*3.3. Energy Diversity Weighted by Energy Import Dependence*

The presented diversity indices, such as the *SWI* and *HHI*, only depend on the quantity and the proportion of each energy resource, considering the proportion of each energy resource is effective when energy resources are less dependent on other countries in the energy supply security of a country. However, its effectiveness could be reduced in a country highly dependent on energy imports. This country could not be evaluated as a secure country in terms of energy supply security, even though the country obtains a higher value of the *SWI* and a lower value of the *HHI*. In other words, these indices seem to lack a fundamental factor indicating the dependence of the target energy source on imports. Therefore, this study proposed modified indices of energy diversity by weighting the import dependence-related parameters. The main concept of these indices is to imply energy import dependence into the diversity indices. Weighted factors stemming from the import dependence of each energy type are multiplied into the energy diversity indices, the *SWI* and *HHI*. The proposed indices are expressed below:

$$D\_{-}SWI = -\sum\_{i=1}^{N} \left(1 - \frac{EI\_i}{ES\_i}\right) p\_i \ln p\_i \tag{8}$$

$$D\_{-}HHI = \sum\_{i=1}^{N} \left(1 + \frac{EI\_i}{ES\_i}\right) P\_i^2 \tag{9}$$

where the *D\_SWI* and the *D\_HHI* demonstrate the modified *SWI* and *HHI*, which imply energy import dependence. In the case of the *D\_SWI*, (1 − *EIi*/*ESi*) is the inverse weight obtained by the share of *i*th energy source imports in supply. Its range is from 0 to 1 and reflects how much the *i*th energy type is self-sufficiently supplied to the country. The theoretical maximum value of the *D\_SWI* may be obtained when the number of types of energy sources is higher and that the quantity of each source is even. In addition, all the considered energy sources should be self-sufficient which means (1 − *EIi*/*ESi*) equals 1. By contrast, the *D\_SWI* becomes smaller when the share of energy imports increases (*EIi*/*ESi* > 0), even though the value of the *SWI* is the *SWIMax*. In the case of *D\_HHI*, however, its theoretical minimum value could be obtained when the share of *i*th energy source imports in supply *EIi*/*ESi* is zero and the *HHI* reaches the *HHImin* simultaneously. As the weighting is a process to assign a relatively important factor in each index [38,39], these proposed indices can be effective, especially to evaluate the primary energy supply security of the countries highly dependent on energy imports such as Singapore, Taiwan, Japan, and Korea.

## *3.4. Data for Evaluation*

In this study, time series data were obtained from a dataset from the Korea Energy Economics Institute [40]. The assessment was conducted with 10 primary energy sources, including anthracite coal, bituminous coal, petroleum for energy use, LPG, petroleum for non-energy use, LNG, general and micro-hydro, pumped hydro, nuclear, and renewables for the period from 1991 to 2018. The data were used for measuring four indices which are the import ratio of energy, energy import dependence, energy diversity represented by the *SWI* and *HHI*, and the mixed indices of energy import dependence and energy diversity.

#### **4. Results and Discussion**
