# Application of Intelligent Systems in Volt-VAr Centralized Control in Modern Distribution Systems of Electrical Energy

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## Abstract

**:**

## 1. Introduction

#### 1.1. Literature Review

#### 1.2. Article Contribution and Organization

- *
- An alternative solution to the problem of centralized control Volt-VAR in modern ESD was proposed based on ISs techniques;
- *
- The proposed methodology allowed one to determine in a simplified way the solution of the centralized control problem Volt-VAR using different ISs techniques such as ANNs, DTs, and SVMs;
- *
- The software WEKA was used as an important computational tool to solve the problem of centralized Volt-VAR control.

## 2. Intelligent Systems

#### 2.1. Artificial Neural Networks

- *
- Input layer: This is a noncomputational layer in which there is no processing; it is responsible for receiving and propagating input information to the next layer;
- *
- Hidden or intermediate layers: These are computational layers that perform processing; the information is transmitted to them through the connections between the input and output units. These connections save the weights that are multiplied by the inputs, ensuring the network knowledge;
- *
- Output layer: This is made of computational neurons and receives information from the hidden layers providing the response.

#### 2.2. Decision Trees

#### 2.3. Support Vector Machines

## 3. Proposed Methodology

#### Machine Learning Platform

## 4. Tests and Results

#### 4.1. Case A—Validation Process Using Input Data Generated by the MILP Model

#### 4.2. Case B—Validation Process Using Load Flow Results as Input Data

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${P}_{t}^{DG}$ | Vector of active power injections of distributed generators in operation at time t. |

${Q}_{t}^{DG}$ | Vector of reactive power injections of distributed generators in operation at time t. |

${T}_{t}^{CB}$ | Vector of modules in operation of capacitor banks at time t. |

${T}_{t}^{T}$ | Vector of tap steps of transformers with on-load tap changers at time t. |

${P}_{t}^{S}$ | Injection of active power of substation at time t. |

${Q}_{t}^{S}$ | Injection of reactive power of substation at time t. |

${P}_{t}^{D}$ | Demand of active system power at time t. |

${Q}_{t}^{D}$ | Demand of reactive system power at time t. |

${V}_{t}^{DG}$ | Vector of voltage magnitudes at nodes of distributed generators in operation at time t. |

${V}_{t}^{CB}$ | Vector of voltage magnitudes at nodes of capacitor banks in operation at time t. |

${V}_{t}^{T}$ | Vector of voltage magnitudes at nodes controlled by the transformers with tap changer under load and voltage regulator in operation at time t. |

${I}_{t}^{T}$ | Vector of current magnitudes in transformers with tap changer under load and voltage regulator in operation at time t. |

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**Figure 1.**(

**a**) Simple neural network with two input nodes and two output nodes. (

**b**) Simple neural network with two input nodes, one hidden layer with two nodes and two output nodes.

Hidden Layer | Learning Rate | Training Time | Correctly Classified (%) |
---|---|---|---|

40 | 0.3 | 100 | 84.89 |

50 | 0.3 | 200 | 86.47 |

80 | 0.3 | 300 | 87.81 |

82 | 0.3 | 100 | 86.67 |

85 | 0.3 | 100 | 87.86 |

85 | 0.2 | 3000 | 94.91 |

90 | 0.3 | 100 | 86.55 |

100 | 0.3 | 400 | 87.12 |

Demand Variation Percentage (5%) | Demand Variation Percentage (20%) | ||||
---|---|---|---|---|---|

Correctly Classified (%) | Correctly Classified (%) | ||||

DT | SVM | ANN | DT | SVM | ANN |

94.6005 | 94.8744 | 91.2536 | 94.1532 | 94.6685 | 91.3600 |

94.7032 | 95.0799 | 92.3025 | 94.3100 | 94.8141 | 91.2569 |

94.6689 | 95.1484 | 92.0415 | 94.2800 | 94.8589 | 91.4879 |

96.8607 | 95.0571 | 92.1698 | 94.1084 | 94.8701 | 91.0025 |

94.7374 | 98.4475 | 93.4890 | 94.1644 | 95.0045 | 91.4300 |

94.0860 | 94.2204 | 91.4875 | 94.1980 | 94.8477 | 91.2547 |

94.0972 | 94.2316 | 91.4045 | 94.3436 | 94.7581 | 91.5478 |

94.1980 | 94.2428 | 90.2568 | 94.4220 | 94.8701 | 91.2560 |

96.1644 | 94.2540 | 91.4050 | 94.3436 | 94.8801 | 91.2589 |

94.0972 | 94.3100 | 91.2356 | 94.2652 | 95.0180 | 91.3692 |

Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | Day 6 | Day 7 | |
---|---|---|---|---|---|---|---|

MPLIM | 11,352.6 | 10,202.8 | 10,139.1 | 10,441.3 | 9464.2 | 9387.9 | 10,266.4 |

SVM | 11,888.0 | 10,684.1 | 10,617.2 | 10,933.7 | 9910.5 | 9830.7 | 10,750.6 |

DT | 12,090.7 | 10,866.2 | 10,798.3 | 11,120.2 | 10,079.5 | 9998.3 | 10,933.9 |

ANN | 12,288.3 | 11,043.8 | 10,974.7 | 11,301.8 | 10,244.2 | 10,161.7 | 11,112.6 |

MPLIM | SVM | DT | ANN | |
---|---|---|---|---|

Hour | Day 1 | Day 1 | Day 1 | Day 1 |

0 | 63.92 | 69.90 | 71.95 | 71.57 |

1 | 71.78 | 71.95 | 71.78 | 71.78 |

2 | 63.92 | 71.78 | 72.15 | 71.78 |

3 | 71.78 | 71.95 | 72.15 | 83.13 |

4 | 71.95 | 71.95 | 72.15 | 83.13 |

5 | 83.13 | 87.54 | 91.40 | 91.40 |

6 | 562.01 | 586.73 | 586.73 | 586.73 |

7 | 531.70 | 562.01 | 586.73 | 586.73 |

8 | 1121.24 | 1146.07 | 1146.07 | 1159.75 |

9 | 586.73 | 586.73 | 586.73 | 655.90 |

10 | 562.01 | 586.73 | 586.73 | 586.73 |

11 | 562.02 | 586.77 | 586.73 | 586.73 |

12 | 531.70 | 586.77 | 586.73 | 562.01 |

13 | 586.73 | 586.77 | 586.77 | 655.90 |

14 | 531.70 | 586.73 | 562.01 | 562.01 |

15 | 562.01 | 586.73 | 586.77 | 562.01 |

16 | 880.87 | 880.87 | 905.62 | 905.62 |

17 | 507.00 | 531.70 | 531.70 | 586.73 |

18 | 1146.07 | 1159.75 | 1159.75 | 1159.75 |

19 | 1146.07 | 1146.07 | 1159.75 | 1159.75 |

20 | 507.00 | 531.70 | 586.73 | 586.73 |

21 | 343.27 | 383.18 | 485.96 | 485.96 |

22 | 189.56 | 335.69 | 335.69 | 343.26 |

23 | 68.46 | 71.95 | 71.95 | 83.13 |

Total | 11,352.61 | 11,888.01 | 12,090.73 | 12,288.22 |

Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | Day 6 | Day 7 | |
---|---|---|---|---|---|---|---|

MPLIM | 6583.94 | 6831.15 | 6342.78 | 6561.45 | 5284.07 | 6119.19 | 6751.01 |

SVM | 6631.58 | 6967.87 | 6412.27 | 6682.32 | 5496.82 | 5496.82 | 6217.77 |

DT | 6716.04 | 6852.01 | 6344.20 | 6597.66 | 5607.33 | 6254.08 | 6887.78 |

NN | 6588.99 | 6956.06 | 6350.29 | 6625.75 | 5547.43 | 6299.38 | 6843.53 |

MPLIM | SVM | DT | ANN | |
---|---|---|---|---|

Hour | Day 2 | Day 2 | Day 2 | Day 2 |

0 | 66.74 | 66.74 | 66.74 | 66.74 |

1 | 66.74 | 66.74 | 66.74 | 66.74 |

2 | 66.74 | 66.74 | 66.74 | 66.74 |

3 | 63.79 | 63.79 | 63.79 | 63.79 |

4 | 66.74 | 66.74 | 66.74 | 66.74 |

5 | 75.47 | 75.47 | 75.47 | 75.47 |

6 | 282.57 | 282.57 | 282.57 | 282.57 |

7 | 302.68 | 302.68 | 302.68 | 302.68 |

8 | 748.05 | 748.05 | 748.05 | 748.05 |

9 | 253.30 | 253.30 | 253.30 | 253.30 |

10 | 282.57 | 282.57 | 282.57 | 282.57 |

11 | 265.99 | 265.99 | 265.99 | 265.99 |

12 | 502.32 | 502.32 | 502.32 | 502.32 |

13 | 599.18 | 724.41 | 548.41 | 724.08 |

14 | 282,57 | 282,57 | 282,57 | 282,57 |

15 | 253.30 | 253.30 | 253.30 | 253.30 |

16 | 217.30 | 217.30 | 217.30 | 217.30 |

17 | 253.30 | 253.30 | 253.30 | 253.30 |

18 | 748.05 | 748.05 | 748.05 | 748.05 |

19 | 748.05 | 748.05 | 748.05 | 748.05 |

20 | 236.72 | 236.72 | 236.72 | 236.72 |

21 | 236.72 | 236.72 | 236.72 | 236.72 |

22 | 145.67 | 157.17 | 217.30 | 145.67 |

23 | 66.61 | 66.61 | 66.61 | 66.61 |

6831.15 | 6967.87 | 6852.01 | 6956.06 |

SVM | DT | ANN | ||||
---|---|---|---|---|---|---|

AMD (%) | Successes (%) | AMD (%) | Successes (%) | AMD (%) | Successes (%) | |

P1 | 0.6550 | 88.6910 | 0.9820 | 86.3090 | 1.2500 | 77.9760 |

P2 | 0.6840 | 87.5000 | 1.2800 | 83.3330 | 1.3090 | 79.1670 |

Q1 | 0.5360 | 89.2860 | 0.5360 | 89.2860 | 0.6840 | 86.9050 |

Q2 | 0.5060 | 89.8810 | 0.7140 | 85.7140 | 0.7140 | 85.7140 |

CB1 | 0.1190 | 97.6190 | 0.2380 | 95.2380 | 0.2080 | 95.8330 |

CB2 | 0.1786 | 97.0238 | 0.4464 | 92.8571 | 0.5060 | 91.0714 |

CB3 | 0.0000 | 100.0000 | 0.0000 | 100.0000 | 0.0000 | 100.0000 |

CB4 | 0.0893 | 98.2143 | 0.1786 | 96.4286 | 0.1786 | 96.4286 |

CB5 | 0.1190 | 97.6190 | 0.2679 | 94.6429 | 0.2976 | 94.0476 |

VR1 | 0.0000 | 100.0000 | 0.0000 | 100.0000 | 0.0000 | 100.0000 |

VR2 | 0.0000 | 100.0000 | 0.0000 | 100.0000 | 0.0000 | 100.0000 |

VR3 | 0.3571 | 92.8571 | 0.4167 | 91.6667 | 0.7738 | 85.7143 |

VR4 | 0.0000 | 100.0000 | 0.0000 | 100.0000 | 0.0000 | 100.0000 |

0.2495 | 95.2839 | 0.3892 | 93.4982 | 0.4556 | 91.7582 |

0–20% | 20–40% | 40–60% | 60–80% | 80–100% | |
---|---|---|---|---|---|

Minimum voltage | 161 | 2 | 1 | 0 | 4 |

Energy losses | 148 | 12 | 4 | 1 | 3 |

0–20% | 20–40% | 40–60% | 60–80% | 80–100% | |
---|---|---|---|---|---|

Voltage Minimum | 139 | 4 | 4 | 0 | 11 |

Energy losses | 127 | 12 | 11 | 2 | 6 |

0–20% | 20–40% | 40–60% | 60–80% | 80–100% | |
---|---|---|---|---|---|

Minimum voltage | 120 | 2 | 6 | 0 | 7 |

Energy losses | 103 | 10 | 10 | 4 | 8 |

Variation | ||||
---|---|---|---|---|

5% | 10% | 15% | 20% | |

Minimum voltage | 95.83 | 82.74 | 75.60 | 71.43 |

Energy losses | 88.10 | 75.60 | 66.07 | 61.31 |

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## Share and Cite

**MDPI and ACS Style**

Florez, H.A.R.; López, G.P.; Carreño-Franco, E.M.; López-Lezama, J.M.; Muñoz-Galeano, N.
Application of Intelligent Systems in Volt-VAr Centralized Control in Modern Distribution Systems of Electrical Energy. *Electronics* **2022**, *11*, 446.
https://doi.org/10.3390/electronics11030446

**AMA Style**

Florez HAR, López GP, Carreño-Franco EM, López-Lezama JM, Muñoz-Galeano N.
Application of Intelligent Systems in Volt-VAr Centralized Control in Modern Distribution Systems of Electrical Energy. *Electronics*. 2022; 11(3):446.
https://doi.org/10.3390/electronics11030446

**Chicago/Turabian Style**

Florez, Hugo A. R., Gloria P. López, Edgar M. Carreño-Franco, Jesús M. López-Lezama, and Nicolás Muñoz-Galeano.
2022. "Application of Intelligent Systems in Volt-VAr Centralized Control in Modern Distribution Systems of Electrical Energy" *Electronics* 11, no. 3: 446.
https://doi.org/10.3390/electronics11030446