Abstract-- Determining the start and end of the voltage
sag event is very important for sag analysis and mitigation.
There are several detection methods for voltage sags in
which sag voltages are usually expressed in the terms of
RMS. The RMS method represents one cycle historical
average value, not instantaneous value which may lead to
long detection time when voltage sag has occurred. This
paper will proposed a novel voltage sag detection method
based on Miss Voltage Technique. Proper dead-band and
hysteresis are used in the method. The actual instantaneous
voltage is compared with certain percentage of desired grid
voltage and certain percentage of the amplitude of the grid
voltage. Through instantaneous value comparison, low
instantaneous value of the grid is shielded which overcome
the mishandling turnover of voltage sags. The approach is
fully described, and the results are compared with other
methods for marking the beginning and end of sag, such as
RMS value evaluation method and Peak-value method and
simulation result provides that the method is efficient and
fast and can be used to determine the initiation and recovery
of voltage sags accompanied by Missing Voltage Technique.
Index Terms—Voltage Sag, RMS, Peak Value, Missing
Voltage.
I. INTRODUCTION
OLTAGE sags are brief reductions in voltage,
typically lasting from a cycle to a second or so, or
tens of milliseconds to hundreds of milliseconds.
Voltage swells are brief increases in voltage over the
same time range.
Power systems have non-zero impedances, so every
increase in current causes a corresponding reduction in
voltage. Usually, these reductions are small enough that
the voltage remains within normal tolerances. But when
there is a large increase in current, or when the system
impedance is high, the voltage can drop significantly.
Voltage sags are the most common power disturbance. At
a typical industrial site, it is not unusual to see several
sags per year at the service entrance, and far more at
equipment terminals. Voltage sags can arrive from the
utility; however, in most cases, the majority of sags are
generated inside a building. For example, in residential
wiring, the most common cause of voltage sags is the
starting current drawn by refrigerator and air conditioning
motors. Sags do not generally disturb incandescent or
fluorescent lighting, motors, or heaters. However, some
electronic equipment lacks sufficient internal energy
storage and, therefore, cannot ride through sags in the
supply voltage. [1].
Some reasons for equipment fail when there are
voltage sags on ac power systems are as follows.
1. Equipment fails because there isn't enough voltage.
2. Equipment fails because an undervoltage circuit
trips.
3. Equipment fails because an unbalance relay trips
4. A quick-acting relay shuts the system down,
typically in the EMO (Emergency Off).
5. A reset circuit may incorrectly trip at the end of the
voltage sag
The costs associated with power outages at commercial
facilities like banks, data centers, and customer service
centers can be tremendous, ranging from thousands to
millions of dollars for a single interruption. The costs to
manufacturing facilities can be just as high, if not higher.
And manufacturing facilities can be sensitive to a wider
range of power quality disturbances than just outages that
are counted in traditional reliability statistics. Voltage dips
that last less than 100 milliseconds can have the same
effect on an industrial process as an outage that lasts
several minutes.
Determining the optimum supply system and electric
system characteristics for industrial facilities requires an
evaluation of many alternatives. Power quality can be
improved by adding power conditioning for selected
equipment or raising the bar for specifications and
equipment design on either the utility or end-user side of
the meter. But as you might imagine, all of these
alternatives have different costs and associated benefits.
Power line conditions which can result in productivity
losses vary from long term power outages to short
duration voltage sags. However, voltage transients and
momentary power interruptions, due to events such as
A Novel Detection Method for Voltage Sags
Kai Ding, K.W.E.Cheng, X.D.Xue, B.P. Divakar,
C.D.Xu, Y.B.Che, D.H.Wang, P.Dong
Power Electronics Research Center
Department of EE, The Hong Kong Polytechnic University
V
2006 2nd International Conference on Power Electronics Systems and Applications
250 of 288
lighting strikes, and line under-voltages(voltage sags)
down to no less than 45-50% of nominal voltage , due to
faults on the utility power system, account for the vast
majority, 90-95%[2].
To face the problem, the existing standards and
recommendations offer some guiding curves to verify the
prescribed maximum magnitude and duration of lower
and upper voltage limits for typical classes of loads. Fig.1
Fig.1 2000 Version of the IT Industry Tolerance Curves (update from
original CBEMA curve)
.
Fig.2. Required semiconductor equipment voltage sag ride-through
capability curve
shows the 2000 Version of the IT Industry Tolerance
Curves. The vertical axis is percent of nominal voltage.
"Well-designed" equipment should be able to tolerate any
power event that lies in the shaded area. Note that the
curve includes sags, swells, and transient overvoltages.
As shown in Fig.2. The semiconductor industry
developed a more recent specification (SEMI F47) for
tools used in the semiconductor industry in an effort to
achieve better ride through of equipment for commonly
occurring voltage dips and therefore improving the
overall process performance[3, 4]. It is basically the same
as the ITI Curve but specifies an improved ride through
requirement down to 50% retained voltage for the first
200 msec. Many short voltage dips are covered by this
additional requirement. IEC 61000-4-11 and IEC 61000-
4-34 provide similar voltage dip immunity standards.
The detection and evaluation of voltage sag is
necessary when mitigating of sag is considered. Precise
and fast and detection of the start and end of the voltage
sags are key important. In this paper, several detection
methods for voltage sags are given. A novel voltage sag
detection method is proposed. The proposed method is
compared with RMS method and Peak-value method. As
shown in simulation results, the method can pick out the
sag beginning and end faster than the other two.
II. D
ETECTION METHODS
Voltage detection is important because it determines
the dynamic performance of the voltage sag regulator.
Precise and fast voltage detection is an essential part of
the voltage sag compensator. Several voltage detection
methods have been documented for use in various voltage
compensation schemes. In this paper, RMS value
evaluation method, Peak value method, and Missing
voltage technique are introduced.
A. RMS Value Evaluation Method[5]
RMS values, continuously calculated for a moving
window of the input voltage samples, provide a
convenient measure of the magnitude evolution, because
they express the energy content of the signal. Assuming
the window contains N samples per cycle (or half cycle).
The resulting RMS value at sampling instant k can be
calculated by:
∑
−
=
−⋅=
1
0
2
][
1
][
N
n
rms
nkv
N
kV
(1)
Suppose
∑
−
=
−=
1
0
2
][][
N
n
nkvkS
(2)
then
∑
−
=
−−=−
1
0
2
]1[]1[
N
n
nkvkS
(3)
from (2) (3) we get
][][
]1[][]1[][
22
1
0
2
1
0
2
Nkvkv
nkvnkvkSkS
N
n
N
n
−−=
−−−−=−−
∑∑
−
=
−
=
(4)
So
]1[][][][
22
−+−−= kSNkvkvkS
(5)
N
z
−
][kv
1−
z
N
1
][kv
rms
][kS
Fig.3 RMS value evaluation using a moving window
Fig.3 illustrates a z-domain representation for the
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voltage RMS magnitude evaluation using a moving
window. The basic idea is to follow the voltage
magnitude changes as close as possible during the
disturbing event. The more RMS values are calculated,
the closer the disturbing event is represented.
B. Peak Value Evaluation Method[6]
Assume that the input voltage v
i
(t) is given by
)sin()( tVtv
Pi
ω
=
(6)
where V
P
, is the peak value of the input voltage. If v
i
(t) is
sent to a 90” phase shift circuit, then v
’
i
(t) is obtained as
) cos(
)90 sin()(
'
tV
tVtv
P
Pi
ω
ω
=
+=
o
(7)
The two signals, v
i
(t) and v
’
i
(t) , are a pair of
orthogonal functions. If they are sent to two separate
multipliers and squared, the following two equations can
be obtained:
) (sin)(
22
01
tkVtv
P
ω
=
(8)
) (cos )(
22
02
tkVtv
P
ω
=
(9)
where k is the multiplication factor of the multipliers. Due
to the characteristic of orthogonal functions v
01
(t) and
v
02
(t), it is easy to obtain the square of the input voltage
peak value by adding (3) and (4):
2
222
02010
)) (cos) ((sin
)()()(
P
P
a
kV
ttkV
tvtvtv
=
+=
+
=
ωω
(10)
In order to measure the peak value, the signal v
0a
(t) is
fed to a square root circuit. Then the output of the square
root circuit is
P
Vktv
10
)( = (11)
where k
1
, is the multiplication factor of the square root
circuit. If the multiplication factors of the multiplier and
the square root circuit are selected properly, the value of
constant k
1
, can be set as 1. The output voltage of the
detector is equal to the peak value of the input voltage.
Because the detector is based on the concept of an
orthogonal function pair, it is called “orthogonal
detector.”
The process of measuring the peak value can be
explained as follows[7]. The single-phase line-to-neutral
voltage is measured, and the cosine value of the voltage is
determined using a 90
o
phase shifter. Assuming a fixed
value (50Hz) for the line frequency, the 90
o
-shifted value
can be found by either an analog circuit or by digital
signal processing. Both components of voltage are
squared and summed to yield V
p
2
. Obtaining the square
root of V
p
2
results in the peak value of the detected
voltage.
Sqrt
×
×
Shifter
90
O
filter
pass Low
p
V
measure
V
) (cos
22
tV
p
ω
+
+
) (sin
22
tV
p
ω
Fig.4 Voltage measurement using the peak detection method
C. Missing Voltage Technique[8]
The RMS value evaluation method is based on the
averaging of previously sampled data for one cycle.
Therefore, it represents one cycle historical average value,
not momentary value. Due to the moving window
retaining almost one cycle of “historical” information in
the calculation, thus the duration of the sag is in error by
almost one cycle if one examines only the RMS plot.
Furthermore, the point on wave of initiation and recovery
of the sag is not clear.
To avoid mis-representing the waveform, reference[8]
proposed another approach, called the Missing Voltage
Technique. The missing voltage is defined as the
difference between the desired instantaneous voltage and
the actual instantaneous value. The desired voltage is
easily obtained by taking the pre-event voltage and
extrapolating this out during the event, similar to the way
a phase-locked loop (PLL) operates. A PLL is basically a
control loop incorporating a voltage-controlled oscillator
and phase sensitive detector in order to lock a given signal
to stable reference frequency. We will call the desired
voltage waveform the desired voltage or reference voltage
and it will be locked in magnitude, frequency, and phase
angle to the pre-event voltage waveform.
The missing voltage can be used to see the real time
variation of the waveform form the ideal, and hence the
actual severity of the sag. Furthermore, it gives a more
accurate indication of the duration of the event.
III. N
OVEL DETECTION METHOD
In the method of missing voltage technique, the missing
voltage (MV) can be obtained by subtracting the actual
instantaneous value from the desired instantaneous
voltage. The start and end of voltage sags can be
determined by MV. A detailed example will be given as
follow for analysis.
A. Problems When Using MV
Assuming the normal grid voltage is 220VAC RMS,
the amplitude of the grid phase voltage is 311V.
Generally, there will be a voltage sag event when voltage
drops to certain value. In this paper, we assumed that
when the voltage depresses to a value lower than 80% of
the desired value will lead to a voltage sag event. When
the voltage is recovered back to more than 80%, we
consider the voltage sag event is over and the grid turns to
normal again.
Under the assumption mentioned above, when the
instantaneous value of MV is equal or larger than 20% of
the reference voltage, start of the voltage sag occurs.
When the instantaneous value of MV is less than the 20%
of the reference voltage, the gird goes back to normal.
Because the MV is very small during the zero-crossing
point, noise, sampling error and delay will affect the
measurement value of MV which will cause mishandling
of the voltage sag restorer.
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Assuming V
s
(t) is the actual instantaneous value, V
ref
(t)
is the desired instantaneous voltage. The voltage sag
starting point can be determined by:
)(%20)()(
000
tVtVtV
refsref
>−
(12)
During the low instantaneous value period, if the value of
V
s
(t) approaches zero, although the grid voltage is normal,
due to the sampling error, sampling delay, noise, there
will be some problems when using (12).
Probelm1: when the grid is 100% normal, during the
low instantaneous value period. For example, assuming at
the point t
0
, V
ref
(t
0
)＝2V,because of the disturbance, a
detection value of 1.5V is possible, and then 25% voltage
drop is recognized by the controller which will lead to
mishandling. So during the low instantaneous value
period, such kind of mishandling will be repeated.
When the gird is 100% normal, during the high
instantaneous voltage period. For example, assuming at
the point t
1
, V
ref
(t
1
)＝170V, V
s
(t
1
)=170V. Although a lot
disturbances may exist, but the detection error above 20%
is rare. That means, obtaining a value of 136V when
detecting the actual voltage value of 170V is almost
impossible. So when the grid is 100% normal, the
mishandling of voltage sag regulator during the high
instantaneous voltage period is rare.
Problem II: Assuming the actual gird is 82% of the
desired grid, during the high value period. For example, at
the point t
1
V
ref
(t
1
)＝170V，V
s
(t
1
)=139.32V. The actual
voltage is normal, but due to some disturbances, the
detected value of V
s
(t
1
) may be 134, the error is 5.32V
which is possible when compared with 139.32V. So when
the actual grid voltage approaches the critical value,
mishandling is also possible.
In like manner, if the grid voltage is abnormal, the
disturbances existing may also lead to incorrect
switchover.
So it is necessary to add dead time and hysteresis band.
B. New Detection Method
Based on the inequality (12), in order to determine the
start and end of a voltage sag event, fist we can add
hysteresis band like this:
For example, when the grid is equal or smaller than
80% of desired grid, enable the voltage sag regulator.
When the grid voltage is equal or bigger than 85% of the
desired grid, disable the regulator, so adding hysteresis
band may avoid wrong switchover at the critical value.
But same as the problem I mentioned above, large error
may appear during the low value period, although adding
hysteresis band, incorrect switchover may also appear.
During the low instantaneous value period, the effect of
voltage sags is smaller when compared with the sags at
high value period. So screening the low voltage
comparison may help solving the mishandling problems.
For example, when the grid voltage is satisfied
AMPtVtV
refs
*%5)(%85)( −≤
(13)
where the AMP is the amplitude of the phase voltage
311V, form (13) we obtain
5.15)(%85)( −≤ tVtV
refs
(14)
When the grid voltage satisfied the inequality (14),
voltage sag event is started, and then during the low
instantaneous value period, (0-15.55V), whatever, the grid
voltage can not be equal or smaller than the value
(85%Vref -15.55), so the low voltage value is shielded. If
the grid voltage is 80%Vref, the grid voltage will be
satisfied the inequality only when the instantaneous grid
voltage reaches the peak value. That means, when the grid
voltage drops to 80% V
ref
, the detection of voltage sags is
very sensitive near the peak value (90degree, or
270degree).
Now, assuming the grid voltage drops x%, θ is the
detection angle when voltage drops x%, as shown in
Fig.5, so from (14), yields
5.15)sin(311%85)sin(*311*)%100( −≤−
θθ
x
(x) (15)
from (15), obtains
)
15
5
(
−
=
x
ArcSin
θ
(16)
Assuming MaxDelay is the max detection delay time. As
shown in Fig.5, assuming the voltage drops more than
20% at the point M, due to the point M is shielded
according the (15), until at the point N , the voltage sag
event is not detected. So
)
15
5
(*22
−
==
x
ArcSinMaxDelay
θ
(17)
θ
θ
−
180
θ
+
180
θ
−
360
θ
θ
−180
θ
+180
θ
−
360
MaxDelay
M
N
Fig.5. Available detection ranges for sag detection (thick line)
4
0
6
0 80
1
00
25
50
75
100
125
150
175
Fig.6. Max detection delay time when voltage drops x% ranges from
20% to 100%
As can seen from fig.6, the more the grid voltage drops,
the less detection delay time. When the grid voltage drops
50%, the max delay time is about 16.4rad, about 0.045
period.
In like manner, gird voltage recovery discussion are as
follows. When the grid voltage is satisfied
AMPVV
refs
%10%75 +≥
(18)
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we consider the voltage sag event is finished, the voltage
sag regulator will be switchover to grid supply. Assuming
the grid voltage drops x%, one obtains
refs
VxV )%100( −=
(19)
substitute (19) in (18), we get
AMPVVx
refref
%10%75*)%100( +≥−
(20)
because
)(* wtSinAmpV
ref
=
(21)
θ
θ
−180
θ
+180
θ
−360
θ
θ
−180
θ
+180
θ
−
360
MaxDelay
Fig.7. Available detection ranges for recovery detection(thick line)
so
AmpwtSinAmpwtSinAmpx %10)(*%75)(**)%100( +≥−
(22)
from (22) we get
x
wtSin
−
≥
25
10
)(
(23)
then, from (23)
)
25
10
(
x
ArcSint
−
≥=
θω
(24)
where
2
0
π
θ
≤≤
For example, as shown in the Fig.7, when the grid voltage
is recovered back to 82% of the desired voltage, the value
θ does not exist. So during this period, it whole power
supply system remains pervious state. Only when the gird
voltage recovered back to more than 85%, the θ exist. For
example when the grid voltage goes back to 100%, the
range of θ is
θ>=23.5782rad
the range is shown in Fig.7 (thick line), the value outside
the rang is screened.
In sum, the above example employs the following
method:
1) When the actual grid voltage satisfied:
5.15%85 −≤
refs
VV
voltage sag regulator is enable, the missing voltage is
added to the actual grid voltage.
2) When the actual grid voltage satisfied:
5.15%851.31%75 −>>+
refsref
VVV
holding the previous state
3) When the actual grid voltage satisfied:
1.31%75 +≥
refs
VV
voltage sag regulator is disable, the power line supply
voltage solely.
Of course, different value of percentage of the desired
voltage and the amplitude will lead to different effects.
The above mentioned parameters are employed in the
example of this paper and the same parameters are also
used in simulation.
IV. S
IMULATION
Simulations have been carried out to verify the
proposed voltage sag detection method. The cases
examined include those when the voltage is depressed to
79% of its nominal value. The sag event lasts for 0.14 s.
As shown in Fig.8, three voltage sag waveforms aregiven,
the first waveform as shown in Fig.8(a) drops at the end
0 0.05 0.1 0.15 0.2 0.25
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
new method Peak Vaule
RMS
(a)
0 0.05 0.1 0.15 0.2 0.25
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
new method Peak Vaule
RMS
(b)
0 0.05 0.1 0.15 0.2 0.25
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
new method Peak Vaule
RMS
(c)
Fig.8. Simulation results
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