# Ultra-Short-Term Forecast of Photovoltaic Output Power under Fog and Haze Weather

^{*}

## Abstract

**:**

## 1. Introduction

_{2}, CO

_{2}, CO and O

_{3}[2]. The AQI level (L

_{AQI}) ranges from Level1–Level6 (0–50, 51–100, 101–150, 151–200, 201–300, and >300), corresponding to excellent condition, good condition, slight pollution, moderate pollution, severe pollution and serious pollution. By the end of February 2017, the Chinese government had set up the National Environmental Air Quality Monitoring Network, consisting of more than 5000 air quality monitoring sites to release AQI and six sub-indexes in real time. They also attempted measures in the long run to restrict the impacts of F-H, such as introducing a variety of energy-saving equipment and employing new energy-saving technology to reduce the consumption of fossil fuels, and substituting electricity for coal in industrial manufacturing to effectively control pollutant emissions. However, F-H weather still exists in many areas of China [3].

## 2. AOD Estimation Model Based on PM Concentration

#### 2.1. Introduction of AOD

#### 2.2. Data Sources

#### 2.3. AOD Estimation Model

#### 2.3.1. BP Neural Network Model

_{PM10}(t), PM2.5 concentration C

_{PM2.5}(t), air relative humidity R(t), aerosol scale height H(t) and air temperature T(t) as input variables, and the 440 nm band AOD τ

_{440}(t), and 1020nm band AOD τ

_{1020}(t) as output variables, a three-layer BP neural network was established with five input neurons, N hidden neurons and two output neurons, and the neural network structure is shown in Figure 2.

_{max}and v

_{min}represent the maximum and minimum values of v respectively, with v

_{norm}being the normalized value of v.

^{−2}, after 54,728 iterations, the training process is finished, the ultimate BP neural network model is obtained.

#### 2.3.2. SVM Estimation Models

_{440}(t), while the output variable of SVM-2 is 1020 nm band AOD τ

_{1020}(t). The Gaussian kernel function is adopted for the two SVM models. The key to getting a high performance SVM model is to set reasonable training parameters, which mainly includes a loss coefficient ε, a penalty factor C, and a kernel function parameter σ

^{2}in this paper. Considering that the loss coefficient ε mainly affects the generalization ability of the model, and is independent of C and σ

^{2}, a constant value to C and σ

^{2}is given respectively, and the optimal value of ε is determined firstly according to the number of support vectors and MSE of estimation results on the training data set. After that, the C and σ

^{2}are determined by the grid search method according to the training accuracy on training data set. Ultimately, the training parameters of the SVM-1 model and SVM-2 model are finally determined as: ε

_{1}= 0.02, C

_{1}= 6, ${\sigma}_{1}^{2}$ = 10, ε

_{2}= 0.01, C

_{2}= 7, ${\sigma}_{2}^{2}$ = 10. The estimation results of the SVM-1 model and SVM-2 model on the training samples are shown in Figure 5. It is known that the estimation results of the 440 nm band AOD and 1020 nm band AOD are both within the same trend with the truth values.

## 3. Calculation of Solar Irradiance

#### 3.1. Introduction and Simplification of REST2 Model

_{0n1}= 635.4 W/m

^{2}and E

_{0n2}= 709.7 W/m

^{2}in the two bands, respectively. Considering Tgi, Toi and Tni have less impact on E

_{bni}, this paper ignores them to simplify the REST2 model, and then total direct irradiance is calculated as:

_{ai}, T

_{ai}is calculated as [29,30]:

_{a}is the optical mass for aerosol extinction, which could be obtained from solar zenith angle Z:

_{h}is the solar hour angle, H

_{s}is the sun time, d is the sequence number of the day of the year.

_{wi}is calculated as [29,30]:

_{w}is the optical mass for water vapor absorption, which could be obtained from solar zenith angle Z:

_{1}, h

_{2}, c

_{1}, c

_{2}, c

_{3}, c

_{4}could be obtained from precipitable water w:

_{Ri}is calculated as [29,30]:

_{d}is the total diffuse irradiance, E

_{di}is band diffuse irradiance, E

_{dpi}is the band incident diffuse irradiance, E

_{ddi}is the band backscattered diffuse irradiance.

_{asi}is the band aerosol scattering transmittance, which could be expressed as:

_{Ri}is the band forward scattering fraction for Rayleigh extinction. For band 2, there is B

_{R2}= 0.5, while for Band 1, B

_{R1}could be obtained from m

_{R}[29,30]:

_{i}is the band correction factor [25,26], for Band 1, there is:

_{a}:

_{a}:

_{a}is the aerosol forward scatterance factor, which could be obtained from solar zenith angle Z:

_{si}is the band sky albedo, which could be obtained from Angstrom wave exponent α

_{i}and Angstrom turbidity factor β

_{i}. For band 1, there is:

_{i}is calculated according to Angstrom equation:

_{gi}is the band ground albedo, and ${\rho}_{g1}={\rho}_{g2}=0.2$ is considered here.

_{a1}, AOD of band 2, τ

_{a2}, are replaced by τ

_{440}and τ

_{1020}as predicted by SVM estimation models. The precipitable water w is calculated by the linear fitting model proposed by Li Chao [31], that is:

_{s}

_{0}is the saturated vapor pressure at 0 °C, with the empirical coefficient at a = 7.5, b = 237.3.

#### 3.2. Total Irradiance Calculation

## 4. Estimation of Efficiency Reduction for Dust Deposition

#### 4.1. Process of the Special Measurement Experiment

- (1)
- The surfaces of the five groups of PV panels were cleaned and placed one by one in the constant irradiance condition (1000 W/m
^{2}) generated by the solar simulator. After the working point was controlled to the maximum power point (MPP) with the conductance incremental method, the output power was measured. The average output power of each group of PV panels was calculated and regarded as P_{0}. - (2)
- The five groups of PV panels were arranged on the open platform to naturally realize the dust deposition, and rain weather and snow weather were avoided.
- (3)
- The PV panels were taken back to the special measurement system periodically (set ΔT = 24 h as time interval) and the average output power of each group of PV panels in the same constant irradiance condition was measured. Meanwhile, the average concentration of PM2.5 and PM10 during the measurement interval is calculated. The group of PV panels with tilt angle β = 0° for example, for the i-th measurement (i = 1, 2, …, M. M is the total number of measure times in one measurement process), were regarded with the average output power as P
_{i}, and the average concentration of PM10 and PM2.5 were calculated as C_{i}_{PM10}and C_{i}_{PM2.5}respectively, then one group of measure samples {(C_{i}_{PM10}, C_{i}_{PM2.5}, P_{i})} was obtained for one measurement process. - (4)
- Return to (1) for the next measurement process if one measurement process is finished, else return to (2).

#### 4.2. Construction and ofAnalysisof Sample Set “Cumulative PMConcentration—Efficiency Reduction”

_{i}are calculated as:

_{i}

_{PM10}, C

_{i}

_{PM2.5}, P

_{i})}, one group of samples “cumulative PM concentration—efficiency reduction” {(${C}_{i\mathrm{PM}10}^{*}$, ${C}_{i\mathrm{PM}2.5}^{*}$, η

_{i})} was obtained correspondingly. After the repetitive measurement processes are accomplished, the sample set of “cumulative PM concentration—efficiency reduction” was constructed. The sample set in three-dimensional space with the least square surface fitting method was drawn, as shown in Figure 10.

^{2}) could be generalized to other irradiance conditions.

#### 4.3. Estimation of Efficiency Reduction Based on Similar-Day Choosing Method

_{1}and β

_{2}adjacent to β* were selected. Then, according to the nearest neighbor principle of cumulative PM concentration, the similar-day sample in each sample set was selected. Eventually the efficiency reduction in current dust deposition state was estimated by implementing linear interpolation on the efficiency reduction of the selected two similar-day samples, according to the distances from tilt angle β* to the tilt angles β

_{1}and β

_{2}.

## 5. Ultra-Short-Term Forecast Method for PV Generation

#### 5.1. Photoelectric Conversion Model

_{0}. Without considering the influence of dust deposition to PV panels, the photoelectric conversion model is [32]:

_{pv}and S are the conversion efficiency and area of the PV panels, respectively. The component working temperature t

_{0}can be estimated according to the received total irradiance E and the air temperature T:

#### 5.2. Process of Ultra-Short-Term Forecast of PV Output Power

## 6. Case Study

_{440}= 0.41 and τ

_{1020}= 0.16) and ignoring the effect of dust deposition on PV panels. The hourly forecasted value and measured value of output power of the PV generation system are shown in Figure 15.

_{PM2.5}= 191 μg/m

^{3}and C

_{PM10}= 252 μg/m

^{3}) was quite close to that at 12 o’clock (C

_{PM2.5}= 206 μg/m

^{3}and C

_{PM10}= 256 μg/m

^{3}); nevertheless, compared with 14 December 2016, the output power of the PV generation system at 9 o’clock and 12 o’clock decreased by 38.09% and 9.91% respectively.

^{3}and 58,183 μg·h/m

^{3}respectively, and the efficiency reduction estimated by similar-day choosing method was 15.46%, which was quite close to the reduction of measured output power, indicating that it is reasonable to represent the dust density by cumulative PM concentration.

## 7. Conclusions

- (1).
- Based on data of PM concentration released by air quality monitoring sites as well as data of other influence factors, an effective AOD estimation model was established using the BP neural network method and SVM method, by which AOD could be accurately obtained in real time, then the total irradiance received by PV panels was calculated with satisfactory accuracy by the simplified REST2 model.
- (2).
- It is feasible to represent dust density by cumulative PM concentration for convenience when analyzing the effect of dust deposition on PV panels’ conversion efficiency. Based on a sample set of “cumulative PM concentration—efficiency reduction” constructed through special measurement experiments, the efficiency reduction of PV panels under certain dust deposition state could be estimated with similar-day choosing method.
- (3).
- The case study indicates that the accuracy of the presented forecast method is satisfactory for it is able to fully reflect the dual effects of F-H on output power of the PV generation system. The forecast error is mainly derived from the error of AOD of as well as the error of estimated efficiency reduction, thus the training data set for AOD and sample set of “PM cumulative concentration—PV power attenuation rate”—should be replenished to achieve better performance on AOD estimation and efficiency reduction estimation, which will be studied in later work.
- (4).
- The presented forecast method could be easily realized in practice as long as there is an air quality monitoring site near the position of the PV generation system.Therefore, it hasbroad prospectsinapplication as the number of air quality monitoring sites continue to grow.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Table 1.**Mean square errors (MSE) of the training results when number of hidden layer neurons N = 8.

Training Process Sequence | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

MSE (10^{−2}) | 7.133 | 7.153 | 7.137 | 7.124 | 7.185 | 7.161 | 7.201 | 7.195 | 7.113 | 7.165 |

N | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Average MSE (10^{−2}) | 7.02 | 7.12 | 7.16 | 7.07 | 6.92 | 6.74 | 6.83 | 6.51 | 6.78 | 7.14 | 7.04 | 6.96 | 7.03 |

Estimation Model | 440 nm Aerosol Optical Depth (AOD) | 1020 nm AOD | ||
---|---|---|---|---|

MAE | MSE | MAE | MSE | |

BP neural network | 0.1869 | 0.0450 | 0.1067 | 0.0154 |

SVM | 0.1591 | 0.0351 | 0.0786 | 0.0109 |

**Table 4.**Specifications of the photovoltaic (PV) panels utilized for special measurement experiment.

Parameters | Values |
---|---|

Cell type | polysilicon |

PV single module nominal efficiency | 11.9% |

Size of the PV module(length × width × thickness) | 536 × 477 × 28 mm |

Maximum output power under standard test condition (STC) | 30 W |

Open-circuit voltage | 21.6 V |

Working voltage at the maximum power point | 17.6 V |

Short-circuit current | 1.7 A |

Working current at the maximum power point | 1.6 A |

Number of Days for Dust Deposition | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Date (Dec.) | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

Air Quality Index (AQI) | 322 | 362 | 318 | 349 | 144 | 172 | 352 | 218 | 48 | 39 | 161 | 228 | 254 | 378 |

AQI Level | 6 | 6 | 6 | 6 | 3 | 4 | 6 | 5 | 1 | 1 | 4 | 5 | 6 | 6 |

PM2.5 (μg/m^{3}) | 275 | 314 | 267 | 301 | 110 | 132 | 303 | 179 | 19 | 18 | 122 | 181 | 203 | 333 |

PM10 (μg/m^{3}) | 349 | 405 | 363 | 391 | 156 | 189 | 397 | 243 | 49 | 40 | 179 | 258 | 270 | 425 |

Parameters | Values |
---|---|

Cell type | polysilicon |

PV single module nominal efficiency | 15.1% |

Size of the PV module(length × width × thickness) | 1640 × 990 × 35 mm |

Maximum output power under STC | 235 W |

Open-circuit voltage | 37.0 V |

Working voltage at the maximum power point | 29.5 V |

Short-circuit current | 8.54 A |

Working current at the maximum power point | 7.97 A |

Date | AQI | AQI Level | PM2.5 (μg/m^{3}) | PM10 (μg/m^{3}) |
---|---|---|---|---|

14 December 2016 | 80 | Good/2 | 56 | 78 |

15 December 2016 | 161 | Moderate/4 | 121 | 160 |

16 December 2016 | 245 | Severe /5 | 194 | 244 |

17 December 2016 | 313 | Serious/6 | 262 | 322 |

18 December 2016 | 336 | Serious/6 | 286 | 357 |

19 December 2016 | 438 | Serious/6 | 408 | 494 |

20 December 2016 | 350 | Serious/6 | 297 | 421 |

21 December 2016 | 432 | Serious/6 | 399 | 513 |

22 December 2016 | 369 | Serious/6 | 316 | 444 |

23 December 2016 | 71 | Good/2 | 50 | 70 |

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## Share and Cite

**MDPI and ACS Style**

Liu, W.; Liu, C.; Lin, Y.; Ma, L.; Xiong, F.; Li, J.
Ultra-Short-Term Forecast of Photovoltaic Output Power under Fog and Haze Weather. *Energies* **2018**, *11*, 528.
https://doi.org/10.3390/en11030528

**AMA Style**

Liu W, Liu C, Lin Y, Ma L, Xiong F, Li J.
Ultra-Short-Term Forecast of Photovoltaic Output Power under Fog and Haze Weather. *Energies*. 2018; 11(3):528.
https://doi.org/10.3390/en11030528

**Chicago/Turabian Style**

Liu, Weiliang, Changliang Liu, Yongjun Lin, Liangyu Ma, Feng Xiong, and Jintuo Li.
2018. "Ultra-Short-Term Forecast of Photovoltaic Output Power under Fog and Haze Weather" *Energies* 11, no. 3: 528.
https://doi.org/10.3390/en11030528