1. Assessment of Harmonic Pollution by LED Lamps
in Power Systems
Hassan Shabbir, Muneeb Ur Rehman, Sohaib Abdul Rehman, Salman Khalid Sheikh, Nauman Zaffar
SBA School of Science & Engineering, LUMS
Abstract—Modern energy-efficient LED lamps do not draw
purely sinusoidal power. Their harmonic distortion level varies
with the quality of their non-linear driver circuit. This paper
studies the problem of system-wide harmonic impact of various
class of market-available LED lamps. Using a classification of
LED lamps based on their harmonic spectrum, we carry out
a study to quantify the distortion and losses possible in power
system if such lamps are to be installed. Unlike prior works,
we use advanced harmonic analysis techniques and conduct
evaluation with voltage-dependent harmonic current model for
LED driver. We conduct our evaluations on IEEE-30 test
bus system and report our results using IEEE standard 1459
which provides modern definitions of power quantities under
non-sinusoidal conditions. Extensive evaluation on a custom-
built simulator shows that poor quality LED lamps can cause
significant distortion in a power system. However, good quality
LED lamps introduce significantly lower distortion and provide
high economic and environmental benefits.
I. INTRODUCTION
Lighting comprises of nearly 20% of world’s electricity con-
sumption [1]. An increased emphasis on energy conservation
has triggered the use of solid-state lighting such as LED lamps
which offer 65% reduction in electricity demand [1]. Therefore
residential and industrial consumers are fast shifting towards
LED technology for economic and environmental reasons.
LED lamps are operated by a power electronics driver which
is a non-linear circuit. Depending upon the quality of driver
circuit, LED lamps can draw significant non-sinusoidal power
and produce harmonic pollution [2]. The negative effects
of harmonic pollution on power system infrastructure (e.g.,
transformers, filter capacitor banks), and user equipment are
well understood [3]. Moreover owing to the billions of dol-
lars invested in existing metering infrastructure, conventional
utility billing is done only on fundamental component (50/60
Hz). Thus any non-fundamental power flowing through the
power system is not accounted and it adds to the system
losses. Therefore LED devices with high harmonic impact
drivers can possibly have a major effect on power system
infrastructure and utility billing. In view of this problem, there
is an urgent need to assess the harmonic pollution due to
the high penetration of market-available LED lamps in power
system.
While it is well known that individual LED lamps can have a
total current harmonic distortion above 100%, it is unclear that
how much distortion and losses can occur system-wide if such
LED lamps are to be installed aggressively. Using a standard
IEEE test bus system, real trace current and voltage data of
market-available LED lamps, and a basic harmonic analysis
technique, we first carry out a detailed study to provide an
estimate of harmonic distortion and losses. We then model
LED driver circuit using converter modeling techniques and
use a high accuracy harmonic analysis method to account
various attenuation and voltage-dependency effects which are
ignored by earlier method. We perform comparisons with
different class of LED lamps which are available in market. We
report our results using IEEE standard 1459 which provides
the modern resolution of apparent power under non-sinusoidal
conditions.
Prior works in the space of system-wide harmonic impact
of LED lamps, use system-monitored data (e.g., [4], [5]), or
consider analysis techniques which do not account attenua-
tion effect and voltage-dependent harmonic behavior of LED
lamps(e.g., [6]). High penetration of poor quality LED lamps
in the future can lead the power system to instability there-
fore on-site measurements to study harmonic impact are not
adequate. Moreover our results show that voltage-dependent
harmonic characteristics and attenuation effect play a key role
in harmonic impact of LED lamps. Hence a generic approach
is required to assess the dynamic harmonic behavior of LED
lamps.
Altogether, this paper makes the following contributions:
• We summarize two advanced harmonic analysis methods
and explain their limitations and data requirements (Sec-
tion II).
• We verify harmonic injection of market-available LED
lamps using measurement data. We classify them as good,
average, or poor based on comparison with accepted
standard harmonic limits (IEC 61000-3-2) (Section III-
B).
• We propose a LED driver model to generate voltage-
dependent harmonic current data (Section III-C).
• We summarize details of IEEE-30 bus system and IEEE-
1459 standard definitions (Section III-A,D).
• We build a custom simulator in Matlab and using rigorous
evaluation via two harmonic analysis methods show the
harmonic impact of each class of LED lamp on a power
system (Section IV).
II. REVIEW OF HARMONIC ANALYSIS TECHNIQUES
Harmonic analysis of power system can be conducted both
in frequency and time domain. The analysis techniques vary in
data requirements, modeling complexity, problem formulation,
and solution accuracy [7]. We consider two advanced fre-

2. quency domain techniques for harmonic analysis in the scope
of this work and provide a brief summary of these techniques.
A. Constant Current Source Injection
Constant current source injection technique is used to eval-
uate the behavior of a power network in the presence of har-
monic sources which can be characterized by a typical current
spectrum (e.g., see [7]). This method requires information
about the magnitude of each harmonic current in the load’s
spectrum and the admittance matrix of power network at each
frequency of interest. Equation 1 is solved at specific harmonic
frequencies using the typical spectrum of nonlinear load to
obtain node voltage at each frequency.
[Yn][Vn] = [In] (1)
where [In] denotes the known nodal current vector, [Yn] is
admittance matrix at given frequency, and [Vn] represents
nodal voltage vector to be solved.
This method is quite beneficial in rough estimation of
distortion and losses in the network. However there are some
limitations of this method. Firstly when a variety of non-
linear loads are present in the network, the typical harmonic
spectrum assumption fails, as each load can have a different
spectrum (both magnitude and phase-wise). In such a situation,
significant cancellation or addition of harmonics (known as at-
tenuation effect) can occur due to phase difference in harmonic
currents. Secondly, the harmonic spectrum of a non-linear load
can vary with change in supply voltage distortion. Therefore
the accuracy of constant current source method is not high in
a realistic scenario. However the method provides us with a
valuable estimate about distortion. We will use this method to
provide an estimate of harmonic distortion due to LED lamps
in a power network.
B. Iterative Harmonic Analysis
Iterative harmonic analysis [8] is an advanced, high ac-
curacy technique. In this technique, each non-linear load is
modelled as a voltage dependent current source (as given by
equation 2).
In = F(V1, V2, V3, ..., VH, c) (2)
Where In is the nth
harmonic current, (V1, V2, V3, ..., VH) are
harmonic voltages at load terminals, and c is a set of control
variables (such as rectifier firing angle or output power).
Eq. 2 in conjunction with Eq. 1 forms a complete mathe-
matical model of the system. These equations can be solved
iteratively for a steady state solution. This method requires
information about the admittance matrix of power network
at each frequency of interest and most importantly a relation
of the form of Eq. 2 for all the non-linear loads under
consideration. Generally such a relation for non-linear loads
is not available (sometimes not possible). So this method is
limited by data availability. However synthetic data can be
generated (with good accuracy) using modeling techniques
for non-linear loads. We will present a frequency domain
harmonic model of LED lamp in Section III-C. We will
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2829
30
AC
AC
AC
AC
AC
AC
(a) IEEE-30 Test Bus System [9]
h
nodenode
(b) Norton equivalent of non-lighting load at
each node
Fig. 1. Test Bus System & equivalent Model to account non-lighting load
generate data from this model to evaluate the behaviour of
LED lamps using iterative harmonic analysis method.
III. OUR SYSTEM MODEL
A. Test System
We select IEEE-30 bus system for analysis and evaluation
purpose. Detailed data for the system is available at Power
Systems Test Case Archive [9]. Figure 1(a) shows one line
diagram of the bus system. The system includes 30 nodes, of
which some are connected to generation sources and others
are connected to loads. We use 11kV as base voltage and 100
MVA as base power of the test system.
Since our focus is to evaluate the effects of harmonics
produced by LED lamps, we use Norton equivalents at each
node to represent all other categories of loads. We use nominal
load values, given in the test case archive, to compute the
Norton equivalent of loads at each node. The equivalent system
is shown in figure 1(b). We use line impedance data and the
Norton equivalents to compute admittance matrix of the power
network at each frequency of interest. For 50 Hz power flow,
we use an impedance model for the overall load connected at
each node.
B. LED Lamps Classification
We verified harmonic injection of LED lamps from ex-
tensive laboratory measurements. Using measurement data
(from our earlier work [2]), we classify LED lamps in three
categories:

3. ‐0.6
‐0.4
‐0.2
0
0.2
0.4
0.6
0 2.5 5 7.5 10 12.5 15 17.5 20
Magnitude (A)
Time (ms)
Good LED
Average LED
Poor LED
(a) Time-domain Current waveforms
0
0.02
0.04
0.06
0.08
0.1
0.12
1 3 5 7 9 11 13 15 17 19 21
Magnitude (A)
Harmonic Order
Good LED
Average LED
Poor LED
(b) Harmonic Spectrum of Current
Fig. 2. Characteristics of some typical LED lamps available in market
Fig. 3. Generic LED Driver Circuit
• Lamps which comply with IEC standard 61000-3-2 (see
[10] for details ) are dubbed as Good LEDs.
• Lamps which partially fail above criteria and have a
current THD below 100% are dubbed as Average LEDs.
• Lamps which do not comply with any standard and have
a THD above 100% are dubbed as Poor LEDs.
Figure 2 shows the time-domain waveforms and harmonic
spectra of LED lamps available in market. All LEDs have
a nominal rating of 20W; however the actual power drawn
differed slightly. Among various LEDs tested, we select labo-
ratory test representatives of each class of LED lamps. We will
use the harmonic spectra of these lamps to conduct harmonics
study with constant current injection method.
C. LED Driver Circuit Model
Prior work on understanding LED harmonics has been
conventionally done via field tests or on-site measurements [4].
Advanced methods (e.g., iterative harmonic analysis) require
extensive measurement data to study interaction of supply
voltage distortion and LED’s nonlinear behavior. Such mea-
surements are generally not feasible and sometime not even
possible. Therefore modeling of LED driver for harmonic stud-
ies is required. Owing to similar motivations, work on compact
florescent light (CFL) modeling has been done previously [11].
In this section, we propose a frequency domain harmonic
model for LED driver circuit and provide its performance
characteristics.
LED driver circuit is essentially a single-phase capacitor
filtered uncontrolled ac/dc converter (as shown in figure 3).
Therefore we build on the techniques used for converter and
CFL modeling in [12] & [11] and report brief derivations
of our LED model to save space. After a series of complex
derivations, the frequency domain LED model can be written
using frequency coupled admittance matrices:


I1
I2
...
IK

 =




Y +
1,1 Y +
1,2 ··· Y +
1,H
Y +
2,1 Y +
2,2 ··· Y +
2,H
...
...
...
...
Y +
K,1 Y +
K,2 ··· Y +
K,H






V1
V2
...
VH

 +




Y −
1,1 Y −
1,2 ··· Y −
1,H
Y −
2,1 Y −
2,2 ··· Y −
2,H
...
...
...
...
Y −
K,1 Y −
K,2 ··· Y −
K,H







ˆV1
ˆV2
...
ˆVH



where Ik is kth
harmonic current phasor, Vh is hth
harmonic
voltage phasor, and ˆVh is conjugate of hth
harmonic voltage
phasor. The model takes four parameters as input to compute
elements of the admittance matrices. These variable comprise
of resistance R, capacitance C, and extinction angle α and
firing angle δ of diode. We select values of C which are close
to the nominal values of components used in LED drivers
where as R is estimated using empirically determined relation
R = 3.927V
I . The expressions for elements of admittance
matrices are:
Y +
k,h =
1 + (hωRC)2
πR
(δ − α)ejarctan(hωRC)
(h = k)
(3)
Y +
k,h =
2 1 + (hωRC)2
πR(h − k)
sin
(h − k)(δ − α)
2
× ej(
(h−k)(δ+α)
2 +arctan(hωRC))
(h = k) (4)
Y −
k,h =
2 1 + (hωRC)2
πR(h − k)
sin
(h + k)(δ − α)
2
× ej(
(h+k)(δ+α)
2 +arctan(hωRC))
) (5)
where ω is fundamental angular frequency. Using this model,
we generate model representatives of actual LED lamp classes.
Our results show that voltage-dependent harmonic current
magnitudes for LED lamps can be generated reliably from
model representatives (see figure 4 for comparison).
D. Measures of Harmonic Distortion & Losses
Prior works (e.g., [13], [14]) provide measures which quan-
tify the harmonic distortion and losses in a comprehensive
way. Most of the research in this domain has been driven
by engineering economics and the need for figures of merit
that help quantify line utilization and utility billing. Recently
proposed IEEE Standard 1459 definitions [15] provide a
detailed resolution of apparent power under non-sinusoidal
conditions. The definitions serve as a good measure of har-
monic distortion and losses in power networks. We provide
here a brief summary of the terms (as defined in IEEE standard
1459) which we will use to report our simulation results.
We assume a balanced three phase system and hence use a
per-phase model for subsequent derivation of measures. The
IEEE standard 1459 resolves current as I2
= I2
1 + I2
H and
voltage as V 2
= V 2
1 + V 2
H; where I (V) is overall current
(voltage), I1 (V1) is the fundamental component of current

4. (a) Good LED (b) Average LED (c) Poor LED
Fig. 4. Comparison of Harmonic Current Characteristics of original LED lamps with corresponding Model representatives
(voltage), and IH (VH) is the harmonic content of current
(voltage). This gives the apparent power as follows:
S2
= V 2
1 I2
1 + V 2
1 I2
H + V 2
HI2
1 + V 2
HI2
H (6)
The first term in Eq 6 is the fundamental apparent power
S1 = V1I1 (7)
S1 can be resolved into fundamental active and reactive
powers, S2
1 = P2
1 + Q2
1, where P1 = V1I1cos(θ1) and
Q1 = V1I1sin(θ1). The active and reactive powers are the
important components required for conventional utility billing
for residential and industrial consumers. The fundamental
reactive power helps estimate the need for linear capacitor
banks to correct fundamental power factor, cos(θ1).
The next three terms in Eq 6 constitute the nonfundamental
apparent power
SN = S2 − S2
1 = V 2
1 I2
H + V 2
HI2
1 + V 2
HI2
H (8)
The non-fundamental apparent power permits us to evaluate
at a glance the severity of distortion. Depending upon the
magnitude of harmonic pollution, SN helps determine the size
of static, active, or other type of compensation equipment.
This quantity also provides a measure for customer penalty
and associated economic charges to discourage harmonic
producing equipment.
Voltage Total Harmonic Distortion (THDV ) is defined as:
THDV =
VH
V1
=
V 2 − V 2
1
V1
(9)
Relative distortion, defined as SN
S1
, provides a relative mea-
sure of harmonics flowing through the monitored bus. Power
Factor, P.F is defined as P1
S and fundamental power factor,
P.Ffund is defined as P1
S1
= cos(θ1). Lastly we account line
losses across distribution line resistance using standard I2
R
method. Harmonic distortion can possibly cause other losses
(e.g., equipment damage) which we do not account in the
scope of this work.
IV. EVALUATION
We implemented the constant current source and iterative
harmonic analysis method in a custom-built simulation in
Matlab. Since replacement of existing lighting infrastructure
with energy efficient LED lamps will result in lower energy
consumption, we use 7% of total load to be lighting load.
We use harmonic spectrum of LED lamps (given in figure 2)
(a) Constant Current Injection (b) Iterative Harmonic Analysis
Fig. 5. Voltage THD observed at each node of System with Average LED
Fig. 6. Maximum THDV observed in the Power System for each Class of
LED lamp
for constant current source method and LED model data for
iterative harmonic analysis.
Table I summarises the results generated by the two meth-
ods. As we replace good LEDs with poor LEDs, both methods
show that distortion and harmonic losses increase significantly.
However iterative harmonic analysis results vary from constant
current injection method. The difference is anticipated as itera-
tive harmonic analysis method accounts for voltage dependent
current behavior of LED lamps and attenuation effect.
Figure 5 presents THDV observed at each node of power
system if average LEDs were to be installed. Figure 6 provides
a comparison of maximum THDV observed in the network
for each class of lamps using both methods. We observe that
distortion in power system increases considerably with poor
LEDs. The difference in THDV calculated by both methods
signifies that iterative harmonic analysis provides a better
assessment of distortion in power system.
Next we use only iterative harmonic analysis method to
report our results. Relative distortion of 0.17 was observed
in the overall system for Poor LEDs (see figure 7). This
means the non-fundamental apparent power is about 17% of
fundamental apparent power flowing in the network. The non-
fundamental power flow should ideally be as small as possible
since conventional utility billing is done only on fundamental
power.
Efficient transmission and distribution of electric power
happens close to unity power factor. Moreover difference

5. TABLE I
BREAKDOWN OF POWER QUANTITIES COMPUTED USING CONSTANT CURRENT INJECTION & ITERATIVE HARMONIC ANALYSIS METHOD
Analysis Method Type of Load Apparent Power (MVA) Fundamental Real Power (MW) Harmonic Line Loss (KW)
Total Fundamental Non-Fundamental Total Linear Lighting Line Loss
Constant Current Source
Good LED 311.93 308.22 6.73 284.87 263.56 19.83 1.486 660.9
Average LED 330.71 308.22 22.51 284.87 263.56 19.83 1.486 1549.6
Poor LED 402.55 308.22 94.35 284.87 263.56 19.83 1.486 3087.8
Iterative Harmonic Analysis
Good LED 312.96 308.22 4.76 284.87 263.56 19.83 1.486 10.95
Average LED 321.69 308.22 13.42 284.87 263.56 19.83 1.486 111.71
Poor LED 361.31 308.22 53.11 284.87 263.56 19.83 1.486 1017.78
(a) Good LED (b) Average LED (c) Poor LED
Fig. 8. Power Factor & Fundamental Power Factor observed at each node of System for each class of LED lamp
Fig. 7. Relative Distortion observed in the Power System for each Class of
LED lamp
in P.F & P.Ffund signifies harmonic content in the power
system. We observe that poor LEDs installation results in
power system operation at a significantly low power factor and
the difference between P.F & P.Ffund is high (see Figure 8).
Low power factor means that excessive current flows for the
same real power delivery thus transmission and distribution
infrastructure such as conductors and transformers have to be
provisioned to carry this extra current.
V. CONCLUSION
In this paper, we studied system-wide harmonic impact of
various class of market-available LED lamps. We considered
real trace current and voltage data of LED lamps to classify
them as good, average, and poor. We also modeled LED
driver circuit as voltage-dependent current source. Using two
advanced harmonic analysis methods, we showed the harmonic
distortion and losses produced by each class of LED lamps
in IEEE-30 bus system. We reported the results using IEEE
standard 1459 definitions. In the future, we plan to analyze a
mixture of LED lamps and other common non-linear appli-
ances for harmonic pollution and losses.
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