Download 2003 SINTES Craiova

PHASE SHIFT AND POWER FACTOR DIGITAL METER
Traian-Titi SERBAN
University of Craiova
e-mail: [email protected], tel: 40-251-435724 ext: 106
Abstract: This paper presents some aspects of the digital
measurement of the phase and the power factor. An
experimental model of a phase shift and power factor
meter is also described.
Keywords: Phase and Power Factor Measurement,
Digital Phase-Meter
INTRODUCTION
In the field of digital measurements, the phase shift
and the power factor are important features that are
usefull in the quality evaluations of various electrical
circuits and power consumers. The phase measurement
is a useful method to estimate the distortions introduced
by a certain electric or electronic circuit. All devices are
characterised by a specific delay or response time that
have different significances depending on the frequency
of the input signal. When periodic signals are applied to
the input of the devices, between the input and the output
signal a delay can be defined and called phase shift. This
delay has frequency dependant weight in the period of
the said signal: the higher the frequency, the higher the
influence of the delay. Measuring the amount of the
delay in the period of the signal is a way to evaluate the
behaviour of the device in the dynamic state.
The digital instruments dedicated to the phase shift
measurement (the phase-meters) evaluate the time lag
between homologue points in the evolution of the two
signals. A time lag “tl” between two signals with the
period “T” means a phase shift of ϕ = tl / T. Usually, the
function of the phase measurement is integrated with
other functions in the complex digital meters.
Nevertheless, dedicated instruments are built on the
principle mentioned above.
In the power systems, the phase shift between the
voltage and the current signals on each phase may be an
important feature when qualitative characterisations must
be made on certain consumers. As the phase shift itself ϕ
is not relevant in the power circuits analysis, a synthetic
value related to it is used instead: the power factor, cosϕ.
The dedicated instrument (cosϕ-meter) displays the
values of the power factor in non-dimensional units. The
present paper presents a digital implementation of a
phase & cosϕ -meter that evaluates both the phase shift
and the power factor in variable frequency environments.
THEORETICAL BACKGROUND
The simplest digital phase-meters are built for fixed
frequency. An oscillator with a constant output
frequency is used to generate pulses counted in the phase
shift corresponding to the time lag “tl” (Serban 1996).
The measured phase shift will be displayed as:
ϕ = 360 tl / Tosc.
Using a digital technique to evaluate the time
intervals tl and T one can get the value of the phase shift.
The method asks only to count the pulses generated by a
quartz-stabilised oscillator in the specified time lag. The
higher the frequency of the oscillator, the better the
precision of the phase-meter. The resolution of the
measurement depends on the number of the pulses that
are count in the minimum time lag. I.e. for a 0,1o
resolution at least one pulse must be counted. For an
entire period, a total number of 360/0,1=3600 pulses
must be counted. If the period of the main signal is
sufficiently long, the pulses may be counted with no
problems, but when the signal’s frequency is high, the
counter’s speed becomes prohibitive and high quality
counters must be used.
Usually, the digital phase-meters are featured with a
few tens of kilohertz bandwidth.
A better instrument could be realised (Nicolau 1979)
if more “tl” and “T” intervals are considered in order to
count the pulses from the oscillator (figure 1). The clock
pulses from the oscillator are validated by the input
AND gates 1 and 2 only on the positive half-periods of
the two signals. The XOR gate selects only the bursts
corresponding to the time lags “tl” when the two signals
evolve in different parts of the time axe. N pulses in the
total number of validated bursts will represent these time
lags. For each period there are two “tl” intervals.
In the first counter the pulses corresponding to a certain
N number of periods are counted. In order to get the
value of the phase shift in the usual format (hexadecimal
degrees), N is chosen as a multiple of 360 (N=360k).
This number prescales the first counter. As long as the
first counter counts the N clock pulses, the output of the
XOR gate is validated and through gate 3 multiple bursts
of pulses corresponding to the phase shift are passed in
the second counter. The displayed value of the phase
shift will be: ϕ = n / k, where n is the number of pulses
counted during all the time-lags corresponding to the
phase shifts along the measuring time, and k is the
number of periods along the measurement is developed.
The global precision does not depend anymore on the
frequency of the oscillator and, moreover, the noise
influence is reduced down to zero as the number of
signal periods that compose the measuring time may be
of hundreds. The bandwidth extends from 1Hz to 1MHz.
The described schematic works when one can specify
the number N of pulses used to prescale the first counter,
representing the number of signal periods that compose
the measuring time. In order to measure the phase shift
for signals with variable frequency, an additional module
must be included in the diagram in figure 1, to evaluate
the unknown period T.
v1
v2
1
3
2
comparator. The main rated features of the input
channels are: Un = 380V; In = 10A.
The minimum values for the input signals are 10mV
for voltage and 10mA for current.
Counter 2
D3
D5
Counter 1
J2
DZ4V7
1N4148
R5
6
D2
1N4148
2
R4
3
1
2
R8
3
7
2
4K7
Q1
1 2N2222A
D6
1N4148
J3
1
R7
+12V
1
2
3
R10
4
R6
1K
470K
-12V
-12V
100
C2
1u
+/-12V
-12V
Figure 3. Voltage Input Channel
In order to avoid the saturation and/or the latch-up of
the amplifier, a limited output voltage configuration was
chosen, with opposite diodes in the negative feedback
loop. For the very low input levels the amplifier acts as
an open loop one, its very high gain producing a fast rise
of the output signal and a well shaped rectangular output
voltage. For normal and high input voltages, the limiting
diodes avoid the saturation of the amplifier itself and of
the next comparator. This way the comparator’s
switching performances are improved and few error
sources are minimised.
D21
D23
R28
DZ4V7
C33 100
1u
+12V
1N4148
D22
J18
8
1N4148
R24
5
8
2
R23
3
U4A
TL082
Q3
1 2N2222A
D24
1N4148
J19
1
R26
+12V
R29
R25
1K
4
1K
Power supply
3
2
4K7
+
Rsh
10m
-
1K
2
1
R27
7
4
J17
1
2
I-OUT
+
47K
+12V
U4B
TL082
-
6
+12V
R22
I-IN
-12V
470K
C34
1u
-12V
100
1
2
3
+/-12V
-12V
Insulation
Input
channel
+12V
4
U1A
TL082
1K
PRACTICAL IMPLEMENTATION
A model for the phase and power factor meter was
built with the main goal of evaluation of the phase shifts
between two voltages (in order to obtain the phase
characteristics for electric and electronic circuits), two
currents or a voltage and a current (in order to evaluate
the power factor in low voltage circuits).
The meter is structured in two modules: the analog
input module and the digital module. Consequently, the
function of the input module is to pick the input signals
and shape them in a rectangular waveform with limited
amplitude.
The input module contains four completely
independent channels, two for current and two for
voltage, with good individual insulation. The maximum
voltage that strains the isolation between the input
channels is the line voltage (380V). Each input channel’s
insulation is distributed in two sections: the power
supply and the digital module input port (figure 2).
5
+
1K
D1
1N4148
U-IN
-
47K/9W
R2
910
8
J1
2
1
The instrument will include, in this case, a digital
measurement controller to manage the operations and
sequences of the measurement process.
47K
R3
100
U-OUT
+
+12V
R1
-
Figure 1. Digital Burst Phase-Meter
C1
1u
U1B
TL082
8
Clock
R9
+12V
1N4148
D4
Figure 4. Current Input Channel
Digital module
U10A
P2.0
1
D29
3
2
1N4148
74HCT00
U1
U10B
Figure 2. The Input Channels’ Insulation
4
D30
VCC
6
P2.4
5
VCC
1N4148
R58
4K7
74HCT00
R55
8K2
INT0
The power supply must have separate outputs for the
four channels, each level of insulation being designed for
the rated line voltage.
The signal transfer between any input channel and
the digital module is made through an optocoupler with
an adequate level of the insulation voltage and dynamic
features.
The voltage and current input channels meet various
conditions, but the most important is to introduce
minimum supplemental phase errors. Noninductive
resistive adapters were chosen in both situations: shunts for current inputs and resistive dividers – for voltage
inputs. The detailed schematics of the voltage and
current input channels are shown in figure 3 and figure 4
respectively. Each input channel includes a simple
protection circuitry, a high gain amplifier and a
U10C
P2.1
9
D31
R56
1N4148
6K2
8
3
2
10
1
74HCT00
Q5
2N2222A
R57
3K9
U2
U10D
12
D32
11
P2.5
13
1N4148
74HCT00
VCC
U11A
P2.2
1
D33
3
2
VCC
R62
4K7
1N4148
74HCT00
I1
R59
8K2
INT1
U11B
4
D34
R60
6
P2.6
3
2
5
1
1N4148
6K2
74HCT00
Q6
2N2222A
R61
3K9
U11C
P2.3
9
D35
8
10
1N4148
74HCT00
I2
U11D
12
D36
11
P2.7
13
1N4148
74HCT00
Figure 5. The Channel Selector
Measuring the phase shift, one must declare first the
“time-fixed” signal considered as a reference and the
“time-floating” signal that is shifted with respect to the
first. The input channel selector is a part of the digital
module and allows selecting the reference and the
secondary signals that define the phase shift.
The detailed schematic of the channel selector is
shown in figure 5.
The digital module makes the selection of the
prescribed input signals and evaluates the main period
and the phase shift of the two signals. The power factor
is also displayed. AT89S52 microcontroller (ATMEL
2001) was chosen to achieve all the operations, mainly
because it allowed to drive also a digital display with no
additional circuits and to select the inputs and the
function of the meter (phase or power factor metering)
using a main menu.
The power factor is displayed after a table search
depending on the value of the measured phase shift.
The experimental model was realised using usual
commercial devices. The analog and digital modules
were built on different PCBs (figure 7).
The model of the digital module is shown in figure 8:
VCC
R70
10K
R69
10K
R68
10K
R67
820
R66
820
R65
820
R64
820
R71
10K
R72
10K
R73
10K
R74
Figure 8. The Digital Module
10K
U12
P1.1
P1.2
P1.3
P1.4
P1.5
P1.6
P1.01
2
3
4
5
6
7
8
9
VCC
C37
10u
D37
1N4148
10
11
12
13
14
15
16
17
INT0
INT1
R63
10K
18
19
P1.0/T2
P1.1/T2-EX
P1.2
P1.3
P1.4
P1.5
P1.6
P1.7
RST
P3.0/RXD
P3.1/TXD
P3.2/INTO
P3.3/INT1
P3.4/TO
P3.5/T1
P3.6/WR
P3.7/RD
XTAL2
XTAL1
X1
20MHz
P0.0/AD0
P0.1/AD1
P0.2/AD2
P0.3/AD3
P0.4/AD4
P0.5/AD5
P0.6/AD6
P0.7/AD7
EA/VPP
ALE/PROG
PSEN
P2.7/A15
P2.6/A14
P2.5/A13
P2.4/A12
P2.3/A11
P2.2/A10
P2.1/A9
P2.0/A8
39
38
37
36
35
34
33
32
SOFTWARE
P0.4
31
P0.5
P0.6
P0.7
VCC
30
29
28
27
26
25
24
23
22
21
P2.7
P2.6
P2.5
P2.4
P2.3
P2.2
P2.1
P2.0
AT89C52
C38
33p
C39
33p
Figure 6. The Digital Module
All four ports of the microcontroller are used: P0 and
P1 - for the human interface control (display and menu
selection), P2 – for the channel selection and P3 – for the
shaped signals inputs as interrupts.
The principle of the meter involves two operations:
the main period “T” measurement and the relative time
delay between the two signals “tl“ measurement. Next
the phase shift is computed using the formula:
ϕ = 360 tl / T
(1)
The software was designed keeping in mind the main
goals: the maximum precision of the phase shift and
power factor measurement and the shortest algorithms.
The time measurement uses 16 bit resolution and the
arithmetic operations – 32 bit resolution, so all additional
errors due to the inherent truncations are avoided.
The measurement is started on the falling edge of the
rising front of the signals applied to the INT0 and INT1
pins of the microcontroller. Both T2L and T2H registers
of the T2 timer in AT89C52 are loaded with 0000h
before any measurement, next INT0 interrupt is enabled.
When the first INT0 comes, timer T2 receives the RUN
command. T2 will be incremented every 0,6ms. When
the second INT0 interrupt comes, the T2 timer will be
stopped. The two registers T2L and T2H are read and the
result will compose the “T” operand that will be saved in
temporary registers. After both registers’ content is
saved, they receive a “reset” command and the timer T2
waits the next INT0 interrupt. T2 is run again until INT1
interrupt becomes active and the timer it is stopped.
The content of the two registers are read and saved in
the special function registers area as the “tl” operand.
Appropriate routines are used to do the arithmetic
calculus in hexagesimal base in order to determine the
phase shift “ϕ”. The corresponding value of cosϕ is
searched in the memorised table. Both values are BCD
and ASCII converted in order to be sent to the display’s
controller. The measuring cycle replays on every 500ms.
ERROR ANALYSIS
Figure 7. The Phase-Meter Experimental Model
Using the 16-bit timer T2 in the AT89C52 and a
20MHz main frequency, the absolute error for the time
measuring is 0,6µs. The basic instrumental error is
o
associated to and equals the phase-shift resolution (0,1 ).
For the power factor measurement, the absolute error is
0,004.
In addition to these main errors, supplemental under
mentioned error components are to be considered:
a) The small signals amplitudes, in conjunction with the
fixed values of the hysteresis windows of the
comparators;
b) The jitter of the commutation moment of the
comparator on each input channel, in conjunction with
the signals’ slew rate;
c) The mis-synchronisation of the clock signal with the
front of the validation signal;
d) The small variations of the frequency of the signals
that define the phase shift.
a) The moment of the comparator’s switching is
delayed from its ideal moment depending on the signal’s
relative amplitude. When the signal is small, then the
moment of the switching comes later, because the fixed
triggering level of the comparator is achieved later. The
higher the signal’s amplitude, the smaller the error
component.
b) The moment that the comparator commutes (on
any channel) strongly depends on the slew rate of the
signal (figure 9). The slower the slew rate, the higher is
the comparator’s commutation delay. When the
amplitude of the signal on the reference channel is much
larger than the amplitude of the secondary signal, the
measured value of the phase shift will be bigger than
real. The error comes from the time lag åt, which delays
the commutation of the comparator on the second
channel with respect to the commutation of the
comparator on the reference channel.
Figure 9. The influence of the signal’s slew-rate
Mutually, when the reference signal’s amplitude is
smaller than the secondary signal’s amplitude, the
measured value of the phase-shift will be smaller than
real.
c) The front of the signal that starts the
incrementation of the phase-shift counter may be
different from the clock front.
One clock tact may be lost because of that. The
corresponding component of the global error will be
equal to the quantum of one single clock period in the
total time delay associated to the phase-shift. The bigger
the phase-shift, the smaller the amount of one single
clock pulse in the time period associated to the measured
phase-shift.
d) The small variations in the frequency of the signals
produced in the measurement time may produce an error
component even if an actual signals’ period
measurement is achieved before any phase-shift
measurement. When the signals’ frequency has a small
increase in the measurement time, the error component
will be positive. At lower frequencies, the component of
the error will be negative. This component must be taken
into account with respect to the small variations in the
main clock’s frequency. A more realistic value can be
predicted if average values are considered. In this case,
this error component can easily be neglected.
The total dynamic error will be calculated by quadratic
summation of the described components.
CONCLUSIONS
A digital phase and power factor meter was designed
and built in order to obtain the phase characteristics of
the electronic circuits and the analysis of the power
transfer in electric circuits. The instrument may be
associated to any power consumer. The use of a
microcontroller for the functional control of the
instrument allowed selecting any of the possible
combinations of the input signals to measure the phase
shift. The power factor has significance only for the
proper combinations of the input channels. An error
analysis reveals the main components of the global error
of the digital meter. The instrument is useful in small
signal circuit’s analysis but also in the high power
circuitry to evaluate the power transfer.
REFERENCES
ATMEL – „Online Products Catalog” – AT89S52, upd. June
2001, www.atmel.com;
Nicolau E. – „Manualul inginerului electronist – Masurari
electronice”, Editura Tehnica, Bucuresti, 1979;
Serban T. – „Masurari electrice si electronice – fazmetru
numeric – note de proiectare” – studiu, 1995-1996;