Identification of Individual Contributions to Total
Flicker Levels in Electric Power Systems
by
Ryan Phillip Gosnell
A thesis submitted to the Graduate Faculty of
Auburn University
in partial fulfillment of the
requirements for the Degree of
Master of Science
Auburn, Alabama
May 14, 2010
Approved by
Mark Halpin, Chair, Professor of Electrical and Computer Engineering
Mark Nelms, Professor and Chair of Electrical and Computer Engineering
Charles Gross, Professor Emeritus of Electrical and Computer Engineering
ii
Abstract
Total flicker levels in an electric power system can be contributed to from
multiple sources of flicker. Methodologies for allocating portions of this total
flicker level to the responsible loads are studied. The representation of flicker is
expanded upon for data generation purposes. Software necessary to both
generate and measure the necessary data is developed. A digital IEEE 1453
flickermeter is examined and implemented as a tool to analyze the total flicker
level in an electric power system. Techniques for identifying individual
contributions to total flicker levels are proposed, tested, and analyzed. The two
methodologies explored are examination of the line current and voltage
difference. Test scenarios compare sources of no flicker, single sources of
flicker, and multiple sources of flicker. Tests range across both lab tests and
computer simulations. The results show evidence of possible statistical
correlation across a range of testing scenarios and identification methodologies
for purely resistive line impedance. Use of more practical RL line impedance
appears to discredit the possibility of correlation for certain identification
methodologies.
iii
Acknowledegments
I would like to express my heartfelt gratitude and appreciation to my
parents. Without their support, patience, and encouragement I could not have
accomplished this. I thank and acknowledge Dr. Mark Halpin, my advisor, for his
time, guidance, and mentoring during my graduate studies. I thank my committee
members, Dr. Mark Nelms and Dr. Charles Gross, for their time and support. I
would also like to recognize the entire Auburn ECE faculty for providing a
wonderful learning experience throughout all the years I?ve spent at Auburn.
iv
Table of Contents
Abstract ......................................................................................................................ii
Acknowledgements .................................................................................................. iii
List of Tables ............................................................................................................vi
List of Figures .......................................................................................................... vii
1 Introduction ............................................................................................................ 1
2 Data Generation and Gathering ........................................................................... 6
2.1 Flicker Waveform Generation ................................................................. 6
2.2 Sampling ................................................................................................. 9
3 Flickermeter Design ............................................................................................ 15
3.1 Block 1 ? R.M.S. and Normalization .................................................... 16
3.2 Blocks 2, 3, and 4 ? Lamp-Eye-Brain Chain Response ...................... 18
3.3 Block 5 ? Statistical Evaluation............................................................. 26
3.3.1 Short-Term Flicker Calculation ............................................... 30
4 Testing & Results ................................................................................................ 34
4.1 First Round of Results & Analysis ........................................................ 36
v
4.2 v1-v2 Results & Analysis........................................................................ 55
4.3 RL Line Impedance Results & Analysis ............................................... 71
5 Conclusions & Future Work ................................................................................ 77
References ............................................................................................................. 79
vi
List of Tables
Table 1. Rectangular Voltage Fluctuations for Pst=1 Test Points [2] ..................... 8
Table 2. Necessary Values for Block 3 Weighting Filters; Parameters of
Lamps .......................................................................................................... 21
Table 3. Pinst Peak Value Results After Scaling .................................................... 24
Table 4. Pst Test Results ........................................................................................ 32
Table 5. Figure List for Obtained First Round of Testing Results ........................ 37
Table 6. Figure List for Obtained v1-v2 Testing Results ........................................ 57
Table 7. Figure List for RL Line Impedance Test Results: Source=110 CPM;
Load=24.4??48.8? Every 1 min .............................................................. 73
vii
List of Figures
Figure 1. Example Power System Diagram ........................................................... 2
Figure 2. Simple Circuit Diagram of Small Scale Problem ..................................... 3
Figure 3. Rectangular Voltage Modulation for 1620 Changes per Minute Test
Point ............................................................................................................... 9
Figure 4. Results of First Round of Testing a 58Hz Sine Wave ........................... 12
Figure 5. Results of Second Round of Testing a 58Hz Sine Wave...................... 12
Figure 6. Block Diagram of IEC Flickermeter ........................................................ 15
Figure 7. R.M.S. Filter Step Response .................................................................. 18
Figure 8. Bode Magnitude Plot of the Block 3 High-pass Filter ............................ 19
Figure 9. Bode Magnitude Plot of the Block 3 Low-pass Section ........................ 20
Figure 10. Bode Magnitude Plot of the Block 3 Weighting Filter .......................... 22
Figure 11. Pinst for the 0.5 Hz Test Point ............................................................... 25
Figure 12. Pinst for the 1620 Changes per Minute Test Point ............................... 26
Figure 13. Histogram of Output Data for the 1620 Changes per Minute Test
Point ............................................................................................................. 28
viii
Figure 14. Complementary Cumulative Probability Distribution for the 1620
Changes Per Minute Test Point .................................................................. 29
Figure 15. Histogram of Pinst of Measured 110 CPM Test Point; Pst=1.023 ........ 39
Figure 16. Histogram of Pinst of v1 with Source=60Hz Sine & Line=48.8?;
Pst=0.0682 ................................................................................................... 40
Figure 17. Histogram of Pinst of v2 with Source=60Hz Sine & Load=48.8?;
Pst=0.0689 ................................................................................................... 40
Figure 18. Histogram of Pinst of Current with Source=60Hz Sine & Load=48.8?;
Pst=0.0874 .................................................................................................. 41
Figure 19. Histogram of Pinst of v1 with Source=110 CPM & Load=48.8?;
Pst=1.009 .................................................................................................... 42
Figure 20. Histogram of Pinst of v2 with Source=110 CPM & Load=48.8?;
Pst=1.009 ..................................................................................................... 42
Figure 21. Histogram of Pinst of Current with Source=110 CPM & Load=48.8?;
Pst=1.026 ..................................................................................................... 43
Figure 22. Histogram of Pinst of v1 with Source=60Hz Sine &
Load=48.8??24.5? Every 1min; Pst=0.3517............................................ 44
Figure 23. Pinst of v1 with Source=60Hz Sine & Load=48.8??24.5?
Every 1min; Pst=1.3517 ............................................................................... 44
Figure 24. Histogram of Pinst of v2 with Source=60Hz Sine &
Load=48.8??24.5? Every 1min; Pst=1.057 .............................................. 45
Figure 25. Pinst of v2 with Source=60Hz Sine & Load=48.8??24.5?
Every 1min; Pst=1.057 ................................................................................. 45
Figure 26. Histogram of Pinst of Current with Source=60Hz Sine &
Load=48.8??24.5? Every 1min; Pst=33.64 .............................................. 46
viii
Figure 27. Pinst of Current with Source=60Hz Sine & Load=48.8??24.5?
Every 1min; Pst=33.64 ................................................................................. 46
Figure 28. Histogram of Pinst of v1 with Source=110 CPM & Load=48.8??24.5?
Every 1min; Pst=1.037 ................................................................................. 47
Figure 29. Pinst of v1 with Source=110 CPM & Load=48.8??24.5?
Every 1min; Pst=1.037 ................................................................................. 48
Figure 30. Histogram of Pinst of v2 with Source=110 CPM & Load=48.8??24.5?
Every 1min; Pst=1.384 ................................................................................. 48
Figure 31. Pinst of v2 with Source=110 CPM & Load=48.8??24.5?
Every 1min; Pst=1.384 ................................................................................. 49
Figure 32. Histogram of Pinst of Current with Source=110 CPM &
Load=48.8??24.5? Every 1min; Pst=29.98 .............................................. 49
Figure 33. Pinst of Current with Source=110 CPM & Load=48.8??24.5?
Every 1min; Pst=29.98 ................................................................................. 50
Figure 34. Histogram of Pinst of v1 with Source=60Hz Sine & Load=48.8??Open
Every 1min; Pst=0.5620 ............................................................................... 51
Figure 35. Histogram of Pinst of v2 with Source=60Hz Sine & Load=48.8??Open
Every 1min; Pst=1.228 ................................................................................. 52
Figure 36. Histogram of Pinst of Current with Source=60Hz Sine &
Load=48.8??Open Every 1min; Pst=560.3............................................... 52
Figure 37. Histogram of Pinst of v1 with Source=110 CPM & Load=48.8??Open
Every 1min; Pst=1.148 ................................................................................. 53
Figure 38. Histogram of Pinst of v2 with Source=110 CPM & Load=48.8??Open
Every 1min; Pst=1.593 ................................................................................. 54
ix
Figure 39. Histogram of Pinst of Current with Source=110 CPM &
Load=48.8??Open Every 1min; Pst=525.9............................................... 54
Figure 40. Current Input at 110 CPM Source Flicker with 48.8??24.5? Load
Switching Every 1min .................................................................................. 56
Figure 41. Input (v1-v2) at 110 CPM Source Flicker with 48.8? Load
Resistance; Pst=2.020 ................................................................................. 58
Figure 42. Pinst of v1-v2 at 110 CPM Source Flicker with 48.8? Load
Resistance; Pst=2.020 ................................................................................. 59
Figure 43. Histogram of Pinst of v1-v2 at 110 CPM Source Flicker with 48.8?
Load Resistance; Pst=2.020 ........................................................................ 59
Figure 44. Pinst of v1 with 60Hz Sine Source with 48.8 ? Load Resistance ........ 60
Figure 45. Input (v1-v2) at 60Hz Sine Source with 48.8? Load Resistance;
Pst=1.808 ..................................................................................................... 61
Figure 46. Pinst of v1-v2 at 60Hz Sine Source with 48.8? Load Resistance;
Pst=1.808 ..................................................................................................... 62
Figure 47. Histogram of Pinst of v1-v2 at 60Hz Sine Source with 48.8?
Load Resistance; Pst=1.808 ........................................................................ 62
Figure 48. Input (v1-v2) at 110 CPM Source Flicker with 48.8??Open Load
Switching Every 1min; Pst=56.50 ................................................................ 63
Figure 49. Pinst of v1-v2 at 110 CPM Source Flicker with 48.8??Open Load
Switching Every 1min; Pst=56.50 ................................................................ 64
Figure 50. Histogram of Pinst of v1-v2 at 110 CPM Source Flicker with
48.8??Open Load Switching Every 1min; Pst=56.50 ............................... 64
Figure 51. Input (v1-v2) at 60Hz Sine Source with 48.8??Open Load
Switching Every 1min; Pst=59.04 ................................................................ 65
x
Figure 52. Pinst of v1-v2 at 60Hz Sine Source with 48.8??Open Load
Switching Every 1min; Pst=59.04 ................................................................ 66
Figure 53. Histogram of Pinst of v1-v2 at 60Hz Sine Source with 48.8??Open
Load Switching Every 1min; Pst=59.04....................................................... 66
Figure 54. Input (v1-v2) at 110 CPM Source Flicker with 24.5??48.8? Load
Switching Every 1min; Pst=38.31 ................................................................ 67
Figure 55. Pinst of v1-v2 at 110 CPM Source Flicker with 24.5??48.8?
Load Switching Every 1min; Pst=38.31....................................................... 68
Figure 56. Histogram of Pinst of v1-v2 at 110 CPM Source Flicker with
24.5??48.8? Load Switching Every 1min; Pst=38.31 .............................. 68
Figure 57. Input (v1-v2) at 60Hz Sine Source with 24.5??48.8? Load
Switching Every 1min; Pst=43.12 ................................................................ 69
Figure 58. Pinst of v1-v2 at 60Hz Sine Source with 24.5??48.8? Load
Switching Every 1min; Pst=43.12 ................................................................ 70
Figure 59. Histogram of Pinst of v1-v2 at 60Hz Sine Source with 24.5??48.8?
Load Switching Every 1min; Pst=43.12....................................................... 70
Figure 60. Simulink Model for Testing with RL Line Impedance .......................... 72
Figure 61. Histogram of Pinst of Current with Line X/R=1; Pst=30.07 .................... 74
Figure 62. Histogram of Pinst of v1-v2 with Line X/R=1; Pst=18.74 ........................ 74
Figure 63. Histogram of Pinst of Current with Line X/R=4; Pst=30.67 .................... 75
Figure 64. Histogram of Pinst of v1-v2 with Line X/R=1; Pst=6.140 ........................ 76
1
Chapter 1
Introduction
Flicker is the term used to describe voltage fluctuations in AC
power systems that are significant enough to cause disturbance. The disturbance
is most notably of visual or perceived nature stemming from lighting systems but
it can sometimes affect equipment operation [1]. Flicker can be caused by many
sources. This is often from industrial facilities that use large induction machines
and non-linear, time-varying loads such as arc welding furnaces [1]. Cyclic flicker
can be represented in the form of rectangular amplitude modulation. Flicker
severity cannot exceed a certain level without disturbing other loads on the
power system. This severity depends largely on the regularity of voltage
fluctuations and the magnitude of voltage change. The frequency range of the
phenomenon is very important as the human eye is most susceptible to flicker in
the frequency range of 5-10Hz while the typical observable range is 0.5-30Hz [1].
Though flicker is described in terms of voltage fluctuations, analysis of
fluctuations in the current will also be explored.
2
In large power systems there are often multiple sources of flicker. The
problem arises when trying to detect how much of the total flicker level an
individual load is responsible for. Such a system can be seen in Figure 1.
G
1
2 3
4
l
4
l
3
L
3
L
4
Figure 1: Example Power System Diagram
Looking at the simple diagram in Figure 1 it becomes obvious that nodes within
the system affect one another. Simple representations of the node voltages can
be seen in (1), (2), and (3).Let [Z] be the bus impedance matrix. L3 and L4
represent high power loads that can generate flicker. l3 and l4 represent a
residential consumer that would be affected by the generated flicker. , , and
are the respective node voltages.
=f1([ ], , ) (1)
=f2([ ], , ) (2)
=f3([ ], , ) (3)
The manner of influence is not as important as the simple fact that since
nodes in a power system are interconnected the node voltages involved are
functions of one another. Before examining an entire utility power system this
problem can be scaled down to allow feasible testing and exploration of various
3
methodologies for analyzing flicker. The small scale problem used to represent
the larger issue at hand can be seen in Figure 2.
Figure 2: Simple Circuit Diagram of Small Scale Problem
This small scale problem reduces the system seen in Figure 1 from a
large utility power system to one with just a source, line impedance, and a load
impedance. The source will be able to generate a flicker signal defined as the
time-domain voltage v1 in Figure 2. The line impedance matrix has been reduced
to an impedance defined as R1+j?L1. The load impedance needs to fluctuate so
as to generate a flicker signal at the load. This can be accomplished by switching
two impedances in parallel at a certain frequency. These resistances are defined
as R2 and R3. The time-domain voltage v2 at the load will then be affected by a
combination of the source flicker, load flicker, and line impedance.
As flicker in one area of the power system could be caused from multiple
other areas, methodologies that can be employed to allocate portions of the total
flicker to the responsible individual sources would be extremely helpful. Proposed
4
methodologies include examining fluctuations in the line current. The results of
subtracting the source and load voltages will be analyzed. Direct analysis of the
voltage present at the source and load shall also be performed. This will allow for
the statistical analysis of the results from a range of tested methodologies by
using the implemented flickermeter to examine current, voltage difference, and
standardized voltage flicker signals. It is important to examine, analyze, and
compare various configurations of flicker sources within the system. The
proposed problem and test setup provides for this eventuality by allowing for
regulation of flicker generation at both the source and load.
With multiple sources of flicker present within the small scale problem it is
necessary to examine how to go about measuring and analyzing this
phenomenon. Standards for measurement of flicker exist both in the US and
Europe. These are the IEEE 1453 [2] and IEC 61000-4-15 Ed. 2 [4] standards
respectively. There are both hardware and software concerns with constructing
the measurement instrument specified by these standards. The flickermeter that
will be proposed is a digital implementation using MATLAB and Simulink similar
to that explored in [3]. There are other possible implementations of the
flickermeter such as those explored in [5], [6], and [7]. Hardware devices
necessary include National Instruments DAQ cards, computer hardware, and
other equipment in the lab. This setup and digital implementation allows for the
measurement, data storage, and analysis of the current and both relevant
voltages in the test system.
5
The flickermeter itself is designed to manipulate and analyze a data signal
spanning a set amount of time. The first part of the flickermeter is designed to
simulate the lamp-eye-brain chain response. The second part of the flickermeter
is for statistical analysis of flicker and providing the corresponding results [2].
Short-term flicker severity, Pst , is the ultimate output of the flickermeter. The
flickermeter?s process of determining Pst provides other meaningful data in the
form of Pinst (instantaneous flicker sensation), which can be examined with
several statistical methods. The results of node voltage and current analysis from
a system that has multiple sources of flicker may provide insight into finding the
portion of flicker disturbance for which each source is responsible.
In Chapter 2 the representation of flicker is explored along with designing
and testing means to gather data. Next, in Chapter 3, design and implementation
of the digital flickermeter is presented. The method of testing and results
obtained are presented and analyzed in Chapter 4, followed by conclusions and
implications of future research in Chapter 5.
6
Chapter 2
Data Generation and Gathering
The first step in solving the problem presented in the Introduction is being
able to generate a flicker waveform. As such it is necessary to expand upon the
representation of flicker. After generating data to act as input into the system it
will be necessary to measure and gather data from the points of interest within
said system. The means of gathering this data should be tested and function
properly so as not to corrupt or influence the results obtained from the
measurement.
2.1 Flicker Waveform Generation
For the purpose of testing the initial flickermeter model, ?perfect? data will
be generated to use as input to the model as opposed to real sampled data. The
representation is that of rectangular amplitude modulation of a sinusoidal
waveform. As is standard in the United States the combination of r.m.s. voltage
and utility frequency examined is 120 Vac/60 Hz. Equation (6) can be used to
generate the voltage fluctuation waveform.
(4)
7
Where ?V/V (%) is the relative voltage change for unit flicker severity and ff (Hz)
is the fluctuation frequency. These values are taken from the IEEE Standard
table of rectangular voltage fluctuation test points shown in Table 1 [2]. The test
points provided will generate a flicker waveform that produces a unit flicker
severity result (Pst=1) in a working flickermeter. Note that different average peak
voltage levels are used in later testing as the voltage sampled by the DAQ card is
normalized by the flickermeter.
8
Changes per minute
Fluctuation Frequenzy (Hz)
Pst=1
Relative voltage changes for
unit flicker severity for 120 Vac
lamps ?V/V (%)
0.1 0.000833 8.202
0.2 0.001667 5.232
0.4 0.003333 4.062
0.6 0.00500 3.645
1 0.00833 3.166
2 0.01667 2.568
3 0.02500 2.250
5 0.04167 1.899
7 0.05833 1.695
10 0.0833 1.499
22 0.1833 1.186
39 0.3250 1.044
38 0.4000 1.000
68 0.5667 0.939
110 0.9167 0.841
176 1.4667 0.739
273 2.2750 0.650
375 3.1250 0.594
480 4.0000 0.559
585 4.8750 0.501
682 5.6833 0.445
796 6.6333 0.393
1020 8.5000 0.350
1055 8.7917 0.351
1200 10.000 0.371
1390 11.583 0.438
1620 13.500 0.547
2400 20.000 1.051
2875 23.9583 1.49
Table 1: Rectangular Voltage Fluctuations for Pst=1 Test Points [2]
It is beneficial to examine a test point that will be used throughout later sections.
Looking at Table 1 it can be seen which values correspond to 1620 changes per
minute for a 120 Vac/60 Hz system: ?V/V=0.547 % and ff=13.5 Hz. To make the
voltage fluctuation more visible ?V/V
has been scaled by a factor of 100. The
resulting waveform for this scaled test point can be seen in Figure 3.
9
Figure 3: Rectangular Voltage Modulation for 1620 Changes per Minute Test Point [2]
From this plot it is possible to calculate that ?v/v=93/170=0.547 and that the two
distinct rectangular voltage changes per period of 0.0741 seconds results in 27
changes per second, or 1620 changes per minute.
2.2 Sampling
After waveform generation the signal can be output through a DAQ card.
For testing this signal will then be amplified, applied to the system, and then
various data will be sampled from the system for analysis. The means for
acquiring this data was accomplished with MATLAB and the Data Acquisition
Toolbox. When generating data, sampling the data, and then writing it to hard-
10
disk, an important concern is the possibility of missed samples. Thus a method
for checking the acquisition and file writing process was employed.
The process for checking for missed samples consists of comparing the
approximate derivative of the sampled data to the maximum analytical derivative
of the generated signal. For these tests a simple sine wave shown in (5) was
used.
(5)
Where is the amplitude and with f being the frequency in Hz. From this
it is easy to determine the analytical derivative and solve for the maximum value.
(6)
(7)
Next it is necessary to calculate the approximate derivative from sampled data.
This can be done by taking the difference between two sampled data points and
dividing by the sample time, seen in (8), where v is a vector of sampled data
points, Ts is the sample time, n is the number of samples in vector v, and d is the
resulting vector of approximate derivatives.
(8)
Now, compare the approximate and analytical derivatives. To do this find
all dk>A?s with s being a scaling factor used to exclude measurement error from
11
the result. By using a range of scaling factors in vector s, the threshold for
measurement error can also be examined.
For analysis it will be helpful to represent the number of approximate derivatives
that exceed the analytical derivative as a percentage of the total approximate
derivatives.
With this information an actual test can be performed. The input signal
will be sampled at a rate of 1920 samples per second by four
different channels on the DAQ card simultaneously. Testing multiple channels
simultaneously is necessary as in lab testing there will be three data channels.
Every two seconds the data will be written to a file for a total of 200 seconds
worth of data. This allows for testing of 100 data acquisition and file writing
procedures. This test will be performed 5 times to allow for comparison. The
results for two of these five tests are shown in Figures 4 and 5. The remaining
tests were very nearly identical. It is also important to note that the largest
approximate derivative calculated is only 18.58% greater than the maximum
analytical derivative without using any scaling factor. This implies that even at
this level the error isn?t great enough to be attributed to missed samples.
12
Figure 4: Results of First Round of Testing a 58Hz Sine Wave
Figure 5: Results for Second Round of Testing a 58Hz Sine Wave
13
If a sample were missed then the distance between two sampled points
would be twice the derivative of the sine wave at that point in time. Depending on
when in the cycle this occurs it could cause an approximate derivative to be up to
twice as large as the maximum analytical derivative; it?s also possible that the
resulting approximate derivative could be less than the maximum analytical
derivative. If several samples were being missed in every cycle the percentage of
approximate derivatives exceeding the analytical derivative would increase
relative to the cyclic rate and depending on where in the cycle the sample is
missed.
To expand on this point a simple test was run with 200 seconds of a 60Hz
sine wave generated in Matlab with a sampling rate of 1920 samples per second.
Then 1 random sample per cycle was removed to simulate it being missed in a
sampling process. The previously described test was performed. For a scaling
factor of 1.1 or less, 4.297% of the approximate derivatives exceeded the
maximum analytical derivative. This value is lower than for measured data due to
the fact that there is no measurement error with the generated data. For a scaling
factor of 1.125 or greater, 3.516% of the approximate derivatives exceeded the
maximum analytical derivative.
From these tests it can be concluded that there are no data samples being
missed in the acquisition and writing processes. Each test is consistent with itself
over a sufficient number of operations. For both tests there is a significantly small
amount of approximate derivatives exceeding the maximum analytical derivative
for a scaling factor of 10%. This implies that the error in approximate derivatives
14
in these cases is most likely due to measurement error. It should be noted that
these conclusions are dependent upon using the same DAQ hardware and
sampling rate tested in this section. If either of these is changed the tests should
be repeated.
After examining the flicker waveform in greater detail, a work means of
accurately generating a flicker signal was implemented and tested. With the
ability to generate the necessary flicker signal and store measured data for
analysis, it is possible to proceed to examining the tools for analyzing flicker.
15
Chapter 3
Flickermeter Design
The flickermeter design itself has several key components. The
flickermeter design process is broken up into several sections represented by
different ?blocks? in the system. A general block diagram of the flickermeter is
provided in Figure 6 [2].
Figure 6: Block Diagram of IEC Flickermeter
The model of blocks 2, 3, and 4 correspond to the lamp-eye-brain chain
response. Block 1 controls the r.m.s. calculation and normalization of the input
voltage signal. Block 5 is responsible for the statistical evaluation necessary to
calculate Pst.
As this is a digital implementation that will ultimately gather and process
data the first consideration is that of sampling rate. It is important to sample fast
enough to retain the integrity of the waveform but without obtaining too many
16
samples to practically handle in a ten minute span of data. The rate is also
somewhat controlled by hardware limitations of the DAQ cards. For this
implementation the rate of 1920 samples per second will be used. This is the
equivalent of 32 samples per cycle (one complete period that repeats) in a 60 Hz
system. Not only will this provide accuracy but the cyclic rate being a power of
two will allow for relatively easy data manipulation in the future, such as Fourier
Transforms. This could be helpful if other design alternatives that implement
Fourier Transforms were explored such as in [5], [7], and [8].
3.1 Block 1 ? R.M.S. and Normalization
Once a signal has been acquired for processing the next necessary step
is normalization of the waveform. Through normalization the magnitude of the
flickermeter input becomes a non-factor. Normally this normalization process is a
simple matter of calculating the r.m.s. value, multiplying it by the square root of
two, and dividing each sample in the time function by the result. To be able to
use this simpler method it must be assumed that the r.m.s. value for the entire
time function is constant. This is not the case for the problem at hand. It must be
kept in mind that the ultimate goal is to examine a utility power system. Over the
period of time required to sample enough data it is quite possible that the signal
level could be altered by a percent significant enough to impact the resulting
analysis. Such changes often occur during particularly high or low load times on
a utility power system. Thus it is necessary to calculate an r.m.s. value
17
corresponding to every sample in the time function. For accurate calculation a full
cycle worth of data must be used. Note that the resulting calculation is only valid
at the point in time for which it is calculated. This leaves the first cycle without a
?valid? r.m.s value; it is necessary to retroactively use the first calculated value for
the entire first cycle.
After the r.m.s. calculation is completed it is necessary to filter the result to
keep it at a constant reference level corresponding to the input. The only
changes that should affect the calculation are magnitude shifts of a relatively
permanent nature. Higher frequency changes will be filtered out to prevent
modification of the flicker modulating fluctuation. This is necessary to follow any
slow changes that occur during the measurement process. The filter has a 10%
to 90% response time step variation equal to 1 minute. The IEEE 1453 standard
stipulates these required specifications [2]. This is accomplished through the use
of a 2nd order low-pass filter. The transfer function (9) was implemented where s
is the Laplace complex variable. A step response of the implemented filter can be
seen in Figure 7.
(9)
18
Figure 7: R.M.S. Filter Step Response
3.2 Blocks 2, 3, and 4 ? Lamp-Eye-Brain Chain Response
This series of blocks is responsible for taking the normalized input
waveform and manipulating it in such a way as to provide an accurate simulation
of the human response to a visibly fluctuating light source. The combined non-
linear response of blocks 2, 3, and 4 simulates human flicker sensation. The first
component of this process, block 2, is a square law demodulator. By squaring the
normalized input voltage the voltage fluctuation is recovered; this, when filtered,
simulates the behavior of a lamp output (light) response. Implementation of this
in Simulink is straightforward as math-function blocks are available.
19
Contained within block 3 is a series of two sets of filters. The purpose of
the first set is to eliminate the d.c. and double mains frequency ripple
components of the block 2 output [2]. This is accomplished through the use of a
first order high-pass filter and a low-pass section implemented as a 6th order
Butterworth filter. The high-pass filter is suggested to have a 3 dB cut-off
frequency of about 0.05 Hz. The transfer function (10) was implemented where s
is the Laplace complex variable. A magnitude response of this filter can be seen
in Figure 8.
(10)
Figure 8: Bode Magnitude Plot of the Block 3 High-pass Filter
20
The Butterworth filter is suggested to have a 3 dB cut-off frequency of 42 Hz for
120 Vac/60 Hz systems. The following transfer function (11) was implemented
where s is the Laplace complex variable. A magnitude response of this filter can
be seen in Figure 9.
(11)
Figure 9: Bode Magnitude Plot of the Block 3 Low-pass Section
The next set of filters is designed to weight the voltage fluctuation according to
the eye-brain sensitivity [2]. The overall transfer function implemented to
accomplish this is specified in the IEEE 1453 standard and given in (12) where s
is the Laplace complex variable [2]. Values required in (12) for a 120 Vac/60 Hz
21
system are specified in the IEEE 1453 standard and given in Table 2. The bode
magnitude plot of the implemented filter can be seen in Figure 10.
(12)
Variable
120 Vac lamp
60 Hz system
? 1.6357
?
?1
?2
?3
?4
Table 2: Necessary Values for Block 3 Weighting Filters; Parameters of Lamps [2]
22
Figure 10: Bode Magnitude Plot of the Block 3 Weighting Filter
The final portion of the lamp-eye-brain chain response is composed of two
sections, a squaring multiplier and a 1st order sliding mean filter [2]. This
simulates the non-linear eye-brain perception and brain storage effect
respectively. As previously implemented the squaring operator can be taken care
of with a squaring math function block. The averaging operator must have the
transfer function of a first order low-pass RC filter with a time constant of 300 ms
as specified in the IEEE 1453 standard [2]. Equation (12) is the transfer function
implemented where s is the Laplace complex variable.
(13)
23
The output of block 4 is the instantaneous flicker sensation Pinst. This
output is defined as one unit of perceptibility which corresponds to the reference
human flicker perceptibility threshold [2]. It is necessary to test this point across a
range of input voltage fluctuations provided in the IEEE 1453 standard. The peak
values from each individual test point were averaged together to calculate the
scalar necessary to achieve a unity peak value. Results for the entire range of
test points are given in Table 3. The calculated scalar was . A plot of
Pinst for the 0.5 Hz test point can be seen in Figure 11. This better illustrates how
Pinst relates to the input voltage fluctuations.
24
Modulation Frequency (Hz) Voltage fluctuation (%) Peak Value Results
0.5 0.600 1.0034
1.0 0.547 0.9935
1.5 0.504 1.0020
2.0 0.471 1.0064
2.5 0.439 0.9965
3.0 0.421 1.0053
3.5 0.407 0.9900
4.0 0.394 0.9993
4.5 0.371 0.9864
5.0 0.349 1.0016
5.5 0.323 0.9873
6.0 0.302 0.9964
6.5 0.282 0.9870
7.0 0.269 0.9922
7.5 0.258 0.9943
8.0 0.255 1.0101
8.8 0.253 1.0072
9.5 0.257 0.9858
10.0 0.264 0.9865
10.5 0.280 1.0092
11.0 0.297 1.0262
11.5 0.309 1.0065
12.0 0.323 0.9920
13.0 0.369 1.0072
14.0 0.411 0.9992
15.0 0.459 1.0058
16.0 0.513 1.0139
17.0 0.580 1.0158
18.0 0.632 1.0105
19.0 0.692 1.0073
20.0 0.752 1.0133
21.0 0.818 1.0100
22.0 0.853 1.0151
23.0 0.946 1.0048
24.0 1.072 1.0273
40.0 3.460 1.3701
Table 3: Pinst Peak Value Results After Scaling
Note that the 40 Hz test point doesn?t fall within the specified Pinst peak
range. This is most likely due to the Butterworth filter implemented in block 3.
The IEEE 1453 standard only recommends a 6th order filter but it may be
necessary to implement a higher order filter for the results to be within the
25
desired range for the higher frequency test points. This isn?t necessary for the
focus of this implementation.
Figure 11: Pinst for the 0.5 Hz Test Point
Note that the peak values here are scaled to unity. This will not be the
case in the unity Pst test points. Scaling from Pinst testing allows the
instantaneous flicker output to be at a proper level for calculating Pst. The
importance of this plot becomes clear upon examining where in time each peak
occurs: they correspond to the number of changes per minute in the input voltage
fluctuation waveform. Two rectangular voltage changes at a frequency of 0.5 Hz
correspond to 2 changes per period of 2 seconds, or 60 changes per minute. A
26
Pinst plot of a unity Pst test point is presented in Figure 12 from which statistical
evaluation will be performed in the following section.
Figure 12: Pinst for the 1620 Changes per Minute Test Point
3.3 Block 5 ? Statistical Evaluation
The purpose of this block is to determine flicker severity by means of
statistical analysis. This is achieved through first sampling the instantaneous
flicker signal generated from the output of block 4 discussed in the previous
section. These resulting samples are counted into a sufficient number of classes
(or ?bins?) corresponding to their magnitude. The sampling frequency chosen for
27
the flickermeter design, 1920 samples per second, is high enough for the
resulting histogram to represent the distribution of flicker level duration in each
bin [2]. It is then necessary to create a cumulative probability distribution function
of the flicker levels by adding each bin count together and dividing by the total
number of samples. Note that this implementation uses the complementary
cumulative probability distribution. From this distribution function relevant
statistical values are easily obtained; this is necessary for calculating Pst.
There are mainly two different ways to approach classifying the
instantaneous flicker signal, a logarithmic classifier and a linear classifier. This
design implements a linear classifier and since it is an off-line flickermeter
implementation a large number of bins can be used. Using a large number of
bins isn?t always practical, particularly in the case of an on-line implementation. In
a situation where processing time is an issue it may be necessary to implement a
logarithmic classifier which significantly reduces the number of bins required for
accuracy.
The statistical evaluation process will be examined in more detail. Assume
that the instantaneous flicker signal Pinst is available and being run through the
classifier. The first step is to create the histogram. This is done through use of
the MATLAB ?hist? command. With this command the number of bins to be used
can be specified. A sufficient number for the purpose of this classifier is 10000
bins. This command now generates 10000 bins centered at linearly spaced
intervals ranging from the minimum to the maximum points of the data set. Such
a histogram is shown in Figure 13 for the 1620 changes per minute test point.
28
Figure 13: Histogram of Output Data for the 1620 Changes per Minute Test Point
With this data it is possible to calculate the complementary cumulative
probability distribution function. Let n be an array of magnitudes corresponding to
the count in each bin of the histogram. Let l be the number of bins which is
10000. The cumulative probability distribution function can be defined as (14).
(14)
This will result in an array of probabilities that correspond to each bin. Shown in
Figure 14 is the result of this process performed on the 1620 changes per minute
test point histogram from Figure 13. The y-axis refers to the array of probabilities
29
while the x-axis refers to the array of magnitudes that correspond to each
percentage. Note that the distribution is of the form P(x)>X.
Figure 14: Complementary Cumulative Probability Distribution for the 1620 Changes per
Minute Test Point
The amount of bins used provides for a large amount of accuracy in the
calculation of Pst. It can be calculated from both Figures 13 and 14 that there are
about 1300 bins over a spacing of 0.1 in magnitude. This shows that the linear
classifier is very accurate when employing a sufficiently large number of bins.
30
3.3.1 Short-term Flicker Calculation
Short-term flicker is the measure of flicker severity over an observation
period of 10 minutes. This measurement is referred to as Pst and is calculated
from the statistical evaluation acquired from the block 5 classifier examined in the
previous section. Pst is calculated from the cumulative probability distribution by
using (15), specified in IEEE 1453.
(15)
, , , , and are the flicker levels that correspond to the
percentiles obtained in the complementary cumulative probability distribution. To
obtain an accurate representation of these percentiles it is necessary to use the
smoothed value obtained from (16) through (19), specified in IEEE 1453. A
smoothed value is not needed for due to the 0.3 second memory time-
constant in the flickermeter.
(16)
(17)
(18)
(19)
It is now possible to examine the process for obtaining the percentiles
necessary for Pst calculation. Let p be the vector of probabilities plotted in Figure
14. Let d be the desired percentage; to find three percentages are needed:
30%, 50%, and 80%. To find the magnitude of the bin corresponding to the
percentages (20) can be employed.
31
(20)
The importance of the value v is only the number of the bin to which it
corresponds. The MATLAB ?min? function can return the index of v along with the
value. This is the index for the magnitude that corresponds to the desired
percentage.
The values calculated with this process for the flicker levels needed to
calculate Pst for the 1620 changes per minute test point are ,
, , , and . With these values it is
possible to calculate Pst which results in Pst=0.9954. As the test point used was
specified to provide it can be seen that the result falls in the required
range. This same process is performed for the entire range of test points
specified in the IEEE 1453 standard. The results can be seen in Table 4.
32
Changes per
Minute (CPM)
Modulation
Frequency (Hz)
Voltage
Fluctuation (%) Pst Results
0.1 0.000833 8.202 0.8860
0.2 0.001667 5.232 0.9921
0.4 0.003333 4.062 0.9884
0.6 0.00500 3.645 0.9890
1 0.00833 3.166 0.9928
2 0.01667 2.568 0.9990
3 0.02500 2.250 0.9969
5 0.04167 1.899 0.9969
7 0.05833 1.695 0.9988
10 0.0833 1.499 1.0029
22 0.1833 1.186 1.0028
39 0.3250 1.044 0.9970
48 0.4000 1.000 0.9927
68 0.5667 0.939 0.9941
110 0.9167 0.841 0.9931
176 1.4667 0.739 0.9924
273 2.2750 0.650 0.9954
375 3.1250 0.594 0.9969
480 4.0000 0.559 0.9998
585 4.8750 0.501 0.9968
682 5.6833 0.445 0.9956
796 6.6333 0.393 0.9958
1020 8.5000 0.350 0.9901
1055 8.7917 0.351 0.9894
1200 10.000 0.371 0.9918
1390 11.583 0.438 0.9996
1620 13.500 0.547 0.9954
2400 20.000 1.051 1.0007
2875 23.9583 1.49 0.9973
Table 4: Pst Test Results
After testing every provided point in the IEEE 1453 standard it can be
concluded that the completed meter is indeed functioning as intended. The Pst
result for every test point falls within the specified margin of error, ,
with the exception of the 0.1 CPM (Changes per Minute) test point. For this test
point only one change occurs within the 10 minute observation period. Unless the
change is perfectly synchronized part of the change will bleed into the next 10
minute period, which is why the Pst value is lower than it should be. If measured
33
continuously the next Pst value would be a bit higher than desired. Note that this
doesn?t impact the results of this implementation.
With these results it is possible to proceed into generating data to analyze
the initial problem presented in the Introduction. The Pst results from the following
sections, presented in Tables 5 and 6, can be compared to the Pst results in
Table 4 to aid in analysis.
34
Chapter 4
Testing & Results
With the flickermeter functioning as specified in the IEEE 1453 standard it
is necessary to move on to lab testing of the problem initially proposed in the
Introduction. This allows for analysis of data that is generated and gathered as it
might be in a practical situation. This data can then be used to examine the
proposed methodologies for analyzing individual flicker levels within the total
flicker signal.
The method of testing should be logically and systematically designed to
measure every value of interest while also examining every possible orientation
between source and load. It is also necessary to generate realistic data in a lab
setting, gather it with the designed meter, and analyze the results. This will be
accomplished with a setup that emulates Figure 2 of the Introduction. The source
flicker levels will be controlled through the use of a C program via desktop
computer and DAQ card. The program is able to generate a flicker waveform
from a given set of flicker frequencies and relative voltage modulation levels by
using the method described in the flicker waveform generation section. The
values for generating these waveforms are contained in Table 1 in the
Introduction.
35
The generated voltage waveform will be amplified to a typical level
(~120Vac) and applied to a series of impedances, a purely resistive impedance
followed by a variable load resistor bank. The constant impedance is to simulate
line impedance. For these tests the impedance is simplified and purely resistive
with a value of 1?. The variable load bank allows for manual control of flicker
generation at a load node by simply varying the resistance every one minute.
From this there will be three relevant data points to gather labeled in Figure 2:
source voltage , load voltage , and current . The voltages will be
stepped down through a voltage divider and gathered via a laptop running the
data gathering program tested in the sampling section. The currents will be
obtained through similar use of a current transformer.
With the testing setup completed a list of testing scenarios must be
compiled. This list will provide for testing the full range of possible source and
load configurations. The source configurations are as follows
? Voltage generated as 120 Vac/60Hz sine wave
? Voltage generated from 2 CPM test point specifications
? Voltage generated from 110 CPM test point specifications
? Voltage generated from 4800 CPM test point specifications
The load configurations are as follows
? Constant 48.8?
? Switching 48.8 ?? Open circuit every one minute
? Switching 24.5 ?? 48.8 ? load resistance every one minute
36
? Switching 24.5 ?? Open circuit every one minute
This results in a total of 16 possible testing configurations. Results from a portion
of these testing configurations will be presented in the following section. The
presented results are sufficient for comparison and analysis.
4.1 First Round of Results & Analysis
In this section, results are presented that were obtained from the various
testing configurations described in the previous section. In most cases plots of
both Pinst and the corresponding histogram will be presented. It is expected that
there can be some statistical correlation found between the various histograms.
This would provide insight as to possibilities in determining which portion of the
flicker signal is attributed to each of the sources. Values calculated for Pst will
also be given. Source and load scenarios are kept consistent between testing
situations to provide meaningful comparisons. In Table 5 the testing scenarios
and Pst values are given along with their corresponding figure number. Note that
the measurement notation corresponds to the system described in Figure 2 in the
Introduction.
37
LABEL SOURCE LOAD MEASUREMENT Pst
Figure 15 110 CPM Open v1 1.023
Figure 16
60Hz Sine
48.8 ?
Constant
v1 0.0682
Figure 17 v2 0.0689
Figure 18 i 0.0874
Figure 19
110 CPM
v1 1.009
Figure 20 v2 1.009
Figure 21 i 1.026
Figure 22
60Hz Sine
24.5?? 48.8?
Switch
Every 1min
v1
0.3517 Figure 23
Figure 24
v2
1.057 Figure 25
Figure 26
i
33.64 Figure 27
Figure 28
110 CPM
v1
1.037 Figure 29
Figure 30
v2
1.384 Figure 31
Figure 32
i
29.98 Figure 33
Figure 34
60Hz Sine
48.8?? Open
Switch
Every 1min
v1 0.5620
Figure 35 v2 1.228
Figure 36 i 560.3
Figure 37
110 CPM
v1 1.148
Figure 38 v2 1.593
Figure 39 i 525.9
Table 5: Figure List for Obtained Testing Results
Looking at the Pst results in Table 5 it can be concluded that the results
are as expected. When there is no flicker in the system the Pst results are very
close to zero. When there is flicker generated only at the source the Pst results
are very close to unity and agree closely with the Pst results in Table 4. This is
expected since the source flicker is generated based on the IEEE 1453
standard?s specifications. When flicker at the load is introduced it starts to
38
influence v1 by increasing the Pst result, though the influence of the source still
dominates the Pst result since v1 involves only the source impedance whereas v2
involves both the source and line impedances. The measurement impacted most
by the load flicker is the current; the fluctuations resulting from such a large
change in load resistance are so severe that it drastically increases the Pst value.
For the case with no load flicker and a 110 CPM test point as the source, it
should be noted that Pst=1 for the current. This is due to the fact that the voltage
is being applied to a fixed resistance of 1?. Since current is equal to voltage
divided by resistance, if the voltage fluctuates then the current fluctuates in the
same manner. The flickermeter examines only the fluctuations and normalizes
everything to the same value so internally there is effectively no difference
between the current and voltage signals in this case.
It is important to note that the flickermeter only holds to linearity over a
certain Pinst magnitude range influenced by the type of interpolation and number
of bins used in the classifier. In this case linearity describes that if the fluctuation
magnitude is doubled the Pst result will also be doubled. With the severe
fluctuations in the current these magnitudes are so large that it exceeds the
flickermeter?s linearity in this implementation. This may be why the Pst values of
the current don?t continue to follow linear growth for the largest load fluctuation
scenario. The 110 CPM test point from the IEEE 1453 standard is measured
directly as output from the amplifier and a histogram of the result is shown in
Figure 15.
39
Figure 15: Histogram of Pinst of Measured 110 CPM Test Point;
Histograms of the Pinst results from a setup where the source output is a
60Hz sine wave from the amplifier while the load is a constant 48.8? resistance
are given in Figures 16, 17, and 18. Note the magnitude of the bin centers for
these plots. Since there is no flicker present at the source or load the majority of
the Pinst data tends toward zero as expected.
40
Figure 16: Histogram of Pinst of v1 with Source=60Hz Sine & Load=48.8?;
Figure 17: Histogram of Pinst of v2 with Source=60Hz Sine & Load=48.8?;
41
Figure 18: Histogram of Pinst of Current with Source=60Hz Sine & Load=48.8?;
Histogram results from a setup where the source output is a 110CPM
flicker test point and the load is a constant 48.8? resistance are given in Figures
19, 20 and 21. As expected the results are scaled versions of the test point result
presented in Figure 15. It also holds true that since there is no flicker present at
the load, the histograms of Pinst of v2 and the current are extremely similar to that
of v1.
42
Figure 19: Histogram of Pinst of v1 with Source=110CPM & Load=48.8?;
Figure 20: Histogram of Pinst of v2 with Source=110CPM & Load=48.8?;
43
Figure 21: Histogram of Pinst of Current with Source=110CPM Sine & Load=48.8?;
Histogram and Pinst results from a setup where the source output is a 60
Hz sine wave and the load changes between 24.5? and 48.8? every one minute
are given in Figures 22 through 27. The large fluctuations of the load provide for
better visual indicators of what is occurring in the flickermeter output. To further
illustrate effects of the load flicker, instantaneous flicker plots have also been
included. The spikes shown in these correspond exactly to the switching points of
the load resistance as expected. Effectively the flickermeter Pinst result is the
same as that from a 60 Hz sine wave with peaks corresponding to the load
flicker. The spikes are so large though that they skew the histogram, forcing the
majority of the information into the first few bins. Note that several histograms
have logarithmic scaling along the x-axis due to this.
44
Figure 22: Histogram of Pinst of v1 with Source=60Hz Sine & Load=48.8?/24.5? Every 1min;
Figure 23: Pinst of v1 with Source=60Hz Sine & Load=48.8?/24.5? Every 1min;
45
Figure 24: Histogram of Pinst of v2 with Source=60Hz Sine & Load=48.8?/24.5? Every 1min;
Figure 25: Pinst of v2 with Source=60Hz Sine & Load=48.8?/24.5? Every 1min;
46
Figure 26: Histogram of Pinst of Current with Source=60Hz Sine & Load=48.8?/24.5? Every
1min;
Figure 27: Pinst of Current with Source=60Hz Sine & Load=48.8?/24.5? Every 1min;
47
Histogram and Pinst results from a setup where the source output is a
110CPM flicker test point and the load changes between 24.5? and 48.8? every
1 minute are given in Figures 28 through 33. Here, as in the 60 Hz variable load
results, the load adds on spikes to the test point response. The histograms
remain similar in shape but since Pinst has several data points larger in
magnitude this causes the histogram to be scaled down. The visible correlation
between these results and those for the constant load scenario, even with the
scaling, supports the prospect of identifying individual contributions to total flicker
levels.
Figure 28: Histogram of Pinst of v1 with Source=110 CPM & Load=48.8?/24.5? Every
1min;
48
Figure 29: Pinst of v1 with Source=110CPM & Load=48.8?/24.5? Every 1min;
Figure 30: Histogram of Pinst of v2 with Source=110CPM & Load=48.8?/24.5? Every 1min;
49
Figure 31: Pinst of v2 with Source=110CPM & Load=48.8?/24.5? Every 1min;
Figure 32: Histogram of Pinst of Current with Source=110CPM & Load=48.8?/24.5? Every
1min;
50
Figure 33: Pinst of Current with Source=110CPM & Load=48.8?/24.5? Every 1min;
Histogram results from a setup where the source output is a 60Hz sine
wave and the load changes between 48.8? and open every one minute are
given in Figures 34, 35, and 36. Instantaneous flicker plots for these cases are
not included as they look very similar to the Pinst plots in Figures 23, 25, and 27
except with much larger peaks every minute. As the results continue to look
similar across the range of test points it becomes clearer that there is correlation
between the histograms of various measurement points.
51
Figure 34: Histogram of Pinst of v1 with Source=60Hz Sine & Load=48.8?/Open Every 1min;
52
Figure 35: Histogram of Pinst of v2 with Source=60Hz Sine & Load=48.8?/open Every 1min;
Figure 36: Histogram of Pinst of Current with Source=60Hz Sine & Load=48.8?/open Every
1min;
53
Histogram results from a setup where the source output is a 110 CPM
flicker test point and the load changes between 48.8? and open every 1 minute
are given in Figures 37, 38, and 39. Instantaneous flicker plots for these cases
are not included as they look very similar to the Pinst plots in Figures 29, 31, and
33 except with much larger peaks every minute.
Figure 37: Histogram of Pinst of v1 with Source=110CPM & Load=48.8?/open Every 1min;
54
Figure 38: Histogram of Pinst of v2 with Source=110CPM & Load=48.8?/open Every 1min;
Figure 39: Histogram of Pinst of Current with Source=110CPM & Load=48.8?/open Every
1min;
55
One of the most important inferences from the various results is that over
a very systematic method of testing the results retain similarities. The nature of
the histograms coupled with the instantaneous flicker severity plots from each
measurement point implies that there is significant statistical correlation. These
results provide reasoning for using both voltage and current measurements in
flicker severity analysis.
4.2 v1-v2 Results & Analysis
In this section, results are presented for the input waveform, Pinst,
histogram, and Pst from the flickermeter after running data for v1-v2 in each setup.
This notation refers again to Figure 2 in the Introduction: v1 being the source
voltage and v2 as the load voltage. The testing scenarios explored here are the
same as those in the previous section of analysis to provide for easy reference.
Due to the nature of the flickermeter and input signals, the results are not
dependent on the order of subtraction. The process can be interpreted in several
ways but ultimately it provides a voltage directly proportional to the load current.
Passing the resulting waveform through the flickermeter should give insight as to
the flicker resulting from the load?s fluctuating current.
An example current input waveform is given in Figure 40. Note that the
input magnitude is lower than the actual value due to a 10:1 current transformer
used for measurement purposes. It can easily be seen from the calculated
voltage input waveform plots in Figures 47, 50, 53, and 56 that the resulting
56
voltage signal closely resembles that of the current. Again, these values are
lower than actual due to a 100:1 voltage divider in the signal conditioning box
used for measurement purposes. The Pinst plots also mimic those of the previous
section. Spikes due to the voltage change caused by the switching load
resistance are stacked on top of the source response. This results in histograms
of similar construction to those in the previous section. Again, this shows
evidence of statistical correlation between the various histograms across
methodologies and test scenarios. In Table 6 the testing scenarios and Pst values
are given along with their corresponding figure number.
Figure 40: Current Input at 110CPM Source Flicker with 48.8?/24.5? Load Switching Every
1min
57
LABEL SOURCE LOAD Pst (v1-v2)
Figure 41
110 CPM
48.8?
Constant
2.020 Figure 42
Figure 43
Figure 45
60Hz Sine
1.808 Figure 46
Figure 47
Figure 48
110 CPM
48.8 ?/Open
Switch
Every 1min
56.50 Figure 49
Figure 50
Figure 51
60Hz Sine
59.04 Figure 52
Figure 53
Figure 54
110 CPM
24.5 ?/48.8 ?
Switch
Every 1min
38.31 Figure 55
Figure 56
Figure 57
60Hz Sine
43.12 Figure 58
Figure 59
Table 6: Figure List for Obtained Testing Results
These Pst results suggest possible anomalies. The summations laws that
exist for mathematically combining multiple flicker sources would suggest that Pst
for two sources of flicker should be greater than when only one source of flicker
is present. Two possible reasons this isn?t the case are that error may be
magnified due to the low signal levels and that depending on when the
fluctuations of each flicker source occur in time, they could partially cancel
instead of add. This could also be why the Pst level isn?t zero when everything is
constant. But the point is that the value of these tests isn?t contained within these
Pst numbers but within the resulting histograms of Pinst that follow and any
noticeable trends therein.
Flickermeter input, histogram, and Pinst results from a setup where the
source output is a 110CPM flicker test point and the load is a constant 48.8?
58
resistance are given in Figures 41, 42, and 43. The histogram results more
closely resemble those of a sine wave source from the previous section. This is
due to the fact that the only source of flicker is at the source.
Figure 41: Input (v1-v2) at 110CPM Source Flicker with 48.8? Load Resistance;
59
Figure 42: Pinst of - at 110CPM Source Flicker with 48.8? Load Resistance;
Figure 43: Histogram of Pinst of - at 110CPM Source Flicker with 48.8? Load
Resistance;
60
Evidence of some measurement error or small signal noise can be seen in
Figures 42, 43, 46, and 47. In these cases the resulting Pinst of the v1-v2
waveform is expected to be effectively zero. With measurement error in the
larger signals (v1 and v2) this error is magnified when subtracting and is larger
relative to the smaller v1-v2 signal. A Pinst result of v1 from a setup where the
source output is a 60Hz sine wave from the amplifier while the load is a constant
48.8? is given in Figure 44. This shows the noise occurring at a much lower level
relative to the large signal, nearly zero, which is as expected.
Figure 44: Pinst of v1 with 60Hz Sine Source and 48.8? Load Resistance
Flickermeter input, histogram, and Pinst results from a setup where the
source output is a 60Hz sine wave from the amplifier while the load is a constant
48.8? resistance are given in Figures 45, 46, and 47. It can be seen that Figure
61
47 closely resembles Figure 18 of the previous section. This is a good sign as it
was expected to resemble the histogram from the Pinst of the current for the same
testing scenario.
Figure 45: Input ( - ) at 60Hz Sine Source with 48.8? Load Resistance;
62
Figure 46: Pinst of - at 60Hz Sine Source with 48.8? Load Resistance;
Figure 47: Histogram of Pinst of - at 60Hz Sine Source with 48.8? Load Resistance;
63
Flickermeter input, histogram, and Pinst results from a setup where the
source output is a 110 CPM flicker test point and the load changes between
48.8? and open every 1 minute are given in Figures 48, 49, and 50. It can be
seen that Figure 50 closely resembles Figure 39 of the previous section. As
expected, the histogram from the Pinst of the current resembles that of v1-v2 for
the same testing scenario. In this case it can be seen that the large Pinst spikes
are driving all the data into the first few bins of the histogram. This becomes a
pattern for all testing scenarios that flicker at the load has introduced. It should
also be noted that small signal noise is likely increasing the value around which
Pinst is centered. This causes the lower bin centers to be higher than expected.
Figure 48: Input ( - ) at 110CPM Source Flicker with 48.8?/Open Load Switching Every
1min;
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Figure 49: Pinst of - at 110CPM Source Flicker with 48.8?/Open Load Switching Every
1min;
Figure 50: Histogram of Pinst of - at 110CPM Source Flicker with 48.8?/Open Load
Switching Every 1min;
65
Flickermeter input, histogram, and Pinst results from a setup where the
source output is a 60Hz sine wave and the load changes between 48.8? and
open every one minute are given in Figures 51, 52, and 53. It can be seen that
Figure 53 closely resembles Figure 36 of the previous section. As expected, the
histogram from the Pinst of the current resembles that of v1-v2 for the same testing
scenario. Again, in this case it can be seen that the large Pinst spikes are driving
all the data into the first few bins of the histogram.
Figure 51: Input ( - ) at 60Hz Sine Source with 48.8?/Open Load Switching Every 1min;
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Figure 52: Pinst of - at 60Hz Sine Source with 48.8?/Open Load Switching Every 1min;
Figure 53: Histogram of Pinst of - at 60Hz Sine Source with 48.8?/Open Load Switching
Every 1min;
67
Flickermeter input, histogram, and Pinst results from a setup where the
source output is a 110CPM flicker test point and the load changes between
24.5? and 48.8? every 1 minute are given in Figures 54, 55, and 56. It can be
seen that Figures 55 and 56 closely resemble the corresponding histogram and
Pinst results from the previous section, seen in Figures 32 and 33.
Figure 54: Input ( - ) at 110CPM Source Flicker with 24.5?/48.8? Load Switching Every
1min;
68
Figure 55: Pinst of - at 110CPM Source Flicker with 24.5?/48.8? Load Switching Every
1min;
Figure 56: Histogram of Pinst of - at 110CPM Source Flicker with 24.5?/48.8? Load
Switching Every 1min;
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Flickermeter input, histogram, and Pinst results from a setup where the
source is a 60 Hz sine wave and the load changes between 24.5? and 48.8?
every one minute are given in Figures 57, 58, and 59. It can be seen that Figures
58 and 59 closely resemble the corresponding histogram and Pinst results from
the previous section, seen in Figures 26 and 27.
Figure 57: Input ( - ) at 60Hz Sine Source with 24.5?/48.8? Load Switching Every 1min;
70
Figure 58: Pinst of - at 60Hz Sine Source with 24.5?/48.8? Load Switching Every 1min;
Figure 59: Histogram of Pinst of - at 60Hz Sine Source with 24.5?/48.8? Load Switching
Every 1min;
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A few conclusions can be drawn from the results of the v1-v2 test
scenarios. As was expected, with purely resistive line impedance, the voltage
v1-v2 closely resembles the corresponding current waveforms from the previous
section. This naturally leads to the same trends in the Pinst and histogram results
and their behavior between test cases. Some small signal noise is likely causing
minor anomalies but doesn?t greatly impact the general behavior or trends seen
between test cases. It is clear that there is some correlation between the
histograms of the current and v1-v2. Though, it should also be noted that these
results may not be indicative of those in a practical scenario due to the nature of
the line impedance. These results also provide insight for analysis and serve as a
base for comparison with results from test scenarios using an RL line impedance
model. Simulations of such scenarios are presented in the following section. It
should be noted that these computer simulations are not affected by the
previously discussed measurement error.
4.3 RL Line Impedance Results & Analysis
To examine a more practical situation, simulations of a model with RL line
impedance were analyzed. Test scenarios will focus on differing X/R ratios as
opposed to various source and load flicker scenarios. Histograms of the Pinst
results for the current and v1-v2 waveforms are presented along with the
corresponding Pst results. Analysis of the results from v1 and v2 was also
72
performed and remains consistent with the corresponding results from section
4.1.
Effects from the RL line impedance are expected to cause the v1-v2
methodology to become unreliable due in part to a phase shift between the node
voltages. Histogram results from the v1-v2 Pinst results would consequently show
no signs of visible correlation with the histograms of the current Pinst results. The
model was implemented within Simulink using the SimPowerSystems Blockset
and can be seen in Figure 60. Note that these results can?t be compared exactly
with those from the previous sections as there is no source output impedance
present in this model.
Figure 60: Simulink Model for Testing with RL Line Impedance
The source flicker in all cases is 110 CPM while the load switching for all
cases is 24.4?? 48.8? every 1 minute. In Table 7 the testing scenarios and Pst
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values are given along with their corresponding figure number. Note that the
x-axis has a log scaling to aid analysis.
LABEL LINE IMPEDANCE MEASUREMENT Pst
Figure 61 X/R=1
R=0.7071 ?
L=1.876 mH
i 30.07
Figure 62 v1-v2 18.75
Figure 63 X/R=4
R=0.2425 ?
L=2.573 mH
i 30.67
Figure 64 v1-v2 6.140
Table 7: Figure List for RL Line Impedance Test Results: Source = 110 CPM;
Load = 24.4?? 48.8? Every 1 min
The histogram of Pinst of the current from a setup where the line
impedance X/R=1 is given in Figure 61. The histogram of the Pinst result of v1-v2
from a setup where the line impedance X/R=1 is given in Figure 62. It starts to
become evident that the histograms aren?t visibly correlated. This is due to the
fact that with the introduction of inductance into the line impedance the v1-v2
voltage fluctuations are slightly less pronounced than those of the current.
74
Figure 61: Histogram of Pinst of Current with Line X/R=1; Pst=30.07
Figure 62: Histogram of Pinst of v1-v2 with X/R=1; Pst=18.74
75
The histogram of Pinst of the current from a setup where the line
impedance X/R=4 is given in Figure 63. The histogram of the Pinst result of v1-v2
from a setup where the line impedance X/R=4 is given in Figure 64. It is clearer
here that the histograms are no longer visibly correlated, as in the previous
sections. With the RL line impedance X/R increasing, the voltage fluctuations of
v1-v2 continue to scale down breaking consistency with the current fluctuations.
Figure 63: Histogram of Pinst of Current with Line X/R=4; Pst=30.67
76
Figure 64: Histogram of Pinst of v1-v2 with Line X/R=4; Pst=6.140
After examining these histograms it is clear that RL line impedance has a
huge impact on visible correlation between the current and v1-v2 results. As the
line impedance X/R increases the v1-v2 voltage fluctuations decrease in
magnitude and in response the histograms of the Pinst results no longer resemble
those of the current. This implies that there wouldn?t be any statistical correlation
between the results and as such the v1-v2 methodology may not be feasible in
practical situations. These results are based on computer simulations and should
be examined in lab and field situations.
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Chapter 5
Conclusions & Future Work
Flicker is a low frequency visual phenomenon that can disturb many
customers on utility power systems. Flicker severity levels generated at one node
must be kept below certain levels. These levels are monitored with a
measurement device known as a flickermeter. A digital implementation of this
device via MATLAB has been presented. The key points of this device are cyclic
r.m.s. signal normalization, lamp-eye-brain chain response, and statistical
evaluation. To use this implementation there are programs and processes
needed for flicker waveform generation, data gathering, and data storage.
As there are typically multiple sources of flicker in a power system,
methodologies for determining how much of the total flicker level an individual
load is responsible for have been proposed, tested, and analyzed. A sufficient
and systematic testing approach has been employed to determine the possibility
of statistical correlation between various measurement and test scenarios. With a
purely resistive line impedance there is evidence of visible correlation between
current and v1-v2 analysis. There isn?t such evidence for a more practical
situation involving RL line impedance. For these various situations there has
been discussion and analysis of flicker waveform generation, instantaneous
flicker levels, and the calculation of short-term flicker severity.
78
This development and testing process has provided a strong foundation
for much further research in this area of study. Employing the designed
flickermeter implementation and testing processes will allow for easy examination
of other proposed methodologies of flicker analysis. It will be important to
examine a larger range of X/R line impedance ratios in both computer simulation
and a lab setting. It would also be valuable to provide for better control over the
variable load so as to allow for easy implementation of other testing scenarios,
particularly using a less exaggerated flicker level at the load node. Most
importantly the similarities between histogram results should be explored
mathematically to determine if any statistical correlation exists. The ultimate goal
is to perform field testing to validate the results from a lab setting.
79
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