3.2.1. The Shannon-Wiener Index (SWI)

The *SWI* is expressed by accounting for the share of each primary energy source as follows:

$$SWI = -\sum\_{i=1}^{N} p\_i \ln p\_i \tag{3}$$

$$p\_i = \frac{ES\_i}{ES\_T} \tag{4}$$

where *pi* is the share of primary energy supply by the *i*th energy source *ESi* in the total primary energy supply *EST*. The smallest value of the *SWI* is zero in the case where there is only one primary energy supply option in the country. It means the sole option takes 100% of the total primary energy supply. Then, the share of this energy source *pi* becomes one. Consequently, ln (1) equals zero, and the *SWI* thus becomes zero. By contrast, the theoretical maximum value of the *SWI* may be obtained when the shares of primary energy sources are even, which means that *pi* equals 1/*N* and that the number of types of energy sources becomes larger. If the share of each option is uneven, the value of the *SWI* is less than its theoretical maximum value, *SWIMax*.

$$SWI\_{\text{Max}} = -N \frac{1}{N} \ln \frac{1}{N} = \ln N \tag{5}$$

## 3.2.2. The Herfindahl-Hirschman Index (HHI)

The *HHI* shows the concentration of the individual share of energy options. It is expressed by the sum of the square of the proportion of each energy source as follows:

$$HHI = \sum\_{i=1}^{N} P\_i^2 = \sum\_{i=1}^{N} (p\_i \times 100)^2 \tag{6}$$

where *Pi* is the percentage of the primary energy supply by the *i*th energy source *ESi* in the total primary energy supply *EST*. As this index uses the square of the percentage of each energy source, the index highlights quantitatively bigger energy resources rather than smaller ones in whole options. This means that the *HHI* emphasizes abundant energy resources. Opposite to the *SWI*, the lower the value of the *HHI,* the higher the diversity. The theoretical minimum value of *HHI* is expressed as follows:

$$HHI\_{\rm min} = N\left(\frac{1}{N} \times 100\right)^2 = \frac{1}{N} \times 10000\tag{7}$$
