Energy and Power E ngineering, 2013, 5, 1503-1507
doi:10.4236/epe.2013.54B284 Published Online July 2013 (http://www.scirp.org/journal/epe)
Copyright © 2013 S ciRes. EPE
Research on C on t rol Method of Inverters for Large-scale
Grid Connected Photovoltaic Power System
Zhuo Zhang, Hongwei Li
Power Supply Company of Zhengzhou, Henan, China
Email: zhang-zhuo@msn.com, lihongwei-6@163.com
Received 2013
ABSTRACT
A grid-connected inverter controlling method to analyze dynamic process of large-scale and grid-connected photo-
voltaic power station is proposed. The reference values of control variables are composed of maximum power wh ich i s
the output of the photovoltaic ar ray of t he photo voltaic p o wer plant, and power factor specified by dispatching, the con-
trol strategy of dynamic feedback linearization is adopted. Nonlinear decoupling controller is designed for realizing
decoupling control of active and reactive power. The cascade PI regulation is proposed to avoid inaccurate parameter
estimation which ge nerates the s ystem static err or. Simulation is carr ied out based on the simplified po wer syste m with
large-scale photo voltaic plan t modellin g, and the po wer factor, solar rad iation strength, and bus fault are considered for
the further research. It’s demonstrated that the parameter adjustment of PI controller is simple and convenient, dynamic
response of s ystem is transient , a nd the stab ility of the inverter control is verified .
Keywords: Large-scale Photovoltaic Grid-connected; Dynamic Feedback Linearization; Nonlinear Decoupling;
Cascade Connection PI Control
1. Introduction
The safety and economy of power system are affected
directly by transformer running states, which play an
i mp ortant role in network. According to the survey, the
total transformer loss of about 8% of electricity genera-
tion, and distribution transformer loss is accounted to
about 60~80% of the entire distribution grid [1, 2]. No-
wadays, a large number of frequency electrical ap-
pliances and devices sorted as non-linear loads in indus-
trial and lives have become increasingly universal, which
have led to harmonic pollution to system and brought
about adverse effects including increased wear and tear,
abnormal temperature rise, insulation reduced life ex-
pectancy shortened to transformers and other electro-
magnetic equipments[3]. Therefore, non-linear load loss
calculation and analysis for transformer has been con-
cerned by the ve ry important.
Traditional transformer loss calculation includes theo-
retical analysis and experimental measurements. In ref-
erence [4], curve fitting method applied, and the har-
monics equivalent parameters are calculated with large
number of experimental information as to harmonic loss
by superposition principle. Co re saturatio n is not put into
consideration, and THD for different parameters can be
corrected. IEEE standards with experimental measure-
ments and operating experience data to calculate the
harmonic losses [5], but DC resistance loss is obtained
roughly, and the eddy current and stray losses are not
distributed considerably. Besides, the conservation is
mentioned [6]. The document [7] studie d the curve fitti ng,
and brought out better method when dealing with high
freq uency harmonic problem.
As studied above, equivalent parameter model has
bee n built , and har monic loss is analyzed in this paper by
considering the winding conductor frequency-dependent
characteristics with model parameters and the non-linear
superposition.
2. Winding Harmonic Model
Transformer total loss includes the copper loss, iron loss
and other stray loss, and copper loss of windings is di-
vided into dc loss and winding eddy loss. The total loss is
consisted of dc transformer winding loss, winding eddy
current loss and other stray loss since iron loss has been
ignored in load operation [8].
The harmonic equivalent circ uit of transformer has
been shown in Figure 1. In which, Rh(1), Rh(2), Xh(1), Xh(2)
is winding equivalent resistance values and reactance
values at order h respectively; Rh(m) and Xh(m) is magnetic
resistance and reactance.
Witho ut regar d t o co r e sa tur at i o n, gr o ups o f e quivalent
parameters information are acquired through no-load,
Z. ZH ANG, H. W. LI
Copyright © 2013 S ciRes. EPE
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U
h
I
h(1)
R
h
1
jX
h
1
R
h
2
jX
h
2
I
h(m)
R
h
m
jX
h
m
I
h
Figure 1 . The harmonic equivalent circuit o f tra nsformer.
short circuit test to test different harmonics effect to the
transformer. The superposition principle is employed to
the harmonic losses while the algebraic sum of the value
of consumed energy. Characterized by curve fitting the
winding resistances under different frequency have been
expressed as harmonic equival ent nonlinear parameters.
(1,2) 1(1,2)
h
h
R eR
β
α
=
( )
2
(1,2)0 121(1,2)h
Xaah ahX=+−
The parameters in the formula are interpreted as fol-
lows :
R1(1,2), Rh(1,2) fundamental and h harmonic equiva-
lent value of former and vice side winding resistance;
X1(1,2), Xh(1,2) fundamental and h harmonic equiva-
lent value of winding reactance;
α coefficient for exponential term;
β polynomial fitting exponent.
Ha rmon i c loss is expressed as:
22
(1) (1)(2) (2)
33
hhhh h
P IRIR= +
The total transformer los ses are shown:
max
22
(1) (1)(2) (2)
1
(33 )
hh
Thhh h
h
PIRIR
=
=
= +
(1)
IEEE / ANSI C57.110 standard made definition of the
total transformer losses under rated cond ition [9]:
2
LL RRdcEC ROSLR
PIR PP
− −−
=++
where, PLL-R is the total loss, RDC is the DC resistance,
PEC-R is rated winding eddy current losses, and POSL-R is
the other stray loss. With non-linear loads, the following
definition is ac hieved [10]:
max
max
max max
2
2
22
11
12
2
111
h
hh
hh
h
HL hhh
h
hh
Ih
Ih I
FI
II
=
=
==



== 


FHL is harmonic loss factor for winding eddy currents.
FHL-STR is the other stray loss factor. It is not considered
about the model parameters of nonlinear problems, har-
monic losses are calculated by overlapping the corres-
pond i ng value .
Tota l loss is defined as belo w:
2
LLRdcHLEC RHL STROSL R
PIRF PFP
− −−
=++
(2)
3. Equivalent Model Frequency
Characteristic
Transformer eddy current loss is generated b y alternating
magnetic flux, follo wed with ther mal effect and mag netic
effect, which is shown in Figure 2.
The eddy currents or magnetic diffusion equation can
be derived in quasi-static magnetic field (MQS).
=∇
=∇
=∇
t
t
t
J
J
E
E
H
H
µγ
µγ
µγ
2
2
2
The distributed electric and magnetic field capacity are
fixed as the magnetic c enter of the dis tr ibution known:
−=
=
)sh(
)ch(
)(
)ch(
)ch(
)(
0
0
Kx
Ka
HK
xE
Kx
Ka
H
xH
y
z
γ
In order to facilitate analysis of conductor in the elec-
tromagnetic field distribution, the following assumptions
are proposed:
1) As l>>ab>>a, it is assumed that conductor di-
mension along y or z direction is much larger than x di-
rection. Otherwise, the geometric size of the thickness is
much smaller. E, H and other field quantity can be ap-
proximated as function of x, y and z independently.
2) Conductor is supposed passed by sinusoidal mag-
netic field and B along the z direction. Then the eddy
current in x- y section was a closed path, but not spread
along direction z. As b>>a mentioned above, the edge
effect of y plane can be ignored. That is, E (J) only has
the component o f y, Ey, Jy, while H only contains Hz.
2a
2b
Bx
y
z
0
J
B
a
-a
Figure 2 . Conductor eddy current distri bution.
Z. ZH ANG, H. W. LI
Copyright © 2013 S ciRes. EPE
1505
Current density analysis of electromagnetic wave
propagation in the conductor:
0
12
()
Kx Kx
z
BK
JC eCeshKx
µ
= +=−
Attenuation of field penetration depth d is estimated
with the expression:
0)
1
(
z
JJsh Kx
Kd
=
=

The harmonics generated in the power density of fer-
romagnetic materials changes as shown below:
Magnetic flux pass through the core along parallel po-
sition of laminations, takes μ1= 1000μ0, γ1= 107S/m, a =
5×10-4m. In the frequency case, the electromagnetic field
penetration depth is of about 7×10-4m, while si licon steel
sheet is always designed in thickness of 3 × 10-4m.
Winding parameter takes μ2≈ 10-3μ1, γ2≈ 10γ1, a= 5×
10-3m, and the magnetic field perpendicular to the circle
direction. Harmonic currents under high frequency
through the conductor reduce the amplitudes, and d=
(2/ωμγ)0.5, The equivalent R has changed accordingly to
d or ω0.5 proportionally. It is known that magnetic field
and eddy current in the conductor are not uniformly dis-
tributed. Correction factor is brought forward as eddy
effect taken into account:
max
2
1
hh h
HL h
hR
K THD
α
ω
ω
=
=

=

Take the variables in the formula, KHL factor for con-
sideration, ωh for the h harmonic angular frequency, ωR
to fundamental wave angular frequency, THDh for the
total h distortion harmonics, α for the frequency- depen-
dent exponent. Non-linear load transformer losses are:
( )
'
''
1
ECHLEC R
LLdc EC OSL
P KP
P PP P
=+×
=++
(3)
IEEE / ANSI C57.110 standard refers only to non- li-
near load current increase in RMS, thus DC resistance
Figure 3 . Current density of the harmonic components.
loss will be increased correspondingly. It is concluded
that the loss calculation is rough under harmonic for
non-linear condition. Therefore, the amended form as
follows:
( )
max 22
1 122
1
hh
dch dchdc
h
PIR IR
=
=
= +
4. Methods Comparation and Simulation
To facilitate the comparative analysis, take the literature
[3] model as an example. Specific parameters and data
are listed in the Table 1, 2.
For simulation, the actual heat pump system has been
taken as example. Frequency control device that produc-
es 6k±1(k=1,2,...) characteristic harmonics is a typical
harmonic source in power system and THD is about 20%
[11]. The circuit principle is shown in Figure 4. Trans-
former model has referred the data provided in Table 1.
Common frequency converter is consisted of the three-
phase bridge uncontrolled rectifier on the r ectifier side
and the PWM control on the inverter side. And squirrel
cage induction motor is exploited as load.
Data of Tabl e 2 is valid in for mula (1) ~ (3) for trans-
former losses ca lculation, the result and si mulatio n value
are gained and compared.
Table 1. Tra nsf ormer parameters.
Rated power 50kVA Load losses 1250W
high voltage (HV) 20kV HV current 1.44A
low voltage (LV) 400V LV current 72A
HV winding resistance 121.5Ω LV winding resistance 0.03Ω
Table 2. The v al ue of the load harmonic current.
h 1 5 7 11 13 17 19
Ih(A) 70.2 12.312 7.7760 3.1680 2.0160 1.0800 0.7056
Z. ZH ANG, H. W. LI
Copyright © 2013 S ciRes. EPE
1506
470000.0 [ u F]
s1 s3 s5
1 3 5
s2 s4 s6
2 4 6
Ia2
Ib2
Ic2
0. 01 [H]
0. 01 [H]
Ia1
Ib1
Ic1
0. 01 [H]
#1 #2
0.2 [MVA]
10.0 [kV] / 0.38 [kV]
V
A
0. 01 [ohm ]
I M
W
S
T
0.0009[H]
0. 0009 [H]
0.0009H]
V
A
DIST
A
B
Ctrl
Ctrl=1
TS
0.5
TIN
0.9798
WIN
StoT
Figure 4 . Adjust able spee d drive sy stem simulation ci r cuit .
Figure 5. Comparison the results of various calculation
me t hods.
Figure 6 . Types of loss and t he relationshi p with THD.
Table 3. Los se s calc ulat i on of m etho ds an d simul ati on.
Curve
fitting Modified
fitting Standard
IEEE Revising
factor Simulation
PLL 1313W 1398W 1670W 1454W 1421W
Exploiting this method calculated transformer losses
of different THD, the results of calculation are shown in
Figure 5.
In the case that tra nsfor mer with a no n-linear load, the
losses increase is mainly caused by the winding eddy
current losses of harmonic, which also determines the
upward trend of the total loss. Figure 6 makes it visible,
which is co nsistent with the I E EE standard.
Revising factor of loss calculatio n is ob tained fro m the
above methods and simulation comparative analysis,
which take into account the frequency harmonics under
different winding parameters and the equivalent non-
linear superposition of harmonic loss calculation. Com-
plexity is the same to the IEEE standard and accurac y is
better than the IEEE standard, curve fitting, and the re-
sults of calculation closer to r e a listic situations.
5. Conclusions
As equivalent parameter model has been established, and
the harmonic winding model frequency-dependent cha-
racteristics analyzed, transformer winding eddy current
equations is derived under high-changed harmonic.
Compared with traditional methods, this method has the
following advantages:
1) Harmonic current of the conductor in the transmis-
sion will produce a frequency-dependent effect, which
has been analyzed from the magnetic field. That is, the
eddy current in the conductor magnetic field is not un-
iformly distribu te d.
2) Taking into account the different frequency har-
monic wave windings of the equivalent nonlinear para-
meter and the harmonic super position calc ulation of loss,
the exponent of frequency change has been amended.
Thus, K and F coefficient are avoided causing conserva-
tive calculations, and result is more reasonable.
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Z. ZH ANG, H. W. LI
Copyright © 2013 S ciRes. EPE
1507
[2] C. J. Liu an d R. G. Yang, “Calculation and Analysis of
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