*3.2. Constraints*

(1) Voltage Constraint: Voltage of each bus must be limited within the lower and upper limit throughout the consideration period set at ±5% of the reference voltage as the expressed equation.

$$V\_{\text{lower}} \le V\_i^t \le V\_{\text{upper}} \tag{15}$$

where *V*lower and *V*upper are the lower bound and upper bound of voltage at *i*th bus, respectively, and *V<sup>t</sup> <sup>i</sup>* is the voltage magnitude at *i*th bus in time *t*.

(2) Battery Constraint: The power and capacity of the battery are bounded to ensure that the battery operation does not exceed the boundary limits during charging or discharging, which can be presented as the equation below.

$$P\_{B-min} \le P\_{\text{chn}'}^t P\_{\text{dis}}^t \le P\_{B-\text{max}} \tag{16}$$

$$E\_{B-\text{min}} \le E\_B^t \le E\_{B-\text{max}}\tag{17}$$

where *PB*−*min*, *PB*−*max* are the minimum and maximum power of BESS, respectively. *Pt cha*, *Pt dis* are the power charge rate and power discharge rate of BESS at time *t*, respectively. *EB*−*min*, *EB*−*max* are the minimum and maximum capacity of BESS, respectively.
