Power Quality in Industrial Commercial Power Systems
Power Quality in Industrial Commercial Power Systems
Power Quality in Industrial Commercial Power Systems
POWER QUALITY
1. Introduction
The quality of the electrical supply is an important
consideration for both power utilities and consumers.
Electrical engineers have always been concerned about power
quality. They see it as anything that affects voltage, current,
and frequency of power being supplied to end-users.
Since the late 1980s, the emphasis has shifted from reliability
concern at generation, transmission and distribution level to
concern about PQ at the customer or end-user level.
2.1 Transients
(1) Overvoltage
(2) Undervoltage
(1) Interruption
1 − 3 − 6β
Percent unbalance = × 100%
1 + 3 − 6β
(2) Harmonics
(3) Inter-harmonics
(4) Notching
(5) Noise
X 1b X 2b
X 0 a = X 0b = X 0 c
X 2 a = X 2b = X 2 c θ 0 a − θ 0 b = 00
X 1a = X 1b = X 1c
θ 2 a − θ 2b = −1200 θ 0 b − θ 0 c = 00
θ1a − θ1b = 1200
θ1b − θ1c = 1200 θ 2b − θ 2c = −1200
X 1a = X 1a ∠θ1a X 2 a = X 2 a ∠θ 2a X 0 a = X 0 a ∠θ 0a
X 1b = a 2 X 1a X 2b = aX 2 a X 0b = 1X 0 a
X 1c = aX 1a X 2c = a 2 X 2 a X 0 c = 1X 0 a
An unbalanced 3φ sequence ( X a , X b , X c )
X a = X a ∠θ a
Xc Xa X b = X b ∠θ b
X c = X c ∠θ c
Xa ≠ Xb ≠ Xc
Xb θ a − θ b ≠ θ b − θ c ≠ θ c − θ a ≠ 1200
1
-a3 a3
a2 -a
Also: 1 + a = 1∠600 = − a 2
1 − a = 3∠ − 300 = 1.5 − j 0.866
1 + a 2 = 1∠ − 600 = − a
1 − a 2 = 3∠300 = 1.5 + j 0.866
a + a 2 = −1
a − a2 = j 3
1 + a + a2 = 0
i.e. X 0a =
1
3
( Xa + Xb + Xc )
1
(
X 1a = X a + aX b + a 2 X c
3
)
1
(
X 2 a = X a + a 2 X b + aX c
3
)
Example:
X 1c X 2a
X 1a X 0a X 0b
X 2c
+ + X 0c
X 1b X 2b
X 0a
Xa
Xc X 2a
X 1a
=
Xb
T
1
where: a0 = ∫ f ( t )dt
T0
T
2
an = ∫ f ( t ) cos ( nωt )dt
T0
T
2
bn = ∫ f ( t ) sin ( nωt )dt
T0
∑ n
V
n=2
2
THDV = × 100%
V1
Note that this is the definition adopted by the IEEE. For the
IEC, THD is calculated as a percentage of the total rms (not
the rms of just the fundamental). The THDI for current is
expressed in a similar manner. THD is related to the rms
value of the total waveform as follows:
∞ 2
⎛ THDV ⎞
V = ∑Vn2 = V1 × 1 + ⎜ ⎟
n=1 ⎝ 100 ⎠
This is not the case for current. A small current may have a
high THDI but not be a problem. However it can be mis-
interpreted as a serious power quality problem. This can be
avoided by referring THDI to the fundamental of the peak
demand current rather than fundamental of present sample.
This is called total demand distortion (TDD).
The total power factor (also called true power factor) is:
pftrue = pf disp × pf dist
Ideal sinusoidal
voltage source -jXc non-linear load
Equivalent circuits:
jXs jnXs
V1 -jXc I1 -jXc In
n
jnXs pcc
jnXd
In
-jXc
n
− jX c ⎞
( Rs + jnX s ) ⎜⎛ jnX d + ⎟
Zn = ⎝ n ⎠
⎛ − jX c ⎞
( Rs + jnX s ) + ⎜ jnX d + ⎟
⎝ n ⎠