Khartonov’s theorem RF Amplifier - UOKeng.uok.ac.ir/bevrani/teaching/Fall 2016/Robust...

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


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!


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


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


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


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


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


43

Continue

System response for step changes in line voltage


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


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


A Classic Reference


Modern Power Grids



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


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


An Update is Required!

20141994


A Solution for Modeling Challenge

Measurement‐based modeling/estimation


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


Example:



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


period of 2～3 sec

0.4[Hz]

Low‐frequency oscillation

FFT filtering

FFT analysis

Single oscillation component

Eigenvalue Estimation

λi＝ σ± jωd


Tuning of Controllers PSS: H∞ Control Design

Two-area system model

Generator 1:

Generators 2-4:

Conventional Exciter and PSS model Control Design Framework


(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

Khartonov’s theorem RF Amplifier - UOKeng.uok.ac.ir/bevrani/teaching/Fall 2016/Robust...

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