Power Quality Issues in Traction Power Systems - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 170

A
B
C

i B i C i A

B A

C

a i a

i b b

c

i c

i rb i ra

i sc

i sb

i sa

i L

i L

Section
insulator

SPC

Figure 9.1 Traction power system with a single feeding wire equipped with a V/V transformer

The load current i L is assumed to be purely sinusoidal without any harmonics for the
moment (the case with harmonic currents will be discussed later) and the power factor is cos θ .

Then, the load current can be expressed as

6 − θ

I L =

I L 1 ∠ (9.2)

where I L 1 is the RMS value of the fundamental load current. The three-phase grid currents
without any compensation are

⎧
⎨

6 − θ

I L 1
K V ∠

I A =

,

I L 1
K V ∠

5
6 π − θ

(9.3)

I B =

− ,

⎩

I C =

0 ,

as shown in Figure 9.2(a). It is obvious that the three-phase grid currents are unbalanced. Both
reactive and active current components are included in I A and I B as they are not in phase
with U A and U B , respectively. Phase-A current leads its voltage by 6 − θ and Phase-B current

− 6 leads its voltage by − θ . A significant amount of negative-sequence currents exists in the

grid currents.