*Appendix A.6. Objective Function*

The objective of the power trade model is to minimize the total cost of electricity during the period of this study. The objective function is written as:

$$\mathbf{b}\mathbf{b}\mathbf{j} = \sum\_{i=1}^{I} \sum\_{\mathbf{v}=1}^{T} \sum\_{\mathbf{m}=1}^{M} \mathbf{c}\_{\mathbf{m}\mathbf{v}} \ast \mathbf{x}\_{\mathbf{m}\mathbf{v}} + \sum\_{t=1}^{T} \left\{ \mathbf{Opex}(\mathbf{t}) + \mathbf{CC}(\mathbf{t}) + \mathbf{TC}(\mathbf{t}) \right\} \tag{A1}$$

#### *Appendix A.7. Constraint Conditions*

There are several constraints that are required to optimize the above objective function.

Equation (A2) shows a first set of constraints, which requires total power capacity to meet total power demand in the region. *Qitp* is the power demand of country *i* in year *t* for load block *p*.

$$\sum\_{i=1}^{I} \sum\_{j=1}^{J} \sum\_{m=1}^{M} \sum\_{v=-V}^{t} \mu\_{mijtvp} \ge \sum\_{i=1}^{I} \mathcal{Q}\_{itp} \tag{A2}$$

The second one, shown in Equation (A3), states the constraint of load factor *l fmi* of each installed capacity of power generation. *kitmi* is the initial vintage capacity of type *m* power plant in country *i.*

$$\|u\_{mijtvp} \le lf\_{mi} \* \left(kit\_{mi} + \mathcal{x}\_{miv}\right) \tag{A3}$$

The third constraint, shown in Equation (A4), says that power supply of all countries to a certain country must be greater than the country's power demand. *tli*,*<sup>j</sup>* is the ratio of transmission loss in cross-border electricity trade between country *i* and country *j*.

$$\sum\_{j=1}^{J} \sum\_{m=1}^{M} \sum\_{v=-V}^{t} u\_{mijtvp} \cdot tl\_{ij} \ge Q\_{itp} \tag{A4}$$

The fourth constraint, shown in Equation (A5), states that total supply of power of one country to all countries (including itself) must be smaller than the summation of the country's available power capacity at the time.

$$\sum\_{j=1}^{J} \mu\_{mijtvp} \le \sum\_{m=1}^{M} \sum\_{v=-V}^{t} l f\_{mi} \ast (kit\_{mi} + x\_{miv}) \tag{A.5}$$

The fifth constraint, shown in Equation (A6), is capacity reserve constraint. *pr* is the rate of reserve capacity as required by regulation. Moreover, *p* = 1 represents the peak load block. *<sup>I</sup>*

$$\sum\_{i}^{I} \sum\_{m=1}^{M} \sum\_{v=-V}^{t} l f\_{mi} \* (k \dot{t}\_{mi} + \mathbf{x}\_{miv}) \ge (1 + pr) \* \sum\_{i}^{I} Q\_{it, p = 1} \tag{A6}$$

Hydro-facilities have the so-called an energy factor constraint as shown in Equation (A7). *e fmi* is the energy factor of plant type *m* in country *i*. Other facilities have *ef* = 1.

$$\sum\_{p=1}^{P} \sum\_{j=1}^{J} u\_{mijtvp} \le cf\_{mi} \* (kit\_{mi} + x\_{miv}) \tag{A7}$$

Lastly, development of power generation capacity faces resource availability constraint, which is shown in Equation (A8). *XMAXmi* is the type of resource constraint of plant type *m* in country *i*.

$$\sum\_{w=1}^{T} x\_{\rm univ} \le X\\MAX\_{\rm mi} \tag{A8}$$
