Analysis of interconnection of permanent magnet generators to the ...

Analysis of interconnection of
permanent magnet generators to the
distribution grid by ATP-EMTP
software tool
Saša Stojković
Technical Faculty, Čačak, Serbia
09. 09. 2009. DEMSEE 2009 1

1. INTRODUCTION
Embedded generation:
• Cage induction
• Double feed induction
• Classic synchronous machines
• Permanent magnet synchronous machines
09. 09. 2009. DEMSEE 2009 2

Permanent magnet generators
• Simplicity
• Cheapness
• Contain permanent magnet instead of rotor winding
• Simple regulation (runner blades)
• Best suited for small heads
• Fairly new concept
• PMGs have never been applied before
• Eliminate the need for an excitation system
• Magnetic field is obtained from permanent magnets
09. 09. 2009. DEMSEE 2009 3

2. MATHEMATICAL MODEL OF PM
GENERATOR
x = x = x
ak d
f k d
a d
⎡ψ
d
⎢
⎢ψ
⎢
⎣ψ
f
v
v
k d
⎡ψ
q
⎢
⎣ψ
⎤ ⎡ x
⎥ ⎢
⎥ = ⎢x
⎥ ⎢
⎦ ⎣
x
k q
d
a d
a d
⎤ ⎡ x
⎥ = ⎢
⎦ ⎣
x
1
dψ
q
a k q
x
x
x
a d
k d
a d
x
x
ω
a k q
k q
x
x
x
a d
a d
f
⎤
⎥ ⋅
⎦
d
d = ⋅ − ⋅ψ
q
ω0
dt ω0
q
1 dψ
q ω
= ⋅ − ⋅ψ
d
dt ω
ω0
0
⎤ ⎡ i
⎥ ⎢
⎥ ⋅ ⎢i
⎥ ⎢
⎦ ⎣
i
⎡ i
⎢
⎣
i
q
k q
a
⎤
⎥
⎦
d
k d
f
+ r ⋅ i
a
d
+ r ⋅ i
q
⎤
⎥
⎥
⎥
⎦
v
v
v
f
=
1
ω 0
dψ
f
⋅
dt
1 dψ
⋅
ω dt
+ r
f
⋅ i
k d
k d = + rk
d ⋅ ik
d
0
1 dψ
k
⋅
ω dt
q
k q = + rk
q ⋅ ik
q
0
T
e
= ψ ⋅ i −ψ
⋅ i
d
2H
dω
⋅ = T e + T m
dt
ω 0
q
q
d
f
= 0
= 0
⎡ψ
d
⎢
⎣ψ
k d
⎡ψ
q
⎢
⎣ψ
k q
ψ = x
−ψ
0 ⎤ ⎡ x
⎥ =
−ψ
⎢
0 ⎦ ⎣
x
−ψ
0 ⎤ ⎡ x
⎥ =
−ψ
⎢
0 ⎦ ⎣
x
⋅ i
0 a d f 0
d
a d
q
a q
x
x
x
x
a d
k d
a q
k q
⎤
⎥ ⋅
⎦
⎡ i
⎢
⎣
i
⎤ ⎡ i
⎥ ⋅ ⎢
⎦ ⎣
i
d
k d
q
k q
⎤
⎥
⎦
⎤
⎥
⎦
CLASSICAL MACHINE
PERMANENT MAGNET MACHINE
09. 09. 2009. DEMSEE 2009 4

Simulation of permanent magnet generator
ATP-EMTP model
09. 09. 2009. DEMSEE 2009 5

Additional work to determine operational regime
j*Xd*I
90°
e0 = u ⋅ cosδ
+ xd
⋅ i ⋅ sinψ
= 1,2
e=1,2
u=1
i=1,00713
s = u ⋅ i
= 1,007136
21°
15°
p = s ⋅ cos ϕ = 0,972819
q = s ⋅ sin ϕ = 0,2606607
φ=15˚. u=1. e=1.2. cosφ=0.9659258. sinφ=0.258819.
2
x d ⋅ i = e − ( u ⋅ cosϕ)
− u ⋅ sinϕ
= 0,4532
2
2
e − ( u ⋅ cosϕ)
− u ⋅ sinϕ
i =
= 1, 007136
x
tgψ
=
q
x d
2
⋅ i + u ⋅ sinϕ
= 0,7371148
u ⋅ cosϕ
ψ = arctg( tgψ ) = 36, 39°
P = p ⋅ S
Q = q ⋅ S
2
U
R = P
X
= Q
U
2
= 972819
= 260666
= 17,78912
= 66,3899
W
VAr
Ω
Ω
X
L = = 211,3257 mH
ω
δ = ψ − ϕ = 21, 39°
09. 09. 2009. DEMSEE 2009 6

4. RESULTS OF SIMULATIONS
Active power as a function of reactive power (left)
Relative apparent. active and reactive power as a function
of angle f (right)
Active power p [p.u.]
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
u=1
u=0.95
u=1.05
p=1
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Apparent, active and reactive power (p. u.)
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
u=1
0.0
-10 0 10 20 30 40 50 60 70 80
s
p
q
Reactive power q [p.u.]
φ [ o ], u=1
09. 09. 2009. DEMSEE 2009 7

Comparison between an analytical method
and ATP-EMTP results
quantyty unity analytical atp-emtp
i p.u. 1.00713 1.03246
ψ ˚ 36.4 35.5
delta ˚ 21.4 20.5
P W 972819 969504
Q VAr 260666 260493
sqrt(3)·If A 1328 1359
T gen
Nm 34521 35088
I md
A 1185 1203
I mq
A 194.9 193.7
ψ md
Wb 14.36 14.58
ψ mq
Wb 2.36 2.35
I R
A 135 135
I X
A 36.17 36.15
09. 09. 2009. DEMSEE 2009 8

Analysis of transient processes by ATP-EMTP
Three-phase short circuit from t=0.05 s to t=0.12 s
Electric torque (left)
Mechanical angular speed (right)
300
38
*10 3 (f ile DEMSEE_01.pl4; x-v ar t) u1:OMEGM
200
34
100
30
0
26
-100
22
-200
0.0 0.4 0.8 1.2 1.6 [s] 2.0
(f ile DEMSEE_01.pl4; x-v ar t) u1:TQGEN
18
0.0 0.4 0.8 1.2 1.6 [s] 2.0
09. 09. 2009. DEMSEE 2009 9

Three-phase short circuit from t=0.05 s to t=0.12 s
machine stator current (left)
part of left figure (right)
1500
1500
1000
1000
500
500
0
0
-500
-500
-1000
0.0 0.4 0.8 1.2 1.6 [s] 2.0
(f ile DEMSEE_01.pl4; x-v ar t) u1:IPA
-1000
0.0 0.2 0.4 0.6 0.8 [s] 1.0
(f ile DEMSEE_01.pl4; x-v ar t) u1:IPA
09. 09. 2009. DEMSEE 2009 10

Three-phase short circuit from t=0.05 s to t=0.15 s
(unstable machine)
electric torque (left)
angular velocity (right)
250
140
*10 3 (f ile DEMSEE_01.pl4; x-v ar t) u1:OMEGM
200
150
100
50
0
-50
-100
-150
0.0 0.4 0.8 1.2 1.6 [s] 2.0
(f ile DEMSEE_01.pl4; x-v ar t) u1:TQGEN
120
100
80
60
40
20
0.0 0.4 0.8 1.2 1.6 [s] 2.0
09. 09. 2009. DEMSEE 2009 11

Three-phase short circuit from t=0.05 s to t=0.15 s
machine current (left)
constant equivalent field current (right)
1500
0
1000
-500
500
-1000
0
-1500
-500
-2000
-1000
-2500
-1500
0.0 0.4 0.8 1.2 1.6 [s] 2.0
(f ile DEMSEE_01.pl4; x-v ar t) u1:IPA
-3000
0.0 0.4 0.8 1.2 1.6 [s] 2.0
(f ile DEMSEE_01.pl4; x-v ar t) u1:IE1
09. 09. 2009. DEMSEE 2009 12

5. CONCLUSIONS
• At this moment permanent magnet
embedded generators are very important
because of their simplicity, cheapness,
and simple regulation. They are best
suited for small heads, which are the most
interesting in embedded generation.
09. 09. 2009. DEMSEE 2009 13

5. CONCLUSIONS
• There are no models for such machines in
most commonly used transient software
tools. The ATP-EMTP software is capable
of modelling such a machine because it
can simulate constant field current.
Unfortunately, this is not easily done, as it
requires additional preparations.
• In this paper an attempt has been made in
that direction.
09. 09. 2009. DEMSEE 2009 14

This work has been supported by the
Ministry of Science and Technology of the
Republic of Serbia, as a part of the project
No. 17001.
09. 09. 2009. DEMSEE 2009 15

THANK YOU FOR YOUR
ATTENTION!
Dr Saša Stojković
Technical Faculty, Čačak, Serbia
sasa.stojkovic@EUnet.rs
09. 09. 2009. DEMSEE 2009 16