# A Probabilistic Ensemble Prediction Method for PV Power in the Nonstationary Period

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## Abstract

**:**

## 1. Introduction

- (1)
- Considering the non-stationary nature of PV power output, the differential theory based on irradiance and power’s ratio is proposed to preprocess the PV historical data.
- (2)
- The Stack-LSTM model, which based on LSTM and Stacking learning, is put forward as a new point prediction model to improve the modeling accuracy.
- (3)
- The multi-objective calibration of ensemble probabilistic photovoltaic power forecasting model (MLBN) is proposed, which can improve prediction accuracy by a large number and help decision-makers control the changes in the power grid planning and scheduling.

## 2. Method Introduction

#### 2.1. Discrimination Method for Radiation Power Ratio Difference (DM)

#### 2.2. Point Prediction Model

- (1)
- Dividing the data set $I={\left\{{x}_{i},{y}_{i}\right\}}_{i=1}^{m}$ into n subsets ${I}_{1},{I}_{2},......{I}_{\mathrm{n}}$;
- (2)
- Based on these n subsets, they are input into the LSTM algorithm to obtain the first prediction result ${w}_{1},{w}_{2},......{w}_{n}$;
- (3)
- The first prediction result is added as an additional feature to the original feature to form a new input feature ${x}_{1}^{\prime},{x}_{2}^{\prime},......{x}_{l}^{\prime}=({x}_{1},{x}_{2},......{x}_{l},{w}_{1},{w}_{2},......{w}_{n})$, which is then input into the LSTM algorithm again to perform the second prediction and obtain a higher precision result [19].

#### 2.3. Interval Prediction Model

#### 2.4. Optimization of the Ensemble Prediction Model

- (1)
- Input selection. Select three points: the deterministic point prediction result, the upper and lower bounds of the interval distribution from the interval prediction, and the actual output value about this point as the input variables of the network.
- (2)
- Model construction. By inputting the relevant variables selected above, a basic NSGA-II network model is constructed to perform multi-objective optimization. The optimization objectives are (PINAW) the smallest interval width and (PICP) the largest interval coverage. Owing to these two indicators are contradictory in the same network, the optimization constraint must weigh them, and choose the smallest interval width under the maximum interval coverage as the restrictions.
- (2)
- Model validation. After experiments in the subsequent part of this article, the feasibility of the model would be verified.

#### 2.5. MIC Theory

## 3. MLBN Model Development

#### 3.1. Model Construction

#### 3.2. Model Prediction Evaluation Index

## 4. Results and Discussion

#### 4.1. Data Description

#### 4.2. Model Input Selection

#### 4.3. Point Prediction Result

#### 4.4. Interval Prediction Result

#### 4.5. Optimization of Ensemble Prediction Results

## 5. Conclusions

- (1)
- The model combines with data preprocessing, non-stationary period discrimination, feature extraction, deterministic prediction, uncertainty prediction, and optimization integration modules to construct a difference in power ratio discrimination method and a Stack-LSTM point prediction model. The proposed MLBN model combines mainstream deterministic forecasting models and interval forecasting models, fusing point forecasting and interval forecasting, and performing multi-objective optimization on two different forms of forecasting results.
- (2)
- After improving the prediction in this article, the prediction accuracy of the Stack-LSTM model is 20% higher than that of the original LSTM model, and compared with the traditional ANN network, the accuracy is improved by nearly 30%, verifying the feasibility and practicality of the model constructed in this article.
- (3)
- Under the PICP of 85%, 90% and 95%, the interval forecast can predict the possible output of this point as far as possible in the non-stationary output period, which enables the dispatching system to timely adjust the dispatching strategy and ensure the safe and stable operation of the power grid to the greatest extent.
- (4)
- Compared with the unoptimized prediction model, the interval width is reduced by 10–20% and the prediction accuracy is improved by at least 10% under the uniform interval coverage, which significantly improves the prediction accuracy of photovoltaic power prediction and verifies the feasibility of the proposed method.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviation

PV | Photovoltaic |

LSTM | long-short-term memory neural network |

Stack-LSTM | Stacking- long-short-term memory neural network |

LSTM-RNN | long-short-term recurrent neural network |

ELM | extreme learning machine |

LUBE | lower and upper bound estimation |

DM | Discrimination method for radiation power ratio difference |

NSGA-II | Non-dominated Sorting Genetic Algorithm-II |

MIC | Maximal Information Coefficient |

RNN | recurrent neural network |

MI | Mutual Information |

MAPE | average absolute percentage error |

RMSE | root mean square error |

PICP | prediction interval coverage probability |

PINAW | prediction interval normalized average width |

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**Figure 5.**BAYES neural network. (

**a**) BAYES neural network structure diagram; (

**b**) Schematic diagram for the hidden layer of the Bayesian neural network.

Number | Variate | Whether |
---|---|---|

1 | The actual output value of photovoltaic power station | |

2 | Wind speed | √ |

3 | Wind direction | √ |

4 | Temperature | √ |

5 | Humidity | √ |

6 | Intensity | |

7 | Irradiance | √ |

Number | Text | ANN (%) | LSTM (%) | Stack-LSTM (%) | Rate of Rise |
---|---|---|---|---|---|

Station 1 | 1 | 1.10306 | 0.72771 | 0.50218 | 0.22553 |

2 | 1.12407 | 0.73006 | 0.49782 | 0.23224 | |

3 | 1.08590 | 0.72827 | 0.50116 | 0.22711 | |

4 | 1.12504 | 0.72735 | 0.49835 | 0.21900 | |

Station 2 | 1 | 0.95952 | 0.70039 | 0.51487 | 0.18552 |

2 | 0.95643 | 0.71264 | 0.51035 | 0.20229 | |

3 | 0.96076 | 0.70982 | 0.50273 | 0.20709 | |

4 | 0.94895 | 0.69331 | 0.51640 | 0.17691 |

Number | PICP | Reference [18] | Before PINAW | After PINAW | Rate of Rise (%) |
---|---|---|---|---|---|

Station 1 | 85% | 9.0342 | 7.4852 | 6.2607 | 17.56 |

90% | 9.4976 | 7.7087 | 6.8395 | 12.84 | |

95% | 10.1306 | 8.2711 | 7.7403 | 10.41 | |

Station 2 | 85% | 9.0342 | 7.2975 | 6.4453 | 13.38 |

90% | 9.4976 | 7.6542 | 7.0842 | 9.86 | |

95% | 10.1306 | 7.9583 | 7.2574 | 9.65 |

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**MDPI and ACS Style**

An, Y.; Dang, K.; Shi, X.; Jia, R.; Zhang, K.; Huang, Q. A Probabilistic Ensemble Prediction Method for PV Power in the Nonstationary Period. *Energies* **2021**, *14*, 859.
https://doi.org/10.3390/en14040859

**AMA Style**

An Y, Dang K, Shi X, Jia R, Zhang K, Huang Q. A Probabilistic Ensemble Prediction Method for PV Power in the Nonstationary Period. *Energies*. 2021; 14(4):859.
https://doi.org/10.3390/en14040859

**Chicago/Turabian Style**

An, Yuan, Kaikai Dang, Xiaoyu Shi, Rong Jia, Kai Zhang, and Qiang Huang. 2021. "A Probabilistic Ensemble Prediction Method for PV Power in the Nonstationary Period" *Energies* 14, no. 4: 859.
https://doi.org/10.3390/en14040859