# Effect of Prediction Error of Machine Learning Schemes on Photovoltaic Power Trading Based on Energy Storage Systems

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## Abstract

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## 1. Introduction

## 2. Background

#### 2.1. Artificial Neural Networks

#### 2.2. Support Vector Machine

## 3. PV Output Power Prediction

#### 3.1. Data for PV Output Power Prediction

#### 3.2. Prediction Results for PV Output Power

#### 3.3. Estimation of Prediction Error Distribution

## 4. ESS-Based PV Power Trading in Energy Markets

#### 4.1. The Importance of the ESS Role for PV Power Trading

#### 4.2. Participation of PV Producers in LMP Markets

#### 4.3. Estimation of Deviation Penalties

#### 4.4. Operation and Sizing of Energy Storage Systems

## 5. Case Study

#### 5.1. ESS Sizing for Machine Learning Prediction Schemes

#### 5.2. Assessment of the Profit for the PV Power Producers

#### 5.3. Benefit-Cost Analysis (BCA) for the ESS in PV Power Trading

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 8.**Operation of the ESS for the ANN scheme with varying time intervals of day time (Tolerance limit = 5%).

**Figure 9.**Operation of the ESS for the SVM scheme with varying time intervals of day time (Tolerance limit = 5%).

Meteorological Parameters | Value Range |
---|---|

Irradiance $[{\mathrm{W}/\mathrm{m}}^{2}]$ | 0–1083 |

Sunshine Duration | 7:00 A.M. to 6:00 P.M. |

Cloud Cover | 0–10 |

Sunshine [hour] | 0–1 |

Humidity [%] | 10–100 |

Precipitation [mm/h] | 0–40 |

Air Temperature [${\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$] | −16–37 |

Wind Speed [m/s] | 0–11 |

Prediction Scheme | $\mathit{\mu}$ | $\mathit{\sigma}$ | $\mathit{\nu}$ |
---|---|---|---|

ANN | −0.0001 | 0.0715 | 10.7179 |

SVM | 0.0001 | 0.0403 | 3.02911 |

**Table 3.**The average amount of the hourly exchanged power [kW] of ESS both the ANN and SVM schemes for a 30-MW PV system (Tolerance limit = 5%).

Power Capacity | ANN | SVM |
---|---|---|

5% | 501.56 | 234.90 |

10% | 707.99 | 301.80 |

15% | 793.95 | 322.45 |

Scheme | Power Capacity | 0% | 2% | 4% | 6% | 8% | 10% |
---|---|---|---|---|---|---|---|

5% | 0.74 | 0.72 | 0.67 | 0.63 | 0.58 | 0.56 | |

ANN | 10% | 1.37 | 1.26 | 1.19 | 1.15 | 1.10 | 1.07 |

15% | 1.83 | 1.77 | 1.70 | 1.65 | 1.56 | 1.48 | |

5% | 0.62 | 0.45 | 0.33 | 0.28 | 0.23 | 0.22 | |

SVM | 10% | 0.84 | 0.61 | 0.51 | 0.44 | 0.43 | 0.34 |

15% | 0.93 | 0.78 | 0.63 | 0.52 | 0.45 | 0.40 |

**Table 5.**Hourly deviation penalties [$/h] of both ANN and SVM schemes with different power capacities and tolerance limits.

Scheme | Power Capacity | 0% | 2% | 4% | 6% | 8% | 10% |
---|---|---|---|---|---|---|---|

ANN | No ESS | 266.27 | 257.01 | 231.48 | 195.38 | 155.57 | 117.81 |

5% | 214.32 | 175.54 | 136.16 | 100.88 | 70.02 | 49.95 | |

10% | 117.81 | 85.59 | 60.17 | 41.26 | 27.80 | 18.52 | |

15% | 49.95 | 33.93 | 22.71 | 15.07 | 9.96 | 6.57 | |

SVM | No ESS | 190.99 | 176.36 | 143.32 | 109.05 | 81.52 | 61.39 |

5% | 125.60 | 94.30 | 70.62 | 53.61 | 41.47 | 32.71 | |

10% | 61.39 | 47.03 | 36.74 | 29.25 | 23.69 | 19.48 | |

15% | 32.71 | 26.27 | 21.45 | 17.76 | 14.88 | 12.61 |

**Table 6.**The maximum benefit-cost ratio (BCR) value of the ANN and SVM schemes for different power capacities of ESSs.

Scheme | Power Capacity | Max. BCR | Tolerance Limit | Penalty Factor |
---|---|---|---|---|

5% | 1.17 | 6% | 2.0 | |

ANN | 10% | 1.10 | 4% | 2.0 |

15% | 0.96 | 3% | 2.0 | |

5% | 2.32 | 4% | 2.0 | |

SVM | 10% | 2.20 | 2% | 2.0 |

15% | 2.11 | 2% | 2.0 |

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**MDPI and ACS Style**

Bae, K.Y.; Jang, H.S.; Jung, B.C.; Sung, D.K.
Effect of Prediction Error of Machine Learning Schemes on Photovoltaic Power Trading Based on Energy Storage Systems. *Energies* **2019**, *12*, 1249.
https://doi.org/10.3390/en12071249

**AMA Style**

Bae KY, Jang HS, Jung BC, Sung DK.
Effect of Prediction Error of Machine Learning Schemes on Photovoltaic Power Trading Based on Energy Storage Systems. *Energies*. 2019; 12(7):1249.
https://doi.org/10.3390/en12071249

**Chicago/Turabian Style**

Bae, Kuk Yeol, Han Seung Jang, Bang Chul Jung, and Dan Keun Sung.
2019. "Effect of Prediction Error of Machine Learning Schemes on Photovoltaic Power Trading Based on Energy Storage Systems" *Energies* 12, no. 7: 1249.
https://doi.org/10.3390/en12071249