# Multi-Criteria Decision Making Approach for Hybrid Operation of Wind Farms

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## Abstract

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## 1. Introduction

## 2. Problem Formulation

- Alternative 1 (${A}_{1}$): Let ${\widehat{p}}_{i}$ represent the forecasted wind power in a particular forecast window and ${p}_{i}$ be the actual wind power from the wind farm. In scenarios where ${\widehat{p}}_{i}$ is greater than ${p}_{i}$, a penalty is paid for the deficit power by the wind farm operator, and the battery bank is left unused. The total cost paid by the operator in such k instances is given as:$$\begin{array}{ccc}\hfill {F}_{1}& =& \beta \sum _{i=1}^{k}\left({\widehat{p}}_{i}-{p}_{i}\right),\hfill \end{array}$$
- Alternative 2 (${A}_{2}$): In this alternative, the deficit power is fed to the grid via a combination of two strategies. Firstly, a threshold battery power (${p}_{b}^{th}$) is identified, and if the deficit (${\widehat{p}}_{i}-{p}_{i}$) is greater than the threshold, the penalty is paid for the said difference. The total cost paid by the operator during such m instances is given as:$$\begin{array}{c}\hfill {F}_{2}=\zeta \sum _{i=1}^{m}\left({p}_{bi}^{th}-{\widehat{p}}_{i}+{p}_{i}\right),\end{array}$$
- Alternative 3 (${A}_{3}$): In this alternative, the deficit wind power is pumped into the grid by neighboring wind farms, and the penalty for the said difference is paid by the wind farm operator. Suppose the actual and forecasted wind powers for Wind Farms 2 and 3 are ${p}_{2i}$, ${\widehat{p}}_{2i}$, ${p}_{3i}$ and ${\widehat{p}}_{3i}$ respectively, then the penalty cost paid by the operator of Wind Farm 1 is given as:$$\begin{array}{c}\hfill {F}_{3}=\left\{\begin{array}{c}\alpha \sum _{i=1}^{l}({p}_{2i}-{\widehat{p}}_{2i}),\phantom{\rule{7.11317pt}{0ex}}\mathrm{if}\phantom{\rule{7.11317pt}{0ex}}{p}_{2i}>{\widehat{p}}_{2i},\hfill \\ \alpha \sum _{i=1}^{l}({p}_{3i}-{\widehat{p}}_{3i}),\phantom{\rule{7.11317pt}{0ex}}\mathrm{if}\phantom{\rule{7.11317pt}{0ex}}{p}_{3i}>{\widehat{p}}_{3i},\hfill \\ \delta \sum _{i=1}^{l}(\widehat{{p}_{i}}-{p}_{i}),\hfill \end{array}\right.\end{array}$$
- Alternative 4 (${A}_{4}$): In this case, the entire deficit power is delivered by the battery bank, and the cost paid by the operator in u such instances is given as:$$\begin{array}{c}\hfill {F}_{4}=\delta \sum _{i=1}^{u}({\widehat{p}}_{i}-{p}_{i}),\end{array}$$

## 3. MCDM: Materials and Methods

#### 3.1. Simple Additive Weighting (Saw) Method

- Step 1: Identify the alternatives (${A}_{1},{A}_{2},\dots ,{A}_{m}$) and criteria (${C}_{1},{C}_{2},\dots ,{C}_{n}$) for the decision making problem.
- Step 2: Develop a decision matrix for the said MCDM problem.
- Step 3: Construct the normalized decision matrix with its elements as:$$\begin{array}{c}\hfill \widehat{{H}_{ij}}=\frac{\mathrm{min}{h}_{ij}}{{h}_{ij}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}i=1,2,\dots ,m;\phantom{\rule{4pt}{0ex}}j=1,2,\dots ,n.\end{array}$$$$\begin{array}{c}\hfill \widehat{{H}_{ij}}=\frac{{h}_{ij}}{\mathrm{max}{h}_{ij}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}i=1,2,\dots ,m;\phantom{\rule{4pt}{0ex}}j=1,2,\dots ,n.\end{array}$$For non-beneficial criteria, the normalized element of the decision matrix is calculated using Equation (6) and for beneficial criteria using Equation (7).
- Step 4: Calculate entropy (${e}_{j}$) and divergence values (${d}_{j}$) for each criteria as:$$\begin{array}{ccc}\hfill {e}_{j}& =& -\frac{1}{\mathrm{log}m}\sum _{i=1}^{m}\widehat{{H}_{ij}}\mathrm{log}(\widehat{{H}_{ij}}).\hfill \end{array}$$$$\begin{array}{ccc}\hfill {d}_{j}& =& |1-{e}_{j}|\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}j=1,2,\dots ,n.\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\hfill \end{array}$$
- Step 5: Calculate the weights for the respective criterion using Equation (10):$${w}_{j}=\frac{{d}_{j}}{{\sum}_{j=1}^{n}{d}_{j}}.$$
- Step 6: Finally, calculate the priority score for each alternative using Equation (10) and arrange them according to highest priority:$$\begin{array}{c}\hfill {S}_{i}=\sum _{j=1}^{n}{w}_{j}{h}_{ij}.\end{array}$$

#### 3.2. Technique for Order or Preference by Similarity to Ideal Solution Method

- Follow Steps 1–2 as in the case of the SAW method.
- Construct the normalized decision matrix with its elements as:$$\begin{array}{c}\hfill \widehat{{H}_{ij}}=\frac{{h}_{ij}}{\sqrt{{\sum}_{j=1}^{n}{h}_{ij}^{2}}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}i=1,2,\dots ,m;\phantom{\rule{4pt}{0ex}}j=1,2,\dots ,n.\end{array}$$
- After calculating weights for each criterion, construct a weighted normalized matrix:$$\widehat{h}={w}_{j}{H}_{ij};\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}i=1,2,\dots ,m;\phantom{\rule{4pt}{0ex}}j=1,2,\dots ,n.$$
- Identify positive and negative ideal solutions ${S}^{+}$ and ${S}^{-}$ respectively as:$$\begin{array}{cc}\hfill {S}_{j}^{+}& =\{\left(\mathrm{max}{h}_{ij}\right|j\in t);\left(\mathrm{min}{h}_{ij}\right|j\in n-t)|i=1,2,\dots ,m\},\end{array}$$$$\begin{array}{cc}\hfill {S}_{j}^{-}& =\{\left(\mathrm{min}{h}_{ij}\right|j\in t);\left(\mathrm{max}{h}_{ij}\right|j\in n-t)|i=1,2,\dots ,m\},\end{array}$$
- The p-norm Euclidean distances ${D}_{i}^{+}$ and ${D}_{i}^{-}$ are determined as:$$\begin{array}{ccc}\hfill {D}_{i}^{+}& =& {\left\{\sum _{j=1}^{n}{\left({\widehat{h}}_{ij}-{S}_{j}^{+}\right)}^{p}\right\}}^{1/p}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}i=1,2,\dots ,m;\phantom{\rule{4pt}{0ex}}j=1,2,\dots ,n.\hfill \end{array}$$$$\begin{array}{ccc}\hfill {D}_{i}^{-}& =& {\left\{\sum _{j=1}^{n}{\left({\widehat{h}}_{ij}-{S}_{j}^{-}\right)}^{p}\right\}}^{1/p}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}i=1,2,\dots ,m;\phantom{\rule{4pt}{0ex}}j=1,2,\dots ,n.\hfill \end{array}$$
- Evaluate the relative closeness of each alternative using Equation (18) and rank them in descending order:$${G}_{i}=\frac{{D}_{i}^{-}}{{D}_{i}^{-}+{D}_{i}^{+}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}i=1,2,\dots ,m;\phantom{\rule{4pt}{0ex}}0\le {G}_{i}\le 1.$$

#### 3.3. Complex Proportional Assessment (Copras) Method

- Construct a hierarchy model for the said MCDM problem.
- Arrive at constructing the normalized decision matrix and determine the weights associated with each criterion as calculated in the case of the TOPSIS method.
- Determine weighted normalized matrix $\widehat{{H}_{ij}}$ using Equation (12).
- Determine the sum of weighted scores for beneficial and non-beneficial criteria using:$$\begin{array}{ccc}\hfill {R}_{i}^{+}& =& \sum _{j=1}^{t}{\widehat{h}}_{ij},\phantom{\rule{3.33333pt}{0ex}}{R}_{i}^{-}=\sum _{j=t+1}^{n}{\widehat{h}}_{ij}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}|\phantom{\rule{3.33333pt}{0ex}}i=1,2,\dots ,m,\hfill \end{array}$$
- Determine relative priorities for each alternative as:$$\begin{array}{c}\hfill {U}_{i}={R}_{i}^{+}+\frac{{\sum}_{i=1}^{m}{R}_{i}^{+}}{{R}_{i}^{-}{\sum}_{i=1}^{m}\frac{1}{{R}_{i}^{-}}}.\end{array}$$
- Arrive at the final priority score for each alternative and arrange them in descending order:$${L}_{i}=\frac{{U}_{i}}{{U}_{max}}\times 100\%.$$

## 4. Results and Discussion

## 5. Comparative Analysis of MCDM Methods

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Abhinav, R.; Pindoriya, N.M. Opportunities and key challenges for wind energy trading with high penetration in Indian power market. Energy Sustain. Dev.
**2018**, 47, 53–61. [Google Scholar] [CrossRef] - Hur, S.-H. Modelling and control of a wind turbine and farm. Energy
**2018**, 156, 360–370. [Google Scholar] [CrossRef] - Majumder, M. Impact of Urbanization on Water Shortage in Face of Climatic Aberrations; Springer: Singapore, 2015. [Google Scholar]
- Keyser, W.D.; Peeters, P. A note on the use of PROMETHEE multicriteria methods. Eur. J. Oper. Res.
**1996**, 89, 457–461. [Google Scholar] [CrossRef] - Haralambopoulos, D.; Polatidis, H. Renewable energy projects: Structuring a multi-criteria group decision making framework. Renew. Energy
**2003**, 28, 961–973. [Google Scholar] [CrossRef] - Georgiou, D.; Mohammed, E.S.; Rozakis, S. Multi-criteria decision making on the energy supply configuration of autonomous desalination units. Renew. Energy
**2015**, 75, 459–467. [Google Scholar] [CrossRef] - Kundakcı, N. An integrated method using MACBETH and EDAS methods for evaluating steam boiler alternatives. J. Multi-Criteria Decis. Anal.
**2018**, 26, 27–34. [Google Scholar] [CrossRef] - Lee, A.H.; Hung, M.C.; Kang, H.Y.; Pearn, W. A wind turbine evaluation model under a multi-criteria decision making environment. Energy Convers. Manag.
**2012**, 64, 289–300. [Google Scholar] [CrossRef] - Mahdy, M.; Bahaj, A.S. Multi criteria decision analysis for offshore wind energy potential in Egypt. Renew. Energy
**2018**, 118, 278–289. [Google Scholar] [CrossRef] [Green Version] - Kolios, A.; Rodriguez-Tsouroukdissian, A.; Salonitis, K. Multi-criteria decision analysis of offshore wind turbines support structures under stochastic inputs. Ships Offshore Struct.
**2016**, 11, 38–49. [Google Scholar] - Garni, H.A.; Kassem, A.; Awasthi, A.; Komljenovic, D.; Al-Haddad, K. A multicriteria decision making approach for evaluating renewable power generation sources in Saudi Arabia. Sustain. Energy Technol. Assess.
**2016**, 16, 137–150. [Google Scholar] [CrossRef] - Jahan, A.; Edwards, K.L. A state-of-the-art survey on the influence of normalization techniques in ranking: Improving the materials selection process in engineering design. Mater. Des. (1980–2015)
**2015**, 65, 335–342. [Google Scholar] [CrossRef] - Deng, Y.; Yu, Z.; Liu, S. A review on scale and siting of wind farms in China. Wind Energy
**2010**, 14, 463–470. [Google Scholar] [CrossRef] [Green Version] - Patel, P.; Shandilya, A.; Deb, D. Optimized hybrid wind power generation with forecasting algorithms and battery life considerations. In Proceedings of the 2017 IEEE Power and Energy Conference at Illinois (PECI), Champaign, IL, USA, 23–24 February 2017. [Google Scholar]
- Henriot, A. Economic curtailment of intermittent renewable energy sources. Energy Econ.
**2015**, 49, 370–379. [Google Scholar] [CrossRef] - Roth, M. Renewable Energy and Landscape Quality; Jovis Verlag: Berlin, Germany, 2018. [Google Scholar]
- Lowson, M.V. Assessment and Prediction of Wind Turbine Noise; Technical report; Flow Solutions Ltd.: Bristol, UK, 1993; ETSU-W–13/00284/REP. [Google Scholar]
- Hwang, C.L.; Yoon, K. Methods for Multiple Attribute Decision Making. In Multiple Attribute Decision Making: Methods and Applications A State-of-the-Art Survey; Springer: Berlin/Heidelberg, Germany, 1981; pp. 58–191. [Google Scholar] [CrossRef]
- Byun, H.; Lee, K. A decision support system for the selection of a rapid prototyping process using the modified TOPSIS method. Int. J. Adv. Manuf. Technol.
**2005**, 26, 1338–1347. [Google Scholar] [CrossRef] - Lourenzutti, R.; Krohling, R.A. A generalized TOPSIS method for group decision making with heterogeneous information in a dynamic environment. Inf. Sci.
**2016**, 330, 1–18. [Google Scholar] [CrossRef] - Balioti, V.; Tzimopoulos, C.; Evangelides, C. Multi-Criteria Decision Making Using TOPSIS Method Under Fuzzy Environment. Application in Spillway Selection. Proceedings
**2018**, 2, 637. [Google Scholar] [CrossRef] - Zolfani, S.H.; Chen, I.S.; Rezaeiniya, N.; Tamošaitienė, J. A hybrid mcdm model encompassing AHP and COPRAS-G methods for selecting company supplier in iran. Technol. Econ. Dev. Econ.
**2012**, 18, 529–543. [Google Scholar] [CrossRef] - Bhowmik, C.; Bhowmik, S.; Ray, A. The effect of normalization tools on green energy sources selection using multi-criteria decision making approach: A case study in India. J. Renew. Sustain. Energy
**2018**, 10, 065901. [Google Scholar] [CrossRef] - Tennekes, H. The Logarithmic Wind Profile. J. Atmos. Sci.
**1973**, 30, 234–238. [Google Scholar] [CrossRef] [Green Version] - Bishop and Clerks, Nantucket Sound|Wind Energy Center. Available online: https://www.umass.edu/windenergy/resourcedata/Bishop_and_Clerks (accessed on 20 February 2019).
- Nguyen, C.L.; Lee, H.H.; Chun, T.W. Cost-Optimized Battery Capacity and Short-Term Power Dispatch Control for Wind Farm. IEEE Trans. Ind. Appl.
**2015**, 51, 595–606. [Google Scholar] [CrossRef] - Saaty, R. The analytic hierarchy process—what it is and how it is used. Math. Model.
**1987**, 9, 161–176. [Google Scholar] [CrossRef] [Green Version]

Label | Criteria | Summary |
---|---|---|

${C}_{1}$ | Wind wakes | Cause power reduction |

${C}_{2}$ | Wind curtailment | Surplus power either fed to battery or used as power loan |

${C}_{3}$ | Forced outage | Reduces wind farm capacity |

Statistic | D1 (January 2011) | D2 (January 2013) | ||||
---|---|---|---|---|---|---|

Farm A | Farm B | Farm C | Farm A | Farm B | Farm C | |

Mean | 8.3364 | 8.3612 | 5.189 | 10.146 | 9.4411 | 6.1096 |

Std. Dev. | 3.2224 | 3.0543 | 2.4075 | 4.2897 | 2.8944 | 2.1752 |

Skewness | −0.0943 | −0.1040 | 0.9670 | −0.3428 | −0.3219 | 0.2102 |

Dataset | BESS Rating | BESS Threshold Limit |
---|---|---|

${D}_{1}$ | 15 MW | 110 kW |

${D}_{2}$ | 50 MW | 955 kW |

**Table 4.**Penalty cost and normalized cost score for Datasets D1 and D2. PC, Penalty Cost; NCS, Normalized Cost Score.

Alternatives | D1 | D2 | ||
---|---|---|---|---|

PC ($) | NCS | PC ($) | NCS | |

${A}_{1}$ | 1971.2 | 1.1665 | 6514.2 | 1.3238 |

${A}_{2}$ | 1689.8 | 1.0000 | 4920.8 | 1.0000 |

${A}_{3}$ | 3916.5 | 2.3177 | 13587 | 2.7612 |

${A}_{4}$ | 2252.8 | 1.3332 | 7444.8 | 1.5129 |

**Table 5.**Performance scores for the decision matrix [27].

Importance | Performance Score as per AHP | Performance Score in Current Work |
---|---|---|

Equally Preferred (EP) | 1 | 9 |

Equally to Moderately Preferred (EMP) | 2 | 8 |

Moderately Preferred (MP) | 3 | 7 |

Moderately to Strongly Preferred (MSP) | 4 | 6 |

Strongly Preferred (SP) | 5 | 5 |

Strongly to Very strongly Preferred (SVP) | 6 | 4 |

Very strongly Preferred (VP) | 7 | 3 |

Very strongly to Extremely Preferred (VEP) | 8 | 2 |

Extremely Preferred (XP) | 9 | 1 |

Alternatives | D1 | D2 | Ranking | ||
---|---|---|---|---|---|

PS | CPS | PS | CPS | ||

${A}_{1}$ | 0.3120 | 0.3640 | 0.3120 | 0.4130 | 3 |

${A}_{2}$ | 0.5021 | 0.5021 | 0.5021 | 0.5021 | 2 |

${A}_{3}$ | 1.0000 | 2.3177 | 1.0000 | 2.7612 | 1 |

${A}_{4}$ | 0.2529 | 0.3372 | 0.2529 | 0.3826 | 4 |

**Table 7.**Cumulative priority score and ranking based on the Complex Proportional Assessment (COPRAS) method.

Alternatives | D1 | D2 | Ranking | |||
---|---|---|---|---|---|---|

PS | CPS | PS | CPS | D1 | D2 | |

${A}_{1}$ | 0.2153 | 0.2511 | 0.2153 | 0.2850 | 4 | 4 |

${A}_{2}$ | 0.3857 | 0.3857 | 0.3857 | 0.3857 | 2 | 2 |

${A}_{3}$ | 1.0000 | 2.3177 | 1.0000 | 2.7612 | 1 | 1 |

${A}_{4}$ | 0.2079 | 0.2772 | 0.2079 | 0.3145 | 3 | 3 |

Alternatives | D1 | D2 | Ranking | ||
---|---|---|---|---|---|

PS | CPS | PS | CPS | ||

${A}_{1}$ | 0.0142 | 0.0166 | 0.0142 | 0.0188 | 3 |

${A}_{2}$ | 0.5323 | 0.5323 | 0.5323 | 0.5323 | 2 |

${A}_{3}$ | 1.0000 | 2.3177 | 1.0000 | 2.7612 | 1 |

${A}_{4}$ | 0.0104 | 0.0139 | 0.0104 | 0.0157 | 4 |

Alternatives | Initial | A_{4} | A_{1} | A_{2} |
---|---|---|---|---|

Rank | ||||

${A}_{4}$ | 4 | |||

${A}_{1}$ | 3 | 3 | ||

${A}_{2}$ | 2 | 2 | 2 | |

${A}_{3}$ | 1 | 1 | 1 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Dhiman, H.S.; Deb, D.; Muresan, V.; Unguresan, M.-L.
Multi-Criteria Decision Making Approach for Hybrid Operation of Wind Farms. *Symmetry* **2019**, *11*, 675.
https://doi.org/10.3390/sym11050675

**AMA Style**

Dhiman HS, Deb D, Muresan V, Unguresan M-L.
Multi-Criteria Decision Making Approach for Hybrid Operation of Wind Farms. *Symmetry*. 2019; 11(5):675.
https://doi.org/10.3390/sym11050675

**Chicago/Turabian Style**

Dhiman, Harsh S., Dipankar Deb, Vlad Muresan, and Mihaela-Ligia Unguresan.
2019. "Multi-Criteria Decision Making Approach for Hybrid Operation of Wind Farms" *Symmetry* 11, no. 5: 675.
https://doi.org/10.3390/sym11050675