# An Ultra-Short-Term PV Power Forecasting Method for Changeable Weather Based on Clustering and Signal Decomposition

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^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Weather Clustering Method Based on Photovoltaic Power Fluctuation Characteristics

#### 2.1. Clear-Sky Normalization

#### 2.2. AP Clustering Algorithm

_{t}(i, j) is the degree to which points other than data point k at time t are suitable as the clustering center of point i, and the values in r(i, k) are all greater than zero. a

_{t}(i, j) is the degree to which point i selects other points, except point k as the clustering center at time t, and the initial value is zero.

_{t+}

_{1}(i, k) is the degree to which point i selects point k as an appropriate clustering center at t + 1 time, and r

_{t+}

_{1}(k, k) is the probability of point k being the clustering center.

## 3. Photovoltaic Power Ultra-Short-Term Forecast Portfolio Model

#### 3.1. CEEMDAN Decomposition Algorithm

_{i}(·) be the i-th modal component obtained by EMD decomposition, ω

^{j}(t) be the j-th added white noise, ε

_{0}be the standard deviation of the white noise, and x(t) be the original power signal. The calculation steps of the CEEMDAN algorithm are as follows [31]:

_{1}

^{j}and the residual signal r

_{1}(t), we can obtain the first-order IMF component IMF

_{1}(t) resulting from CEEMDAN decomposition by finding the mean value of IMF

_{1}

^{j}.

_{1}(t), continue the EMD decomposition to obtain the second-order IMF component IMF

_{2}

^{j}and the residual r

_{2}(t), and derive the second-order component IMF

_{2}(t).

_{n}

^{j}and the residual r

_{n}(t) to find the nth-order component IMF

_{n}(t).

_{n−1}is the weight coefficient of the n-1th-order white noise.

#### 3.2. BiLSTM Neural Network

_{t}, ${\overrightarrow{h}}_{t}$, and ${\overleftarrow{h}}_{t}$ denote the input data at time t, the output of the forward LSTM implicit layer, and the output of the reverse LSTM implicit layer, respectively, and α and β are constant coefficients that denote the weights corresponding to ${\overrightarrow{h}}_{t}$ and ${\overleftarrow{h}}_{t}$, respectively.

#### 3.3. Combined Model Forecasting Process

- Clear-sky normalization: Using the PV power history data of the whole year as the dataset, the maximum value of each moment in each month in the dataset was extracted to form the monthly clear-sky curve, which represents the standard “clear-sky days” of each month. The historical power data and the preliminary forecasted value of future power were normalized with the clear-sky curve as the standard, and the CSPC (including the real value in the past and the forecasted value in the future) was obtained;
- AP weather clustering: The mean and variance of daily CSPC were calculated and subsequently used as clustering indicators for AP clustering, classifying data points into three weather types based on PV output characteristics: sunny, cloudy, and changeable weather;
- Combined CEEMDAN-BiLSTM model: The CEEMDAN decomposition algorithm was used to decompose the changeable day data into n IMF components and one residual component in order to reduce the non-stationarity of the data, and they were then input into the BiLSTM network for the forecasting;
- Clear-sky denormalization: The CSPC was denormalized according to the clear-sky curve in order to obtain the final power forecasting results.

## 4. Results and Analysis

#### 4.1. Data Description

#### 4.2. Model Evaluation Criteria

#### 4.3. Experimental Results and Analysis

_{1}to IMF

_{4}showed the characteristics of high frequency and strong randomness, which makes it difficult to forecast, but it cannot be removed as the randomness component because of its large amplitude change, otherwise it will affect the forecasting accuracy. IMF

_{5}to IMF

_{12}had a lower frequency and certain periodic change pattern, which makes the forecasting less difficult; Res was the trend component, and its trend indicated the overall decreasing trend of PV power. Therefore, it is important to build BiLSTM models for each component separately for training and forecasting.

## 5. Conclusions

- The normalized daily CSPC could reflect the weather changes that affect photovoltaic power generation to a certain extent. In this paper, the weather types were divided into sunny days, cloudy days, and variable days, which can be further divided into more complex types based on the curve characteristics of the daily CSPC.
- Due to the complexity of changeable days, the PV power curve has a very strong non-stationary feature, which is liable to cause low forecasting accuracy. The PV output power curve in a day can be linearized by the clear-sky normalization method, the method of modal decomposition, and the strategy of forecasting each component separately are helpful to improve the accuracy.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Comparison of the PV power and the CSPC for the sunny, cloudy, and changeable days for each season.

Method | Changeable Day | ||
---|---|---|---|

MAE/MW | MAPE/% | RMSE/MW | |

BP | 0.421 | 68.755 | 0.682 |

BiLSTM | 0.226 | 36.643 | 0.382 |

CEEMDAN-BiLSTM | 0.096 | 15.221 | 0.133 |

The proposed method | 0.029 | 2.771 | 0.055 |

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**MDPI and ACS Style**

Zhang, J.; Hao, Y.; Fan, R.; Wang, Z. An Ultra-Short-Term PV Power Forecasting Method for Changeable Weather Based on Clustering and Signal Decomposition. *Energies* **2023**, *16*, 3092.
https://doi.org/10.3390/en16073092

**AMA Style**

Zhang J, Hao Y, Fan R, Wang Z. An Ultra-Short-Term PV Power Forecasting Method for Changeable Weather Based on Clustering and Signal Decomposition. *Energies*. 2023; 16(7):3092.
https://doi.org/10.3390/en16073092

**Chicago/Turabian Style**

Zhang, Jiaan, Yan Hao, Ruiqing Fan, and Zhenzhen Wang. 2023. "An Ultra-Short-Term PV Power Forecasting Method for Changeable Weather Based on Clustering and Signal Decomposition" *Energies* 16, no. 7: 3092.
https://doi.org/10.3390/en16073092