*4.1. Test System*

The distribution network used to evaluate the optimal siting and sizing of the BESS was the IEEE 33-bus distribution network shown in Figure 1, and the detailed data can be obtained from [14]. The values of load power at each bus can be obtained from the voltage magnitude at each bus (in per unit) without any RES connection according to Equations (18) and (19).

$$P\_{L-i} = P\_{0i}(a\_p + b\_p|V\_i| + c\_p|V\_i|^2) \tag{18}$$

$$Q\_{L-i} = Q\_{0i}(a\_q + b\_q|V\_i| + c\_q|V\_i|^2) \tag{19}$$

where *PL*−*i*, *QL*−*<sup>i</sup>* are the active power and reactive power at the *i*th bus, respectively. *P*0*i*, *Q*0*<sup>i</sup>* are the initial active power and reactive power at the *i*th bus, respectively, *ap* + *bp* + *cp* = 1, *aq* + *bq* + *cq* = 1, base voltage (*V*base) = 12.66 kV, base power (*MVA*base) = 10 MVA. The two types of RESs, wind turbines (WTs) and photovoltaics (PVs), were connected in the distribution network. Two WTs (1 MW) were each located at buses 18 and 24, three PVs (400 kVA) each were installed at buses 5, 21, and 31, and four PVs (500 kVA) each were installed at buses 8, 12, 28, and 33. In this test system, the parameters were set as *ap* = *aq* = 0.4, *bp* = *bq* = 0.3, and *cp* = *cq* = 0.3. Peak active and reactive powers of the test system were 3.556 MW and 2.191 MVar, respectively. The detailed data of load magnitude and the output generations of WTs and PVs can be found in [14,21].

**Figure 1.** IEEE 33 bus distribution network [14].
