Energy and Power Engineering, 2013, 5, 1083-1088
doi:10.4236/epe.2013.54B206 Published Online July 2013 (http://www.scirp.org/journal/epe)
Influence Caused by Harmonic and Filtering Methods of
Synchronous Generator in Short-capacity System
Chunming Wang, Cong Pan, Jingjing Chen, Pengchao Song, Jian-ke Li
Engineering Institute of Engineering Corps, PLA University of Science and Technology, Nanjing, China
Received March, 2013
ABSTRACT
Relative to the power grid, the short-capacity system has smaller inertia and weaker ability to bear disturbance. As a
result, the synchronous generator in short-capacity system will be greatly influenced by harmonic. To reveal how har-
monic influence the generator, this article analyzed how harmonic current will influence the output voltage. Deduced a
formula that can describe the electromagnetic torque pulsation brought by the theory of Instantaneous Power, which can
explain why generator’s shaft vibrates. Then this article evaluated the applicability of current filtering methods in view
of characteristics of the small capacity of the system. As a result, it was demonstrated that active filtering method is best
suited for small capacity system. At last, it conducted the experiment that diesel generator set supply power to non-liner
load to demonstrate the conclusion of theoretical analysis.
Keywords: Short-capacity System; Synchronous Generator; Harmonic; Instantaneous Power; Active Filtering
1. Introduction
The increasing nonlinear loads in the power system have
brought serious harmonic pollution to the grid. Power
quality problems caused by the harmonic have given rise
to widespread attention [1, 2]. Relative to the power grid,
the short-capacity system has smaller short-circuited ca-
pacity and relatively large internal impedance [3], the
synchronous generator in short-capacity system will be
greatly influenced by harmonic. Harmonic may cause
electromagnetic torque and bring mechanical vibration of
the generator’s shaft. Meanwhile, harmonic bring a lot of
heat loss, which can reduce the power generation effi-
ciency, even will burn unit. Moreover, harmonic current
in armature may cause distortion of the output voltage of
the synchronous motor, which will degrade power qual-
ity seriously [4-6].
With the development of short- capacity power grid,
its suppression technology has attracted wide attention.
In utility grid, harmonic should be reduced by some me-
thods, such as the technology of passive filtering or ac-
tive filtering, power factor correction technology. While,
it need feasibility study that if these methods will also
work effectively in short- capacity.
2. The Change of Electromagnetic Relation
Compared with linear load, harmonic current will be su-
perimposed to the normal armature current when syn-
chronous generator supplies power to nonlinear load.
And the magneto motive (MMF) force caused by this
part of harmonic components will affect the reaction of
the armature of the generator. But also due to the pres-
ence of the resistance and inductance of the armature
windings, the output terminal voltage will occur distor-
tion. The inner electromagnetic relation of the non sali-
ent-pole synchronous generator, which is often used in
short-capacity systems, can be shown as Figure 1.
The output voltage of generator Uo give nonlinear load
the current I, which contains harmonic current. The fun-
damental current generates MMF Fa1, and the harmonic
current generate MMF Fan. Superimposing Fan to the
original Fa1 will change the form of armature reaction
and make the total MMF F pulsation, which leads to the
pulsation of the total Emf E.


E
I
1

I
RI

1

XIj

1




2n
n
RI




2n
nn
XjI





2n
n
I


2n
an
F
1a
F
f
I
f
F

F

B
o
U I
e
T
Figure 1. Electromagnetic relation when harmonic current
flow through armature.

C. M. WANG ET AL.
1084
3. Analysis of the Motor Operating
Characteristics under the Influence of
Harmonic
3.1. The Distortion of Output Voltage
The rotating magnetic filed generated by the harmonic
currents will also cut the stator windings and cause har-
monic voltage. But the rotary magnetic field generated
by the sinusoidal current is not a sine law standards change;
it contains space harmonic components which have the
same speed with the fundamental. The n-th harmonic
component of fundamental, for example, the cycle of
wave as the fundamental wave of 1/n, which as same as
the pole pitch. While, the rotating magnetic field gener-
ated by the n-th harmonic current contrast is different, it
has the same pole pitch with but n times spatial rotational
speed than fundamental wave. Therefore, instantaneous
value of electromotive force in the stator conductors
induced by harmonic current should be:
0
0
00
sin
sin2 sin
nn nm
nm p
n
eblvBlvnt
nB lntE nt







(1)
bn—Density of magnetic flux generated by harmonic n
l —Length of conductor
v —Relative line speed
In above equation:
02.22
2
nm p
n
nB l
En



n
f (2)
Bnm—Amplitude of rotate magnetic field generated by
harmonic n
τp —Pole pitch
f —Frequency of fundamental
Φn —Air-gap flux per pole of harmonic n
For the full-pitched coil, the RMS of its Emf Elec-
tromotive force is:
24.44
K
nkn k
ENE nfN n  (3)
Nk——Total series turns per phase
Since any harmonic rotate magnetic field has the same
polar distance with the fundamental, we can know that
for any harmonic current, its distribution factor is the
same as the fundamental. Assume that the air gap between
rotor and stator is uniform and ignore the magnetic satu-
ration of generator, we can know the relationship of Fn
∝
In, and then E
n
∝ nIn. This means that synchronous gen-
erator is more sensitive to the high-order harmonic cur-
rent. It is because the magnetic field generated by the
high-order harmonic rotates faster and has the higher
cutting speed.
3.2. The Electromagnetic Torque of Synchronous
Generator Caused by Harmonic
What nature of the synchronous generator is to convert
mechanical energy into electricity by the action of the
magnetic field? The relationship of energy conversion
inside motor can be shown as Figure 2.
In the process of energy conversion, the winding coil
is the only element that can store large numbers of en-
ergy. Therefore, if it can be demonstrated that magnetic
field energy stored in the winding coil is not variable, we
can draw a conclusion that the input mechanical energy
of the motor and the electric energy transformed are al-
ways equal.
When the motor is working under steady state, the
magnetic field energy in the winding coil is[7]:
 
2 2
0
0,,
2sr
RL
WFtFt

d






 (4)
Fs—Amplitude of the fundamental part of stator MMF
Fr—Amplitude of the fundamental part of rotor MMF
α—Mechanical angle
R—Radius of stator
L—Effective length of the shaft
Λ0—Permeability of the air gap
It can be seen, W is an invariant in the case of stable
load. Therefore, the input mechanical energy is:
efh out
Tppp


 (5)
Te——Electromagnetic torque
ω——Speed of rotor
pf——Mechanical loss
ph——Electric loss
pout——Output power
To simplify the calculation, pf and ph can be ignored:
e out
Tp


 (6)
Thus, Te can be approximated by computing the gen-
erator output power and motor speed. And the derivation
of the formula does not depend on the waveforms of the
output voltage and current, which has a wide range of
applicability. The pout in formula (6) stands for the tran-
sient power of the motor, which can not calculated as
average power. Here, the concept of instantaneous power
[8] can be introduced to understand pout. This concept is
more in line with the original definition p=u*i, without
extra secondary derivation process. In addition, the active
power, reactive power and distortion power can not be
normalized to the instantaneous power, which can avoid
the calculation error of the distortion power. Following
ex- ample is given to illustrate the applicability of the
theory:
Figure 2. Relationship of electrical energy conversion.

C. M. WANG ET AL. 1085
Assuming that the output voltage of diesel generator
has no distortion, the output current contains the 5th and
7th harmonic:
10
sin( )
A
ut

  (7)
10
(120
B
ut)

  (8)
10
(120 )
C
ut

 
5
(9)
105 0
707
sin() sin(5)
sin(7)
A
it t
t





 
 (10)
105 05
707
sin(120 )sin(5120 )
sin(7120)
B
it t
t
 

 



(11)
105 05
707
sin(120 )sin(5120 )
sin(7120)
C
it t
t
 


 (12)
The calculated value based on instantaneous output
power of the diesel generator sets is:
0
cos(6 )
4
AAB BCC
puiui uiabt



  (13)
In above equation:
'
11 1
3cos
2
a

  (14)
'
177 55
32 (sin sin)
2
b

 
(15)
Then:
0
0
cos 64
e
p
Tab t




   




(16)
In above equation:
'
11 1
0
3cos
2
a



  (17)
'
1775 5
0
32
b= α(βsinθ-βsinθ)
2ω (18)
In formula (16), the former represents the constant part
of electromagnetic torque, and the latter represents the
pulsation part of electromagnetic torque, which suggests
that 5th and 7th harmonic can both caused pulsating com-
ponent with 6 times frequency than fundamental fre-
quency. This conclusion is the same as what literature [8]
expresses, which can prove the theory of instantaneous
power is suitable for use to analysis the system. More-
over, the study about the theory of instantaneous power
will do good to search suitable filtering technology for
short- capacity.
3.3. Loss Caused by Harmonic
The stator windings of the synchronous generator are
densely wound by a large number of winding, the total
length of the winding is generally greater than the total
length of the cable in the small capacity systems, which
actually increased the total amount of heat generated due
to the skin effect. Moreover, the winding densely wound
in a small space, which lead that the stator winding
cooling capacity is much weaker than the distribution
cable and greatly exacerbate the effects of the proximity
effect. Under the combined action of skin effect and
proximity effect, the synchronous generators will severe
fever even burn unit components?
4. Study of Harmonic Suppression Method
4.1. Evaluation of Existing Methods
Currently, the used suppression methods for harmonic
can be divided into active management and passive gov-
ernance.
Active governance is to make harmonic work in higher
frequency or let different harmonics cancel each other
out with technology as power factor correction, PWM,
increase the number of fairing pulsating or Change the
configuration of harmonic source. These measures work
effective in power grid, but it will cost too much in re-
construction of the existing small system.
Different from the Active governance, passive gov-
ernance measures may filter devices to absorb the har-
monic currents generated by the harmonic source in
place, which is most widely used in field of harmonic
suppression. Power filter devices can usually be divided
into passive filters and active filters.
Passive Power Filter (PPF) usually consist of capaci-
tances, inductances and resistances in accordance with
certain topology certain parameters [9]. They always
have a simple structure, low cost and high reliability. In
addition to absorb harmonic basis, they can also com-
pensate reactive power, improve power factor. A typical
single tuned filter is shown as Figure 3 (a).
Active filter (APF) is invented based on the instantaneous
power theory and principle of cancellation, which can
dynamic tracking load harmonic changes and filtering in
real-time. Its principle is shown in Figure 3(b) above. As
one of the harmonic suppression strategies used in large
grid or grid of short- capacity, it have unparalleled
n
L

1
n
C

(a) (b)
Figure 3. The principle diagram of the filter.

C. M. WANG ET AL.
1086
advantage. It has the following advantages on the basis
of theoretical study and practical [5][10]:
1) Can not only filter most harmonics, but also
inhibited the flicker and compensating reactive power. 2)
Filtering properties will not affected by the system im-
pedance and avoid the risk of series or parallel resonant
with the system impedance. 3) Overload problem will not
occur. 4) With automatic tracking and compensating
harmonic changes. 5) Fast dynamic response.
4.2. Filtering Options
Although passive filter harmonic suppression technique
is widely used in the grid，But for small independent
capacity supply network, when grid load changes,
parallel resonant or series resonant may occur between
the system impedance and LC filter. If it happens, not
only can’t the filter eliminate specific frequency
harmonic currents, but will magnify the harmonic, which
bring a serious decline in quality of power supply. The
property of a filter depends on grid parameter, which
changes along with the impedance and resonant
frequency of the short- capacity operating conditions.
Thus, it’s difficult to design an LC network for short-
capacity grid [11].
In addition, the frequency of short- capacity power
supply is sensitive and influenced by load fluctuations.
For example, as a single-tuned filter branch shown in
Figure 3, its expression of the impedance for the n-th
harmonic is:
1
(-
nn
n
ZRjL C   )
1
(19)
Under disturbance, the frequency of grid will occur
some drifts, and the n-th harmonic impedance Zn will
increases. Assuming the parameters of filter branch is
stable, In1 means the n-th harmonic current of the filter
branch undisturbed, In1
’ means means the n-th harmonic
current of the filter branch disturbed.It is clear that:
1nn
I
I  (20)
Therefore, the filtering capacity of passive filter will
decline when power frequency drifts. As a result, the
quality of power supply will decline, particularly for
loads as meters.In consideration of the advantages and
disadvantages of these filtering measures, this paper
recommended the active filter as independent short-
capacity grid filtering means.
5. Experimental Study
Currently, most of the studies about the impacts on diesel
generator sets caused by nonlinear loads are limited to
qualitative analysis; the conclusions are often wide of the
engineering practice. In order to study about the impacts
of nonlinear loads on diesel generator sets, this article
conducted an experiment with a 50kw diesel generator
set produced by the Feng-Ling company of special power
plant in Taizhou City. The experimental principle is
shown in Figure 4:
The above nonlinear load is three-phase controlled
rectifiers with rated current of 500 A, linear load is a
resistance box with rated power of 200 kW. The active
power filter is invented by China University of Petroleum.
5.1. Experiment about Impacts of Harmonic on
Generator Sets
This article will measure the vibration signal and the
noise signal during this experiment. The tap of vibration
signal measurement is in chassis of the generator. Then
we will select four points in four sides’ each 1 meter
from the fuselage as the measuring point of the noise
signal. We will test output voltage and current
waveforms by using electric energy analyzer.
First, launch the diesel generator sets with linear load;
regulate the load power from no-load to full-load. Then,
test the working condition of diesel with nonlinear load.
In the progress of experiment, we select four power
points as 0 kW, 20 kW, 35 kW, 50 kW to test vibration,
noise, and frequency of the diesel generator set, the
measured data are shown in the Figures 5-7 below:
A
B
C
N
K
L
i
S
i
C
i
1
K
A
B
C
N
2
K
3
K
Figure 4. Experiment principle.
Figure 5. The change curve of unit vibration signal.

C. M. WANG ET AL. 1087
Figure 6. The change curve of unit noise.
Figure 7. The change curve of unit frequency.
The figures show that when genets nonlinear load,
there will be component of pulsating torque in the shaft
under the influence of the harmonic current. The pulsating
component will force the shaft always in unbalanced
state and bring about frequent acceleration and decelera-
tion. As a result, the frequency of generator will swing,
which can swing range from 40Hz to 60Hz, even it may
overcome the rotational inertia of the flywheel and force
the generator set to shut down. This is the root cause of
diesel generator set’s poor ability to supply for non-linear
load. Moreover, the pulsating electromagnetic torque will
apply periodic stress to the shaft, which will reduce life
expectancy of shafting components. It may also cause
high-frequency tensional vibration of shafting.
5.2. Experiment about Active Filter
First, close switch K1, the diesel generator sets grid work
with three-phase rectifier, use clamp and oscilloscope to
observe load current waveform and filtered current wave-
form of power supply side. And analysis distortion rate
of current waveform by Matlab. Then, close switch K3,
the active filter storks work, test the same data as the first
step. The waveforms of three-phase load current are
shown in Figure 8 and Figure 10; the current harmonic
content analyses by software are shown in Figure 9 and
Figure 11.
Figure 8. Current waveform of the three-phase load.
Figure 9. Current waveform spectrum analysis of the three-
phase load.
Figure 10. Current waveform of the three-phase load after
filtered.
Figure 11. Current waveform spectrum analysis of the three-
phase load after filtered.

C. M. WANG ET AL.
1088
As shown in Figure 15-16, when the three-phase
rectifier works, the current waveform of load distort
seriously, the THD of current waveform is 27.9%. After
the current compensated by active filter, the current
waveform is close to sine wave, the degree of waveform
distortion is reduced to 4.19%.The phenomenon demon-
strates that active filter can overcome fluctuation of
frequency and defect of system’s resonance.
6. Conclusions
This article analyzed the changes of electromagnetic
relations inside the motor caused by harmonic, and ana-
lyzed how harmonic current will influence the output
voltage, electromagnetic torque and fever characteristics.
Then this paper has evaluated the applicability of current
filtering methods and selected active filter as the filtering
device for short- capacity system.
At last, an experiment was conducted to demonstrate
the influence of harmonic and the availability of active
filter, the experimental results and theoretical analysis
are consistent. In addition, we found that the unit had
relatively poor capacity to provide active power for the
non-linear load, which leads to the problem about power
matching for nonlinear load. It needs further study.
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