Author: M. R. Tavakoli, et al. Esfahan University Department of - - PowerPoint PPT Presentation

Electricity Beyond Borders

A Central Asia Power Sector Forum

The Conrad Hotel, Istanbul, Turkey June 12-14, 2006

BF-NM Optimization Algorithm Based LFC for Interconnected Power System

Author: M. R. Tavakoli, et al.

Esfahan University Department of Electrical Engineering

Presenter :Maryam Nasri

2

Introduction

• Load Frequency Control(LFC)

The frequency of the power system can be maintained constant by eliminating the mismatch between generation and load.

The goals of LFC

regulates the power flow between different areas.

holds the frequency constant. maintain zero steady state errors.

3

Modeling

• Power System Modeling

The power system used here is two-area thermal power

system including governor dead-band and generation rate constraints

4

• governor dead-band nonlinearity

The range of sustained speed change to the governor in which there is neither an increase nor decrease in valve position of the turbine.

( , ) y F x x =

• 2

1

( , ) ... N dx F x x F N x dt ω = + + +

• 2

1

( , ) N dx F x x N x DB x dt ω = + =

• 0.2

0.8 1

g g

s G T s π − = +

x : a sinusoidal oscillation with f0=0.5 Hz.

sin( ) x A t ω

• The F function can be evaluated as a Fourier series

The dead-band nonlinearity is symmetrical about the origin thus the constant term F0 is equal to zero

.

The Fourier coefficients of a backlash of 0.5 % are obtained as and .

1

0.8 N =

2

0 .2 N = −

Modeling

5

• Generation rate constrate

The practical limit on the rate of change in the generating power.

m m m m m

d P d P P d P d d d P − < −  = − < <   < 

• The linear model of a turbine is replaced by a nonlinear model introduced above.

Modeling

6

Hybrid BF-NM Algorithm

• Hybrid BF-NM Algorithm

The optimization hybrid method to tune the parameters of the Load frequency contorl Bacterial foraging (BF) oriented by Nelder-Mead (NM) algorithm

• Bacterial Foraging Algorithm

Chemotactic step

A bacterium can swim or tumble, and shifts between these two positions during its life-span

Swarming step

exchange of signals between the bacteria through absorbing food materials

Reproduction step

S shows the number of all bacteria and is divided into two parts, Sr=S/2

Elimination and dispersal step

Elimination and dispersal step moves to another position in the environment based on the selected probability (Ped) These step can effectively prevent from trapping in local optimal points

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Hybrid BF-NM Algorithm

• Nelder-Mead method
• A simplex method for finding a local minimum point
• Example : NM method which is a pattern search for a problem with two

variables

1) Determination of the initial triangle BGW

• The algorithm starts with three initial points (B , G , W)

2) Determination of the midpoint of the good side

• midpoint (M) is obtained from the middle of the line between G and B

3) Reflection using the point R

• Point R is obtained using reflection on side BG

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Hybrid BF-NM Algorithm

• Nelder-Mead method

4) Expansion using point E

• If fR < fW , a correct direction will be obtained for minimization
• In this state, the expanded triangle BGE is used and point E is calculated
• If fE < fR , point E will be better than point R and is replaced by point W and point

E is consider as new vertex of triangle

5) Contraction using point C

• If fR = fW , another point should be obtained
• middle points between M and W (C1) , M and R (C2) are considered
• Each of C1 and C2 points with smaller function value is named C and it is consider

as new vertex of triangle

6) Shrink towards B

• If fC > fW , points W and G should be shrunk towards B
• point G is replaced with point M and W is replaced with S

9

Hybrid BF-NM Algorithm

• Flowchart of the Hybrid bacteria foraging algorithm with

Nelder–Mead

10

Simulation Modeling

• The control strategy of LFC for two-area power system

1 1 1 tie

ACE B f P = ∆ + ∆

2 2 2 tie

ACE B f P = ∆ + ∆

The inputs of the PI-controllers are used together with area control errors, ACE1 and ACE2

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Simulation Formula

1 1 1 1 1 p i

u K ACE K ACE = +

∫

2 2 2 2 2 p i

u K ACE K ACE = +

∫

• The control inputs of the power system

2

.( )

sim

t i

Min ITSE t A CE = ∫

• Objective Function

min max min max

: ,

p p p i i i

subject to K K K K K K ≤ ≤ ≤ ≤

12

Simulation Results

• The frequency deviation of area 1 for pu.MW

1

0.01

L

P ∆ =

13

Simulation Results

• The frequency deviation of area 2 for pu.MW

1

0.01

L

P ∆ =

14

Simulation Results

• Tie-line power deviation for pu.MW

1

0.01

L

P ∆ =

15

Simulation Results

• The frequency deviation of area 1 when all the parameters
• f the power system increase 25% from their nominal values

16

Conclusions

• new control scheme for designing the load frequency control

parameters was proposed

• optimization technique was based on a hybrid method called BF-

NM

wide search region with a high convergence speed

• Simulation and analytical results for two-area power systems

confirmed the effectiveness and the robustness of the proposed design technique to enhance the dynamic characteristics of the power system

Electricity Beyond Borders

A Central Asia Power Sector Forum

The Conrad Hotel, Istanbul, Turkey June 12-14, 2006

Please refer your questions to: mr.tavakoli1986@eng.ui.ac.ir BF-NM Optimization Algorithm Based LFC for Interconnected Power System