Application of Swarm Mean-Variance Mapping Optimization on Location and Tuning Damping Controllers, Jose Luis Rueda - Francisco M. Gonzalez-Longatt

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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

http://www.fglongatt.org/

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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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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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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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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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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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Search range of all

optimization variables

normalized to [0, 1].


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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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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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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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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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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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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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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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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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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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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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Questions and Answers

Thank you!

Dr. Jose Luis Rueda

[email protected]

Dr. Francisco M. Gonzalez-Longatt

[email protected]


Engineering

Application of Swarm Mean-Variance Mapping Optimization on Location and Tuning Damping Controllers, Jose Luis Rueda - Francisco M. Gonzalez-Longatt