enhanced velocity differential evolutionary particle swarm
TRANSCRIPT
Enhanced Velocity DifferentialEvolutionary Particle Swarm Optimization (EVDEPSO)
Developers: Kartik S. Pandya ,Dharmesh A. DabhiDepartment of Electrical Engineering, CSPIT ,CHARUSAT UNIVERSITY,GUJARAT,INDIA
[email protected] [email protected]
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OutlineØParticle Swarm OptimizationØDifferential Evolutionary PSO (DEEPSO)ØResearch challengeØEnhanced Velocity Differential Evolutionary Particle
Swarm Optimization (EVDEPSO)ØCharacteristics of ProblemØObjective functionØConstraintsØScenarios OverviewØSimulation ResultØReferences
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Particle Swarm Optimization[1] J. Kennedy and R. Eberhart
• Particles: Possible solutions in the feasible space• New position of a particle i:
• Velocity (Step-length) of a particle i:
• Velocity of a particle is influenced by:(1) Inertia
Follow in the same direction
(1) Personal memoryAttraction by particle past best
(1) CooperationFollow the global best particle
kXi
i
Cooperation Gbest
Memory Pbest_i
iV k
V k+1 Step-length
1 1k k ki i iX X V+ += +
11 _ 2. . . . ( ) (. )k k k k
i I i M best i i C best iV w V R w P X R w G X+ = + - + -
X k+1
i
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Differential Evolutionary PSO [2] V. Miranda and R. Alves
• New position of a particle i:
(1) InertiaFollow the same direction
(2) PerceptionFollow the randomly sampled particle chosen from the matrix of
individual past bests
(3) CooperationFollow the mutated global best particle
1 * * * *. .( ) . .( )k k k ki i i iI M Crand bestV w V w X X w P G X+ = + - + -
1 1k k ki i iX X V+ += +
• Velocity updating rule:
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Differential Evolutionary PSO Continue…….
• Each weight and global best particle are subject to mutation as follows
• P= communication probability• Allow communication Ûrand()<P• sampled particle chosen from the matrix of individual past bests
*( , , ) ( , , ) [0,1]I M C I M Cw w Nt= +*( ) ( ) (1 [0,1])best best bG G w N= +
randX
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Research challenge
v Optimization involves….
• Global Exploration: To explore unknown and large-scale search space
• Local Exploitation
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Enhanced Velocity Differential EvolutionaryParticle Swarm Optimization (EVDEPSO)
{ }1
* *
*1 [0,1
0.52[1 (0,
(1) (0,1)]
)
]kk
ki
i i
C bes
I
tw G
V w N
ra
V
Xnd U
+ +
+ +
=
++
-
• New position of a particle i:
• Velocity (Step-length) of a particle i:
1 1(2* ) / 3k k ki i iX X V+ += +
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(1) Enhanced VelocityFollow the mutated current velocity
(2) CooperationFollow the mutated global best particle
(3) Stochastic Uniform Distribution (SUD)
Enhanced Velocity Differential EvolutionaryParticle Swarm Optimization (EVDEPSO)
i
k+1Xi
Cooperation
Current position
SUD
X k-1
Old position
X ki
1kiV+
Enhanced velocity
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• N[0,1] :Normal Distribution• U[0,1] :Uniform Distribution• r(0,1) :Random value between (0,1)• Global best particle are subject to
mutation
• Each weight is subject to mutations
• τ=Mutation Rate
*( , , ) ( , , ) (0,1)I C E I C Ew w Nt= +
* (1 )best best EG G w= +
Enhanced Velocity Differential EvolutionaryParticle Swarm Optimization (EVDEPSO)
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ParametersParameters Value
Populations size (N) 10
No. of Iteration (I_itermax) 285
No. of Scenario 10
Local Search Probability 0.3
Mutation Rate (τ ) 0.7
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Characteristics of Problem
• Day-ahead energy resource management problem in smart gridsunder environments with uncertainty related to EV Trip,renewable generation, variable load consumption, market price.
• In this context, operational problems posse highly complexmathematical properties like:
Ø Non-convexityØ DiscontinuityØ High-dimensionality
• which emphasizes the need of advanced optimization solvers inorder to find optimal solutions that guarantee efficient andflexible operations.
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Objective functions• Objective: Maximize the profit of VPP
Profit of VPP = Income - Operating Cost (OC)Objective function: Minimze Z= Operating Cost (OC)- Income
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
L M
ST V
Load L, Load L, Sell M, Sell M,T L 1 M 1
t 1Ch ST, Ch ST, Ch V, Ch V,
ST 1 V 1
MP MPIncome t
MP MP
= =
=
= =
´ ´é ùæ ö+å åê úç ÷= • Dê úç ÷å
ê úç ÷å åç ÷+ ´ + ´ê úè øë û
N N
t t t t
N N
t t t t
P P
P P
( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( )
SP
ST V
S L
L
DG DG, DG DG, SP SP, SP SP,t 1DG 1 SP 1
PV PV, PV PV, Dch ST, Dch ST, Dch V, Dch V,DG 1 ST 1 V 1
GCP DG, GCP DG, NSD L, NSD L,S 1 DG 1 L 1
Cut L,L 1
c
c c
c
O.C c
c
c
c
DG
PV_DG
DG
N NT
t t t t
N N N
t t t t t t
N N N
t t t t
N
t
P P
P P P
P P
P
= = =
= = =
= = =
=
´ ´
´ ´ + ´
+
= +å å å
+å å å
å å+ ´ ´å
å
+
´ ( )
( )T
t 1
Cut L,
S
t
=
é ùæ öê úç ÷ê úç ÷ê úç ÷ •på ê úç ÷ê úç ÷ê úç ÷ç ÷ê úè øë û
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Constraints:
v Equality constraints:
• Power balance equationsv Inequality constraints:• Distributed generation constraints • Max. active power output of slack generator• Nodal voltages and load angles for load buses• Allowable branch power flows• External supplier constraints• Electric vehicles constraints• Energy Storage Constraints
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Scenarios OverviewTable 1. Available Energy Resources [22]
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Simulation Results: EVDEPSORow AvgFit stdFit minFit maxFitRun 1 18.29978 1.935962 13.68005 23.79353Run 2 17.0305 2.051103 12.24396 22.86369Run 3 17.93517 1.893092 13.42795 23.21843Run 4 17.59375 1.98978 12.91211 23.24552Run 5 18.49571 1.935768 13.83458 23.90411Run 6 18.08487 1.924987 13.46798 23.49525Run 7 18.11005 1.756328 13.95512 22.95723Run 8 18.14271 1.945139 13.56755 23.65157Run 9 18.7998 1.863772 14.31799 23.88956
Run 10 18.09776 1.910083 13.57313 23.35899Run 11 17.4468 1.797446 13.21725 22.51312Run 12 17.97835 1.811764 13.73231 23.04904Run 13 18.14957 1.909128 13.60455 23.46674Run 14 18.30368 1.803799 14.01402 23.24459Run 15 17.91566 1.731264 13.8702 22.63402Run 16 17.91001 1.890555 13.44915 23.21442Run 17 17.87666 2.100027 12.95505 23.7512Run 18 17.01954 2.019215 12.29765 22.74517Run 19 17.37858 1.928871 12.8291 22.80545Run 20 17.0047 1.853347 12.66079 22.21759
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Simulation Results: EVDEPSO
RankingIndex PAvgFit PstdFit PminFit PmaxFit
19.5954 17.6882 1.90715 13.18682 23.04330
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Simulation Results cont.…EVDEPSO
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AvgFit stdFit minFit maxFit
Fitn
ess V
alue
No. of Iteration
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References1.) J. Kennedy and R. Eberhart, “Particle Swarm Optimization”, proceedings of IEEEInternational Conference on Neural Networks (ICNN’95), vol. IV, Perth, Australia,1995, PP.1942-1948.
2.) V. Miranda and R. Alves, “Differential Evolutionary Particle SwarmOptimization(DEEPSO): Asuccessful hybrid”, proceedings of 2013 BRICS Congress on
Computational Intelligence & 11thBrazilian congress on Computational Intelligence,
Ipojuca, Brazil, Sept. 2013, pp. 368-374.
3)V.Miranda and Leonel Carvalho (2014), “DEEPSOEvolutionary Swarms in the OPFchallenge”, [online] Available http://sites.ieee.org/psace-mho/panels-and-competitions-2014-opf-problems/, pp. 16.
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THANK YOU
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