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IEEE Power and Energy Society ISGT Asia 2015 1/19
APPLICATION OF SWARM MEAN-VARIANCE MAPPING OPTIMIZATION ON LOCATION AND TUNING DAMPING CONTROLLERS
Dr. Jose Luis RuedaDelft University of Technology, Netherlands
Dr. Francisco M. Gonzalez-Longatt*Loughborough University, UK
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IEEE Power and Energy Society ISGT Asia 2015 2/19
I. Introduction (1/2)
• The most common practice on the problem of placement
and tuning of power system damping controllers
• It have been solve it as individual problems based on
participation factors, residues, damping torque, sensitivity
coefficients and singular value decomposition.
• Alternatively, the simultaneous solution for both tasks has also
been investigated from optimization problem point of view.
• Particularly, the joint determination of optimal placement
and coordinated tuning of power system damping
controllers (OPCDC) constitutes a challenging optimization
problem due to the mix-integer combinatorial nature as well
as to the nonlinearity, multimodality, and no convexity of the
search space
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IEEE Power and Energy Society ISGT Asia 2015 3/19
I. Introduction (2/2)
• OPCDC using optimization approaches.
• Earlier reported approaches based on modified versions of
genetic algorithm (GA), particle swarm optimization (PSO),
and differential evolution (DE) highlight the potential of
metaheuristic optimization algorithms for solving the OPCDC.
• This paper presents an approach based on the Swarm Mean-
Variance Mapping optimization (MVMO-S), which extends
the single-solution variant of MVMO to a population based
strategy.
• This paper introduces the use of the MVMO-S to solving
the multi-scenario problem of the optimal placement and
POCDCs.
OPCDC: optimal placement and coordinated tuning of power system damping controllers
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IEEE Power and Energy Society ISGT Asia 2015 4/19
II. A. Optimization problem statement (1/2)
• The OPCDC problem is mathematically formulated as
follow:
• Minimize:
• Subject to:
• where th is a predefined threshold for minimum acceptable
modes’ real part (i.e. damping factor).
• *sys and *
sys correspond to the global damping ratio and
damping factor of the system (among the nm critical OMs)
throughout nsc representative scenarios.
2 2
* *
sys th 1 sys thOF ζ ζ +w
min max x x x
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IEEE Power and Energy Society ISGT Asia 2015 5/19
II. A. Optimization problem statement (2/2)
• The vector x constitutes the solution of the problem, so it
contains the damping controller’s tuning parameters (gains
KSDC, and time constants T1 to T4), which are continuous
variables, and their locations, which are coded by using
logical variables.
• The weighting factor w1 is a positive number that is used for
combining the squared difference between *sys and th
with the squared difference between *sys and ζth.
• *sys and *
sys are determined as follows:
*
sys kj 1 nsc k 1 nm
ζ min min
*
sys kj 1 nsc k 1 nmmax max
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IEEE Power and Energy Society ISGT Asia 2015 6/19
II.B. Mean-variance mapping optimization (MVMO)
• Mean-variance mapping optimization (MVMO) is a recently
introduced evolutionary algorithm, which has some basic
conceptual similarities to other heuristic approaches, but it
constitutes a fundamentally new evolutionary mechanism with
two salient features.
• Swarm Mean-Variance Mapping optimization (MVMO-S),
which adopts a swarm intelligence scheme and
incorporates a multi-parent crossover strategy to increase
the search diversity while striving for a balance between
exploration and exploitation.
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IEEE Power and Energy Society ISGT Asia 2015 7/19
II.B. Mean-variance mapping optimization (MVMO)
Search range of all
optimization variables
normalized to [0, 1].
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IEEE Power and Energy Society ISGT Asia 2015 8/19
II.B. Mean-variance mapping optimization (MVMO)
MVMO-SH - Some highlights
1. Winner of IEEE competitions on Expensive optimization: CEC-2014
(Beijing, July 2014), and CEC-2015 (Sendai, Japan, May 2015)
2. 3rd out of 13 place in the competition on real-parameter single
Objective optimization at CEC-2015, Sendai, Japan, May 2015.
3. 4th out of 17 place in the competition on real-parameter single
Objective optimization at CEC-2014, Beijing, PR-China, July 2014.
4. 6th out of 21 place in the real-parameter single Objective
optimization at CEC-2013, Cancun, Mexicom June 2013.
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IEEE Power and Energy Society ISGT Asia 2015 9/19
II.B. Mean-variance mapping optimization (MVMO)
MVMO-SH – Improved offspring generationAll solutions ranked according to their individual best
Global
Best
Global
Worst
Good solutions Bad solutions
Last
Good
First
BadRandom
Good
Selection of m dimensions out of D
for mutation via mapping function
k k,s d
best best bestRG GB LG
parent
parent
=
=
i
ii ii , ,
x
x x
x
s
x x
d
bestGBx best
RGx bestLGx
besp tareGB
be
nt
stRG
=
=
k
k
x
x
x
x
k i
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IEEE Power and Energy Society ISGT Asia 2015 10/19
II.B. MVMO
Offspring
generation
Yes No
Start
Initialize algorithm parameters
Generation and normalization of initial population
i=0
Fitness evaluation
Termination criteria satisfied?Stop
Classification of good and bad particles
and parent selection
Mutation through mapping of m selected
dimensions based on mean and variance
Bad particle?
k=1
k=k+1k<NP
i=i+1
No Yes
No
Yes
Multi-parent crossover based
on a subset of good particlesSingle parent crossover
based on local best
Fill/Update individual archive
Selected scenarios
System model
Damping performance criteria
MVMO-S based solution
procedure for OPCDC
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IEEE Power and Energy Society ISGT Asia 2015 11/19
III. Study Case
• The approach is tested using a slightly modified version of the
IEEE New England 39 bus test system, which includes two
Thyristor-Controlled Series Capacitors (TCSCs),
G10
G8
G9
G2
G3
G4
G5
G6
G7
1
2
3
18 17
30
37
25 26 28 29
38
27
4
15
16
21
24
514
19
22
236
11
12
13
33 20
34
10
32
31
35
36
8
7
9
39
G1
TCSC1
TCSC2
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IEEE Power and Energy Society ISGT Asia 2015 12/19
III. Study Case
• The approach presented in was used to determine the representative scenarios from probabilistic model based Monte Carlo simulations (MCS).
• OPCDC is solved by considering the representative scenarios and potential addition of damping controllers at generators G2 to G10 as well as at both TCSCs.
• The damping controllers at generators are assumed to have speed as input signals from local generators and are superimposed to the excitation control system, whereas those at TCSCs have line currents as inputs and are superimposed on the device’s main control loop, whose output signal is the series compensation susceptance.
• The parameters of each controller were adjusted considering typical limits, i.e. KSDC [1, 100], T1 and T3 [0.2, 2], T1/T2 and T3/T4 [1, 30], whereas the location is decided by using logical variables. Therefore, the search space has 66 dimensions, comprising to 55 continuous variables and 11 two-state discrete variables.
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III. Study Case
• A static penalty scheme is defined for MVMO and the
compared algorithms in order to properly consider the
fulfillment degree of constraints as well as to ensure fair
comparison.
• The fitness is calculated as follows:
• where f stands for objective function value, Ncon is the number
of constraints, gi denotes the i-th constraint, and is the
penalty coefficient for each constraint.
2*
1
max 0,conN
i i
i
f f g
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IEEE Power and Energy Society ISGT Asia 2015 14/19
III. Study Case
• Average convergence of the fitness, among 30 independent optimization repetitions
• Comprehensive learning particle swarm optimization (CLPSO)
• Genetic algorithm with multi-parent crossover (GA-MPC)
• Differential evolution DE algorithm with adaptive crossover operator,
• Linearized biogeography-based optimization with re-initialization (LBBO)
• Covariance matrix adaptation evolution strategy (CMA-ES).
0 200 400 600 800 1000 1200 1400 1600 1800 20000
50
100
150
200
250
300
350
400
450
500
Number of function evaluations
Fit
ness
MVMO-SM
CLPSO
GAMPC
DE-ACO
LBBO
CMA-ES0 400 800 1200 1600 20000
0.01
0.02
0.03
0.04
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IEEE Power and Energy Society ISGT Asia 2015 15/19
III. Study Case
• Mote the excellent performance of MVMO-SM in terms of
both convergence speed and the minimum reached, since
after the first 1,600 function evaluations, it is able to locate
the global optimal solution in the search space (when the
thresholds for damping performance are reached, i.e. OF = 0)
without being trapped in a local optimum.
0 200 400 600 800 1000 1200 1400 1600 1800 20000
50
100
150
200
250
300
350
400
450
500
Number of function evaluations
Fit
ness
MVMO-SM
CLPSO
GAMPC
DE-ACO
LBBO
CMA-ES0 400 800 1200 1600 20000
0.01
0.02
0.03
0.04
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IEEE Power and Energy Society ISGT Asia 2015 16/19
III. Study Case
• A statistical survey of the achieved fitness values for all
optimization repetitions is given in following Table:
• The outstanding performance of MVMO-S can be more clearly
appreciated by comparing different statistical attributes.
• It can be seen that there are some slight differences, which
are due to inherent algorithmic characteristics of each
method.
Fitness (p.u.)Algorithm
MVMO-S CLPSO GA-MPC DE-ACO LBBO CMA-ES
Min. 1.669110-7 8.830210-3 5.071410-3 4.933910-3 4.785510-3 8.532310-5
Max. 1.065910-4 4.173910-2 1.151710-2 9.840710-3 1.151710-2 6.972310+1
Mean 1.519910-5 1.550910-2 1.059010-2 8.422810-3 1.017810-2 0.780910+1
Std. 2.986710-5 1.134110-2 2.113710-3 1.308710-3 2.218010-3 2.190610+1
Average
execution time
(min)
26.2537 26.6231 29.7757 26.6538 25.9259 26.5142
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IEEE Power and Energy Society ISGT Asia 2015 17/19
III. Study Case
• Time domain simulation was also performed to confirm the
effectiveness of the obtained results.
• For this purpose, the simulation was conducted for one of the
scenarios considered in the OPCDC by applying a three-
phase fault at bus 15 at t = 1.0 s, with a duration of 100 ms
0 5 10 15 20-1000
-500
0
500
1000
1500
Time (s)
Pij
lin
e 9
-39
(M
W)
Baseline
After OPCDC
Simulation response of the active power flow (Pij) in line 9-39 (MW).
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IEEE Power and Energy Society ISGT Asia 2015 18/19
IV. Conclusions
• This paper presents a metaheuristic based approach to
tackle the problem of optimal placement and coordinated
tuning of power system supplementary damping
controllers.
• The optimization task is solved via MVMO-S.
• Numerical results attest the outstanding performance of the
proposed MVMO-SM in terms of convergence behaviour and
lowest statistical attributes associated to optimization
repetition.
MVMO-S: Swarm Mean-Variance Mapping optimization
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IEEE Power and Energy Society ISGT Asia 2015 19/19
Questions and Answers
Thank you!
Dr. Jose Luis Rueda
Dr. Francisco M. Gonzalez-Longatt