ELE 806 Midterm: ELE806 Winter 2012 Midterm Solutions
31 Jan 2019
School
Department
Course
Professor
Department of Electrical and Computer Engineering
Solution
ELE806 Alternative Energy Systems
Winter 2012
MIDTERM EXAMINATION
(Closed Book)
Duration: 2 hours
Date: March 2, 2012
Instructor: Dr. Bin Wu
Instructions
(1) This is a closed-book exam. No aids other than basic calculators and two formula
sheets are permitted.
(2) Answer all four questions. You must show your steps and derivations clearly to be
awarded part marks for your answer.
(3) If in doubt on any question, clearly state your own assumptions.
Q1. 25% ______________
Q2. 25% ______________
Q3. 25% ______________
Q4. 25% ______________
Student Name: ____________________________
Student Number: ____________________________
Midterm Examination ELE806 W2012
1
Question 1 (25%)
A general dq-axis dynamic model of synchronous generator (SG) in the rotor field reference frame is shown in Fig. 1, based on which
answer the following three questions.
s
R
ds
i
ls
L
dm
i
dm
L
ds
v
ds
p
dr
p
dsr
s
R
qs
i
ls
L
qm
i
qm
L
qs
v
qs
p
Fig. 1 General dq-axis dynamic model of SG in the rotor field synchronous reference frame.
1.1) (15%) Derive a simplified dq-axis dynamic model of synchronous generator based on the general model shown in Fig. 1. Use the
rotor flux linkage λr , and the dq-axis stator self inductances Ld and Lq in your derivation.
(1)
qsdsrqssqs
dsqsrdssds
piRv
piRv
(2)
qsqqsqmlsqs
rdsdfdmdsdmlsdsfdmdslsds
iLiLL
iLILiLLiILiL
)(
)(
(3)
qmlsq
dmlsd
fdmr
LLL
LLL
IL
(4)
qsqrrdsdrqssqs
dsdqsqrdssds
piLiLiRv
piLiLiRv
1.2) (5%) Based on your derivations, draw a simplified dq-axis dynamic equivalent circuit of the SG in the rotor field synchronous
reference frame.
1.3) (5%) Derive a dq-axis steady-state equivalent circuit for the synchronous generator. Show your derivation steps.
Midterm Examination ELE806 W2012
2
Question 2 (25%)
A two-channel interleaved boost converter is used in a 1.5MW/690V/50Hz PMSG wind energy conversion system as shown in Fig. 2.
The boost inductance L1 (L2 = L1) and capacitance Co of the boost converter are 300 μH and 3000 μF, respectively. The switching
frequency of the boost converter is 2.5kHz. The output voltage vo of the boost converter is set by the inverter to 1200 V. At a given
wind speed, the generator is delivering the rated power to the grid and its line-to-line stator voltage is 690 V. Assuming that the
rectifier and boost converter are idea (no power losses) and the grid line-to-line voltage is 690V, answer the following questions.
Fig. 2 A 1.5MW/690V/50Hz PMSG wind energy conversion system using two-channel interleaved boost converter.
2.1) (5%) Assuming that the converter is operating in the continuous current mode (CCM), find the boundary inductor currents and
boundary output currents of each converter channel.
V 5.93169035.1
23 LLi VV
2238.0
1200
5.931
11
o
i
V
V
D
The boundary inductor currents for each channel:
A97.138
103002
2500
1
1200
7762.02238.0
2
16
21
L
TV
DDIII so
LBLBLB
The boundary output currents for each channel:
A87.10797.1387762.0)1(
21 LBoBoBoB IDIII
2.2) (5%) Verify that the boost converters are operating in the continuous current mode.
A1250
1200
105.1 6
o
i
o
o
oV
P
V
P
I
from which the average output current for each channel can be obtained by
A6252/12502/
21 ooo III
Since oBoo III 21 , the converter operates in the CCM. Therefore, the assumption is valid.
Document Summary
No aids other than basic calculators and two formula sheets are permitted. (2) answer all four questions. You must show your steps and derivations clearly to be awarded part marks for your answer. (3) if in doubt on any question, clearly state your own assumptions. A general dq-axis dynamic model of synchronous generator (sg) in the rotor field reference frame is shown in fig. 1, based on which answer the following three questions. srdsi lsl dsv dsp dmi dml srqsi r ds lsl drp qsv qsp qmi qml. 1 general dq-axis dynamic model of sg in the rotor field synchronous reference frame. 1. 1) (15%) derive a simplified dq-axis dynamic model of synchronous generator based on the general model shown in fig. Use the rotor flux linkage r , and the dq-axis stator self inductances ld and lq in your derivation. ds qs r qs ds. L qm i qs p ds p qs ds i f il qsq.
