Loads currents are exactly the same as in above example (delta connected reactive loads).

Next , analyze currents to terminals of connected capacitors

Id = { Sxn /Vxn}* = { -jQ/V_p/_0°}* = { (Q/V_p) /_-90°}* = { (Q/V_p) /_90°}

Ie = { Syn /Vyn}* = { -jQ/V_p/_-120°}* = { (Q/V_p) /_(-90° + 120°) } * = { (Q/V_p) /_30°}*= { (Q/V_p) /_-30°}

If = { Szn /Vzn}* = { -jQ/V_p/_-240°}* = { (Q/V_p) /_(-90° + 240°)}* = { (Q/V_p) /_150°}*= { (Q/V_p) /_-150°}

Ia = Id + Ig = { (Q/V_p) /_90°} + | Ig | /_ - cos ^-1 pfi

Ib = Ie+ Ih = { (Q/V_p) /_-30°} + | Ih | /_ { (- cos ^-1 pfi ) - 120° }

Ic = If+ Ii = { (Q/V_p) /_-150°} + | Ii | /_ { (- cos ^-1 pfi ) - 240° } Let's find value of capacitance, C :

Xc = V_p / i = 1/(wC)
V_p/ (Q/Vp) = 1/wC
C= Q/(w x V_p ²) where w= 2 x pi x f.

Similarly, the resultant currents at load side and supply side are identical to that calculated in the case of delta connected reactive load

A 3-phase 415V supply delivers a balanced 3-phase load of 300kW , power factor lagging 0.75 is to be corrected to 0.87

Load current of line R, Ig = | Ig | /_ - cos ^-1 pfi = 100kW /(240V x 0.76) /_- cos ^- 0.75 =555.55 /_-41.4° A

From Table 4D1A of 16th Edition IEE Wiring Regulation (BS 7671), 4 x 1core mm 185 sq PVC Cu carry 296A
Therefore use cable 8 x 1core 185 mm sq PVC Cu (carry 2 x 296A=592A > 555.55A) ok.

Reactive power (single phase), Q=100kW x [ ( tan cos ^-1 0.75 ) - (tan cos ^-1 0.87) ] = 31.5kVar

Capacitor line current, Id = (Q/Vp) /_90° = 31,500/240 /_90°A = 131.25 /_90°
Use 150A 3-pole MCCB and 3 x single core 70 mm sq PVC (171A capacity)

Supply current of line R,    Ia = Ig + Id = 555.55 /_-41.4° + 131.25 /_90° = 416.7 - j236.1 =478.9 /_ -29.5°

From Table 4D1A of 16th Edition IEE Wiring Regulation (BS 7671), 4 x 1core 120 mm sq PVC Cu carry 296A
Therefore use cable 8 x 1core 150 mm sq PVC Cu (carry 2 x 262A=524A > 478.8A) ok.
or use cable 4 x 1core 500 mm sq PVC Cu (carry 533A > 478.8A) ok

Notice that besides PF is improved from 0.75 to 0.87, smaller sized cables of 2 x 150mm per phase is required to carry supply current when cap bank is installed as compared to bigger cable of 2 x 185 mm sq at load side.

• Required final power factor can be achieved by either using wye or delta connected reactive loads
• delta connected capacitor:
  • used for low voltage application
  • phase voltage (Vp) equals line voltage (V_L). Because of this it's not recommended for high voltage use since high insulation is required.
  • capacitance, C=1.732 Q/(wV_L²)
• wye connected capacitors
• used for high voltage installation
• phase voltage (Vp) equals V_L/1.732
• capacitance, C=Q/(wVp²)