Electric Distribution Systems from Facilities to End Users - Energy Conversion and Management - page 115

7.7 Practical Examples

Example 1 Calculate the losses in an electric industrial distribution line with
different levels of power factor control.
Below is a practical example of the calculation of losses in an industrial electric
distribution line with different levels of power factor control at load nodes. This
approach must be followed in order to evaluate the economic validity of installing
capacitors near the loads instead of placing them at the utility nodes (see Sect. 7.3 ).
In reference to Fig. 7.10 and on the assumption that load voltage V is kept
constant, the formulae used for calculation are
- Line current

P

I ¼

p V cos

φ

- Total line losses

P 2

RT

I 2 PL ¼ 3 RT ¼

2

ð V cos φ Þ

- Line voltage drop

p 3

Δ V ¼ I ð RT cos φ þ XT sin φ Þ

- Maximum loading power with a voltage drop of 5 %

V 2

5
100

φ
RT cos φ þ XT sin φ

cos

¼

PMV

- Maximum loading power with rated current I n

Fig. 7.10 Simplified equivalent circuit for a distribution line