# Spatiotemporal Complementary Characteristics of Large-Scale Wind Power, Photovoltaic Power, and Hydropower

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## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Complementary Characteristic Analysis Based on the Correlation Coefficient

_{1}, y

_{1}),(x

_{2}, y

_{2}),…,(x

_{N}, y

_{N})} is a sample space composed of N sets of observations of random vectors (X, Y), where X and Y are continuous random variables, and x

_{i}and y

_{i}are one-to-one in time. (x

_{i}, y

_{i}) and (x

_{j}, y

_{j}) are any two sets of observations in the sample space. If (x

_{i}, y

_{i})(x

_{j}, y

_{j}) > 0, then (x

_{i}, y

_{i}) and (x

_{j}, y

_{j}) are consistent; if (x

_{i}, y

_{i})(x

_{j}, y

_{j}) < 0, then (x

_{i}, y

_{i}) and (x

_{j}, y

_{j}) are inconsistent. The Kendall correlation coefficient represents the difference between the consistent and inconsistent probability of two groups of observations randomly selected from the sample. The calculation method is as follows:

_{k}is (−1, 1).

#### 2.2. Multidimensional Complementary Index Based on a Space Vector

_{i}, and the sum of their variances is:

_{i}, there is always ${D}_{x}\ge 0$; that is, $Var\left({\sum}_{i=1}^{n}{x}_{i}\right)\ge 0$. Therefore:

## 3. Case Study

#### 3.1. Study Area

#### 3.2. Power Modeling

- (1)
- Wind Power Model

_{w}, is the power generation of wind turbines under different wind speed conditions, and will be calculated as follows [24]:

_{r}denotes the rated wind output under the rated conditions; v denotes the real-time wind speed; v

_{i}denotes the cut-in wind speed; v

_{o}denotes the cut-out wind speed; v

_{r}denotes the rated wind speed.

- (2)
- Photovoltaic Model

_{p}, is linearly related to the solar light intensity, and is calculated as follows [25]:

_{r}denotes the rated photovoltaic output under the rated conditions; G denotes the actual solar irradiance (W/m

^{2}); G

_{r}denotes the rated solar irradiance (1000 W/m

^{2}); α

_{T}denotes the temperature coefficient; T denotes the actual surface temperature of the photovoltaic cells (°C); T

_{r}denotes the rated surface temperature of the photovoltaic cells (25 °C).

- (3)
- Hydropower Model

_{h}will be calculated as follows [26]:

^{2}); η

_{h}denotes the efficiency of the generator; ρ denotes the density of the water (1000 kg/m

^{3}); Q denotes the water flow (m

^{3}/s); h denotes the height of the water drop (m).

_{W,max}denotes the wind power rated output (MW);

_{P,max}denotes the photovoltaic rated output (MW);

_{t}

_{+1}and V

_{t}denote the reservoir storage (m

^{3}) at the end and the beginning; I

_{t}denotes the reservoir inflow (m

^{3}/s);

^{3});

^{3}/s);

_{s}denotes the schedulable output (MW), which refers to the output that hydropower can offer on the satisfying water-dispatching premise.

## 4. Results and Discussion

#### 4.1. Analysis of Wind-Power–Photovoltaic-Power–Hydropower Complementary Characteristics at the Annual Scale

#### 4.2. Analysis of Wind-Power–Photovoltaic-Power–Hydropower Complementary Characteristics at the Monthly Scale

#### 4.3. Analysis of Wind-Power–Photovoltaic-Power–Hydropower Complementary Characteristics at the Daily Scale

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

CC | Correlation coefficient |

CIMISS | China Integrated Meteorological Information Sharing System |

C1 | Combination 1 |

C2 | Combination 2 |

## References

- Shafiekhani, M.; Ahmadi, A.; Homaee, O.; Shafie-khah, M.; Catalão, J.P.S. Optimal bidding strategy of a renewable-based virtual power plant including wind and solar units and dispatchable loads. Energy
**2022**, 239, 122379. [Google Scholar] [CrossRef] - Sharma, P.; Chhillar, A.; Said, Z.; Memon, S. Exploring the Exhaust Emission and Efficiency of Algal Biodiesel Powered Compression Ignition Engine: Application of Box–Behnken and Desirability Based Multi-Objective Response Surface Methodology. Energies
**2021**, 14, 5968. [Google Scholar] [CrossRef] - Stevović, I.; Mirjanić, D.; Stevović, S. Possibilities for wider investment in solar energy implementation. Energy
**2019**, 180, 495–510. [Google Scholar] [CrossRef] - Sezer, N.; Biçer, Y.; Koç, M. Design and analysis of an integrated concentrated solar and wind energy system with storage. Int. J. Energy Res.
**2019**, 43, 3263–3283. [Google Scholar] [CrossRef] - Zhang, Y.; Lian, J.; Ma, C.; Yang, Y.; Pang, X.; Wang, L. Optimal sizing of the grid-connected hybrid system integrating hydropower, photovoltaic, and wind considering cascade reservoir connection and photovoltaic-wind complementarity. J. Clean. Prod.
**2020**, 274, 123100. [Google Scholar] [CrossRef] - Jurasz, J.; Canales, F.A.; Kies, A.; Guezgouz, M.; Beluco, A. A review on the complementarity of renewable energy sources: Concept, metrics, application and future research directions. Sol. Energy
**2020**, 195, 703–724. [Google Scholar] [CrossRef] - Cantao, M.P.; Bessa, M.R.; Bettega, R.; Detzel, D.H.M.; Lima, J.M. Evaluation of hydro-wind complementarity in the Brazilian territory by means of correlation maps. Renew. Energy Feb.
**2017**, 101, 1215–1225. [Google Scholar] [CrossRef] - Xu, L.; Wang, Z.; Liu, Y. The spatial and temporal variation features of wind-sun complementarity in China. Energy Convers. Manag.
**2017**, 154, 138–148. [Google Scholar] [CrossRef] - De Jong, P.; Sanchez, A.S.; Esquerre, K.; Kalid, R.A.; Torres, E.A. Solar and wind energy production in relation to the electricity load curve and hydroelectricity in the northeast region of Brazil. Renew. Sustain. Energy Rev.
**2013**, 23, 526–535. [Google Scholar] [CrossRef] - Moura, P.S.; de Almeida, A.T. Multi-objective optimization of a mixed renewable system with demand-side management. Renew. Sustain. Energy Rev.
**2010**, 14, 1461–1468. [Google Scholar] [CrossRef] - Rosa, C.D.C.S.; Costa, K.A.; Christo, E.D.; Bertahone, P.B. Complementarity of Hydro, Photovoltaic, and Wind Power in Rio de Janeiro State. Sustainability
**2017**, 9, 1130. [Google Scholar] - François, B.; Borga, M.; Creutin, J.D.; Hingray, B.; Raynaud, D.; Sauterleute, J.F. Complementarity between solar and hydro power: Sensitivity study to climate characteristics in Northern-Italy. Renew. Energy
**2016**, 86, 543–553. [Google Scholar] [CrossRef] - Ma, T.; Yang, H.X.; Lu, L.; Peng, J.Q. Technical feasibility study on a standalone hybrid solar-wind system with pumped hydro storage for a remote island in Hong Kong. Renew. Energy
**2014**, 69, 7–15. [Google Scholar] [CrossRef] - He, C.; Liu, T.; Wu, L.; Shahidehpour, M. Robust coordination of interdependent electricity and natural gas systems in day-ahead scheduling for facilitating volatile renewable generations via power-to-gas technology. J. Mod. Power Syst. Clean Energy
**2017**, 5, 375–388. [Google Scholar] [CrossRef] [Green Version] - Philip, E.B.; Hazel, E.T. The climatological relationships between wind and solar energy supply in Britain. Renew. Energy
**2016**, 86, 96–110. [Google Scholar] - Priscilla, S.; da Silva, A.S.A.; Stošić, B.; Stošić, T. Long-term correlations and cross-correlations in wind speed and solar radiation temporal series from Fernando de Noronha Island, Brazil. Phys. A
**2015**, 424, 90–96. [Google Scholar] - Schindler, D.; Schmidt-Rohr, S.; Jung, C. On the spatiotemporal complementarity of the European onshore wind resource. Energy Convers. Manag.
**2021**, 237, 114098. [Google Scholar] [CrossRef] - Prasad, A.A.; Taylor, R.A.; Kay, M. Assessment of solar and wind resource synergy in Australia. Appl. Energy
**2017**, 190, 354–367. [Google Scholar] [CrossRef] - Canales, F.A.; Jurasz, J.; Beluco, A.; Kies, A. Assessing temporal complementarity between three variable energy sources through correlation and compromise programming. Energy
**2020**, 192, 116637. [Google Scholar] [CrossRef] [Green Version] - Sharma, P.; Said, Z.; Kumar, A.; Nižetić, S.; Pandey, A.; Hoang, A.T.; Huang, Z.; Afzal, A.; Li, C.; Le, A.T.; et al. Recent Advances in Machine Learning Research for Nanofluid-Based Heat Transfer in Renewable Energy System. Energy Fuels
**2022**, 13, 6626–6658. [Google Scholar] [CrossRef] - Fang, W.; Huang, Q.; Huang, S.; Yang, J.; Meng, E.; Li, Y. Optimal sizing of utility-scale photovoltaic power generation complementarily operating with hydropower: A case study of the world’s largest hydro-photovoltaic plant. Energy Convers. Manag.
**2017**, 136, 161–172. [Google Scholar] [CrossRef] - Zhang, Y.; Ma, C.; Lian, J.; Pang, X.; Qiao, Y.; Chaima, E. Optimal photovoltaic capacity of large-scale hydro-photovoltaic complementary systems considering electricity delivery demand and reservoir characteristics. Energy Convers. Manag.
**2019**, 195, 597–608. [Google Scholar] [CrossRef] - Chang, R.; Luo, Y.; Zhu, R. Simulated local climatic impacts of large-scale photovoltaics over the barren area of Qinghai, China. Renew. Energy
**2020**, 145, 478–489. [Google Scholar] [CrossRef] - Heide, D.; von Bremen, L.; Greiner, M.; Hoffmann, C.; Speckmann, M.; Bofinger, S. Seasonal optimal mix of wind and solar power in a future, highly renewable Europe. Renew. Energy
**2010**, 35, 2483–2489. [Google Scholar] [CrossRef] - Ceran, B. The concept of use of PV/WT/FC hybrid power generation system for smoothing the energy profile of the consumer. Energy
**2019**, 167, 853–865. [Google Scholar] [CrossRef] - Ming, B.; Liu, P.; Guo, S.; Zhang, X.; Feng, M.; Wang, X. Optimizing utility-scale photovoltaic power generation for integration into a hydropower reservoir by incorporating long- and short-term operational decisions. Appl. Energy
**2017**, 204, 432–445. [Google Scholar] [CrossRef] - Wang, S.; Jia, R.; Shi, X.; An, Y.; Huang, Q.; Guo, P.; Luo, C. Hybrid time-scale optimal scheduling considering multi-energy complementary characteristic. IEEE Access
**2021**, 9, 94087–94098. [Google Scholar] [CrossRef]

**Figure 4.**Contribution of each complementary portfolio for complementary combination 1 (C1) at the annual scale.

**Figure 5.**Contribution of each complementary portfolio for complementary combination 2 (C2) at the annual scale.

**Figure 6.**Contribution of each complementary portfolio for complementary combination 1 (C1) at the monthly scale.

**Figure 7.**Contribution of each complementary portfolio for complementary combination 2 (C2) at the monthly scale.

**Figure 8.**Contribution of each complementary portfolio for complementary combination 1 (C1) at the daily scale.

**Figure 9.**Contribution of each complementary portfolio for complementary combination 2 (C2) at the daily scale.

Correlation Coefficient (r) | Meaning | |
---|---|---|

Correlation | 0.9 ≤ r ≤ 1.0 | Very strong correlation |

0.6 ≤ r < 0.9 | Strong correlation | |

0.3 ≤ r < 0.6 | Moderate correlation | |

0.0 ≤ r < 0.3 | Weak correlation | |

Complementarity | −0.3 < r ≤ 0.0 | Weak complementarity |

−0.6 < r ≤ −0.3 | Medium complementarity | |

−0.9 < r ≤ −0.6 | Strong complementarity | |

−1.0 ≤ r ≤ −0.9 | Very strong complementary |

Year | Complementary Vector c | Spatial Optimal Solution $\mathit{L}\left(\mathit{c}\right)$ | Total Complementary Index ${\mathit{k}}_{\mathit{t}}\left(\mathit{c}\right)$ |
---|---|---|---|

2019 | −0.693ph + 0.036pw + 0.148wh | 1.246 | 77.96% |

2018 | −0.535ph − 0.524pw + 0.237wh | 1.089 | 84.93% |

2017 | −0.611ph − 0.134pw + 0.420wh | 1.338 | 73.87% |

Year | Complementary Vector c | Spatial Optimal Solution $\mathit{L}\left(\mathit{c}\right)$ | Total Complementary Index ${\mathit{k}}_{\mathit{t}}\left(\mathit{c}\right)$ |
---|---|---|---|

2019 | −0.355ph − 0.126pw + 0.148wh | 1.334 | 74.07% |

2018 | −0.612ph − 0.375pw + 0.237wh | 1.125 | 83.33% |

2017 | −0.421ph − 0.158pw + 0.420wh | 1.421 | 70.20% |

**Table 4.**The complementary characteristics of the complementary combination 1 based on monthly data.

Month | Complementary Vector c | Spatial Optimal Solution $\mathit{L}\left(\mathit{c}\right)$ | Total Complementary Index ${\mathit{k}}_{\mathit{t}}\left(\mathit{c}\right)$ |
---|---|---|---|

1 | −0.356ph + 0.041pw − 0.175wh | 1.255 | 77.56% |

2 | −0.403ph − 0.119pw + 0.871wh | 1.675 | 58.91% |

3 | 0.858ph + 0.362pw + 0.433wh | 2.327 | 29.93% |

4 | 0.294ph − 0.478pw − 0.337wh | 1.340 | 73.80% |

5 | 0.375ph + 0.093pw + 0.617wh | 2.043 | 42.56% |

6 | 0.114ph + 0.195pw − 0.392wh | 1.477 | 67.69% |

7 | 0.639ph − 0.286pw − 0.565wh | 1.394 | 71.38% |

8 | 0.451ph − 0.129pw + 0.704wh | 2.013 | 43.87% |

9 | 0.267ph − 0.082pw − 0.415wh | 1.385 | 71.78% |

10 | 0.339ph − 0.383pw − 0.069wh | 1.444 | 69.18% |

11 | 0.594ph + 0.061pw − 0.288wh | 1.684 | 58.51% |

12 | −0.383ph + 0.144pw − 0.279wh | 1.241 | 78.18% |

**Table 5.**The complementary characteristics of the complementary combination 2 based on monthly data.

Month | Complementary Vector c | Spatial Optimal Solution $\mathit{L}\left(\mathit{c}\right)$ | Total Complementary Index ${\mathit{k}}_{\mathit{t}}\left(\mathit{c}\right)$ |
---|---|---|---|

1 | −0.274ph − 0.121pw − 0.175wh | 1.270 | 76.91% |

2 | −0.525ph − 0.263pw + 0.871wh | 1.542 | 64.82% |

3 | 0.641ph − 0.011pw + 0.433wh | 2.032 | 43.04% |

4 | 0.556ph − 0.452pw − 0.337wh | 1.384 | 71.84% |

5 | 0.272ph − 0.081pw + 0.617wh | 1.904 | 48.71% |

6 | 0.305ph − 0.149pw − 0.392wh | 1.382 | 71.91% |

7 | 0.512ph + 0.037pw − 0.565wh | 1.492 | 67.02% |

8 | 0.219ph − 0.663pw + 0.704wh | 1.630 | 60.89% |

9 | 0.369ph − 0.152pw − 0.415wh | 1.401 | 71.07% |

10 | 0.291ph − 0.476pw − 0.069wh | 1.373 | 72.31% |

11 | 0.407ph − 0.196pw − 0.288wh | 1.462 | 68.38% |

12 | −0.517ph − 0.021pw − 0.279wh | 1.092 | 84.82% |

Day | Complementary Vector c | Spatial Optimal Solution $\mathit{L}\left(\mathit{c}\right)$ | Total Complementary Index ${\mathit{k}}_{\mathit{t}}\left(\mathit{c}\right)$ |
---|---|---|---|

S1 | −0.005ph + 0.564pw − 0.177wh | 1.691 | 58.18% |

R1 | 0.080ph + 0.434pw − 0.126wh | 1.694 | 58.04% |

S2 | −0.467ph + 0.125pw − 0.391wh | 1.134 | 82.96% |

R2 | −0.171ph − 0.038pw − 0.249wh | 1.271 | 76.84% |

S3 | 0.263ph + 0.131pw − 0.087wh | 1.654 | 59.84% |

R3 | 0.192ph + 0.212pw − 0.153wh | 1.626 | 61.09% |

S4 | −0.723ph − 0.286pw + 0.397wh | 1.194 | 80.27% |

R4 | −0.496ph − 0.129pw + 0.351wh | 1.363 | 72.76% |

Day | Complementary Vector c | Spatial Optimal Solution $\mathit{L}\left(\mathit{c}\right)$ | Total Complementary Index ${\mathit{k}}_{\mathit{t}}\left(\mathit{c}\right)$ |
---|---|---|---|

S1 | −0.165ph + 0.378pw − 0.177wh | 1.518 | 65.87% |

R1 | −0.013ph + 0.587pw − 0.126wh | 1.724 | 56.71% |

S2 | −0.561ph − 0.024pw − 0.391wh | 1.012 | 88.36% |

R2 | −0.203ph + 0.151pw − 0.249wh | 1.350 | 73.36% |

S3 | −0.217ph − 0.036pw − 0.087wh | 1.330 | 74.22% |

R3 | −0.183ph + 0.327pw − 0.153wh | 1.496 | 66.87% |

S4 | −0.492ph + 0.126pw + 0.397wh | 1.516 | 65.98% |

R4 | −0.721ph − 0.307pw + 0.351wh | 1.162 | 81.71% |

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**MDPI and ACS Style**

Wang, S.; Jia, R.; Luo, C.; An, Y.; Guo, P.
Spatiotemporal Complementary Characteristics of Large-Scale Wind Power, Photovoltaic Power, and Hydropower. *Sustainability* **2022**, *14*, 9273.
https://doi.org/10.3390/su14159273

**AMA Style**

Wang S, Jia R, Luo C, An Y, Guo P.
Spatiotemporal Complementary Characteristics of Large-Scale Wind Power, Photovoltaic Power, and Hydropower. *Sustainability*. 2022; 14(15):9273.
https://doi.org/10.3390/su14159273

**Chicago/Turabian Style**

Wang, Songkai, Rong Jia, Chang Luo, Yuan An, and Pengcheng Guo.
2022. "Spatiotemporal Complementary Characteristics of Large-Scale Wind Power, Photovoltaic Power, and Hydropower" *Sustainability* 14, no. 15: 9273.
https://doi.org/10.3390/su14159273