Integration of PMSG-Based Wind Turbine into Electric Power
Distribution System Load Flow Analysis
RUDY GIANTO, MANAGAM RAJAGUKGUK
Department of Electrical Engineering, University of Tanjungpura, INDONESIA
Abstract: In this paper, a simple method for modeling and integrating PMSG (Permanent Magnet
Synchronous Generator)-based WPP (Wind Power Plant) for load flow analysis of electric power
distribution systems is proposed. The proposed model is derived based on: (i) the PMSG torque
current equations, (ii) the relationships between PMSG voltages/currents in q-axis and d-axis, and (iii)
the equations of WPP powers (namely: turbine mechanical power input, WPP power loss and power
output). Application of the proposed model in representative electric power distribution system is also
investigated and presented in this paper. The results of the investigation confirm the proposed model
validity. The confirmation can also be verified by observing the load flow analysis results where, for
each value of turbine power, the substation power output plus the WPP power output is always equal
to the total system load plus total line loss (the line loss has been calculated based on the impedances
and currents of the distribution lines).
Key-Words: PMSG, wind power plant, steady state model, load flow analysis, distribution system
Received: March 21, 2021. Revised: January 8, 2022. Accepted: February 18, 2022. Published: March 14, 2022.
1 Introduction
Based on the rotational speed, WPPs can be
classified into two groups, namely: (i) fixed or
near-constant speed WPP and (ii) variable speed
WPP. Since variable-speed WPP can capture or
extract wind energy in a more optimal way than
fixed-speed WPP, its application is currently much
more popular. Two types of generators that are
often used in variable-speed WPP configurations
are DFIG (Doubly Fed Induction Generator) and
PMSG [1,2]. Compared to DFIG, PMSG has an
advantage in that it does not require direct current
(DC) excitation because the magnetic field is
obtained from permanent magnets. Thus, PMSG
does not require slip rings and brushes, which
reduces power losses and simplifies maintenance.
Furthermore, the PMSG-based WPP can operate at
low speed, so it does not need a gearbox.
Therefore, the construction can be made simpler,
more robust, efficient, and the cost is also cheaper
[1,2].
Load flow analysis provides information about
the steady-state conditions of an electric power
system. In load flow analysis, a conventional
synchronous generator is generally expressed as a
generator with constant active power and voltage
magnitude (commonly known as the PV model).
However, with the penetration of WPP, which
usually does not use conventional synchronous
generator, the PV model can no longer be used to
represent the WPP, and consequently the load flow
analysis cannot be carried out. Therefore, to enable
of such analysis to be carried out, developing a
valid model for the WPP and modifying the
traditional load flow analysis is necessary. Several
researchers have conducted studies on the modeling
and integration of WPP in load flow analysis, and
some of the recent methods are reported in [3-18].
References [3-11], propose some interesting
methods to incorporate fixed-speed WPP into load
flow analysis of multi-bus electric power system.
On the other hand, researchers in [12-18] propose
several DFIG-based variable speed WPP models to
be used in load flow analysis of electric power
systems. However, steady state modeling of
PMSG-based WPP for load flow analysis has not
been much investigated and reported in the
literatures.
This paper proposes a simple method for
modeling and integrating PMSG-based variable
speed WPP in the electric power distribution
system load flow analysis. The proposed model is
derived based on (i) the PMSG torque current
equations, (ii) the relationships between PMSG
voltages/currents in q-axis and d-axis, and (iii) the
WPP powers (namely: turbine mechanical power
input, WPP power loss, and power output).
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Furthermore, this paper also discusses a case study
where validation of the proposed method is carried
out.
2 Formulation of DSLF Problem
As previously mentioned, load flow study is
normally carried out to evaluate the steady-state
performance of an electric power system. The
electrical quantities such as bus voltages, power
generations, transmission/distribution line power
flows (and losses) can be determined from the
study. It can be shown that the load flow problem
of an electric power distribution system has the
following formulations [19-21]:
0)cos(VYVPP n
1j ijjijijiLiGi
(1a)
0)sin(VYVQQ n
1j ijjijijiLiGi
(1b)
By observing (1), it can be seen that for each
system bus, there will be two equations and four
unknown quantities (i.e. PG, QG, |V| and
).
Therefore, in order to find a unique solution to (1),
two of the four quantities values must be
determined or specified. For this purpose, it is a
common practice in distribution load flow analysis
to define two types of buses, namely: (1) substation
bus (reference); and (2) load bus (see Table 1).
Table 1. Known and unknown quantities
Known Quantities
Unknown Quantities
|V| and
=0
PG and QG
PG=QG= 0
|V| and
*SS: Substation
3 PMSG-Based Wind Turbine
3.1 Basic Structure
Figure 1 shows a basic configuration of PMSG-
based WPP [1,2,22]. Power electronic devices
(such as converter, inverter, and DC link) connect
the PMSG to the electric power system (or power
grid). With these power electronic devices, the
PMSG rotation speed can be isolated from the
frequency of the power system where the WPP is
connected. This isolation makes the PMSG-based
WPP can be operated at a broader generator speed
range than other WPP types. Therefore, the wind
energy extraction can be carried out more
optimally. It is to be noted that in PMSG-based
wind turbine, the power converter based on IGBT
(Insulated Gate Bipolar Transistor) is usually
employed for the power electronic device topology.
Fig. 1: PMSG-based wind turbine structure
In Figure 1, Pm is wind turbine mechanical
power input; VS is PMSG stator voltage; Vg is WPP
terminal voltage; PS and QS are PMSG active and
reactive power outputs (powers at PMSG stator);
Pg and Qg are WPP active and reactive power
outputs. It should also be noted that PMSG-based
WPP has the ability to deliver or absorb reactive
power (leading or lagging power factor operation)
However, the unity power factor mode of operation
is more often adopted. In this mode of operation,
the WPP does not deliver or absorb reactive power
to or from the power grid.
3.2 PMSG Equivalent Circuits
Figure 2 shows the PMSG equivalent circuits in d-q
reference frame [22-26]. In the figure, Vq and Vd are
q- and d-axis terminal voltages; Iq and Id are q- and
d- axis terminal currents; Iwq and Iwd are q- and d-
axis torque currents; RS is stator winding resistance;
Lq and Ld are PMSG inductances in q- and d-axis;
r is rotor angular speed; and
f is permanent
magnet flux. It is to be noted that in Figure 2, Rfe
and RS are used to represent PMSG iron and copper
losses, respectively. Copper loss occurs in the
PMSG stator winding, while iron loss occurs in the
PMSG iron core. Also, in Figure 2, Ifeq and Ifed
quantities are used to express the currents flowing
in Rfe in q- and d-axis, respectively.
Based on Figure 2, the PMSG terminal voltages
will have the following forms:
qswddfrq IRILV
(2a)
dswqqrd IRILV
(2b)
On the other hand, the PMSG torque currents
can be formulated as:
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fe
wddfr
qfeqqwq R
IL
IIII
(3a)
fe
wqqr
dfeddwd R
IL
IIII
(3b)
(a)
(b)
Fig. 2: PMSG equivalent circuits
The relationships between q- and d-axis
quantities of the PMSG terminal voltage and
current can be expressed as (see Figure 7 in
Appendix A.1):
tanVV qd
(4a)
tanII qd
(4b)
where
is the angle of PMSG rotor relative to the
stator voltage/current.
3.3 PMSG Power Formulations
By looking at Figure 1, it can be seen that the
PMSG power output equals to turbine mechanical
power input minus PMSG copper loss (Pcu) and
PMSG iron loss (Pfe), or:
fecumS PPPP
(5)
It should be noted that in (5) the mechanical or
friction loss due to rotation of the PMSG rotor have
been neglected because their value is much smaller
than the other losses [23,24]. On the other hand, the
PMSG power output can also be formulated as a
function of the stator voltage and current as follows
(derivation can be found in Appendix A.1):
ddqqS IVIV5.0P
(6)
Also, the PMSG copper loss (Pcu) and PMSG
iron loss (Pfe) in (5) can be calculated using the
following formulas [23,24]:
2
d
2
qscu IIR5.0P
(7)
2
fed
2
feq
fefe IIR5.0P
(8)
Therefore, on using (6) - (8) in (5), the turbine
power can be formulated as:
2
fed
2
feq
fe
2
d
2
qsddqqm
IIR5.0
IIR5.0IVIV5.0P
(9)
3.4 PMSG Modeling and Integration
Based on (3), (4) and (9), the proposed steady state
model of PMSG-based WPP is:
0ILIIR wddfrqwqfe
(10a)
0ILIIR wqqrdwd
fe
(10b)
0tanVV qd
(10c)
0tanII qd
(10d)
0IIR5.0
IIR5.0IVIV5.0P
2
fed
2
feq
fe
2
d
2
qsddqqm
(10e)
In (10a) and (10b), the torque currents (Iwq and
Iwd) are calculated based on (2) as follows:
qrdsdwq L/IRVI
(11a)
drqqsfrwd L/VIRI
(11b)
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It can be seen from (11) that the PMSG torque
currents have been represented in terms of PMSG
terminal voltage and current. Based on Figure 2, Ifeq
and Ifed in (10e) can also be expressed in terms of
PMSG terminal voltage and current as follows:
q
qr
dsd
qwqfeq I
L
IRV
III
(12a)
d
dr
qqsfr
dwdfed I
L
VIR
III
(12b)
Therefore, for electric power system embedded
with PMSG-based WPP, solution to the load flow
problem is found by simultaneously solving the
nonlinear equations (1) and (10). Table 2 shows the
known (specified) and unknown (to be calculated)
quantities in the equations. It should be noted that,
in the load flow analysis, the following
relationships also apply:
ddqqPEC
SPECgG
IVIV5,0
PPP
(13a)
0QQQ SPECgG
(13b)
where
PEC is efficiency of the power electronic
converter. In (13b), the WPP reactive power output
is zero because the PMSG-based WPP is assumed
to be operated at unity power factor or no reactive
power exchange between the WPP and the power
grid. It is also to be noted that since set of equations
(1) and (10) is nonlinear, iterative techniques (for
example Newton-Raphson method) are often
employed to solve the set of equations. Brief
explanation of Newton-Raphson method is given in
Appendix A.2.
Table 2. Known and unknown quantities for system
with WPP
Bus
Known Quantities
Unknown Quantities
SS
|V| and
=0
PG and QG
Load
PG=QG= 0
|V| and
WPP
r, Pm,
RS, Rfe, Ld, Lq,
f, and
PEC
|V=|Vg|,

g, Vq,
Vd, Iq, Id and
4 Case Study
4.1 Test System
Distribution system shown in Figure 3 will be used
in the case study to investigate the application of
the proposed model in load flow analysis of electric
power distribution system containing PMSG-based
WPP. The system in Figure 3 has 33 buses and is
adopted from [19,20]. The system has a voltage of
12.66 kV with a total three-phase load of 11.145
MW and 6.900 MVAR. The system is then
modified by adding a PMSG-based WPP in the
system. The WPP is connected to bus 33 via a step-
up transformer. All of the system data (including
WPP data) are shown in Tables 3 and 4. Unless
otherwise stated, all data are in pu on the basis of 1
MVA.
Fig. 3: Test system
Table 3. Test system data
Br.
No
Send
Bus
Rec.
Bus
R (pu)
X (pu)
PL*
(pu)
QL*
(pu)
1
1
2
0.000575
0.000293
100
60
2
2
3
0.003076
0.001567
90
40
3
3
4
0.002284
0.001163
120
80
4
4
5
0.002378
0.001211
60
30
5
5
6
0.005110
0.004411
60
20
6
6
7
0.001168
0.003861
200
100
7
7
8
0.010678
0.007706
200
100
8
8
9
0.006426
0.004617
60
20
9
9
10
0.006514
0.004617
60
20
10
10
11
0.001227
0.000406
45
30
11
11
12
0.002336
0.000772
60
35
12
12
13
0.009159
0.007206
60
35
13
13
14
0.003379
0.004448
120
80
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14
14
15
0.003687
0.003282
60
10
15
15
16
0.004656
0.003400
60
20
16
16
17
0.008042
0.010738
60
20
17
17
18
0.004567
0.003581
90
40
18
2
19
0.001023
0.000976
90
40
19
19
20
0.009385
0.008457
90
40
20
20
21
0.002555
0.002985
90
40
21
21
22
0.004423
0.005848
90
40
22
3
23
0.002815
0.001924
90
50
23
23
24
0.005603
0.004424
420
200
24
24
25
0.005590
0.004374
420
200
25
6
26
0.001267
0.000645
60
25
26
26
27
0.001773
0.000903
60
25
27
27
28
0.006607
0.005826
60
20
28
28
29
0.005018
0.004371
120
70
29
29
30
0.003166
0.001613
200
600
30
30
31
0.006080
0.006008
150
70
31
31
32
0.001937
0.002258
210
100
32
32
33
0.002128
0.003308
60
40
*Load connected to receiving bus
Table 4. Wind turbine generator data
Turbine
Length of turbine blade: 38 meter
Power rating: 2.0 MW
Speed:
Cut-in: 3 m/s; Rated: 14 m/s; Cut-
out: 23 m/s
Gearbox
None (Direct drive)
Generator
Type: PMSG
Power rating: 2.0 MW
Number of pole pairs: 26
Voltage: 690 Volt
Speed rating: 22.5 rpm
Resistance/Induktance/Flux:
RS=0.02; Rfe=80; Ld=2.0; Lq=3.0;
f =2.3
Power electronic
converter
Efficiency:
PEC = 95%
Transformer
Impedance: j0.1 Ohm
4.2 Calculation of Wind Power
Turbine mechanical power and rotor speed can be
calculated using the formulas given [15]. In the
calculation it is assumed that the air density is
1.225 kg/m3, tip speed ratio is 7.0, and turbine
performance coefficient is 0.4. Table 5 shows the
calculation results of turbine mechanical power and
rotor speed for wind speed values ranging from 5 to
12 m/s.
Table 5. Turbine power and rotor speed
Vw
(m/s)
r
(rad/s)
Pm
(MW)
5
23.9474
0.1389
6
28.7368
0.2401
7
33.5263
0.3812
8
38.3153
0.5691
9
43.1053
0.8102
10
47.8947
1.1114
11
52.6842
1.4793
12
57.4737
1.9206
4.3 Results and Discussion
Tables 6 and 7 show the load flow analysis results
for various values of turbine mechanical power as
listed in Table 5. Some of the results are also
presented in graphical forms (see Figures 4 - 6). It
can be seen that as the turbine mechanical power
increases, PMSG power losses also increase. The
increase in power losses is due to the increase in
PMSG power output which can be explained as
follows. As the PMSG power output raises, the
generator currents and losses will also increase.
Due to power loss in the power electronic
converter, the power output of WPP (Pg) is slightly
smaller than PMSG stator power (PS) (see Figure
4). In this paper, it has been assumed that the power
converter has the efficiency of 95%. It is also to be
noted that the WPP power output and the PMSG
stator power vary linearly with the increase in
turbine mechanical power.
Table 6. PMSG losses and WPP output
Pm
(MW)
Pcu
(MW)
Pfe
(MW)
PS
(MW)
Pg
(MW)
0,1389
0.0003
0.0151
0.1236
0.1174
0,2401
0.0006
0.0215
0.2180
0.2071
0,3812
0.0014
0.0379
0.3419
0.3248
0,5691
0.0024
0.0401
0.5266
0.5003
0,8102
0.0032
0.0456
0.7614
0.7234
1,1114
0.0052
0.0534
1.0528
1.0001
1,4793
0.0085
0.0587
1.4120
1.3414
1,9206
0.0118
0.0605
1.8483
1.7559
Table 7. WPP voltage, SS output and line loss
Pm
(MW)
Vg
(pu)
SS Power
(MW, MVAR)
Line Loss
(MW, MVAR)
0,1389
0.9836
11.5683+j7.2663
0.5406+j0.3663
0,2401
0.9849
11.4692+j7.2599
0.5313+j0.3599
0,3812
0.9866
11.3396+j7.2519
0.5194+j0.3519
0,5691
0.9892
11.1444+j7.2405
0.4997+j0.3405
0,8102
0.9924
10.9045+j7.2276
0.4828+j0.3276
1,1114
0.9963
10.6053+j7.2132
0.4605+j0.3132
1,4793
1.0012
10.2399+j7.1981
0.4362+j0.2981
1,9206
1.0070
9.7908+j7.1833
0.4017+j0.2833
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0 0.5 1 1.5 2
0
0.5
1
1.5
2
Turbine Power (MW)
WPP Power (MW)
Ps
Pg
Fig. 4: Variation of WPP power
The load flow study results also show that with
the increase in WPP power output, the voltage
profile will also improve (see Figure 5). This
voltage profile improvement can occur because
with the increase in WPP power output, more loads
can be supplied by the WPP, and the line losses
will be decreasing since the WPP is located at the
end of the distribution line. In turn, this line losses
decrement reduces the line voltage drop and
improves the system voltage profile.
0 0.5 1 1.5 2
0.98
0.985
0.99
0.995
1
1.005
1.01
1.015
Turbine Power (MW)
WPP Terminal Voltage (pu)
Fig. 5: Variation of WPP voltage
0 0.5 1 1.5 2
9.5
10
10.5
11
11.5
12
Turbine Power (MW)
Substasiun Power (MW)
Fig. 6: Variation of substation power
Beside the system voltage profile improvement,
another advantage of the WPP installation is that it
can reduce the power supply from distribution
system substation (see Figure 6). It is to be noted
that power supply from distribution substation
usually comes from conventional power plants that
use non-renewable energy sources. It is to be noted
the results of the above study also confirm the
proposed method validity. More confirmation can
also be obtained by observing the results of load
flow analysis where, for each value of turbine
power, the substation power output plus the WPP
power output is always equal to the total system
load plus total line loss. Where the line loss has
been calculated based on the impedances and
currents of the distribution lines.
5 Conclusion
In this paper, a simple method for modeling and
integrating PMSG-based variable speed WPP for
load flow analysis of electric power distribution
systems has been proposed. The proposed model is
derived based on: (i) the PMSG torque current
equations, (ii) the relationships between PMSG
voltages/currents in q-axis and d-axis, and (iii) the
equations of WPP powers (namely: turbine
mechanical power input, WPP power loss and
power output). Application of the proposed model
in load flow analysis of representative electric
power distribution system has also been
investigated and presented in this paper. The results
of the investigation (i.e., the load flow analysis
results for various values of turbine mechanical
power) confirm the proposed model validity.
The confirmation can also be obtained by
observing the results of load flow analysis where,
for each value of turbine power, the substation
power output plus the WPP power output is always
equal to the total system load plus total line loss,
where the line loss has been calculated based on the
impedances and currents of the distribution lines.
However, in this paper, the PMSG-based WPP has
been assumed to be operated at unity power factor.
Extension of the method so that it can be applied to
PMSG operating at lagging and leading power
factors is probably an interesting topic for future
research.
Appendix
A.1 PMSG Power Output
Figure 7 shows phasor diagrams of PMSG stator
voltage and current [21,22]. In the figure,
is the
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angle of PMSG rotor relative to the stator
voltage/current. At steady state condition, this
angle is constant. On the other hand,
is the angle
of stator voltage/current to the reference. It is to be
noted that VS and IS are in phase because the PMSG
is operated at unity power factor (QS=0). Based on
Figure 7, the formulas for stator voltage and current
phasors are:
)(j
dqS ejVV
2
1
V
(A.1)
)(j
dqS ejII
2
1
I
(A.2)
PMSG stator power can be calculated using:
SSS IVS
(A.3)
Substituting (A.1) and (A.2) into (A.3), the PMSG
stator power becomes:
qddqddqqS IVIVjIVIV5,0S
(A.4)
Fig. 7: Phasor diagrams of stator voltage and
current of PMSG
By separating the real and imaginary parts of (A.4),
the formulas for PMSG stator active and reactive
powers are:
ddqqSS IVIV5,0SReP
(A.5)
0IVIV5,0SImQqddqSS
(A.6)
A.2 Newton-Raphson Method
In general form, a set of nonlinear equations can be
written as:
0xF
),,,(
),,,(
),,,(
)(
n21n
n212
n211
xxxf
xxxf
xxxf
(A.7)
In Newton-Raphson method, the calculation of
unknown variables xi, is conducted by solving:
)()()( kk1k dxx
(A.8)
where:
)()( )()()( k
1
kk xFxJd
(A.9)
In (A.9), J(x) is the Jacobian of F(x), and is
determined using:
n
n
2
n
1
n
n
2
2
2
1
2n
1
2
1
1
1
x
f
x
f
x
f
x
f
x
f
x
fx
f
x
f
x
f
)(xJ
(A.10)
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Volume 17, 2022
[5] Wang, J., Huang, C., and Zobaa, A.F., ‘Multiple-
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WSEAS TRANSACTIONS on POWER SYSTEMS
10.37394/232016.2022.17.5
Rudy Gianto, Managam Rajagukguk
E-ISSN: 2224-350X
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