu, T.; Overbye, T.J.; Scaglione, A.; Wang, Z.
A Metric-Based Validation Process to Assess the Realism of Synthetic Power Grids. *Energies* **2017**, *10*, 1233.
https://doi.org/10.3390/en10081233

**AMA Style**

Birchfield AB, Schweitzer E, Athari MH, Xu T, Overbye TJ, Scaglione A, Wang Z.
A Metric-Based Validation Process to Assess the Realism of Synthetic Power Grids. *Energies*. 2017; 10(8):1233.
https://doi.org/10.3390/en10081233

**Chicago/Turabian Style**

Birchfield, Adam B., Eran Schweitzer, Mir Hadi Athari, Ti Xu, Thomas J. Overbye, Anna Scaglione, and Zhifang Wang.
2017. "A Metric-Based Validation Process to Assess the Realism of Synthetic Power Grids" *Energies* 10, no. 8: 1233.
https://doi.org/10.3390/en10081233