# A New Prediction Model for Transformer Winding Hotspot Temperature Fluctuation Based on Fuzzy Information Granulation and an Optimized Wavelet Neural Network

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Fuzzy Information Granulation

_{1}, t

_{2}, …, t

_{n}] is considered to be a time window in data fuzzification. Additionally, the objective is to establish a fuzzy particle P on the basis of T, that is, to determine the function:

- (1)
- Determine the mean value R. R = median(T) where T is the time series put in ascending order.
- (2)
- Determine the lower bound LOW.$$MaximizeQ(LOW)=\frac{{\displaystyle {\sum}_{{t}_{k}\le R}A({t}_{k})}}{R-LOW}.$$
- (3)
- Determine the upper bound UP.$$MaximizeQ(UP)=\frac{{\displaystyle {\sum}_{{t}_{k}R}A({t}_{k})}}{UP-R}.$$
- (4)
- Determine the fuzzy particle P.$$P=(LOW,R,UP).$$

## 3. Chaotic Particle Swarm Optimized Wavelet Neural Network

_{1}, …, x

_{i}, …, x

_{n}} is the input of WNN as well as the TWHT historical data after fuzzy granulation; y is the prediction output data of WNN; w

_{ij}is the weight coefficient from the input layer to the hidden layer; w

_{j}is the weight coefficient from the hidden layer to the output layer; Ψ is the excitation function of the hidden layer nodes, and Morlet-base wavelet function is used here.

_{i}(i = 1, 2, …, n), the input to the jth hidden layer node is:

_{j}is the stretching factor and b

_{j}is the translation factor. Considering the Morlet-base wavelet function.

^{−x}). So the final prediction result of the model can be expressed as:

_{P}and y

_{P}are, respectively, the measured data and the predicted data for the Pth sample.

_{ij}and w

_{j}, the stretching factor a

_{j}, and the translation factor b

_{j}. Therefore, it is necessary to select reasonable model parameters. The traditional WNN uses the gradient descent method to select parameters. However, the convergence is slow and it cannot effectively search for the global optimal result [16,17,18]. To solve this problem, this paper introduces the chaotic particle swarm optimization (CPSO).

- (1)
- The randomness of the initialization process may result in inferior solutions, affecting the convergence of the evolutionary process.
- (2)
- The solution obtained by this algorithm may be a local optimal solution rather than a global optimal solution.

_{0}< 1, it will generate a complete chaotic series. Therefore, any arbitrary initial value z

_{0}(0 < z

_{0}< 1) can generate a chaotic series (z

_{1}, z

_{2}, z

_{3}, …) by iteration.

_{ij}, the output weight w

_{j}, the stretching factor a

_{j}, and the translation factor b

_{j}, which are the parameters that need to be optimized, are taken as the position vectors of each particle, as shown in

- (1)
- Initialize the parameters to generate a random D-dimensional vector (z
_{1}= (z_{11}, z_{12}, …, z_{1D})) with the value of each component being between 0 and 1. Get N vectors z_{1}, z_{2}, …, z_{n}by iteration according to Equation (9). Additionally, transform the components of each vector into the corresponding value range. - (2)
- Call the WNN to obtain the fitness value of the particles. Select M particles from the N populations to form the initial population. Additionally, generate the initial velocity of the M particles by chaotic series.
- (3)
- Update the individual extremum pBest if the particle fitness value is superior to pBest. Additionally, update the global extremum gBest if the particle fitness value is superior to gBest. Then update the particle’s position and velocity.
- (4)
- Perform chaotic optimization to the current optimal position P
_{gBest}= (p_{g}_{1}, p_{g}_{2}, …, p_{gD}). Additionally, map P_{gBest}to 0–1 according to:$${y}_{i}=\frac{{p}_{gi}-{p}_{\mathrm{min}}}{{p}_{\mathrm{max}}-{p}_{\mathrm{min}}},i=1,2,\dots ,D.$$_{1}, y_{2}, …, y_{D}]. The chaotic series Y_{1}, Y_{2}, …, Y_{m}is generated after m times iterations by Logistic equation. The chaotic series is then mapped back to the original solution space according to:$${P}_{gj}^{*}=({p}_{\mathrm{max}}-{p}_{\mathrm{min}})\times {Y}_{j}+{p}_{\mathrm{min}},j=1,2,\dots ,m.$$_{g}_{1}*, P_{g}_{2}*, …, P_{gm}*. - (5)
- Calculate the fitness value of the new solution and replace the position of any particle in the current population with the best solution P*.
- (6)
- Determine whether the termination condition is reached. If not, return to step (3) to continue iteration. Otherwise, the flow terminates and the selected parameters are obtained.

## 4. Prediction Model for Transformer Winding Hotspot Temperature Fluctuation Range

- (1)
- Extract the sample data. Determine the size of granulation time window according to the sample data. The granulation data should be able to describe the trend of the original sample data. Perform FIG to sample data to obtain LOW, R, and UP.
- (2)
- If the amount of data is huge, the output layer node shall be determined according to forecast demand. The input layer node n shall be determined according to the intrinsic regularity of the historical data. Additionally, the number of hidden layer node shall be m = 2n + 1.If the amount of data to be processed is limited, the output layer node shall be determined according to forecast demand, while the input layer node and the hidden layer node shall be determined by traversing method.
- (3)
- The structural parameters that need to be optimized are determined when the input layer, the hidden layer, and the output layer are determined. Encode the optimization object according to Equation (13), and take Equation (11) to be the fitness value function. Screen the structural parameters of the WNN by CPSO.
- (4)
- Use the designed WNN to predict LOW, R, and UP to obtain the fluctuation range of the TWHT.
- (5)
- Evaluate the performance of the model by the mean square error (MSE), the mean absolute error (MAE), and the correlation coefficient (r), calculated as:$$MSE=\frac{1}{N}\sqrt{{\displaystyle \sum _{i=1}^{N}{({y}_{i}-{\widehat{y}}_{i})}^{2}}},$$$$MAE=\frac{1}{N}{\displaystyle \sum _{i=1}^{N}\left|{y}_{i}-{\widehat{y}}_{i}\right|},$$$$r=\frac{Cov(y,\widehat{y})}{\sqrt{D(y)}\sqrt{D(\widehat{y})}}.$$

## 5. Case Study

#### 5.1. Fuzzy Information Granulation

#### 5.2. Establishment of Optimized WNN Prediction Model

- (1)
- The selection of wavelet function.
- (2)
- The number of nodes for the input layer and the hidden layer.
- (3)
- The selection of the input weight w
_{ij}, the output weight w_{j}, the translation factor b_{j}, and the stretching factor a_{j}.

#### 5.3. Comparison of Four Prediction Models

#### 5.4. Comparison of the Predicted Fluctuation Range with the Measured Data

## 6. Conclusions

- (1)
- Information granulation can extract useful information from the raw data, which reduces the complexity of target data. Additionally, the wavelet neural network (WNN) has a strong nonlinear mapping capability. In this paper, the two methods are combined to make effective predictions of the transformer winding hotspot temperature fluctuation range.
- (2)
- By designing the WNN according to the field data, we obtain a superior prediction performance compared with various prediction models. The feasibility of the FIG-CPSO-WNN model for predicting the transformer winding hotspot temperature fluctuation range is thereby demonstrated.
- (3)
- The proposed model has a high prediction accuracy and guiding significance to the operation and maintenance of transformers. The new model can not only be used in the prediction of transformer winding hotspot temperature fluctuation range, but also provides ideas for prediction modeling in other areas.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 7.**(

**a**) Comparison of LOW predictions; (

**b**) comparison of R predictions; (

**c**) comparison of UP predictions.

Rated Parameters | Basic Structural Parameters | ||
---|---|---|---|

rated capacity | 24/24/16 MVA | oil weight | 62,000 kg |

rated voltage | 220/115/37 kV | winding weight | 39,482 kg |

rated current | 630/1205/2497 A | core weight | 99,658 kg |

rated frequency | 50 Hz | tank length | 10 m |

connection type | YNyn0d11 | tank width | 2.5 m |

cooling method | ONAN | tank height | 4 m |

Serial Number | w_{ij} | a_{j} | b_{j} | w_{j} |
---|---|---|---|---|

1 | 0.8199 | 0.3208 | 0.1225 | 0.3837 |

2 | 0.2874 | 0.4802 | 0.6329 | 0.6052 |

3 | 0.8830 | 0.2729 | 0.9809 | 0.5076 |

4 | 0.5415 | 0.5215 | 0.0292 | 0.3290 |

5 | 0.5623 | 0.2805 | 0.4745 | 0.6701 |

6 | 0.9254 | 0.2475 | 0.7413 | 0.4753 |

Prediction Model | SVR | Elman | WNN | FIG-CPSO-WNN | |
---|---|---|---|---|---|

MSE | 1.3812 | 1.7679 | 1.1170 | 0.8385 | |

LOW | MAE | 1.2786 | 1.2362 | 1.0265 | 0.7290 |

r | 0.9379 | 0.9708 | 0.9457 | 0.9681 | |

MSE | 1.1378 | 1.6338 | 0.9209 | 0.6830 | |

R | MAE | 0.9269 | 1.2716 | 0.7743 | 0.5954 |

r | 0.9785 | 0.9863 | 0.9665 | 0.9689 | |

MSE | 1.092 | 1.8314 | 1.2137 | 0.9779 | |

UP | MAE | 0.9432 | 1.5108 | 1.1000 | 0.8828 |

r | 0.9725 | 0.9946 | 0.9483 | 0.9729 |

Time Window | Measured Data | Predicted Data | ||||
---|---|---|---|---|---|---|

MIN | MEAN | MAX | LOW | R | UP | |

1 | 57.1 | 57.2 | 57.4 | 55.8 | 56.1 | 55.6 |

2 | 56.7 | 56.8 | 57 | 55.8 | 56 | 55.6 |

3 | 56.4 | 56.5 | 56.6 | 55.6 | 55.9 | 55.7 |

4 | 56.1 | 56.2 | 56.2 | 55.6 | 56.1 | 55.9 |

5 | 56.3 | 56.3 | 57.2 | 55.6 | 56 | 55.7 |

6 | 57.9 | 60 | 61.9 | 55.8 | 59.4 | 60.9 |

7 | 62.8 | 62.8 | 62.9 | 61.9 | 61.7 | 62.1 |

8 | 62 | 62.5 | 62.9 | 61.7 | 61.8 | 62 |

9 | 60 | 61 | 61.7 | 60 | 61.2 | 60.7 |

10 | 59 | 59.4 | 59.6 | 58.6 | 59.7 | 60.3 |

11 | 58.2 | 58.8 | 60 | 56.7 | 58.3 | 58.3 |

12 | 56 | 57 | 57.6 | 56.1 | 56.8 | 56.2 |

Evaluation Index | LOW | R | UP |
---|---|---|---|

MSE | 0.9836 | 0.6318 | 1.1951 |

MAE | 0.7917 | 0.5417 | 1.1167 |

r | 0.9666 | 0.9823 | 0.9692 |

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**MDPI and ACS Style**

Zhang, L.; Zhang, W.; Liu, J.; Zhao, T.; Zou, L.; Wang, X.
A New Prediction Model for Transformer Winding Hotspot Temperature Fluctuation Based on Fuzzy Information Granulation and an Optimized Wavelet Neural Network. *Energies* **2017**, *10*, 1998.
https://doi.org/10.3390/en10121998

**AMA Style**

Zhang L, Zhang W, Liu J, Zhao T, Zou L, Wang X.
A New Prediction Model for Transformer Winding Hotspot Temperature Fluctuation Based on Fuzzy Information Granulation and an Optimized Wavelet Neural Network. *Energies*. 2017; 10(12):1998.
https://doi.org/10.3390/en10121998

**Chicago/Turabian Style**

Zhang, Li, Wenfang Zhang, Jinxin Liu, Tong Zhao, Liang Zou, and Xinghua Wang.
2017. "A New Prediction Model for Transformer Winding Hotspot Temperature Fluctuation Based on Fuzzy Information Granulation and an Optimized Wavelet Neural Network" *Energies* 10, no. 12: 1998.
https://doi.org/10.3390/en10121998