Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
a~
BACKGROUND OF INVENTION:
_
(a) Field of the Invention
The present invention relates to a method
and a system for measuring the amplitude and phase
angle of harmonics in a periodic signal by utilizing
a tunable tracking filter which is connected to receive
the periodic signal having a frequency within a predict-
able range. The tunable tracking filter may be a
switch capacitor filter or an analog-type filter.
(b) Description of Prior Art
As far back as the 1920's, power system
harmonics were an important matter under investigation
by power utilities and telephone companies. Early
problems were mainly related to low-order current
harmonics generated by transformers and induction
motors. The most successful effort to reduce these
harmonics utilized the transEormer connections. For
example, delta transformer connections act as a blocking
filter for the 3rd, 6th, 9th, etc. harmonics. Today,
the proliferation of non-linear loads, created mostly
by static power converters, has increased the level
of power harmonics and represents a growing source
of problems afflicting other customer loads and the
power network itself.
The sources of harmonics are multiple:
transformers, induction motors, arc furnaces and static
power converters for electrochemical processes, dc
and ac drives, HVDC transmission and var control.
Most of these sources act as non-linear loads affecting
primarily the current waveform. Some common cases
of distortion are as follows:
a) rectangular shapes due to the rectifying
process;
b) stair-step shapes generated in the synthesis
of sinusoidal waveform;
c) high frequency pulses caused by direct
ac to ac conversion involving constant switching from
one phase to another.
Even in the presence of pure sine wave voltages,
the effect of current harmonics produced by a specific
load will affect the distribution system. Considering
the power system example of Fig.l, one can see that
the distortecl currents, Elowing through the characteristic
impedance oE the transmission line, will generate
voltage harmonics. The other customer loads connected
to the same network will suffer from this electrical
pollution.
The evaluation oE the efEects of harmonics
on power sys-tems is a complex task. Sc;me valuab]e assessments are
given in an article of the I.E.E.E., Working Group on Power System
Harmonics, 84 EH0221-2PWR, New York, 1984, which also listrnany
interesting studies on the subject. Moreover, utilities
are very concerned about the growing level of system
harmonics and about the application of measures to
temper this phenomenon. Many measurement techniques
have been suggested in the prior art literature.
Phase angle and amplitude measurement of
harmonics can be classified according to two procedures.
The first method performs selective null detection
in conjunction with a wave analy er. The second method
is based on Fourier series (orthogonality). Both
procedures yield acceptable results if the instruments
used are properly designed and calibrated. However,
-- 3
their implementation on a large scale could suffer
from drawbacks like the high overall cost, the sensitivity
of critical components and the time needed to process
the information.
Many methods are known for measuring electrical
parameters such as active power and apparent voltamperes.
The most common are: electrodynamometers, thermoinstru-
ments, electronic multipliers, Hall effect transducers,
fast Fourier transform systems, dedicated distortion
~10 analy~ers, and frequency selective voltmeters. However,
most of these methods fail to provide an easy measurement
of the displacement power factor. For example, in
single phase, single frequency, the measurement can
only be performed by uslng a high-Q tuned filter or
with the help of elaborate methods. Both analog and
digital techniques currently used to extract the funda-
mental component of an electrical signal are plagued
with severe shortcomings. The analog techniques involve
serious delays due to the low-pass filters required while
digital ones suffer due to the considerable computing
time required by FFT techniques. Therefore, these
methods are ill-suited to measure the power displacement
factor of variable frequency power conditions, where
both current and voltage may be heavily distorted,
;~ 25 and where the frequency may well vary between 1 Hz
and 200 Hz.
SUMMARY OF THE INVENTION:
It is a feature of the present invention
to provide a system and method capable of detecting,
simultaneously, the amplitude and phase of any given
-- 4
harmonic and to maintain the amplitude and phase despite
variations in the incoming periodic signal. Known
tracking filters are una~le to perform such a detection
in the presence of a variable frequency signal (periodic
signal).
It is a feature of the present invention
to provide a novel harmonics detection and measuring
system for measuring the amplitude and phase angle
of harmonics in a periodic signal by utilizing a
tunable tracking filter connected to the periodic
signal which has a frequency within a predictable
range.
Another feature of the present invention
ls to provide a method of detecting and measuring
the amplitude and phase angle of harmonics in a periodic
signal by utilizing a tunable tracking filter which
is connected to the periodic signal which has a frequency
within a predictable range.
Another feature of the present invention
is to provide a new technique for detecting and measuring
the amplitude as well as the phase angle of harmonics,
using a tracking filter. The measurement is performed
by a selective filtering of each harmonic, using program-
mable switched-capacitor-filters, constantly tuned
by a synchronized clock derived from the fundamental
component of the line voltage.
According to a broad aspect of the present
invention, there is provided a harmonics analy~er
system for simultaneously detecting the amplitude
and phase angle of harmonics in a periodic signal.
-- 5 --
The system comprises a tunable tracking filter connected
to an input of the system for receiving the periodic
signal having a frequency within a predictable range.
Conditioning circuit means are connected to the input
S to tune the tracking filter,~ ~ selected harmonic
in the periodic signal, and a programmable frequency multiplier
circuit receives the pulses and connects to the tracking
rl;~
filter for locking the clock frequency thereof,
tune~ the tracking filter to the selected harmonic
of the periodic signal to provide at its output an
output signal having the amplitude and corresponding
phase of the selected harmonic.
According to a still further broad aspect
of the present invention, there is provided a method
for detecting the ampl.itude and phase angle oE harmonics
in a periodic signal whieh comprises selectively filter-
ing a harmonie using a tunable traeking :Eilter whieh
is locked on a selected harmonic by means of a frequency
multiplier which is synehronized by the fundamental
frequeney of the periodie signal.
~RIEF DESCRIPTION OF DRAWINGS:
A preferred embodiment of the present invention
will now be deseribed with reference to the examples
thereof as illustrated in the aeeompanying drawings,
in which:
FIGURE 1 is a simplified view illustrating
a power system with a non-linear load;
FIGURE 2 is a simplified block diagram illus-
trating the non-linear load supplied by sinusoidal
voltage;
-- 6 ---
FIGURE 3 is a simplified block diagram illus-
trating a linear load supplied by sinusoidal voltage;
FIGURES 4A and 4B are simplified schematic
diagrams illustrating a basic inverting integrator
5with switch-capacitor and with an effective resistance;
FIGURES 5A and 5B are characteristic curves
illustrating the first order low-pass filter tuned
at two different cut-off frequencies illustrating
the magnitude of the signals and the phase shift of
10the signals;
FIGURE 6 is a block diagram of the harmonics
detection and measuri.ng system of the present invention;
FIGURE 7 is a block diagram showing a phase-
lock loop frequency mu}.tiplier;
FIGURE 8 is a block diagram of a synchronized
15digi.tal frequency multip.l.ier;
FIGURE 9 is a block di.agram of an experimental
test set-up;
F:[GURE 10 is a schematic diagram illustrating
the basic configuration :Eo:r a second order low-pass
filter using a national universal monolithic MF10;
20FIGURE ll is a characteristic representation
of the experimental filter using an 8th order Butterworth
filter;
FIGURE 12 is a frequency characteristic
illustrating absolute phase offset as a function of
25input frequency;
FIGURE 13 is a characteristic curve illustrating
the normalized frequency ratio thus illustrating the
absolute phase offset as a function of center frequency
ratio and quality factor;
; 30FIGURES 14A and 14B are photographs illustrating
the waveforms of the supply voltage, supply current
-- 7
:
and supply fundamental current of actual tests.
DESCRIPTION OF PREFERRED EMBODIMENTS:
Figure 1 give$ a simplified view of a power
system 10 comprising three main parts: part 11 repre-
sents the power source, producing an almost purelysinusoidal voltage lthe internal impedance of the
generator is voluntarily omitted); part 12 depicts
the characteristic impedance of the transmission line
and part 13 shows a non-linear load connected to the
system along with other non-identified loads 14.
For the sake of simplicity, all loads are assumed
to be connected to a single point in the system.
Even with a pure generated sine wave, the line voltages
appearing at the terminals of the non-linear load
can be quite distorted due to the non-sinusoidal currents
Elowing through the 1 ~e impedances. Both the relative
importance oE the l.oad and the distortion level of
current waveforms can affect line voltages at this
point. For other loads connected to this distribution
system, line voltages will appear distorted. In such
a case, when both current and voltage are distorted,
the performance analysis of a specific load or part
of an ac network becomes complex.
'P~r~
The operation of most power ~e~*~ can
be represented as illustrated in Figure 2, by a non-linear
time-varying load 15. Assuming an ideal (undistorted)
voltage supply e, such a load 15 can draw line currents
which consist of fundamental and harmonic components.
Instantaneous supply voltage and current can be expressed
as
~2~
e = ~ E sin ~t (1)
i = ~ n In sin(n~t + en~ (2)
: 1
This expression (2) assumes that the line
current does not contain a dc. component. Electrical
evaluation and comparison of non-linear loads can
be performed using certain parameters such as distortion
and displacement factors. The simple power system
of Figure 2 can be described by the following expres-
slons,
a) Active Power (P)
Pl = 2~ e i d(~t) = E Il cos ~1 (3)
b) Reactive Voltamperes (Q)
Ql = E Il sin ~1 (4)
c) Displacement Power Factor (Al)
~1 = cos Hl (5)
d) Distortion Power Factor (~)
~ Il ' (6)
I
e) Power Factor (~)
= p = 1 cos Hl =~ (7)
S
f) Apparent Voltamper~s (S)
S = E I - E [~ 2 ~ 1/2 (8)
g) Distortion Voltamperes ~D)
D = S -(P + Q ) (9a)
D2 = E2 (I2 _ I2) E2 r~ I2l (9b)
1 ~2 n~
It should be noted that the numeral one
subscript for P and Q means that only the fundamental
components of voltage and current produce active power
g
and reactive voltamperes in a non-linear load supplied
by sinusoidal voltage. The power factor is made up
of two components: displacement (A~l) and distortion
(,~5 ). The displacement component is related to the
displacement of the fundamental component of the
current; the distortion component is associated with
harmonics in the current. Unity represents the best
achievable value for each term.
A non-linear load, such as a power connector,
acts as a harmonic current generator. Figure 2
illus-trates such a non-linear load supplied by a
sinusoidal voltage. Because of -the finite impedance
of the transmission line, including transformers,
current harmonics, circulating in the power system
of Figure 1, generate harmonic voltage components.
These components exist at the same Erequencies as
those oE the current harmonics. The electrical evalua-
tion of a linear load, connected in parallel with
such a system, can be performed following a procedure
similar to the one used in the previous case.
Considering the simplified system of Figure
3, supply voltage and load current can be expressed as
e = ~ æ En sin(n~t + ~n) (lO)
i = ~ ~ In sin(n~t +~n + ~n (ll)
where n represents the phase angle for the sinusoidal
excitation of the nth harmonic fre~uency. Based on
a similar analysis presented in (8), active power,
reactive and apparent voltamperes, and distortion
voltamperes resulting from the operatlon of Fig.
3 system are
-- 10 --
~ ~4~
1 n In co5 ~n (12)
Q = ~ En In sin ~ (13)
S = E I = E ~2 E2 ~ I2 ~ 1/2 (14)
l n 1 n
n 2 n 2 n
D2 ~' E ~ In 1 n n (15)
In a typical power network, Fig. l, power
is shared between linear and non-linear loads. A
Eull analysis of the electrical parameters at each
major load becomes complex if one must account for
the harmonics present in the network. The harmonic
measurement technique proposed provides a valuable
tool for the evaluation oE the performance oE each
load as well as the overall system.
The availability oE programmable switched-
capacitor Eilters make it possible to design filters
which maintain an almost constant phase shift despite
wide variations in the frequency of the input signal.
Most of the time, realizing a sharp variable
filter with passive components requires costly hybrid
devices. On the other hand, digital filters need
analog to digital conversion and complex clock require-
ments, and therefore, also generate expensive solutions.
Switched-capacitor techniques make it possible to
design high order filters with an absolute control
of the cutoff frequency.
The basic operation of the switched-capacitor
simulates a variable resistor being adjusted by means
of a clock frequency. Figures 4A and 4B present an
-- 11 --
integrator using this technique~ With simple circuit
analysis, it can be shown that the switched-capacitor
,imulates a resistor of value
Req = l (16)
5 Cs U~s
The transfer function of this integrator
becomes
sC(i~) M (17)
j~) ~,~
where M = C/Cs is a design constant. This relation
means that the time constant can be tuned via the
clock frequency C~s. Also, the stability of the function
is very good because the integrator time constant
relies on the ratio of two capacitors physically located
in the same silicon chip. Such an integrator serves
as the building block for realizing very predictable
state-variable filters. For example, the transfer
function of a first order low-pass filter is expressed
as:
20Hlp(j~) = 1 = 1 (18)
+ 1 i,~/~S +
It becomes obvious that the cutoff frequency of this
filter, ~c = ~s/M~ is directly dependent on the clock
frequency. Furthermore, because of the good approximation
with a linear filter, when using a high enough value
for the ~/~s ratio, it is possible to control the
amplitude as well as the phase characteristics of
the filter.
30Figures 5A and 5B illustrate the characteris-
tics of a first order low-pass filter tuned at two
- 12 -
difEerent cutoff frequencies. Without altering the
topology of the filter or changing any value of the
external passive components, it is possible to move
the corner frequency of the filter to a specific value ,
just by adjusting the filter clock frequency. Moreover,
phase shift will be precisely altered in the same
way as the amplitude. The stability and the accuracy
of the filter characteristics at any new adjusted
cutoff frequency depend solely on the accuracy and
stability of the clock frequency.
This simple method of tuning a switched-capacitor
filter (SCF) opens the way to the design of devices
Eor harmonic measurements in power electronics and
other field.s. By locking the filter clock frequency,
through a frequency multiplier, to the fundamen-tal
frequency of a periodic signal, it is possible to
tune the SCF exactly on the fundamental component
or on any harmonic component of this signal.
Referring now to Figure 6, there is shown
a simplified block diagram of the measurement system
17 of the present invention. Basically, the system
works as follows: A periodic signal 18 of unknown
frequency, but within a predictable range, passes
through a sharp low-pass filter l9 to remove medium
and high order harmonics. The output 20 of the filter
19 enters a zero crossing detector 21 which produces
pulses at the fundamental frequency of the periodic
signal. These pulses serve to synchronize a program-
mable frequency multiplier 22 with a NxM ratio, where
N stands for the harmonic order. The output signal
at output 23 forms a pulse train of NxM times the
fundamental frequency of the input signal. The signal
at output 23 becomes the input clock of a high order
lband-pass switched-capaci-tor filter 24 whichhas a selected clock-to-
center frequency ratio of M. This means that the center frequencyof the filter 24 is tuned to N times the fundamental
frequency of the input signal 18. The SCF 24 output
signal on output 25 resembles a synthesized sinusoid
made of a hundred discrete levels, resulting from
the commutation action inside the SCF 24. A conventional
analog low-pass filter 26 is then used to clean the
signa] of any clock residues. Analog measurement
of the desired output signal 27 will yield the amplitude
of the Nth harmonic, or Cn. Phase measurement is
accomplished by digitally comparing the zero-crossing
mark of the signal 27 with the reference mark produced
by the fundamental component of the input signal 18
in a detector 28.
In order to maintain an accurate measurement
of both the amplitude and the phase oE any selected
harmonic, the clock frequency of the SCF 24 must be
precisely adjusted to NxM times the fundamental frequency
of the incoming signal 18. Furthermore, frequency
drift in this signal can be expected, particularly
when the measurement is performed on a small network
or an unsynchronized source like a UPS or a windmill
generatorO For both these reasons, a precise frequency
multiplier is needed. Two possible solutions are
disclosed and namely the phase-locked loop (PLL) and
the digital frequency multiplier.
- 14 -
The phase-locked loop ( PLL ) is a well-known
analog method used to perform a frequency multiplication.
Figure 7shows the basic block diagram of a PLL 29 .
In the locked condition, the output frequency
~s becomes
~ s = N ~R (19)
~y properly designing the low-pass filter 31 and by
choosing the right value for the gain constant, Kv,
of the voltage controlled oscillator (VCO) 30, a con-
siderable locking range can be obtained. However,transients on the reference signal, ~R~ can be such
that an unlocked condition may exist for some time during
which the VCO output frequency, ~s' is unstable.
This condition may be minimized by selecting appropriate
characteristics for the phase detector 32. It is
recommended to use a voltage pump phase frequency
detector 32 resulting in a positive action of the
circuit during the unlocked condition of the PLL 29.
Despite the best PLL design, an unlocked
condition during transient typically lasts for three
or more periods of the reference frequency. A shorter
lock time can be achieved by using a digital method
of frequency multiplication. Such a device was introduced
many years ago. An improved version is illustrated
in Figure 8. For each half period of the reference
signal, a short pulse is generated by a zero-crossing
detector 33. This pulse synchronously resets a free-
running counter 34 clocked by a high frequency clock
35 divided by a prescaler ~, N) 36. At the end of each
half reference period, the content of the counter
~2~
34 is moved to an accumulator 37 which sets up the
input bits of a programmable counter 38. The program-
mable counter 38 is clocked directly by the high frequency
oscillator throu~h connection 39. A down-count end
pulse automatically reloads the content of the accumulator
37 through a logic circuit 40. The frequency of this
down-count end signal is expressed by:
wM/ = 2 N ~ (20)
The signal wM/M is passed through a divide-by-
two counter 41 which produces a square wave of frequency
N~R .
One application of the proposed measurement
technique i9 shown in the block diagram of Figure
9. This circuit represents the basis for an instrument
capable of measuring the power displacement factor
in a single-phase, variable-frequency power system.
Thisapplication assumes that a sinusoidal supply voltage
is applied to the terminals of a linear or non-linear
load 43. A linear load will be used for the performance
analysis regarding the amplitude and the phase response
of the SC tracking filter 44 and its sensitivity to
deviation of parameters.
The SCF 44 forms an 8th order Butterw~th
filter usin~ two National universal monolithic MF10
45 as shown in Figure 10. The basic filter building
block for a 2nd order low-pass configuration (see
Fig. 10), needs only two external resistors Rl and
R2 to set the quality factor (Q) of the function's
complex zero pairs. The low-pass gain is unity
(HoLp = -1) and the clock to cutoff frequency ratio
- 16 -
is set to lOO. The resistor values used in the
design of the Butterworth filter are listed below.
An 8th order configuration giving a 48 dB attenuation
at twice the filter cutoff frequency was chosen as
the design objective.
Resistor values for the 8th orde~ sutterworth
filter using two National~MF10
Stage Q R
# (k~) (kn)
. . .
1 0.51 22 11
2 0.60 22 13
3 0.90 22 20
4 2.56 22 56
The SCF clock signal (Wh) comes from a PLL
46 built around an RCA~CD4046A; the overall configuration
of the PLL is similar to the one in Figure 7. The
reference frequency derived from the sinusoidal
line voltage is produced by a variab]e frequency generator
42. The zero-crossing circuit 47 assures proper voltage
levels to the logic circuits.
The SCF 44 input receives the signal produced
by a current shunt 48 mounted in one of the supply
linesO The shunt signal is amplified, by an amplifier
49, to a proper level allowing a good signal-to-noise
ratio with the operation of the MF10. The output
50 of the SCF passes through a conventional RC low-pass
filter 51 which cleans the signal of any clock residues.
During the test, the cutoff frequency of this filter
is tuned at ten times the cutoff frequency of the
SCF. Bearing in mind that the clock to cutoff frequency
ratio of the SCF is 100, this calibration represents
the best compromise between the phase shift introduced
into the measured analog signal and the attenuation
of the clock residues.
Test Results
-
Tests were conducted to verify the basic
characteristics of the SCF 24, its phase behavior
as a function of the tuning frequency and finally
its phase and amplitude sensitivity to deviation in
the values of the components.
As mentioned above, the SCF forms an 8th
order Butterworth configuration. Using resistors
with 5% tolerance to adjust the four stages of 2nd
order basic filter, the characteristics obtained were
very close to that of the ideal Butterworth filter.
Figure 11 shows the experimental results
near the cutoff Erequency: the center curves for
amplitude and phase shiEt depict test results corresponding
to the nominal values of the resistors. At twice
the cutoff frequency, the attenuation reaches 46 dB,
or 2 dB less than the ideal value. Outer curves in
Figure 11 give the changed amplitude and phase shift
when, through the variation of resistor values, the
quality factor of all the 2nd order stages are shifted
by +10~ or -10~. One should note that, at the cutoff
frequency, the phase shift is not affected by variation
of Q- This means that the phase offset introduced
by the SCF is almost independent of the absolute values
of the external components. However, the gain of the
SCF suffers from the variation of Q and an appreciable
error can result in the amplitude measurement of the
fundamental component, appearing at -the output of
- 18 -
the filter. Hence, it is advisable to modify one
of the four stages in the SCF to allow some gain adjust-
ment.
Figure 12 shows an important performance
characteristic of the system of the present invention.
As the input frequency changes from 10 Hz to 100 Hz,
the absolute phase shift of the SCF 24 stays within
a two-degree deviation. The test was performed using
in-phase signals for both voltage and current, sinusoidal
waveforms. The phase difference was measured by means
of a calibrated zero-crossing detector 21. The good
performance is attributed -to the fact that the SCF
is precisely tuned by the input voltage frequency
via the PLL 29. In its locked condition, the PLL
produces zero frequency error, allowing ultimate per-
formance; the digital frequency multiplier has a non-zero
frequency error which can increase the phase shift
deviation at some frequencies. Also, one should note
the additional phase shift introduced by the analog
low-pass filter 31. The constant phase offset produced
by this filter results from the fact that the filter
was tuned at ten times the cutoff frequency of the
SCF for each measured point. This was done manually
during the present test but a tunable analog filter,
adjusted by the VCO 30 input voltage, can be designed.
The last test concerned the SCF phase sensiti-
vity to Q's variation. As previously mentioned, the
phase shift of the filter was unaffected, at the cutoff
frequency, by variations of the Q values. In fact,
operation of the MFlO introduces some phase variation;
- 19 -
-` ~2~
as shown in Fig. 13, a typical clock-to-cutoff frequency
ration offset exists with a value of 0.985 or 1.5%
off the ideal ratio. This results from the fabrication
of the MF10 integrated circuit. Operation with such
an offset, even relatively small, results in some
sensitivity of the phase to variations of the Q values.
In the present case, an 8th order filter is implemented;
this results in a deviation of +0.75 for a -10% varia-
tion of the quality factor. In applications where
a lower order filter should prove satisfactory, the
same shift would yield less deviation because of the
lower slope of the phase characteristic around cutoff
frequency.
Tests have also been performed with a non-
linear load. The performance of this system is also
well demonstrated in an application where the power
displacement factor of a single phase ac chopper,
operating with a complex load, has to be measured.
The chopper is made of two bidirectional MOSFET switches
which are turned-on and off according to a scheme
for nulling or at least minimizing the displacement
of the fundamental component of the line current.
The photographs of Figure 14A and 14B show examples
of the line current produced by the chopper supplying
two diEferent passive loads: in Figure 14A, the load
is slightly inductive (~load = 30) and the discontinuous
line current looks like a part of a sinusoid, with
the fundamental component in phase with the supply
voltage; in Figure 14B, the reactive nature of the
load is increased (~load = 60) and by proper adjustment
- 20 -
of turn-on and turn-off instants, the displacement
angle can be set to zero. In such an application,
the use of the harmonic analy~er based on SCF greatly
eased the measurement procedure.
In summary, a new technique for measuring
the amplitude as well as the phase angle of harmonics
is provided with its principle of operation based
on selective filtering of each harmonic, using a program-
mable switched-capacitor filter or analog filter.
The method has some advantages: constant phase offset
value of the tracking filter as a function of the
operating frequency, zero-frequency error on the filter
cutoff frequency, low phase sensitivity to variations
of Q values and low cost implementation. A practical
application of the technique has been demonstrated
with the measurement of power displacement factor
of a heavily distorted line current, produced by the
operation of a single-phase ac chopper.
The switched-capacitor filter harmonic ar.aly~er
of this invention has many applications, for example,
it can be used for general measurement of reactive
and distortion voltamperes in power converter applica-
tions; regulation involving power displacement factor
or low order harmonics; accurate harmonic analy~er
for network var compensation; quasi-analog fast Fourier
transform; and selective waveform analysis or generation.
It is within the ambi~ of the present invention
to cover any obvious modifications thereof provided
such modifications fall within the scope of the appended
claims.
- 21 -
