J V Milanović

M T Au

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C I R E D 18th International Conference on Electricity Distribution Turin, 6-9 June 2005 
 
 
ESTABLISHMENT OF LOAD COMPOSITION IN AGGREGATE HARMONIC LOAD MODEL AT 
LV BUSES BASED ON FIELD MEASUREMENTS 
 
M. T. Au    
Universiti Tenaga Nasional – Malaysia  
mtau@uniten.edu.my 
 
J. V. Milanović 
The University of Manchester – U.K 
jovica.milanovic@manchester.ac.uk
 
INTRODUCTION 
 
This paper presents the methodology developed to derive the 
linear and nonlinear load composition of an aggregate 
harmonic load model based on harmonic measurements taken 
at the service entrance feeder.   Based on harmonic current 
spectra of typical nonlinear loads and aggregate harmonic 
loads obtained through measurement at service entrance, a 
weighted coefficient representative of the percentage 
combination of each type of nonlinear load is determined by 
solving a set of simultaneous equations with complex 
variables. Subsequently, linear load fraction is determined 
through SUPERHARM simulation of the modeled aggregate 
load.     
 
 
BACKGROUND 
 
Power electronics technology has advanced so extensively 
that present day electrical loads found in all sectors of 
consumers of electricity i.e industrial, commercial and 
residential consists of a significant portion of power 
electronic/nonlinear loads such as adjustable speed drives, 
converters, fluorescent lamps, personal computers and 
television sets. Connected to the same bus with the power 
electronic/nonlinear loads are the linear loads such as motor 
loads, heater/conventional ovens and air conditioning. While 
power electronic loads generate harmonics, the linear loads 
act as damping elements to harmonics propagation and alter 
the resonance frequency of the distribution system [1]. As 
there are usually a large number of power electronics and 
linear loads of medium and small power range connected to 
the same bus, it is not practical to model each load 
individually for a harmonic propagation study. Hence, an 
aggregate harmonic load model representative of the 
aggregate sum of power electronic/nonlinear loads and linear 
loads are desired. In the case of current source model, an 
independent harmonic current source is used to represent the 
power electronic/nonlinear loads and resistive, inductive and 
capacitive elements are used to represent linear loads.   
In developing aggregate harmonic load model, it is crucial 
that both the linear and nonlinear loads percentage 
composition be reasonably accurate so that frequency 
response curves and voltage distortion levels at distribution 
buses obtained through simulation are in close agreement 
with those of real distribution network. Published papers on 
aggregate harmonic load model typically refer to specific 
groups of nonlinear loads [2-5] and have not considered 
aggregate harmonic loads made up of linear and a variety of 
nonlinear loads with medium and small power range such as 
those classified based on customers activities.  
This paper presents a methodology to determine the fraction 
composition of linear and nonlinear loads through harmonic 
measurements taken at low voltage (LV) bus of the aggregate 
harmonic loads classified based on customer types/activities.  
           
 
GENERIC LOAD REPRESENTATION AT LV BUSES   
  
Load Representation  
 
A generic comprehensive load representation at LV buses for 
harmonic studies is shown in Fig. 1. Computation of the 
model parameters are explained and elaborated in reference 
[1]  :      
)1(
1 hIa
)2(
2 hIa
)(m
hm Ia
SV
)(hZS
1L
3R
)()( hZ LLeq
Harmonic
Recorder
)(NL
hI
S
hI
)(LL
hI
SI1
)(
1
NLI )(1
LLI
Electronic/Nonlinear Loads
1C)(2 hR
Low Voltage Load Bus
Linear Loads
LL
 
Fig. 1. General load representation for harmonic studies 
 
Circuit Analysis of The Model 
 
The nonlinear load composition at the LV bus typically 
consists of magnetic ballast discharge lamps (DL), compact 
fluorescent lamps (CFL), television sets (TV), converters 
(CONV), computers (PC) and adjustable speed drives (ASD) 
depending on the class of consumers. The net total harmonic 
current  is the vector sum of the harmonic current 
generated by the individual nonlinear load connected to the 
bus. With reference to Fig. 1, for a 1 p.u fundamental current 
of the individual nonlinear load, the harmonic current 
generated based on its fractional active power a of the total 
nonlinear load can be written as
)(NL
hI
i
)(i
hi Ia . 
Hence, the net total harmonic current generated by the 
nonlinear loads is,  
  
CIRED2005 
 
Session No 2 
C I R E D 18th International Conference on Electricity Distribution Turin, 6-9 June 2005 
 
)()()2(
2
)1(
1
)( m
hm
i
hihh
NL
h IaIaIaIaI +++++= KK    (1) 
 
where  are weighted coefficients representing the 
respective individual nonlinear load fraction active power  of 
the total nonlinear load at the LV bus, and ∑ , 
 
maaa K,, 21
0.1≤
0.1
1
=
m
ia
0 < ia
Also, let  represents the nonlinear loads fraction of the 
active power of the total plant load. Assuming that the 
fundamental current is approximately equal to load rms 
current, one can write: 
EK
 
S
E
NL IKI 1
)(
1 =                                    (2) 
 
As )()( hZ LLeq >>
S
hZ , it can be further approximated that, 
 
S
h
NL
h II =
)(     (3) 
 
where )(1
NLI and )(NLhI is total fundamental and harmonic 
current generated by the nonlinear loads respectively, SI1 and 
S
hI is the fundamental and harmonic current at the source 
(service entrance) branch respectively, )()( hZ LLeq is the 
equivalent impedance of linear loads, )(hZ s is the equivalent 
source impedance. 
Substituting (3) into (1) and writing in matrix form to indicate 
each harmonic current (up to the 11th) we have, 
 
































=
















−
S
S
S
S
S
I
I
I
I
I
IIIII
IIIII
IIIII
IIIII
IIIII
a
a
a
a
a
11
9
7
5
3
1
)5(
11
)4(
11
)3(
11
)2(
11
)1(
11
)5(
9
)4(
9
)3(
9
)2(
9
)1(
9
)5(
7
)4(
7
)3(
7
)2(
7
)1(
7
)5(
5
)4(
5
)3(
5
)2(
5
)1(
5
)5(
3
)4(
3
)3(
3
)2(
3
)1(
3
5
4
3
2
1
              (4) 
 
It should be noted that (4) has been formulated with the 
assumption that there are five distinctly dominant individual 
or groups of individual nonlinear loads fed from the particular 
low voltage bus. With this assumption, a 5X5 matrix is set up, 
hence limiting the harmonic to be considered to the 11th. This 
is justified by the fact that field measurements indicated that 
individual harmonic distortion for harmonic order larger the 
11th is relatively small and can be ignored.  
Note that all quantities on the right hand side of (4) are 
obtained from harmonic field measurements.  
 
 
HARMONIC MEASUREMENTS AT LV  BUSES 
 
Ideally, in congruence with the establishment of parameters of 
the aggregate harmonic load model shown in Fig. 1, separate 
sets of current measurements should be obtained for the 
branch that feeds the nonlinear loads and the branch that feeds 
linear loads in addition to voltage measurement at the 
common low voltage load bus. However, in practice, only   
one set of current measurements is taken at the service 
entrance feeder, as linear and nonlinear loads are not grouped 
separately and supplied by different cables.  
Therefore, the fraction of induction motors and other linear 
loads, )1( EK− , together with the fraction of individual/group 
of nonlinear loads will have to be derived based on measured 
power and individual harmonic current distortion at the 
service entrance and harmonic current spectra of 
individual/group of nonlinear loads.  
Sample of results indicating current total harmonic distortion 
(THDI) measured at the service entrance are shown in Fig 2. 
It can be observed that THDI varies randomly with a trend 
component that is dependent on time of the day. For 
simplicity, the trend component can be divided into daytime 
(9.00 hrs – 18.00 hrs) and nighttime (18.00 hrs – 24.00 hrs). 
Histogram of the THDI during daytime and nighttime is 
approximately a normal distribution. 
 
0
5
10
15
20
9:03 11:08 13:13 15:18 17:23 19:28 21:33 23:38
Time
TH
D
I(%
)
 
(a) 
 
(b) 
 
(c) 
Fig. 2. Bank aggregate harmonic load, (a) THDI variation with respect to 
time, (b) THDI histogram during daytime period, (c) THDI histogram 
during nighttime period 
 
 
DERIVATION OF LOAD COMPOSITION 
 
A simulation model as shown in Fig. 3, using probabilistic 
values of a  obtained by solving (4) is used to determine the 
effective harmonic current spectrum at the aggregate 
nonlinear load branch. 
i
Characteristic curves indicating variation of THDI with 
respect to , are obtained through SUPERHARM 
simulation using model shown in Fig. 4. Aggregate nonlinear 
load is represented by a single harmonic current source with 
the effective harmonic current spectrum derived based on Fig. 
3. Linear loads are assumed to be made up of 10% resistive 
load and 90% induction motor load modeled in 
EK
CIRED2005 
 
Session No 2 
C I R E D 18th International Conference on Electricity Distribution Turin, 6-9 June 2005 
 
SUPERHARM based on standard locked rotor KVA/HP 
ranges provided in NEMA MG-1-1993 [6]. 
Fundamental current at the source branch ( ) is fixed and 
set equal to field measured values. Values of  are then 
varied from 1 to 0.1 resulting in corresponding variation in 
THD
SI1
EK
I at the source branch (service entrance). The influence 
of  variation on THDEK I at the service entrance is illustrated 
in Fig. 5 
 
)1(
1
)1(
1
I
I
a h KK
)2(
1
)2(
2
I
I
a h )5(
1
)5(
5
I
I
a h
)(
1
)(
NL
NL
h
I
I
Effective harmonic current
spectrum
 
Fig. 3. Simulation Model of Nonlinear Loads 
 
)(LL
eqZ
)(NL
hI
S
hZ
)(LL
hI
S
hI
SV
SI1
S
E IK 1
S
E IK 1)1( −
Utility Source
Effective harmonic
current spectrum
 
Fig. 4. SUPERHARM Simulation Model 
 
 
ILLUSTRATION OF THE METHODOLOGY 
 
Harmonic measurement results of individual harmonic 
distortion at the service entrance (source) and for the 
respective individual nonlinear loads shown in Table 1 and 2 
are used as illustration. It is assumed that all the three classes 
of consumers have nonlinear loads that can be categorized 
into five categories as indicated in Table 2.  
Coefficients  are obtained by solving (4) using the data 
provided in Tables 1 and 2.  These coefficients (shown in 
Table 3) are subsequently used to calculate (in custom made 
MATLAB subroutine based on the single line diagram 
illustrated in Fig. 3.) effective harmonic current spectrum. 
ia
Measured values of THDI at the service entrance are then 
used to trace the corresponding fraction of nonlinear loads (in 
total aggregate load at the bus) operating during the day load 
and night load period for different types of consumers, as 
indicated in Fig. 5.   
The analysis performed showed that for all the three classes 
of aggregate loads magnetic ballast discharge lamps made up 
about 30-60% of the total nonlinear loads. The ratio of linear 
to nonlinear loads varies between different classes of 
aggregate loads. For example, the bank aggregate load has a 
ratio of 50:50, the hospital a ratio of 54:46 and the hotel a 
ratio of 85:15. High proportion of nonlinear loads is found in 
bank installations mainly due to discharge lamps, six pulse 
converters and computers. Linear/nonlinear load composition 
is also influenced by energy usage as indicated by   the bank 
aggregate load which shows a reduction in linear loads during 
the night as most air-conditioners are switched off. The 
hospital and hotel aggregate loads linear loads remain about 
the same throughout the day and night due to the nature of 
their business needs. The results can be taken as an added 
value feature to harmonic measurements taken at LV buses as 
it provides insight into the types and proportion of linear and 
nonlinear loads found in aggregate loads.    
 
 
TABLE 1 - Measured harmonic current distortion at the service entrance 
SS
h II 1  
Day Night 
 
 
h 
Bank Hosp. Hotel Bank Hosp Hotel 
3 
5 
7 
9 
11 
3.0% 
5.1% 
8.1% 
1.3% 
2.1% 
3.4% 
1.3% 
1.8% 
1.1% 
0.4% 
1.6% 
1.3% 
0.9% 
1.0% 
1.0% 
5.0% 
10.0% 
3.2% 
0.3% 
5.1% 
3.9% 
1.6% 
1.6% 
1.2% 
0.3% 
1.3% 
2.0% 
1.0% 
0.9% 
0.8% 
THDI 10.3% 4.2% 2.65% 12.7% 4.7% 2.9% 
 
TABLE 2 - Measured harmonic current spectra and THDI of individual 
nonlinear loads 
)(
1
)( ii
h II  
 
 
h T 1  
(e.g.,  
6-pulse 
Converter) 
T2 
(e.g.,   
P.C) * 
T 3  
(e.g., 
Compact 
Fluorescent 
Lamp) * 
T 4  
(e.g., 
Discharge 
Lamp) 
T5 
(e.g., 
TV) * 
3 
5 
7 
9 
11 
1.9% 
4.3% 
11.0% 
1.0% 
4.5% 
65% 
23% 
21% 
27% 
13% 
90% 
72% 
51% 
23% 
15% 
15.0% 
8.9% 
3.0% 
1.7% 
1.2% 
84% 
68% 
53% 
36% 
22% 
THDI 13% 78% 129% 18% 122% 
*Diversity factor=0.8 applied [3] 
 
TABLE 3 - Derived nonlinear load composition 
Installation / Time of 
Day 
T1 
( ) 1a
T 2 
( ) 2a
T 3 
( ) 3a
T 4 
( ) 4a
T 5 
( ) 5a
Day 0.117 0.144 0.115 0.521 0.103 Bank 
Night 0.086 0.152 0.112 0.544 0.106 
Day 0.326 0.121 0.074 0.463 0.016 Hosp. 
Night 0.221 0.146 0.033 0.568 0.032 
Day 0.354 0.163 0.065 0.324 0.094 Hotel 
Night 0.289 0.152 0.057 0.403 0.099 
 
  
 
CIRED2005 
 
Session No 2 
C I R E D 18th International Conference on Electricity Distribution Turin, 6-9 June 2005 
 
 
(a) 
 
(b) 
 
(c) 
Fig. 5. Characteristic curves of nonlinear load fraction , against THDEK I, 
(a) bank aggregate load, (b) hospital aggregate load, (c) hotel aggregate 
load 
 
 
CONCLUSIONS 
 
A methodology to derive approximate percentage 
composition of linear load and nonlinear loads found in 
aggregate harmonic loads of different classes of customers is 
presented. Results of this study concur with findings based on 
a rough inspection of loads found at the respective customer 
sites.  
 
 
 
 
As most utilities do not have information about customers 
load composition, the results are important inputs to aggregate 
harmonic load modeling which is particularly useful for 
distribution network harmonic simulation studies. With 
sufficient amount of harmonic measurements, the 
methodology presented can be used to further develop 
harmonic current spectra of typical aggregate loads found in 
distribution systems. 
 
 
ACKNOWLEDGMENTS 
 
The authors would like to thank Mr. Ganesan and Mr. 
Ghazali Jati from TNB Melaka, Malaysia for their assistance 
in performing harmonic measurements at distribution 
substations. 
 
 
REFERENCES 
 
[1]     Task Force on Harmonics Modeling and Simulation, 
2003, "Impact of Aggregate Linear Load Modeling on 
Harmonic Analysis: A Comparison of Common 
Practice and Analytical Models," IEEE Transactions 
on Power Delivery, vol. 18, pp. 625 - 630. 
[2]      A. Mansoor, W. M. Grady, P. T. Staats, R. S. Thallam, 
M. T. Doyle, and M. J. Samotyj, 1995, "Predicting the 
Net Harmonic Currents Produced by Large Numbers 
of Distributed Single Phase Loads," IEEE 
Transactions on Power Delivery, vol. 10, pp. 2001 - 
2005. 
[3]      A. Mansoor, W. M. Grady, A. H. Chowdhury, and M. 
J. Samotyj, 1995, "An Investigation of Harmonics 
Attenuation and Diversity Among Distributed Single 
Phase Power Electronic Loads," IEEE Transactions on 
Power Delivery, vol. 10, pp. 467 - 473. 
[4]    J.A. Orr, A. E. Emanuel, and K. W. Oberg, 1982, 
"Current Harmonics Generated by a Cluster of Electric 
Vehicle Battery Chargers," IEEE Transactions on 
Power Apparatus and Systems, vol. 101, pp. 691 - 700. 
[5]   J. M. Crucq, A. Robert, and B. Laborelec, 1989, 
"Statistical Approach For Harmonics Measurements 
and Calculations," presented at CIRED. 
[6]     Electrotek Concepts, 2000, Users Guide SuperHarm. 
Knoxville, Tennessee: Electrotek Concepts. 
 
 
 
CIRED2005 
 
Session No 2 


ESTABLISHMENT OF LOAD COMPOSITION IN AGGREGATE HARMONIC LOAD MODEL AT LV BUSES BASED ON FIELD MEASUREMENTS

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ESTABLISHMENT OF LOAD COMPOSITION IN AGGREGATE HARMONIC LOAD MODEL AT LV BUSES BASED ON FIELD MEASUREMENTS

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