Two-port network model of fixed-speed wind turbine generator for distribution system load flow analysis

TELKOMNIKA, Vol.17, No.3, June 2019, pp.1569~1576
ISSN: 1693-6930, accredited First Grade by Kemenristekdikti, Decree No: 21/E/KPT/2018
DOI: 10.12928/TELKOMNIKA.v17i3.11866 ◼ 1569
Received November 21, 2018; Revised January 27, 2019; Accepted February 20, 2019
Two-port network model of fixed-speed wind turbine
generator for distribution system load flow analysis
Rudy Gianto*, Kho Hie Khwee, Hendro Priyatman, Managam Rajagukguk
Department of Electrical Engineering, Tanjungpura University,
Prof. Dr. H. Hadari Nawawi St., Pontianak 78124, Indonesia
*Corresponding author, e-mail: rudygianto@gmail.com
Abstract
Load flow analysis has always been used in determining the steady-state operation of an electric
power or distribution system. For conventional power system without wind turbine generator, the method
for load flow analysis has been well established. However, for modern system embedded with wind turbine
generator, the investigation of analysis method is still an active research area. This paper proposed a new
method to integrate fixed-speed wind turbine generator into distribution system load flow analysis.
The proposed method is derived based on two-port network theory where the parameters of induction
generator of the wind turbine generator are embedded in general constants of the two-port network.
The proposed method has been tested and verified using a representative electric distribution system.
Keywords: distribution system, load flow, two-port network, wind turbine
Copyright © 2019 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
It has widely been known that the steady-state operation of a power grid is usually
evaluated by load flow analysis. For conventional power system without wind turbine generating
system (WTGS), the method for load flow analysis has been well established. However, for
modern power system containing WTGS, the method of analysis is still under development.
To perform the load flow analysis for system with WTGS, the first step is to develop a valid
model for the WTGS. After the model has been developed, the next step is to incorporate the
model into the analysis. The load flow problem is then solved, and the steady-state operation of
the system (including the WTGS) can be evaluated properly. Some researchers have
investigated the WTGS modeling and its integration into load flow analysis [1-18]. In [1-15], a
mathematical model of a WTGS has been proposed. The equations from the model are then
combined with the equations arising from load flow formulation of the system without WTGS.
The whole set of equations is then iteratively solved to obtain the load flow solution. However, the
proposed WTGS model is quite complicated, and therefore, its application in power or distribution
system containing multiple WTGS can be difficult.
In [16-18], a method has been proposed to incorporate fixed-speed WTGS into a standard
load flow program. The proposed model in [16-18] adds two buses, two series elements, one shunt
element and one load to the existing power network. Obviously, the addition will increase the size of
the power system and also the number of equations in the load flow formulation. As a consequence,
the load flow problem will be more difficult to solve, especially if the system has many WTGSs. In
the present paper, the proposed model for fixed-speed WTGS is based on two-port network
model. In the model, the parameters of induction generator of the WTGS are embedded in
general constants of the two-port network. The WTGS mathematical model is then derived
based on the equations of two-port network theory. The proposed model is simpler and can
easily be integrated into the power or distribution system load flow analysis. Moreover, its
application in the system containing multiple WTGSs is also simple and straightforward. Results
of the proposed model validation and verification using a representative test system, i.e. 33-bus
distribution network, are also presented in this paper.
2. Research Method
2.1. Formulation of Distribution System Load Flow Problem
In distribution system load flow (or power flow) analysis, the study is carried out to
determine the following quantities: (i) bus or nodal voltages, and (ii) substation power. These
quantities can be calculated by solving a set of nonlinear equations as follows:

◼ ISSN: 1693-6930
TELKOMNIKA Vol. 17, No. 3, June 2019: 1569-1576
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0VYVSS =−− **)(diagLG (1)
In (1), SG, SL, V and Y are generated power vector, load power vector, nodal voltage
vector and nodal admittance matrix, respectively. For n-node power system, these vectors and
matrix are of the forms:
 T
GnSGSGSG 21=S
(2a)
 T
LnSLSLSL 21=S (2b)












=
nnYnYnY
nYYY
nYYY




21
22221
11211
Y (2c)
where:
SGi : generated power flowing into node i
SLi : load power flowing out node i
Vi : voltage at node i
Yij : element ij of admittance matrix
After (1) has been solved and all of the quantities have been determined, the line flows
and losses can also be calculated. It is to be noted that distribution system is usually fed at one
bus (substation bus), and the voltage at this bus is known or specified. Therefore, only the
voltages at the remaining buses (load buses) need to be computed. Table 1 shows the known
and unknown quantities of the distribution system load flow formulation. For conventional
system without WTGS, (1) is the only set of equations that needs to be solved to obtain the load
flow solution. However, for modern system with WTGS, additional equation is needed to
facilitate and incorporate the WTGS into the load flow analysis. The modeling and integration of
the WTGS will be discussed in the following section.
2.2. Proposed Model of WTGS and Its Integration
2.2.1. Two-Port Network Theory
In the present work, development of fixed-speed WTGS model will be based on
two-port network mathematical model where nodal power equations are used in the model
derivation. The general two-port network containing passive impedances is presented in
Figure 1. In two-port network theory, it can be shown that the voltage/current relationship is of
the form:






−





=





− 1
1
2
2
I
V
HG
FE
I
V
(3)
where:
1
DC
BA
HG
FE
−






=





(4)
In (4), A, B, C and D are the general two-port network constants. The values of these
constants depend on the network components, i.e. their impedances and admittances.
The (3) is equivalent to the following two (5a) and (5b). The development of the proposed
WTGS model based on (5) will be explained in the next section.

TELKOMNIKA ISSN: 1693-6930 ◼
Two-port network model of fixed-speed wind turbine generator for distribution... (Rudy Gianto)
1571
112 FIEVV −= (5a)
112 HIGVI +−= (5b)
Table 1. Bus Types and Quantities
Bus Type Known Quantity Unnown Quantity
Substation SLi and Vi = 1.0 SGi
Load SLi and SGi = 0 Vi
Figure 1. General two-port network
2.2.2. Proposed Model of WTGS
Figure 2(a) shows fixed-speed WTGS connected to a distribution system [16-20]. Power
converter of the WTGS is squirrel cage induction generator (SCIG). The SCIG has mechanical
power input Pm and electrical power output Sg= Pg+jQg as can be seen in Figure 2(b).
(a) (b)
Figure 2. WTGS connected to distribution system
Figure 3(a) shows steady-state equivalent circuit of the SCIG [21-23] where R1, X1, R2,
X2, Rc and Xm denote stator resistance, stator leakage reactance, rotor resistance, rotor leakage
reactance, core loss resistance and magnetic reactance, respectively. R2(1-s)/s is the dynamic
resistance and its value depends on slip s. Power of the dynamic resistance represents the
mechanical power Pm delivered by the wind turbine to SCIG. The value of this power depends
mostly on the wind speed and it can be determined using the power curve provided by the
turbine manufacturer. In the proposed method, the WTGS model is obtained by viewing the
SCIG equivalent circuit of Figure 3(a) as the two-port network depicted in Figure 3 (b).
In Figure 3 (b), the impedances Z1, Z2 and Z3 are given by:
)/(3
222
111
mjXcRmXcjRZ
jXRZ
jXRZ
+=
+=
+=
(6)
it is to be noted that for the two-port network of Figure 3 (b), the formulas for general network
constants are of the forms [24]:
k
SCIGDistribution
System
PmSg=Pg+jQg
SCIG
I2I1
V1 V2
A B
C D

◼ ISSN: 1693-6930
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3/21
3/1
3/2121
3/11
ZZD
ZC
ZZZZZB
ZZA
+=
=
++=
+=
(7)
(a) (b)
Figure 3. Steady-state equivalent circuit of SCIG
based on Figure 3 (b), the SCIG electrical power output is formulated as:
*11IVgjQgPgS =+= (8)
and the mechanical power delivered by wind turbine to the SCIG is calculated as:
*220 IVjmPmS =+= (9)
Application of two-port network equations in the above SCIG mechanical power input
equation, or by substituting (5a) and (5b) into (9), gives:
*)1**1*)(11( IHVGFIEVmS +−−= (10)
or:
*11*1*1**11**11* IIFHIVFGIVEHVVEGmS −++−= (11)
on using (8) in (11), i.e. substituting I1 in (11) by Sg*/V1*, the following equation is obtained:
0
*11
*
*****11* =+−−+
VV
gSgS
FHgSFGgSEHVVEGmS (12)
In (12) is the proposed model for fixed-speed WTGS. It is to be noted that V1 in (12) is
the voltage at WTGS bus (or it is equal to Vk in Figure 3 (a)). Incorporation of the model into the
load flow formulation (1) will be discussed in the next section.
2.2.3. Integration of WTGS Model
For modern system containing fixed-speed WTGS, solution to the power flow problem
can be found by simultaneously solving (1) and (12). It can be seen that (12) is the additional
equation to the formulation in (1). Whereas, the additional quantity that need to be calculated is
the WTGS power output Sg. Table 2 shows the known and unknown quantities in the load flow
formulation of the system with WTGS. It is to be noted that since sets of the equations, i.e
R2(1-s)/s
R2+jX2
jXmRc
Pm
k
Sg=Pg+jQg
R1+jX1
V2
I2I1
Z3
PmZ2Sg Z1
V1

1573
(1) and (12), are nonlinear; they are usually solved using iterative technique (for example:
Newton-Raphson method).
3. Results and Analysis
3.1. Test System
The proposed method for incorporating WTGS in distribution system load flow analysis
is tested by using the 33-bus system [25]. This distribution network has the system voltage of
12.66 kV. One line diagram of the distribution system is shown in Figure 4, and the detail of the
system data can be found in [25]. In the present work, it is assumed that the distribution system
has one WTGS and it is connected to bus 33. Data for the SCIG of WTGS is shown in Table 3.
All of the data are in pu on 1 MVA base. Results of the load flow analysis for the test system are
presented in the following section.
Figure 4. 33-Bus distribution network
Table 2. Bus Types and Quantities for
System with WTGS
Bus Type Known Quantity Unnown Quantity
Substation SLi and Vi = 1.0 SGi
Load SLi and SGi = 0 Vi
WTGS SLi and SGi = 0 Sg and Vi
Table 3. SCIG Data
Parameter R1 X1 R2 X2 Rc Xm
Value 0,01 0,05 0,01 0,05 100 5
3.2. Results and Analysis
In this paper, power flow calculations were carried out for various values of mechanical
power Pm. The mechanical powers ranging from 0.1 to 1.0 pu were taken in the investigation.
These values represent the low speed and higher speed wind conditions. It is to be noted that
all of the computations were done on PC, and the proposed method were implemented as
MATLAB codes (m-files).
Results of the calculations (in terms of WTGS voltage/power and substation power) are
shown in Table 4. It is to be noted that the results of the proposed method are accurate and in
excellent agreement with those of the method in [16-18]. These results confirm that the
proposed two-port model is valid and can be used as a method for incorporating fixed-speed
wind turbine generator into distribution system load flow analysis.
Since fixed-speed WTGS is usually equipped with shunt capacitance to support the
reactive-power consumed by induction generator of the WTGS, the effects of the capacitance
installation are also investigated in this paper. Table 5 shows the results of load flow analysis (in
terms of WTGS voltage/power and substation power) when the capacitance with the capacity of
0.5 pu is installed. To observe the effects more clearly the results are also presented in
graphical forms in Figures 5 and 6.

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(a)
(b)
Figure 5. WTGS power versus mechanical power
Table 4. WTGS Voltage/Power and
Substation Power
Pm
WTGS
Voltage
WTGS Power
Substation
Power
0,1 0.91419 0.0912-j0.1670 3.8423+j2.6135
0,2 0.91866 0.1904-j0.1724 3.7326+j2.6140
0,3 0.92296 0.2892-j0.1801 3.6249+j2.6158
0,4 0.92710 0.3875-j0.1899 3.5190+j2.6208
0,5 0.93108 0.4854-j0.2018 3.4148+j2.6289
0,6 0.93492 0.5828-j0.2157 3.3124+j2.6400
0,7 0.93861 0.6799-j0.2315 3.2116+j2.6540
0,8 0.94217 0.7765-j0.2493 3.1125+j2.6709
0,9 0.94559 0.8728-j0.2689 3.0149+j2.6906
1,0 0.94888 0.9687-j0.2904 2.9189+j2.7131
Table 5. WTGS Voltage/Power and Substation
Power for System with Capacitance
Pm
WTGS
Voltage
WTGS Power
Substation
Power
0,1 0.93305 0.0909-j0.1738 3.7969+j2.0911
0,2 0.93744 0.1901-j0.1792 3.6874+j2.0895
0,3 0.94167 0.2889-j0.1866 3.5796+j2.0911
0,4 0.94575 0.3873-j0.1961 3.4735+j2.0956
0,5 0.94968 0.4852-j0.2076 3.3689+j2.1031
0,6 0.95348 0.5828-j0.2211 3.2660+j2.1133
0,7 0.95715 0.6799-j0.2364 3.1645+j2.1264
0,8 0.96069 0.7767-j0.2536 3.0645+j2.1421
0,9 0.96411 0.8731-j0.2726 2.9659+j2.1604
1,0 0.96740 0.9692-j0.2934 2.8688+j2.1814
Table 5 clearly shows that shunt capacitance is able to support the WTGS
reactive-power demand as indicated by the improvement of WTGS voltage profile. Although its
value is slightly less than mechanical power input (due to losses in induction generator),
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Mechanical Power
WTGSActive-Power
without capacitor
with capacitor
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
Mechanical Power
WTGSReactive-Power
without capacitor
with capacitor

1575
active-power generation of WTGS is always proportional to the mechanical power input as
shown in Figure 5 (a). However this is not the case for the variation of WTGS reactive-power.
With the increase in mechanical power, the WTGS reactive-power increases almost
exponentially as shown in Figure 5 (b). In other words, the increase in WTGS active-power
generation requires higher increase in WTGS reactive-power demand. This result is also
confirmed by Figure 6 (b). Figure 6 (a) shows that with the increase in mechanical power, the
active-power supplied by distribution substation decreases linearly. This result is expected
because with the increase in mechanical power, the WTGS active-power generation also
increases, and therefore more active-power can be delivered by WTGS to support the system
load demand. Consequently, with the increase in WTGS mechanical power, distribution
substation can deliver less active-power since part of the system load is supplied by WTGS.
(a)
(b)
Figure 6. Substation power versus mechanical power
4. Conclusion
A simple method for incorporating fixed-speed WTGS into a distribution system load
flow analysis has been presented in this paper. The development of the proposed method is
based on two-port network theory where equations from the electric circuit theory have been
utilized to derive the proposed WTGS mathematical model. By integrating the model into the
load flow analysis, the steady-state operations of the system (including the WTGS) can then be
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2.8
3
3.2
3.4
3.6
3.8
4
Mechanical Power
SubstationActive-Power
without capacitor
with capacitor
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
Mechanical Power
SubstationReactive-Power
without capacitor
with capacitor

◼ ISSN: 1693-6930
1576
evaluated. The proposed method has been tested and verified using a representative test
system, i.e. 33-bus distribution network.
Acknowledgement
The author would like to express special appreciation to the Ministry of Research,
Technology and Higher Education of Indonesia (Kemenristek Dikti Indonesia) for funding the
research reported in this paper.
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