*4.5. System Performance Evaluation*

To evaluate the system performance after the BESS installation based on the objective function, voltage deviation, power loss, and peak demand were investigated. The details are as follows.

#### 4.5.1. Voltage Deviation Index (VDI)

To evaluate the voltage profile improvement, the VDI was applied to represent the voltage deviation of each case. The VDI compared the voltage level of each bus (*Vbi* in p.u.) with the reference voltage (*V*ref = 1 p.u.) and is presented in percent (%*VDI*). The VDI can be calculated by the expressed equations.

$$\%VIDI\_i = \max\_{i}^{T} \left( \frac{|V\_{\text{ref}} - V\_{bi}|}{V\_{\text{ref}}} \right) \times 100 \tag{22}$$

$$\%VDI = \sum\_{i=1}^{N} \%VDI\_i \tag{23}$$

where %*VDIi* is the VDI of the *i*th bus, and %*VDI* is the total VDI of the distribution network.
