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

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 Electricity Beyond Borders A Central Asia Power Sector Forum The Conrad Hotel, Istanbul, Turkey June 12-14, 2006

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. 2

Modeling • Power System Modeling The power system used here is two-area thermal power system including governor dead-band and generation rate constraints 3

Modeling . • 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 ( , ) x : a sinusoidal oscillation with f 0 =0.5 Hz. � x A sin( ω t ) 0 The F function can be evaluated as a Fourier series N dx � 2 F x x ( , ) = F + N x + + ... dt 0 1 ω 0 The dead-band nonlinearity is symmetrical about the origin thus the constant term F 0 is equal to zero N dx � 2 F x x ( , ) = N x + = DB x dt 1 ω 0 0.2 0.8 − s The Fourier coefficients of a π backlash of 0.5 % are obtained G = g 1 + T s as and . N = 0.8 N = − 0 .2 g 4 1 2

Modeling • Generation rate constrate The practical limit on the rate of change in the generating power. �  − < − d P d m  � � �  P = P − d < P < d m m m  � d d < P  m � The linear model of a turbine is replaced by a nonlinear model introduced above. 5

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 6

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 7

Hybrid BF-NM Algorithm • Nelder-Mead method 4) Expansion using point E � If f R < f W , a correct direction will be obtained for minimization � In this state, the expanded triangle BGE is used and point E is calculated � If f E < f R , 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 f R = f W , another point should be obtained � middle points between M and W (C 1 ) , M and R (C 2 ) are considered � Each of C 1 and C 2 points with smaller function value is named C and it is consider as new vertex of triangle 6) Shrink towards B � If f C > f W , points W and G should be shrunk towards B � point G is replaced with point M and W is replaced with S 8

Hybrid BF-NM Algorithm • Flowchart of the Hybrid bacteria foraging algorithm with Nelder–Mead 9

Simulation Modeling • The control strategy of LFC for two-area power system The inputs of the PI-controllers are used together with area control errors, ACE1 and ACE2 ACE = B ∆ f + ∆ P 1 1 1 tie ACE = B ∆ f + ∆ P 10 2 2 2 tie

Simulation Formula • The control inputs of the power system ∫ u = K ACE + K ACE 1 p 1 1 i 1 1 ∫ u = K ACE + K ACE 2 p 2 2 i 2 2 • Objective Function Min = ∫ t sim 2 ITSE t .( A CE ) i 0 subject to : min max min max K ≤ K ≤ K , K ≤ K ≤ K p p p i i i 11

Simulation Results • The frequency deviation of area 1 for pu.MW ∆ = 0.01 P L 1 12

Simulation Results • The frequency deviation of area 2 for pu.MW ∆ = 0.01 P L 1 13

Simulation Results • Tie-line power deviation for pu.MW ∆ = 0.01 P L 1 14

Simulation Results • The frequency deviation of area 1 when all the parameters of the power system increase 25% from their nominal values 15

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 16

BF-NM Optimization Algorithm Based LFC for Interconnected Power System Please refer your questions to: mr.tavakoli1986@eng.ui.ac.ir Electricity Beyond Borders A Central Asia Power Sector Forum The Conrad Hotel, Istanbul, Turkey June 12-14, 2006