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Classical-Equivalent Bayesian Portfolio Optimization for Electricity Generation Planning^{ †}

^{1}

^{2}

^{3}

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^{†}

## Abstract

**:**

## 1. Introduction

_{2}emission and the corresponding mechanisms will surely impact the electricity generation costs. Precisely, the future price of an emitted ton of CO

_{2}is uncertain and this uncertainty should be considered in the planning process. Consequently, electricity generation policies solely relying on the evolution of historical average costs of electricity generation technologies are unsatisfactory. The careful consideration of the uncertainties associated with the current and the prospective costs of such technologies is fundamental for planning purposes.

## 2. Classical or Naive Mean-Variance Approach

## 3. Classical-Equivalent Bayesian Mean-Variance Approach

#### 3.1. Improper Prior Case

#### 3.2. Proper Prior Case

## 4. Results

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

MPT | Modern Portfolio Theory |

USD | United States Dollar |

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**Figure 1.**Efficient frontiers using naive and classical-equivalent Bayesian approaches for the improper prior case for some values of T.

**Figure 2.**Efficient frontiers using naive and classical-equivalent Bayesian approaches for the proper prior case for some values of $\tau $.

**Table 1.**The means and standard deviations of costs for existing plants and prospective ideas of building new plants for different energy generation technologies from [35] (values are in cents of USD/kWh).

Energy Generation Technology | ${\widehat{\mathit{\mu}}}_{\mathit{i}}^{\mathit{e}}$ | ${\widehat{\mathit{\mu}}}_{\mathit{i}}^{\mathit{p}}$ | ${\widehat{\mathit{\sigma}}}_{\mathit{i}}^{\mathit{e}}$ | ${\widehat{\mathit{\sigma}}}_{\mathit{i}}^{\mathit{p}}$ |
---|---|---|---|---|

gas | 09.9010 | 09.2770 | 0.1500 | 0.1500 |

coal | 11.5560 | 11.1180 | 0.1125 | 0.1187 |

nuclear | 10.1260 | 10.0110 | 0.0625 | 0.1500 |

fuel oil | 19.0980 | 16.4680 | 0.2250 | 0.2188 |

biomass | 14.0390 | 13.4560 | 0.0813 | 0.0875 |

large hydropower | 04.1200 | 05.0240 | 0.0313 | 0.2062 |

wind | 10.9860 | 10.4440 | 0.0250 | 0.1187 |

small hydropower | 06.8850 | 06.9090 | 0.0187 | 0.1187 |

**Table 2.**The correlations of the fuel costs between different energy generation technologies from [35].

Energy Generation Technology | 1. | 2. | 3. | 4. | 5. | 6. | 7. | 8. |
---|---|---|---|---|---|---|---|---|

1. gas | 01.00 | |||||||

2. coal | 00.47 | 01.00 | ||||||

3. nuclear | 00.06 | 00.12 | 01.00 | |||||

4. fuel oil | 00.49 | 00.27 | 00.08 | 01.00 | ||||

5. biomass | −0.44 | −0.38 | −0.22 | −0.17 | 01.00 | |||

6. large hydropower | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 01.00 | ||

7. wind | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 01.00 | |

8. small hydropower | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 00.00 | 1.00 |

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## Share and Cite

**MDPI and ACS Style**

Takada, H.H.; Stern, J.M.; Costa, O.L.V.; Ribeiro, C.O. Classical-Equivalent Bayesian Portfolio Optimization for Electricity Generation Planning. *Entropy* **2018**, *20*, 42.
https://doi.org/10.3390/e20010042

**AMA Style**

Takada HH, Stern JM, Costa OLV, Ribeiro CO. Classical-Equivalent Bayesian Portfolio Optimization for Electricity Generation Planning. *Entropy*. 2018; 20(1):42.
https://doi.org/10.3390/e20010042

**Chicago/Turabian Style**

Takada, Hellinton H., Julio M. Stern, Oswaldo L. V. Costa, and Celma O. Ribeiro. 2018. "Classical-Equivalent Bayesian Portfolio Optimization for Electricity Generation Planning" *Entropy* 20, no. 1: 42.
https://doi.org/10.3390/e20010042