Post on 13-May-2018
Advanced Mathematical Programming 1
H. BevraniSmart/Micro Grids Research Center
University of Kurdistan
Fall Semester, 2016
Lectures and Presentations
Robust Control Applications: Challenges and SolutionsKasetsart university, Thailand (April 5, 2012)
Robust Control Applications in Modern Power SystemsOsaka University, Japan (August 21, 2015)
3
Robust Control System
Conventional control fails to meet the specified objectives in new environment.
H2
µ
LQGLQR
MPC
H∞
H2/H∞
QFT
Kharitonov
Robust Control Techniques
5
Khartonov’s theorem
• A polynomial such:
with real coefficients is Hurwitz if and only if the following four
extreme polynomials are Hurwitz:
• The “-“ and “+” show the minimum and maximum bounds.
6
RF Amplifier
Advanced Mathematical Programming 2
7
Quadratic Buck Converter (QBC)
Step change of load between 3 and 6 ohms Variation in line voltage from 12 V to 17 VUniversity of KurdistanUniversity of Kurdistan8/70H. BevraniH. Bevrani
An Experience (Japan, 2003)
After implementationusing analog parts
Robust ControllerSMPS
9
A Challenge!
Robust control theorems usually provide complex structures and some times infeasible solutions.
10
Industry Requirements
Practically,Simple structures are desirable.
11
A future Direction
Robust/OptimalControl Theorems
Robustness+
Optimal performance
Real-world Control Systems
Simple structure+
Simple procedure
12
An effective solution
Starting the control design using a more simple control structure, for example Static Output Feedback control configuration.
A Challenge!
Advanced Mathematical Programming 3
13
Proposed Strategies
Tracking
Relaxation
Compromising
Develop new control algorithmsbased on following 3 key points:
14
Point 1: Tracking
Track the robust performance index ( )γ
15
Example: H∞ performance index
Find an admissible SOF control law:
iii yKu sofi KK ,
Such that*
(s)Tz w *and
is the optimal H∞ Performance Index, yielded byfull order dynamic H∞ controller.
γ(s)Tzw
γ
16
Point 2: Relaxation
Invoke the strict conditions using relaxationand proper reformulation.
17
Point 3: Compromising
Trade-off between various requirements
RobustnessReality
18
Overall framework
Advanced Mathematical Programming 4
19
Mixed H2/H∞ based LFC control
_______________________________________________________________________________________[1] H. Bevrani, T. hiyama On load-frequency regulation with time delays: design and real-time implementation, IEEETrans. On Energy Conversion, 24(1): 292-300, 2009.
20Power System Laboratory
Real-Time Simulation
21
Time delay as uncertainty
22
wDxCyuDwDxCz
uDwDxCzuBwBAxx
y1y
21
21
21
2222
2 wzKK
2
IS
T inf
wzTSubject to
23
Control framework
2 wzKK
2i2i
ISi
T inf
1T 1i wiz Subject to
)( ACEkCEAktu IP
)(
] [)(
tky
ACEACEkktuT
IP
PI to SOF
Advanced Mathematical Programming 5
25
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
10-3
10-2
10-1
100
101
102
frequency (rad/sec)M
agni
tude
W1(s)
ILMI algorithm
] [ IiPii kkK sofi KK
22i w2izsofKiK
T inf
subject to
1T 1i wiz
Multiobjective Robust AGC
26
Synthesis framework
Control strategy and ILMI
28
Study system
0AA d 9714.12)(
29
Real-time lab. experiment
Analog Power System Simulator, Research Lab., Kyushu Electric Power Co.30
PC based control loop
Advanced Mathematical Programming 6
31
0 50 100 150 200-0.05
0
0.05
(ra
d/s)
0 50 100 150 200-0.2
0
0.2
P
tie (
pu)
0 50 100 150 200-0.2
0
0.2
u1 (
pu)
0 50 100 150 200-0.2
0
0.2
u2 (
pu)
0 50 100 150 200-0.1
0
0.1
u3 (
pu)
0 50 100 150 200-1
0
1
AC
E (
pu)
Time(s)
System response for 10 sec delay; following 10% step load change.
More continue
32
Motor Motor
+
Position Position
Position Error
Force Communication
33
Laboratory Experiment
34
Switching Converter
ISIE 2004 35
s0.010t V, 25Vref
s0.0150.01t V, 20Vref
ISIE 2004 36
s0.0080t V, 20Vref
s0.0130.008t V, 15Vref
s0.0180.013t V, 20V ref s0.0250.018t V, 25Vref
Advanced Mathematical Programming 7
ISIE 2004 37
Load is changed to 1Ω and 10Ω at 0.007s
ISIE 2004 38
s0.0070t V, 3Vi 0
s0.0150.007t V, 3Vi 30
39
Power Rectifier
15 kW active rectifiers [1]
Three phase circuit diagram40
Control framework
41
Problem formulation via H∞-SOF
xCy
uDxCz
uBwBAxx
2
121
21
:)(sG
42
Simulation results
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5300
400
500
600
700
v ref (
V)
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5300
400
500
600
700
v dc (
V)
Time (sec)
System response for step changes in reference voltage
Dynamic H∞ and PI designs
Advanced Mathematical Programming 8
43
Continue
System response for step changes in line voltage
Dynamic H∞ and PI designs
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65200
300
400
500
600
Vm
(V
)
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65550
555
560
565
570
575
v dc (
V)
Time (sec)
44
Continue …
System response for step changes in line voltage
Dynamic H∞ and PI designs
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.650
10
20
30
40
50
Rlo
ad (
)
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65540
550
560
570
580
v dc (
V)
Time (sec)
Hassan Bevrani
University of Kurdistan
Osaka University, August 21-2015
University of KurdistanUniversity of Kurdistan46/70H. BevraniH. Bevrani
Stability Analysis/Control Synthesis: Conv. Scheme
University of KurdistanUniversity of Kurdistan47/70H. BevraniH. Bevrani
A Classic Reference
University of KurdistanUniversity of Kurdistan48/70H. BevraniH. Bevrani
Modern Power Grids
Advanced Mathematical Programming 9
University of KurdistanUniversity of Kurdistan49/70H. BevraniH. Bevrani
Wide network of monitoring units: IEDs/PMUs
New Characteristics and Challenges
Highly decentralized property and fully control
Increase of size/complexity
Emerging DGs/RESs, MGs and new functions(Diversity in generation and load)
Huge amount of data
Require fast data processing/calculation
University of KurdistanUniversity of Kurdistan50/70H. BevraniH. Bevrani
Low inertia due to use of electronic interfaces
Continue
Conv. stability/security analysis methods fail
Update conventional modelling and control
Variable nature of RESs and continues changes (uncertainty)
Decrease of stability
Update the methods and revise control performance standards
University of KurdistanUniversity of Kurdistan51/70H. BevraniH. Bevrani
An Update is Required!
20141994
University of KurdistanUniversity of Kurdistan52/70H. BevraniH. Bevrani
A Solution for Modeling Challenge
Measurement‐based modeling/estimation
University of KurdistanUniversity of Kurdistan53/70H. BevraniH. Bevrani
Measurement‐based Modeling/Estimation
Real-time monitoring/WAM
Data storage/analysis
Dynamic estimation
Real-time monitoring/WAM
Data storage/analysis
Dynamic estimation
Controller design/tuning
University of KurdistanUniversity of Kurdistan54/70H. BevraniH. Bevrani
Example:
Advanced Mathematical Programming 10
University of KurdistanUniversity of Kurdistan55/70H. BevraniH. Bevrani
Wide‐Area Measurement System (WAMS)
NAS: Network Attached Storage
Fault analysis
Eigenvalues estimation
Overall stability analysis
Tuning of controllers
PMUs
Data C
ommunicatio
n Channel
Data Collection
Site
Data Collection
Site
Database
University of KurdistanUniversity of Kurdistan56/70H. BevraniH. Bevrani
period of 2~3 sec
0.4[Hz]
Low‐frequency oscillation
FFT filtering
FFT analysis
Single oscillation component
Eigenvalue Estimation
λi= σ± jωd
University of KurdistanUniversity of Kurdistan57/70H. BevraniH. Bevrani
Tuning of Controllers PSS: H∞ Control Design
Two-area system model
Generator 1:
Generators 2-4:
Conventional Exciter and PSS model Control Design Framework
Advanced Mathematical Programming 11
(1) Phase difference
(2) Oscillation time series
(3) Oscillation model
(4) G(s)
2
121
2
1
01 x
xaa
x
x
sx 11
)( 112 seesx
j
)()(
222 s2s
1sG
0.44 Hz
Oscillation Model Identification Steps
α±jβ = -0 137±j3 720
2
121
2
1
01 x
xaa
x
x
sx 11
)( 112 seesx
Oscillation model
Eigenvalues
Nodes1 and 3 FFT Spectrum
Filtering
Oscillation model
Then:
86.13274.0
12
ss
sG
s2201s3101s4501
s5801s8201870
sF
...
...
The model F(s) is identified using a procedure given in
The filtered phase difference and the output signal of low-order model
01
66
77
801
66
77
bsbsbsbs
asasasasPg
The H controller is obtained as:
4523
6726
1047.51089.13068
1048.11005.31039.1
sss
sssP
Balanced realization technique
The eigenvalues of the simple-two area system
Step response with the low-order model Simulation result with the original two-area system
Mode Inter-areaWithout PSS 0.123 j3.710
Initial PSS 0.201 j3.814Designed PSS 0.322 j4.071