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Statistical Inference for Visualization of Large Utility Power Distribution Systems

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## Abstract

**:**

## 1. Introduction

## 2. Analysis and Validation in Multi-Agent Smart Grids

#### 2.1. Time-Sequential Simulation

- Alternative solution methods;
- Fault location;
- Network reconfiguration;
- Power quality;
- Short-circuit analysis;
- State estimation;
- Steady state power flow;
- System’s planning;
- System’s reliability;
- Voltage regulation.

- Advanced voltage control technologies;
- Controller’s interoperability;
- Custom power devices;
- Cyber-physical analysis;
- Distributed control schemes;
- Distributed generation;
- Distribution management strategies;
- Electric transportation analysis;
- Energy efficiency improvements;
- Energy storage;
- Maintenance scheduling;
- Microgrid operation;
- Power systems communications;
- Resiliency and protection;
- Smart metering applications.

^{6}voltage computation results in one hour of operation, 421.3 × 10

^{6}for one day, and 153.8 × 10

^{9}for one year. The comparative analysis of multiple operative conditions usually requires independent simulations; therefore, the validation based on long-term simulation is restricted by the capability to generate, process and analyze big amounts of data. This characteristic of time-sequential simulations constitutes a major challenge for validations on future distribution systems.

#### 2.2. Real-Time Simulation

#### 2.3. Visualization of Large Utility Power Distribution Systems

#### 2.4. The Problem of Worst Voltage Condition Allocation

## 3. Meaningful Visualization for Voltage Analysis

#### 3.1. Statistical Inference

#### 3.2. Time Sequential Visualization

## 4. Test Case on Large Feeder and Discussion

^{®}(Version 8.6.0, The MathWorks, Natick, MA, USA) in co-simulation with OpenDSS.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Voltage profile for IEEE 8500 nodes test feeder. One phase per color, where continuous lines represent primary voltages and dashed lines represent secondary voltages.

**Figure 3.**Three-dimensional visualization for time-sequential simulation. Warmer colors represent higher voltage magnitudes.

**Figure 4.**Time-sequential simulation of 2354 loads. Each load line is associated with a different color.

**Figure 5.**Voltage magnitude (

**a**) and geographical locations (

**b**) for loads of interest in time-sequential simulation.

Reference | Nodes | Electrical Simulation | Validation Variable | Visualization | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Snapshot | Time-Sequential | Real-Time | V | I | P | Other | Figure | Table | ||

[7] | 123 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||

[8] | 123 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||

[9] | 37 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||

[10] | 8500 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||

[11] | 8500 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||

[12] | 8500 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||

[13] | 8500 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||

[14] | 7000 ^{a} | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||

[15] | 200 ^{a} | ✓ | ✓ | ✓ | ✓ | ✓ | ||||

[16] | 8500 | ✓ | ✓ | ✓ | ||||||

[17] | 8500 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||

[18] | 8500 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||

[19] | 8500 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||

[20] | 738 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||

[21] | 9 ^{a} | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||

[22] | 8500 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||

[23] | 13 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||

[24] | 400 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||

[25] | >200 ^{a} | ✓ | ✓ | ✓ | ✓ | |||||

[26] | 15 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||

[27] | 6999 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||

[28] | 60 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||

[29] | 8500 | ✓ | ✓ | ✓ | ✓ | ✓ | ||||

[30] | 60 | ✓ | ✓ | ✓ | ✓ | ✓ |

^{a}Approximate count of calculated node voltages.

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**MDPI and ACS Style**

Hernandez, M.; Ramos, G.; Padullaparti, H.V.; Santoso, S.
Statistical Inference for Visualization of Large Utility Power Distribution Systems

. *Inventions* **2017**, *2*, 11.
https://doi.org/10.3390/inventions2020011

**AMA Style**

Hernandez M, Ramos G, Padullaparti HV, Santoso S.
Statistical Inference for Visualization of Large Utility Power Distribution Systems

. *Inventions*. 2017; 2(2):11.
https://doi.org/10.3390/inventions2020011

**Chicago/Turabian Style**

Hernandez, Miguel, Gustavo Ramos, Harsha V. Padullaparti, and Surya Santoso.
2017. "Statistical Inference for Visualization of Large Utility Power Distribution Systems

" *Inventions* 2, no. 2: 11.
https://doi.org/10.3390/inventions2020011