Mean-Variance Mapping Optimization Current developmental status and application to power system problems Dr. –Ing. José L. Rueda 9 September

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.

The hybrid variant: MVMO-SH 3

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

MVMO-SH: solution archive 5

MVMO-SH: parent selection 6

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)

MVMO-SH: selection of dimensions for mutation 8 8 Random-sequential selection mode

MVMO-SH: mutation based on mapping function x i x i * 10 (2)(2) (3)(3) (4)(4)

MVMO-SH: mapping function features 10

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 doesn’t change (5)(5)

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

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

Optimal Reactive Power Dispatch 14 Minimize (16) (17) (19) Losses subject to (18) (20) (21) (22) (23) Operational constraints

Optimal Reactive Power Dispatch 15 IEEE 118 bus system 77 dimensions (54 gen, 9 OLTCs, 14 compensators)

Optimal Reactive Power Dispatch 16 IEEE 118 bus system : Average convergence performance

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 Max Mean Std

Identification of dynamic equivalent 18 Ecuador-Colombia interconnected system 320 buses generators 3.23 GW installed capacity 2.66 GW peak load Ecuador (study area) 1729 buses generators GW installed capacity 8.78 GW peak load Colombia (external area) 22 dimensions (reactances, gains, time constants) Opt. problem

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

Identification of dynamic equivalent 20 Optimization & Dynamic simulation

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

Identification of dynamic equivalent 22 DE for Colombia: comparison of heuristic methods

Identification of dynamic equivalent 23 DE for Colombia: comparison of dynamic responses Fault 1 Fault 2 Full system model With DE

Online optimal control of reactive sources 24

Online optimal control of reactive sources 25

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

Highlights 27 1.Winner of the competition on Expensive optimization at CEC-2014, Beijing, PR-China, 6-11 July th out of 17 place in the competition on real-parameter single Objective optimization at CEC-2014, Beijing, PR-China, 6-11 July th out of 21 place in the real-parameter single Objective optimization at CEC-2013, Cancun, Mexico June 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 (

28 Thanks! Dr. José L. Rueda

MVMO-SH: parent selection 29 GoodBad All particles ranked according to their local best (2)(2) (3) (4)(4)

MVMO-SH: parent selection 30 (6)(6) (5) Alternatively: (7)(7) (8)(8)