Mean-Variance Mapping Optimization Current developmental status
and application to power system problems Dr. Ing. Jos L. Rueda 9
September 2014 1
Slide 2
Rationale behind MVMO 2 Introduced by I. Erlich (University
Duisburg- Essen, Germany ) in 2010 Internal search range of all
variables restricted to [0, 1]. Solution archive: knowledge base
for guiding the searching direction. Mapping function: Applied for
mutating the offspring on the basis of the mean and variance of the
n-best population attained so far.
Slide 3
The hybrid variant: MVMO-SH 3
Slide 4
MVMO-SH: launching local search 4 (1) : local search
probability, e.g. Local search performed according to Different
methods can be used: Classical: Interior-Point Method (IPM)
Heuristic: Hill climbing, evolutionary strategies where D: Problem
dimension
Slide 5
MVMO-SH: solution archive 5
Slide 6
MVMO-SH: parent selection 6
Slide 7
MVMO-SH: selection of dimensions for mutation 7 8 Two different
strategies are available: a)The full range corresponds with the
number of mutated variables, e.g. m =7 b)The number of mutated
variables estimated randomly in the given range, e.g. m =
irand(7)
Slide 8
MVMO-SH: selection of dimensions for mutation 8 8
Random-sequential selection mode
Slide 9
MVMO-SH: mutation based on mapping function 9 8 0 1 01 x i x i
* 10 (2)(2) (3)(3) (4)(4)
Slide 10
MVMO-SH: mapping function features 10
Slide 11
MVMO-SH: assignment of shape and d-factors 11 d r is always
oscillating around the shape s r and is set to 1 in the
initialization stage d 0 0.4 d = The d-factors remain dynamic with
the mapping even the corresponding shape doesnt change (5)(5)
Slide 12
MVMO-SH: assignment of shape and d-factors 12 (5)(5) CEC2013
function F1, single particle MVMO without local search, fs=1.0, d 0
=0.15
Slide 13
Application to power system problems 13 1.Optimal reactive
power dispatch 2.Identification of power system dynamic equivalent
3.Online optimal control of reactive sources
Slide 14
Optimal Reactive Power Dispatch 14 Minimize (16) (17) (19)
Losses subject to (18) (20) (21) (22) (23) Operational
constraints
Slide 15
Optimal Reactive Power Dispatch 15 IEEE 118 bus system 77
dimensions (54 gen, 9 OLTCs, 14 compensators)
Slide 16
Optimal Reactive Power Dispatch 16 IEEE 118 bus system :
Average convergence performance
Slide 17
Optimal Reactive Power Dispatch 17 IEEE 118 bus system :
Statistics of active power losses P loss (MW) Algorithms MVMO S
MVMOCLPSOSPSOUPSOFDRPSO DMS- PSO-HS DEJADE-vPS Min
117.0802117.0074120.2117121.8049123.1174119.1387123.4717118.7199118.1047
Max
118.1662125.1501132.0461125.4654130.2011123.5461128.5504121.1128120.2177
Mean
117.4251119.3353122.2499123.6784125.6709121.6536125.0562119.7737118.9533
Std. 0.22851.93862.05330.91451.76631.05011.20330.62890.5321
Identification of dynamic equivalent 19 Dynamic equivalent for
Colombia 22 dimensions (Reactances, gains, time constants)
Optimization problem - Sixth order generator model - AVR model -
Governor model
Slide 20
Identification of dynamic equivalent 20 Optimization &
Dynamic simulation
Slide 21
Identification of dynamic equivalent 21 Parameter
identification problem statement Minimize subject to From PMU or
simulations System with component model to be identified Parameters
of the model
Slide 22
Identification of dynamic equivalent 22 DE for Colombia:
comparison of heuristic methods
Slide 23
Identification of dynamic equivalent 23 DE for Colombia:
comparison of dynamic responses Fault 1 Fault 2 Full system model
With DE
Slide 24
Online optimal control of reactive sources 24
Slide 25
Online optimal control of reactive sources 25
Slide 26
Other applications to power system problems 26
1.Active-reactive power dispatch 2.Short-term transmission planning
3.Location and tuning of damping controllers 4.Optimal transmission
pricing 5.Optimal allocation and sizing of dynamic Var sources
Slide 27
Highlights 27 1.Winner of the competition on Expensive
optimization at CEC-2014, Beijing, PR-China, 6-11 July 2014. 2.4 th
out of 17 place in the competition on real-parameter single
Objective optimization at CEC-2014, Beijing, PR-China, 6-11 July
2014. 3.6 th out of 21 place in the real-parameter single Objective
optimization at CEC-2013, Cancun, Mexico 21-23 June 2013. 4.Used
for benchmarking in 2014 Competition on OPF problems organized by
the Working Group on Modern Heuristic Optimization (WGMHO) under
the IEEE PES Power System Analysis, Computing, and Economics
Committee
(https://www.uni-due.de/ieee-wgmho/)https://www.uni-due.de/ieee-wgmho/
Slide 28
28 Thanks! Dr. Jos L. Rueda [email protected]
http://www.uni-due.de/mvmo/
Slide 29
MVMO-SH: parent selection 29 GoodBad All particles ranked
according to their local best (2)(2) (3) (4)(4)