# A WGAN-GP-Based Scenarios Generation Method for Wind and Solar Power Complementary Study

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## Abstract

**:**

## 1. Introduction

- In complementary characteristics of VRE research, most studies only focus on the complementary performance of wind and solar resources, while the matching degree of the combined output to the load is usually ignored. Moreover, the impact of the volatility of VRE output itself is overlooked by correlation coefficients, which only pay attention to the wholeness of data.
- The traditional probabilistic model does not fully consider wind and solar resources’ historical and unknown relationship. In addition, these methods require a prior assumption that the data obeys a specific probability distribution, such as a Weibull distribution, Beta distribution, etc. However, the actual environment is complex, and the assumed distribution may not fit the real condition. On the other hand, existing research based on deep learning lacks relevant research on the complementary properties of new energy sources.

- Two types of complementary indicators are defined, aiming at total output smoothing and source-load matching, respectively. The significance of two types of complementary indicators in different regions is studied. Moreover, the complementary rate of fluctuation (CROF), complementary rate of ramp (CROR), and complementary rate of offset (CRO) are added to the correlation analysis to consider the volatility of VRE output itself. The photovoltaic capacity ratio corresponding to the maximum CROF is proposed as the basis for the hybrid system’s capacity allocation to stabilize the wind and solar output volatility.
- WGAN-GP, based on a data-driven deep learning method, is used for wind and solar scenario generation, and an unsupervised k-means clustering method is used for scenario reduction. At the same time, we compared the traditional statistical methods of MC and Copula, and the results showed that WGAN-GP generated scenarios could be applied to the VRE output complementary study, which may balance the relevance of the historical with the uncertainty in future production.

## 2. Complementary Indicators of Wind and Solar Hybrid System

#### 2.1. Two Types of Complementary Indicators

#### 2.2. Correlation Coefficient

#### 2.2.1. Pearson Correlation Coefficient

#### 2.2.2. Spearman Correlation Coefficient

#### 2.2.3. Kendall Correlation Coefficient

#### 2.2.4. Complementary Rate of Fluctuation (CROF)

#### 2.2.5. Complementary Rate of Ramp (CROR)

#### 2.2.6. Complementary Rate of Offset (CRO)

## 3. Study on Complementary Characteristics of Wind and Solar

#### 3.1. Data

^{2}, except for region 8. The average monthly and yearly peak sunshine hours (PSH) in Haixi are presented in Table 3, and the annual mean PSH is 4.88 h, the highest in Qinghai Province. Moreover, the Gobi Desert area, which is situated in Haixi, contains the most wind and solar energy-rich regions that require low operation and maintenance costs, thereby highlighting the benefits of wind and solar energy potential in Haixi.

#### 3.2. Data-Processing

#### 3.2.1. Output Power of Photovoltaic (PV) Power Station

^{2}, G

_{STG}is the standard irradiance, 1000 W/m

^{2}, P

_{cs}is the installed capacity of the PV power station, and R

_{PV}is the comprehensive efficiency of the PV power station, 0.81.

#### 3.2.2. Output Power of Wind Farm

_{WG}is the rated capacity of the wind turbine, P

_{cw}is the installed capacity of the wind farm, and R

_{V}is the comprehensive efficiency of the wind farm, 0.7.

#### 3.2.3. Normalization

#### 3.2.4. Output Power of the Hybrid System

#### 3.3. The First Type of Complementarity

#### 3.3.1. Wind-Wind and Wind-Solar Mode

#### 3.3.2. Solar-Solar and Solar-Wind Mode

#### 3.4. The Second Type of Complementarity

#### 3.4.1. Wind-Wind and Wind-Solar Mode

#### 3.4.2. Solar-Solar and Solar-Wind Mode

## 4. Scenario Generation and Complementary Analysis Based on WGAN-GP

#### 4.1. Scenario Generation of Wind and Solar Output Based on WGAN-GP

Algorithm 1: Pseudo-code of WGAN-GP |

Algorithm WGAN-GP. We use default values of $\lambda =10$, ${n}_{critic}=5$, $\alpha =0.0002$, ${\beta}_{1}=0.5$, ${\beta}_{2}=0.999$ |

Require: The gradient penalty coefficient $\lambda $, the number of critic iterations per generator iteration ${n}_{critic}$, the batch size $m$, Adam hyperparameters $\alpha $, ${\beta}_{1}$, ${\beta}_{2}$. |

Require: initial critic parameters ${\omega}_{0}$, initial generator parameters ${\theta}_{0}$ |

1: While $\theta $ has not converged do |

2: for $t=1,\dots ,{n}_{critic}$do |

3: for $i=1,\dots ,m$ do |

4: Samples real data $x~{P}_{r}$, latent variable $z~p\left(z\right)$, a random number $\u03f5~U\left[0,1\right]$ |

5: $\tilde{x}\leftarrow {G}_{\theta}\left(z\right)$ |

6: $\widehat{x}\leftarrow \u03f5x+\left(1-\u03f5\right)\tilde{x}$ |

7: ${L}^{\left(i\right)}\leftarrow {D}_{\omega}\left(\tilde{x}\right)-{D}_{\omega}\left(x\right)+\lambda {\left(\parallel {\nabla}_{\widehat{x}}{D}_{\omega}\left(\widehat{x}\right){\parallel}_{2}-1\right)}^{2}$ |

8: end for |

9: $\omega \leftarrow Adam\left({\nabla}_{\omega}\frac{1}{m}{\sum}_{i=1}^{m}{L}^{\left(i\right)},\omega ,\alpha ,{\beta}_{1},{\beta}_{2}\right)$ |

10: end for |

11: Sample a batch of latent variables ${\left\{{z}^{\left(i\right)}\right\}}_{i=1}^{m}~p\left(z\right)$ |

12: $\theta \leftarrow Adam\left({\nabla}_{\theta}\frac{1}{m}{\sum}_{i=1}^{m}-{D}_{\omega}\left({G}_{\theta}\right)),\theta ,\alpha ,{\beta}_{1},{\beta}_{2}\right)$ |

13: end while |

#### 4.2. Scenario Generation Results by Three Methods

#### 4.3. Complementary Analysis Based on Scenario Generation

## 5. Conclusions

- This paper focuses on wind and solar complementarity in Haixi, Qinghai. It proposes using the deep learning method WGAN-GP for complementary studies, which shows that the proposed method can comprehensively analyze the correlation of resource contributions and improve the robustness of the results. This proposed method has a high coverage rate for measured values, which can accurately describe the uncertainty of renewable energy output. In addition, the proposed methodology reduces the RMSE of the generated output by 4% and 3.4% in independent renewable energy systems and hybrid power systems, respectively, compared to the Copula function method. Additionally, compared to the MC method, the RMSE decreases to 9.7% and 6.7%.
- In the first type of complementarity study, wind-solar and solar-wind modes significantly enhance the overall output’s smoothness and stabilize fluctuations in hybrid systems. In the second type of complementarity study, the wind-solar mode also significantly improves source-load matching, making it easier to integrate wind and solar resources to accommodate. However, the solar-wind mode’s improvement effect is less pronounced than that of the first complementarity type.
- In this paper, we found that combining wind energy from region six with solar power from region three showed the best complementary effects in the first type of study. Similarly, combining wind energy from region seven with solar energy from region three yielded the best results in the second type of complementarity study.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

${r}_{p}$ | Pearson correlation coefficient | ${\tau}_{k}$ | Kendall correlation coefficient |

${r}_{s}$ | Spearman correlation coefficient | n | sample size |

$\tau $ | the first type of complementary indicator | ${\tau}_{L}$ | the second type of complementary indicator |

${C}_{\tau}$ | the number of concordant pairs | ${D}_{\tau}$ | the number of discordant pairs |

$\alpha $ | photovoltaic capacity ratio | ${\alpha}_{k}$ | the kth VRE ratio in the hybrid system |

$R{R}^{k}$ | the ramp ratio of the kth VRE power system | ${\epsilon}^{k}$ | the offset ratio of the kth VRE power system |

${\gamma}_{i}^{k}$ | the volatility ratio of the kth VRE power system | $\lambda $ | the gradient penalty coefficient |

R_{V} | the comprehensive efficiency of the wind farm | R_{PV} | the comprehensive efficiency of the PV power station |

P_{cw} | installed capacity of the wind farm | P_{cs} | installed capacity of the PV power station |

${P}_{wj}$ | output of the wind farm at the jth region | ${P}_{sj}$ | output of the PV power station at the jth region |

${P}_{T}^{i}$ | actual output of a single wind turbine | ${G}_{T}^{i}$ | total radiation of the slanted plane |

P_{WG} | rated capacity of the wind turbine | G_{STG} | standard irradiance |

${P}_{nw}^{i}$ | normalized wind farm output power | ${P}_{ns}^{i}$ | normalized PV power station output power |

${P}_{j}$ | output of the hybrid system at the jth region | ${\overline{P}}_{j}$ | average output of the hybrid system at the jth region |

${P}_{r}$ | the probability distribution of real data | ${P}_{g}$ | the probability distribution of generated data |

C | generator | D | discriminator |

CROF | complementary rate of fluctuation | CROR | complementary rate of ramp |

CRO | complementary rate of offset | VRE | variable renewable energy |

RMSE | root mean square error | MAE | mean absolute error |

MC | Monte Carlo |

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**Figure 3.**The first type of complementary indicator under different time scales (the blue box represents the wind-wind mode, and the red box illustrates the wind-solar mode).

**Figure 4.**The first type of complementary indicator under different time scales (the blue box represents the solar-solar mode, and the red box illustrates the solar-wind mode).

**Figure 7.**The second type of complementary indicator under different time scales (the blue box represents the wind-wind mode, and the red box illustrates the wind-solar mode).

**Figure 8.**The second type of complementary indicator under different time scales (the blue box represents the solar-solar mode, and the red box illustrates the solar-wind mode).

Article | Location | Data Resolution | Correlation Coefficient |
---|---|---|---|

Cantão et al. [13] | Brazil | Hourly, monthly | Pearson, Spearman |

Kapica et al. [14] | global | Daily | Kendall |

Couto et al. [15] | Portugal | Hourly, daily | Pearson, capacity factor |

Frank et al. [16] | European countries | Daily | Pearson |

Lv et al. [17] | China | Daily | Spearman |

Dirk et al. [18] | Germany | Daily, seasonal | Kendall |

Hoicka et al. [19] | Canada | Hourly | Kendall |

Jurasz et al. [20] | Poland | 15-min, hourly | Capacity factor |

Sterl et al. [21] | Africa | Hourly | Proposed one index |

Prasad et al. [22] | Australia | Hourly | Proposed two indexes |

Bett et al. [23] | the United Kingdom | 6-hourly, Daily | Pearson |

Shaner et al. [24] | the United States | Hourly | Kendall |

Costoya et al. [25] | North America | Hourly | Proposed two indexes |

Region | Location | Longitude | Latitude | Mean Solar Irradiance (W/m^{2}) | Mean Wind Speed (m/s) |
---|---|---|---|---|---|

1 | Wulan | 99.20 E | 36.34 N | 203.64 | 5.04 |

2 | Dachaidan | 95.11 E | 37.35 N | 223.65 | 6.02 |

3 | Delingha | 97.24 E | 37.06 N | 202.91 | 6.56 |

4 | Dulan | 96.25 E | 36.22 N | 219.64 | 6.24 |

5 | Golmud | 95.5 E | 36.23 N | 220.47 | 5.86 |

6 | Mangnai | 92.48 E | 37.95 N | 221.83 | 5.71 |

7 | Lenghu | 93.27 E | 35.54 N | 208.59 | 5.30 |

8 | Tianjun | 98.49 E | 37.22 N | 199.13 | 5.35 |

Month | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | Mean |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

PSH (h) | 3.20 | 4.13 | 5.17 | 6.11 | 6.29 | 6.06 | 5.99 | 5.71 | 5.01 | 4.49 | 3.50 | 2.89 | 4.88 |

Region | Kendall | Spearman | Pearson |
---|---|---|---|

1 | 0.0392 | 0.1051 | 0.0281 |

2 | −0.0966 | −0.0643 | −0.0706 |

3 | −0.1042 | −0.1139 | −0.0754 |

4 | −0.0255 | −0.0348 | −0.0184 |

5 | −0.0089 | −0.0488 | −0.0068 |

6 | −0.2956 | −0.2772 | −0.2184 |

7 | −0.1214 | −0.0727 | −0.0878 |

8 | 0.0625 | −0.0050 | 0.0452 |

WGAN-GP | Copula | MC | ||||
---|---|---|---|---|---|---|

RMSE | MAE | RMSE | MAE | RMSE | MAE | |

${P}_{s1}$ | 0.036 | 0.024 | 0.089 | 0.059 | 0.112 | 0.059 |

${P}_{w1}$ | 0.091 | 0.079 | 0.100 | 0.083 | 0.321 | 0.214 |

${P}_{s2}$ | 0.056 | 0.033 | 0.109 | 0.065 | 0.167 | 0.090 |

${P}_{w2}$ | 0.158 | 0.150 | 0.172 | 0.154 | 0.251 | 0.212 |

${P}_{s3}$ | 0.041 | 0.027 | 0.112 | 0.068 | 0.085 | 0.049 |

${P}_{w3}$ | 0.172 | 0.139 | 0.170 | 0.155 | 0.325 | 0.267 |

${P}_{s4}$ | 0.047 | 0.026 | 0.092 | 0.053 | 0.084 | 0.047 |

${P}_{w4}$ | 0.190 | 0.182 | 0.204 | 0.181 | 0.207 | 0.163 |

${P}_{s5}$ | 0.086 | 0.054 | 0.113 | 0.069 | 0.126 | 0.061 |

${P}_{w5}$ | 0.134 | 0.122 | 0.172 | 0.134 | 0.245 | 0.208 |

${P}_{s6}$ | 0.065 | 0.044 | 0.073 | 0.048 | 0.140 | 0.068 |

${P}_{w6}$ | 0.088 | 0.079 | 0.191 | 0.151 | 0.153 | 0.116 |

${P}_{s7}$ | 0.024 | 0.015 | 0.075 | 0.049 | 0.113 | 0.059 |

${P}_{w7}$ | 0.095 | 0.068 | 0.159 | 0.100 | 0.213 | 0.149 |

${P}_{s8}$ | 0.039 | 0.023 | 0.082 | 0.051 | 0.092 | 0.053 |

${P}_{w8}$ | 0.091 | 0.078 | 0.137 | 0.128 | 0.263 | 0.207 |

mean | 0.088 | 0.071 | 0.128 | 0.097 | 0.181 | 0.126 |

$\Delta $ | 0.040 | 0.026 | 0.093 | 0.055 |

WGAN-GP | Copula | MC | |||||
---|---|---|---|---|---|---|---|

$\mathit{\alpha}$ | RMSE | MAE | RMSE | MAE | RMSE | MAE | |

${P}_{1}$ | 0.35 | 0.065 | 0.056 | 0.085 | 0.065 | 0.205 | 0.132 |

${P}_{2}$ | 0.46 | 0.097 | 0.090 | 0.124 | 0.101 | 0.165 | 0.139 |

${P}_{3}$ | 0.56 | 0.085 | 0.072 | 0.113 | 0.095 | 0.153 | 0.126 |

${P}_{4}$ | 0.42 | 0.117 | 0.110 | 0.134 | 0.113 | 0.124 | 0.099 |

${P}_{5}$ | 0.43 | 0.107 | 0.091 | 0.127 | 0.092 | 0.147 | 0.129 |

${P}_{6}$ | 0.44 | 0.039 | 0.031 | 0.112 | 0.090 | 0.096 | 0.071 |

${P}_{7}$ | 0.45 | 0.058 | 0.043 | 0.097 | 0.064 | 0.120 | 0.085 |

${P}_{8}$ | 0.47 | 0.046 | 0.038 | 0.095 | 0.082 | 0.139 | 0.108 |

mean | 0.45 | 0.077 | 0.066 | 0.111 | 0.088 | 0.144 | 0.111 |

$\Delta $ | 0.034 | 0.022 | 0.067 | 0.045 |

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## Share and Cite

**MDPI and ACS Style**

Ma, X.; Liu, Y.; Yan, J.; Wang, H.
A WGAN-GP-Based Scenarios Generation Method for Wind and Solar Power Complementary Study. *Energies* **2023**, *16*, 3114.
https://doi.org/10.3390/en16073114

**AMA Style**

Ma X, Liu Y, Yan J, Wang H.
A WGAN-GP-Based Scenarios Generation Method for Wind and Solar Power Complementary Study. *Energies*. 2023; 16(7):3114.
https://doi.org/10.3390/en16073114

**Chicago/Turabian Style**

Ma, Xiaomei, Yongqian Liu, Jie Yan, and Han Wang.
2023. "A WGAN-GP-Based Scenarios Generation Method for Wind and Solar Power Complementary Study" *Energies* 16, no. 7: 3114.
https://doi.org/10.3390/en16073114