Decision tools from index fund finance to explore the path towards a scenario of renewable energy generation with globalization and high specialization of regional electricity markets

.title[
# Decision tools from index fund finance to explore the path towards a scenario of renewable energy generation with globalization and high specialization of regional electricity markets
]
.author[
### Orlando Joaqui-Barandica <strong>|</strong> Diego F. Manotas-Duque <strong>|</strong> Jorge M. Uribe
]
.date[
### <br> 8° ELAEE 2022 <br> BOGOTÁ, COLOMBIA
]

---

]
]

.center[
<img style="border-radius: 50%;" src="img/avatar.png"
width="100px" href="https://www.joaquibarandica.com"
/>

[Orlando Joaqui-Barandica, M.Sc.](https://www.joaquibarandica.com) <br/>
Universidad del Valle
]

[Diego F. Manotas-Duque, Ph.D.](http://industrial.univalle.edu.co/profesores/diego-fernando-manotas-duque) <br>
Universidad del Valle
]

[Jorge M. Uribe, Ph.D.](https://jorgemuribe.com/) <br>
Universitat Oberta de Catalunya
]

]

???

Buenas tardes, el día de hoy socializaré mi propuesta de investigación doctoral en tópicos de activos y pasivos: una visión comparativa entre economías emergentes y desarrolladas.

Esta propuesta doctoral está bajo la dirección del profesor Diego Manotas de la Escuela de Ing. Industrial de la Universidad del Valle. Y el profesor Jorge M. Uribe de la Universitat Oberta de Catalunya..

Este trabajo de investigación está integrado al grupo de investigación GIFINC de la Esc. de Ing. Ind.

---

# Motivation

???

---

# Motivation

### Three fundamental characteristics of future energy markets are:

]

> - Almost all electricity will be generated by variable renewable energy technologies (VRE) such as wind turbines and solar cells, and by hydropower sources.

<hr>

> - Further transnational integration of energy markets will be required with the aim of diversifying the climate and weather risk.

<hr>

> - Energy storage, especially green hydrogen technologies, will play a critical role.

]
]
]

---

# Motivation

<br>

.font170[Literature has extensively explored `portfolio optimization techniques` similar to those developed from a capital allocation perspective in finance...

]
]

<br>

.right[
.font170[...to construct an optimal generation mix of electricity that consists of different renewable energy technologies `(wind, sun, hydro)` and diverse geographical locations to conduct the energy transformation.
]
]

---

# We consider a different although 
<br>
# related problem

.center[<svg aria-hidden="true" role="img" viewBox="0 0 352 512" style="height:5em;width:3.44em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M96.06 454.35c.01 6.29 1.87 12.45 5.36 17.69l17.09 25.69a31.99 31.99 0 0 0 26.64 14.28h61.71a31.99 31.99 0 0 0 26.64-14.28l17.09-25.69a31.989 31.989 0 0 0 5.36-17.69l.04-38.35H96.01l.05 38.35zM0 176c0 44.37 16.45 84.85 43.56 115.78 16.52 18.85 42.36 58.23 52.21 91.45.04.26.07.52.11.78h160.24c.04-.26.07-.51.11-.78 9.85-33.22 35.69-72.6 52.21-91.45C335.55 260.85 352 220.37 352 176 352 78.61 272.91-.3 175.45 0 73.44.31 0 82.97 0 176zm176-80c-44.11 0-80 35.89-80 80 0 8.84-7.16 16-16 16s-16-7.16-16-16c0-61.76 50.24-112 112-112 8.84 0 16 7.16 16 16s-7.16 16-16 16z"/></svg>]

???

---

# Motivation

<br>

.center[<svg aria-hidden="true" role="img" viewBox="0 0 496 512" style="height:7em;width:6.78em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M248 8C111.03 8 0 119.03 0 256s111.03 248 248 248 248-111.03 248-248S384.97 8 248 8zm82.29 357.6c-3.9 3.88-7.99 7.95-11.31 11.28-2.99 3-5.1 6.7-6.17 10.71-1.51 5.66-2.73 11.38-4.77 16.87l-17.39 46.85c-13.76 3-28 4.69-42.65 4.69v-27.38c1.69-12.62-7.64-36.26-22.63-51.25-6-6-9.37-14.14-9.37-22.63v-32.01c0-11.64-6.27-22.34-16.46-27.97-14.37-7.95-34.81-19.06-48.81-26.11-11.48-5.78-22.1-13.14-31.65-21.75l-.8-.72a114.792 114.792 0 0 1-18.06-20.74c-9.38-13.77-24.66-36.42-34.59-51.14 20.47-45.5 57.36-82.04 103.2-101.89l24.01 12.01C203.48 89.74 216 82.01 216 70.11v-11.3c7.99-1.29 16.12-2.11 24.39-2.42l28.3 28.3c6.25 6.25 6.25 16.38 0 22.63L264 112l-10.34 10.34c-3.12 3.12-3.12 8.19 0 11.31l4.69 4.69c3.12 3.12 3.12 8.19 0 11.31l-8 8a8.008 8.008 0 0 1-5.66 2.34h-8.99c-2.08 0-4.08.81-5.58 2.27l-9.92 9.65a8.008 8.008 0 0 0-1.58 9.31l15.59 31.19c2.66 5.32-1.21 11.58-7.15 11.58h-5.64c-1.93 0-3.79-.7-5.24-1.96l-9.28-8.06a16.017 16.017 0 0 0-15.55-3.1l-31.17 10.39a11.95 11.95 0 0 0-8.17 11.34c0 4.53 2.56 8.66 6.61 10.69l11.08 5.54c9.41 4.71 19.79 7.16 30.31 7.16s22.59 27.29 32 32h66.75c8.49 0 16.62 3.37 22.63 9.37l13.69 13.69a30.503 30.503 0 0 1 8.93 21.57 46.536 46.536 0 0 1-13.72 32.98zM417 274.25c-5.79-1.45-10.84-5-14.15-9.97l-17.98-26.97a23.97 23.97 0 0 1 0-26.62l19.59-29.38c2.32-3.47 5.5-6.29 9.24-8.15l12.98-6.49C440.2 193.59 448 223.87 448 256c0 8.67-.74 17.16-1.82 25.54L417 274.25z"/></svg>]
]

.font120[
> We provide a way for a government to decide, in a globalized market of electricity:
- Which firms (and power plants) should be ideally preserved (and encourage) in case that specialization dictates concentrating the national generation efforts on a fixed number of firms (or a few locations), and therefore, on fewer power plants than those already in operation.

]

---

# Methodology and Data

???

---

# Optimization model

> <span><i class="fas  fa-angle-double-right faa-passing animated "></i></span> We perform an optimization using the correlation matrix of observed weather configurations and progressively reducing the number of power plants that better preserve the actual weather/climate risk configuration.

<br>

`$$ρ_{ij}: \text{Correlation between plant i and plant j}$$`

`$$x_{ij} = \left\{\begin{matrix}
1 & \text{if j is the most similar plant} \\
  & \text{in the optimal portfolio} \\
0 & otherwise 
\end{matrix}\right.$$`

`$$y_{j} = \left\{\begin{matrix}
1 & \text{if the plant j is selected} \\
  & \text{in the optimal portfolio} \\
0 & otherwise 
\end{matrix}\right.$$`

]

Objective function

`$$Z=Max\ \ \sum_{i=1}^{n}\sum_{j=1}^{n}{\rho_{ij}x_{ij}}$$`

Subject to:

- `$$\sum_{j=1}^{n}y_j=q$$`

- `$$\sum_{j=1}^{n}x_{ij}=1\ \ \ \ \ \ \ \ \ \ \ \ \ \ for\ i=1,\ \ldots,n$$`

- `$$x_{ij}\le y_j$$`

]

---

# Data

<br>

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</style>
<table class="gt_table">
  <thead class="gt_header">
    <tr>
      <th colspan="3" class="gt_heading gt_title gt_font_normal gt_bottom_border" style><strong>Sources of energy generation in Argentina</strong></th>
    </tr>
    
  </thead>
  <thead class="gt_col_headings">
    <tr>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">Type</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">n = 106</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">MW = 16,746 *</th>
    </tr>
  </thead>
  <tbody class="gt_table_body">
    <tr><td class="gt_row gt_left">Wind plants</td>
<td class="gt_row gt_left">38</td>
<td class="gt_row gt_left">16.3%</td></tr>
    <tr><td class="gt_row gt_left">Solar plants</td>
<td class="gt_row gt_left">34</td>
<td class="gt_row gt_left">9.0%</td></tr>
    <tr><td class="gt_row gt_left">Hydraulic plants</td>
<td class="gt_row gt_left">34</td>
<td class="gt_row gt_left">74.7%</td></tr>
  </tbody>
  <tfoot class="gt_sourcenotes">
    <tr>
      <td class="gt_sourcenote" colspan="3">*These plants represent an installed power capacity of more than 16,747 MW</td>
    </tr>
  </tfoot>
  
</table>
</div>

<br>

> <span><i class="fas  fa-angle-double-right faa-passing animated "></i></span> We select the country of Argentina and use 106 main power generation plants that use different production technologies associated with wind, solar and hydraulic sources.

]

<br>

> <span><i class="fas  fa-angle-double-right faa-passing animated "></i></span> We extract for each coordinate according to its type of generation, information on wind speed at 2m, solar irradiation (JM/m2) and precipitation (mm). Climate information is extracted from 01/01/2000 to 01/01/2022 with a daily frequency.

]
]

---

# Results and Conclusion

???

---

# Results

<br>

> <span><i class="fas  fa-angle-double-right faa-passing animated "></i></span> Distribution of the number of plants for each optimal portfolio. **Note:** The axis of the optimal portfolio represents the number q of plants specialized in preserving the correlation structure of the energy network.

---

# Results

<br>

> <span><i class="fas  fa-angle-double-right faa-passing animated "></i></span> Geographic distribution of plants optimally selected. **Note:** We select some values of q to identify as our model achieves in diversifying climatic variability from a geographic perspective.

---

# Results

<br>

> <span><i class="fas  fa-angle-double-right faa-passing animated "></i></span> Averages of the meteorological series. **Note:** This figure shows the behavior of all the climatic series associated with an optimal portfolio with *q=30*. We use this value of *q* to exemplify the climatic variability of each type of source.

---

# Results

<br>

> <span><i class="fas  fa-angle-double-right faa-passing animated "></i></span> 12 months Moving average for meteorological series. **Note:** This figure shows some optimal portfolio for *q = 5, 30, 60, 100,* where each series is the moving average of the set of meteorological series by generate source.

---

# Conclusion

]

.right-column[
.font120[
> We adapt integer portfolio optimization tools from finance to show how a government can transit, if required, to a scenario of electricity generation based on renewable energy sources, and fewer power plants than those already operating in the country.

<br>

<hr>

<br>

> The main objective of the government is to preserve the configuration of weather risks, which is determinant for variable renewable energy technologies, as stable as possible during such a transition.

]
]

???

---

# Conclusion

]

.right-column[
.font120[
> We resort to these fundamental weather factors and show that our model is able to provide the path that could be optimally transited during the transition to a more specialized electricity market in Argentina.

<br>

<hr>

<br>

> An extension would be to incorporate more than one country in the model, in order to directly target the problem of globalized markets, from a supranational perspective, instead of a restricted optimization problem that only concerns a single national unit.

]
]

???

---

<br>

]

# Gracias !!!

.font140[**|**] <span><i class="fas  fa-envelope faa-passing animated "></i></span> orlando.joaqui@correounivalle.edu.co

.font140[**|**] <span><i class="fas  fa-envelope faa-passing animated "></i></span> diego.manotas@correounivalle.edu.co

]

???