Evaluating the Long-term Impact of a Continuously Increasing Harmonic Load
Demand on Feeder Level Voltage Distortion
Kerry D. McBee
Member, IEEE
Colorado School of Mines
1500 Illinois Street
Denver, CO 80223
power.engineer@ymail.com
Abstract –The increasing implementation of nonlinear
devices in residential homes may have a significant impact
on feeder level harmonic distortion. Because most utilities do
not monitor feeder level harmonics, the existing levels of
harmonic distortion are unknown, which hinders a utility’s
ability to forecast future feeder level harmonic distortion.
Within this paper the authors analyze the long-term feeder
level distortion possibilities based on a large number of
residential customers producing harmonic currents near
and above the IEEE 519 harmonic current threshold limits.
Field experiments were performed to determine the
relationship between the harmonic current produced by a
single residential customer and the corresponding customer
harmonic impedance. Utilizing the IEEE 13 Node Test
Feeder and the developed harmonic impedance function, the
authors utilized the current injection method with
residential customers represented by a Norton equivalent
circuit to evaluate the aggregate effects of customers with
high harmonic load demand. Also included is an analysis of
the effects that the increased harmonic demand will have on
harmonic resonance points on the feeder.
Index Terms-- Current Injection, Harmonics, IEEE 519,
Harmonic Resonance, THD
I.
INTRODUCTION
The increased implementation of nonlinear devices
within residential households has led some electric utility
companies to become more concerned about the resulting
harmonic distortion that is induced onto the distribution
system. From a distribution planning perspective the
question becomes how will the increased use of these
nonlinear devices affect future distribution operation and
designs, which have historically ignored the effects of
harmonics. In the last 20 years nonlinear devices such
adjustable speed driven air conditioning units, fluorescent
tube lighting, pc’s and laptops have become more
prominent in the residential household. With an
expectation of higher penetrations of electric vehicle
chargers and renewable energy devices on the distribution
system, the utility engineer must forecast how these new
nonlinear devices will add to the existing harmonic
distortion.
For the last 30 years researchers have investigated the
Marcelo G. Simões
Member, IEEE
Colorado School of Mines
1500 Illinois Street
Golden, CO 80401, USA
mgodoysimoes@gmail.com
increased use of nonlinear devices on the distribution
system. Most of the research has focused on the
implementation of a specific type of nonlinear device. The
impact of adjustable speed driven air conditioning units
was studied in [1]. The authors of [2] - [5] analyzed the
effects of residential PV installations. The harmonic
impact of compact fluorescent lighting was analyzed in
[6] – [10]. Because of the expectation that electric vehicle
purchase will increase, the authors of [11]-[13] evaluated
the impact of a high penetration of electric vehicle
chargers on feeder level harmonic distortion. Although
some of these papers incorporate a limited amount of
other nonlinear devices within their models, the authors
mainly address the harmonic distortion as a result of the
subject matter of the paper and not the aggregate sum of
all devices with increased penetration levels.
These research endeavors mostly focused on the
harmonic impact of specific devices based on a given
penetration level. Little concern was given to how the
harmonic distortion will increase yearly, which is the
concern of utility planning engineers. One exception is
the work performed by the authors in [14], who attempted
to predict the yearly rate of harmonic distortion increase
by forecasting the increased usage of nonlinear devices by
type. The disadvantage to this approach is that it relies
upon knowing specifics of customers load types and how
they change over time, which is typically inaccessible to
utility companies on a regular basis. For distribution
planning purposes, utility engineers rely upon indicators,
usually in the form of load demand, to signify when
design standards require revision or system infrastructure
requires upgrades.
With so many harmonic producing customers, the
question that many utilities must answer is “Will the
harmonic distortion produced by the aggregate sum of all
customers result in operational or system deficiencies that
should be considered when planning future system
upgrades, including capacitor bank and harmonic filter
installation?”
This paper describes the research performed by the
authors to evaluate the long-term effect of a continuingly
increasing harmonic demand. As with most forecasting
techniques, the authors evaluated the harmonic distortion
on 134 feeders to understand the existing conditions of a
typical system. The second part of the evaluation consists
of applying the current injection method to an expanded
version of the IEEE 13 Node Test Feeder to evaluate how
voltage distortion will be affected by increased nonlinear
device usage. The amount of current injected into the
system was varied between 3% and 30% of the residential
peak demand. Residential customers with linear and
nonlinear loads were represented by a Norton equivalent
circuit, which required the authors to determine the
relationship between the current injected into a
distribution system by a single customer and the harmonic
impedance of that customer. Field measurements were
acquired from residential customers located throughout
Denver, Colorado to determine the harmonic impedance
and current injected relationship.
II.
EXISTING LEVELS OF DISTORTION
Many utilities believe that customer current limitations
set forth by IEEE 519 will prevent any adverse harmonic
distortion effects at the system level. Within IEEE 519 are
current harmonic limits for customers and voltage
harmonic limits for utility companies [15]. The thought
behind the standard is that customers are responsible for
the amount of harmonic current demanded, while the
utility company is responsible for the resulting voltage
harmonic distortion. Unfortunately the document was
developed in 1992 when most of the harmonic current
sources were located at industrial and commercial
facilities. Because of the “push” for energy efficiency
appliances and lighting, today many residential homes
could be considered small harmonic sources, suggesting
that the limitations set forth in IEEE 519 may be too
stringent for the utility company and too relaxed for
customers.
Since the implementation of power electronics 25 years
ago, harmonic current distortion has only resulted in
isolated voltage distortion problems, which where
typically traced back to large industrial customer. With so
few problems associated with harmonic distortion, utilities
have essentially ignored monitoring customer and feeder
level harmonics. This lack of historical and active data
prevents utility planning engineers from accurately
predicting the long-term effects even if they so desired.
Typical forecasting approaches, whether for long-term
or short-term planning, utilize historical data and
regression curve fitting to predict demand growth [16].
The accepted growth pattern for demand takes the shape
of the typical S-Shape curve, which is illustrated in figure
1. Without information regarding historical harmonic
load demand, it’s nearly impossible to apply any existing
forecasting techniques to the future feeder level harmonic
distortion.
Fig. 1. Typical load growth S-Curve
The authors surveyed seven utility distribution
companies in regards to their increased number of
harmonic related issues and the implementation of
proactive monitoring programs. The results indicated that
only 2 of the utilities were implementing a proactive
program and none of them had seen an increase in
harmonic related problems.
One of the utility companies performed a detailed
feeder level voltage total harmonic distortion (THDv)
study. Utilizing Outram Ranger 7000 power quality
recorders, the THDv was measured for a week on 134
different 13.2kV feeders. The measurements were
required over a two year period in an urban environment.
The penetration of EVs and PVs on the monitored circuits
was less than 1% of the total customers.
Fig. 2. Histogram illustrating the voltage THD of 134 13.2kV feeders.
The monitoring revealed that the average THDv was
4.73%, which is just below the 5% voltage limit set forth
by IEEE 519 for utility voltage distortion. Although the
monitoring revealed that some feeders possessed voltage
distortion above the IEEE 519 thresholds, the distribution
company did not experience any adverse effects or record
any complaints related to harmonic distortion on any of
the monitored feeders. Figure 2 illustrates a histogram of
the THDv monitoring results.
The results of the monitoring study suggests that even
today many distribution feeders may have voltage
distortion levels that exceed IEEE 519 even if customers
or utilities are not witnessing the destructive impact of
harmonics. Although harmonics can disrupt electronic
control equipment that rely upon sinusoidal waveforms,
the largest impact of harmonics on power delivery devices
consists of long-term effects [17]-[19]. Harmonics
increase the heat generated by electrical devices. The
increased thermal environment essentially degrades
equipment insulation properties and can significantly
reduce the life of equipment depending upon the
magnitude of the distortion. However most utility
equipment is manufactured to operate for 20, 30, and
possible 40 years [20]; therefore noticing a reduced life
between 0 – 40% may be impossible.
With levels of harmonic distortion increasing on the
distribution system, the questions that utility engineers
must answer are:
•
•
•
•
•
How will existing harmonic distortion levels be
affected by the increased use of nonlinear devices?
If customers produce harmonic currents below IEEE
519 limitations will the resulting feeder level
voltage distortion exceed IEEE 519 limitations?
Does increased nonlinear device implementation
affect existing harmonic resonance points?
Where does the existing level of harmonic
distortion level fall on the typical load growth SCurve?
Will there be a saturation point for harmonic
distortion as with the typical load growth S-Curve?
III. AGGREGATE HARMONIC LOAD EFFECTS
A.
Development of Analysis Model
The traditional current injection method was utilized to
evaluate the effects of increasing customer harmonic
demand. Residential customers are modeled by their
Norton equivalent circuit as described in [21] - [24]. For
large scale distribution analysis regarding harmonics,
current injection method has proven to be an accepted
technique [25]. The current injection is based on upon (1).
Historically nonlinear devices have been modeled as
current sources. However, research has proven that some
nonlinear devices that utilize diode bridge rectifiers with
capacitive filter outputs can have characteristics that
resemble harmonic voltage sources instead. [26][27].
Because a utility company is concerned about the voltage
at the PCC, other linear devices that are connected to the
voltage source acting nonlinear device must be included
in the home representation.
These linear devices along with the resistance of
conductors are seen as impedances from the point of view
of the utility. Residential conductors sized 10awg – 18awg
possess resistance between 0.1 and 0.6 Ohms for distances
of 100ft, which is an average distance for residential
wiring [28]. These impedances when combined with the
nonlinear devices that have voltage source characteristics
can be represented by a Thevenin or Norton equivalent
circuit, which is utilized in this analysis. The authors do
agree that for analyses that evaluate the effects that a
voltage source acting device has on other household
appliances, the Norton equivalent circuit cannot be
utilized if the nonlinear device acts like a pure voltage
source [27].
The main focus of the analysis performed in this paper
is the bus voltage as a function of a fixed harmonic
current magnitude, which is the attribute that IEEE 519
limits for customers. For example, if all residential
customers demand 5th harmonic current in access of the
15% allowed by IEEE 519, will the resulting PCC
voltages exceed the voltage thresholds set forth by IEEE
519?
[ I Sh ] = [Yh −1 ][Vnh ]
(1)
Where:
ISh – Norton Current source at frequency h
Yh – System admittance matrix at frequency h
Vnh – Voltage node n at frequency h
The model utilized by the authors was developed from
the IEEE 13 Node Test Feeder [29]. The test system was
expanded to include lateral conductors, 50 kVA
transformers, secondary conductors, and individual
residential customers. Figure 3 illustrates the general
expansion of the 13 Node Test Feeder. The load delivered
through each lateral, which are connected to one of the 13
test nodes, was set equal to the amount of kVA specified
by [29]. This demand information was utilized to
determine the number of homes and transformers per
lateral. Each home was rated at 5kVA, while the lateral
conductors were sized in accordance to the current
demanded by the aggregate sum of the homes it serves.
With the transformers being rated at 50kVA, the
maximum number of homes per transformer was 10. All
secondary conductors were comprised of 350 kcmil 600V
triplex cable. Conductor sizes for lateral conductors are
listed in Table II. The laterals were designed in radial
pattern as illustrated in figure 4. Combining all of the
transformers, residential customers, and primary busses,
the final model consisted of a Y matrix with 298 buses.
With the system impedances determined, the authors were
left with modeling the individual homes.
TABLE II
Load Information for Test System
Fig. 3. IEEE 13 Node Test Feeder with load expansions.
Fig. 4. Representation of lateral connected IEEE 13 Node Test Feeder.
The authors utilized the Norton equivalent circuit
model as described in [21] - [24], which consists of a
current source in parallel with an impedance as illustrated
in figure 5. Although the current can be adjusted to inject
any amount of current back into the distribution system,
an impedance that represents the typical residential
customer impedance is unknown. Since the harmonic
current (Idh ) demanded by customers is a representation of
the type and number of devices drawing power, it can be
inferred that customer harmonic impedance varies with
Idh. Therefore utilizing an assumed fixed value that is
unrelated to Idh would lead to inaccurate analysis results.
To determine the relationship between residential
customer harmonic impedance and the amount of
harmonic current demanded by the customer, the authors
monitored 25 residential homes located in an urban area.
Bus 634
Load A
Load Amps
Lateral Size
Cable Rating
Transformers
Homes
Bus 611
Load B
Load Amps
Lateral Size
Cable Rating
Transformers
Homes
Bus 671
Load C
Load Amps
Lateral Size
Cable Rating
Transformers
Homes
Bus 675
Load D
Load Amps
Lateral Size
Cable Rating
Transformers
Homes
160kW, 110kVAr
80 amps
#4
120 amps
3
32
170kW, 80kVAr
78 amps
#4
120 amps
3
34
385kW, 220kVAr
184 amps
.1/0
275 amps
8
77
460kW, 360kVAr
242 amps
1/0
275 amps
10
95
Harmonic impedance of a load is determined by
measuring harmonic current and voltage at the frequency
of concern while varying the system impedance. The
voltage and current from the two operating conditions are
utilized in (2) to calculate the harmonic impedance. For
the analysis, current and voltage were monitored on the
customer side of the revenue meter, which is considered
the PCC. Once again Outram PM7000 power quality
recorders were utilized to acquire the field readings.
While the recorders were set, capacitor banks rated
between 900kVAr and 1500kVAr were operated so as to
satisfy the required system impedance fluctuation as
described in [21].
Zh =
∆Vh
∆I h
(2)
Where:
Zh – Harmonic impedance of current source
ΔVh – Change in harmonic voltage at frequency h
ΔIh – Change in harmonic current at frequency h
The results of the harmonic impedance analysis
revealed a nonlinear relationship between the harmonic
impedance and the amount of harmonic current demanded
by the customer. The nonlinear relationship for the 3rd, 5th,
and 7th harmonic frequencies is illustrated in (3).
Attributes for other frequencies were too diminished to
rely upon the outcome. These results match the measured
harmonic current and voltage magnitudes acquired in the
city networks monitoring study performed in [30], which
identified the 3rd, 5th, and 7th harmonics as the most
dominant in urban areas. Figures 6-8 illustrate the results
for the three different frequencies.
Evident in the results is the high harmonic impedance
associated with little harmonic current demand. Although
further research is required in this area, the authors
believe that this occurrence may reflect a low number of
connected appliances within the home. As more devices
are energized within the home, which are connected in
parallel to other devices, the home impedance as seen
from the utility decreases.
A × I dh
−( B )
I dh ≤16 amps
Fig. 5. Diagram of residential home model.
(3)
Where:
A
– Constant between 10.2 and 11.2
B
– Constant between 1.5 and 1.7
Idh – Harmonic current demanded by
customer at frequency h
The observed phase angle of the harmonic impedance
varied between 68° and -53°. To implement these angle
fluctuations into the analysis, harmonic impedance angles
of 45°, 0°, and -45° were evaluated.
The final component of the model was determining
how to adjust the current source so that the desired
amount of current was injected into the Y matrix. To
actually solve for the proper amount of current with every
residential home connected would require solving a
system of nonlinear equations, each representing all 298
buses of the system. To simplify the approach, the authors
determined the equivalent impedance of the distribution
system as seen from each home assuming that none of the
other homes were connected. This approach assumes that
the majority of the impedance seen from each home is
driven mostly by transformer impedance and
conductor/cable impedance. Utilizing current division and
(3), the magnitude of the current source (IS) can be
determined with (4). Results of the analysis revealed that
this approach was accurate within 0.1 - 0.2% for adjusting
IS for a specific Idh.
Diversity between residential customers was accounted
for by varying the phase angle of IS in accordance with
[31]. The authors utilized the number of residential homes
on each lateral to determine how to apply diversity
calculation from [31].
Fig. 6. Graph illustrating 3rd harmonic impedance as a function of current
injected.
Fig. 7. Graph illustrating 5th harmonic impedance as a function of current
injected.
Fig. 8. Graph illustrating 7th harmonic impedance as a function of current
injected.
I S = I dh + Z th AI dh
(1+ B )
(4)
B.
Aggregate effects on harmonic voltage
Harmonic current was equally injected into the Ymatrix to calculate the resulting voltage harmonic
distortion. The amount current injected represented the
average customer harmonic current demanded.
The results revealed that the IEEE 519 voltage
threshold limit for individual harmonic voltages, which is
3%, are exceeded for some instances when the average
customer injected current is greater than 3%. Figures 9 14 illustrate the resulting harmonic voltage at the
customers’ PCC on laterals A, B, C, and D as a function
of injected harmonic current.
The results indicate that the peak voltage is followed
by a saturation zone. The “harmonic peak” occurs at the
point where the customer harmonic impedance is
equivalent to the distribution system impedance as seen
from the customer, which can be describe by the
maximum power transfer theorem. These results suggest
that the impedance of the system as seen from the
customer’s PCC and the harmonic impedance of said
customer dictate the occurrence of peak voltage values.
For the IEEE 13 Node Test feeder, these matching
impedances occur between 3% and 15% injected current.
For a distribution system that has a higher impedance, the
peak voltage will occur at lower levels of injected current.
Conversely, having low system impedance will shift the
peak to the right.
These results should not be surprising considering that
harmonic devices are modeled as voltage and current
sources. The maximum power delivered to any network by
a source is dependant upon the impedance of the network
and the source. The only difference in this case is that
there are hundreds of sources and the harmonic
impedance of the homes fluctuates.
The PCC experiences “harmonic saturation” after the
occurrence of the harmonic peak. The magnitude of the
harmonic saturation can be as low as a 30% of the peak
harmonic value. The characteristics of the saturation
follow the characteristics of the nonlinearly declining Zh.
The results also indicate that voltage harmonic
distortion increases with harmonic frequency, which is
evident when comparing analysis results for the 3rd and 5th
harmonic frequencies. This occurrence reflects the
frequency dependant nature of inductive and capacitive
impedance.
Although the individual harmonic voltages at high
current injection levels are less than the individual
harmonic voltage thresholds set by IEEE 519, the
resulting THDv can be significantly higher than the 5%.
Because THD is the normalized aggregate of each
individual harmonic voltage, having a number of
frequencies with voltages near the IEEE 519 individual
harmonic threshold can result in high voltage distortion.
Fig. 9. Illustration of the 3rd harmonic voltage as function average harmonic
injected by customers. Residential harmonic impedance is purely resistive.
Each lateral is represented by A, B, C, and D.
Fig. 10. Illustration of the 3rd harmonic voltage as function average
harmonic injected by customers. Residential harmonic impedance is
inductive. Each lateral is represented by A, B, C, and D.
Fig. 11. Illustration of the 3rd harmonic voltage as function average
harmonic injected by customers. Residential harmonic impedance is
capacitive. Each lateral is represented by A, B, C, and D.
Fig. 12. Illustration of the 5th harmonic voltage as function average
harmonic injected by customers. Residential harmonic impedance is purely
resistive. Each lateral is represented by A, B, C, and D.
indicates that harmonic filters, which are designed to
eliminate harmonics at a given frequency, may require
retuning as the amount of current injection changes over
time. Other devices that may be affected are capacitor
banks, which may have been installed at locations to
prevent harmonic resonance. Tables 3 and 4 list the
changing ZD for several mainline buses along with the
impedance of the capacitor bank.
Fig. 13. Illustration of the 3 harmonic voltage as function average
harmonic injected by customers. Residential harmonic impedance is
inductive. Each lateral is represented by A, B, C, and D.
TABLE III
ZD and Capacitor Impedance at the 5th Harmonic
rd
Harmonic
Impedance Bus
(Ohms)
650
1000
1.3
100
1.3
10
1.3
1
1.1
0.1
1.1
Bus
632
5.1
5.1
5.0
3.9
3.4
Bus
633
8.5
8.4
8.4
5.8
4.1
Bus Bus Bus Bus Bus Cap
634 611 684 671 675 Z
9.5 10.9 9.5 10.0 10.0 10.7
9.4 10.9 9.4 9.9 9.9 10.7
9.1 10.4 8.7 9.1 9.1 10.7
5.5 5.9 3.5 3.4 3.4 10.7
4.0 4.0 2.5 2.4 2.4 10.7
TABLE IV
ZD and Capacitor Impedance at the 7th Harmonic
Fig. 14. Illustration of the 5th harmonic voltage as function average
harmonic injected by customers. Residential harmonic impedance is
capacitive. Each lateral is represented by A, B, C, and D.
C.
Impact on Harmonic Resonance
Since customer harmonic impedances vary depending
upon the amount of current injected into the system, it is
perceivable to believe that existing harmonic resonance
points on the distribution system will fluctuate as more
nonlinear devices are utilized. To examine this
occurrence, the authors calculated the driving reactance
(ZD) as seen from each bus located on the backbone of the
test feeder. Utilizing the approach defined in [11], the
authors calculated ZD at different system buses for average
customer impedances ranging between 0.1 – 1000 Ohms,
which represent harmonic current injections of 0.07 –
62amp (.2pu – 1.5pu). To evaluate the occurrence of
resonance, ZD is compared to the impedance of a
1200kVAr capacitor bank, which is 10.7 Ohms at the 5 th
harmonic and 7.6 Ohms at the 7th harmonic. Harmonic
resonance will occur when ZD is equal to the impedance of
the capacitor bank.
The results indicated that ZD fluctuates by several ohms
when transitioning between low current injection and
high current injection. For Bus 611 at the 5th harmonic
frequency, ZD is equivalent to the capacitor bank
impedance at low injection levels but transitions out of
this harmonic resonance zone as harmonic current
increases. For Buses 633, 634, 611, and 675 the increase
of current injection moves the resonance point from the 5 th
harmonic frequency to the 7th harmonic frequency. This
IV. CONCLUSION
The results of the analysis revealed that utility
companies should be concerned with the amount of
harmonic distortion that is produced by the increased
implementation of nonlinear devices. The preliminary
analysis revealed that even at today’s low levels of
nonlinear device penetration that voltage distortion can
exceed levels set by IEEE 519. The amount of voltage
distortion is dependant upon the system impedance as
viewed from the residential customer. These results
suggest that a utility may be able to predict the maximum
levels of voltage distortion based on its system
infrastructure. Through field measurements the authors
were able to determine harmonic impedances associated
with residential customers will decrease the more
nonlinear devices are implemented, which also suggests
that existing harmonic resonance points on the system
may change.
V.
[1]
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VI. BIOGRAPHIES
Kerry D. McBee (BS’99-MS’00) is pursuing his
Ph.D. degree in the Department of Engineering at
Colorado School of Mines, Golden, Colorado,
which is where he received his B.Sc. degree in
1999. He received his M.Sc. degree in Electric
Power Engineering at Rensselaer Polytechnic
Institute, Troy, New York, in 2000. During his
career he has focused on power quality, reliability,
forensic engineering, and distribution design for
companies such as NEI Power Engineers, Peak
Power Engineering, Knott Laboratory, and Xcel Energy. His field of
interest is Smart Grid implementation affects upon distribution engineering
and utility operations.
Marcelo G. Simões (IEEE S’89–M’95–SM’98)
received his Ph.D. from the University of
Tennessee, Knoxville, in 1995. He is with
Colorado School of Mines, Department of
Electrical Engineering and Computer Science,
where he is the director of the Center for
Advanced Control of Energy and Power Systems
(ACEPS). He has been conducting research and
education activities in the development of
intelligent control for high-power-electronics
applications in renewable- and distributed energy
systems and smart-grid technology. He is currently Past-Chair for the IEEE
IAS IACC and Co-Chair for the IEEE IES Smart Grid Committee. He has
been involved in activities related to the control and management of smartgrid applications since 2002 with his NSF CAREER award “Intelligent
Based Performance Enhancement Control of Micropower Energy
Systems.”