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Intelligent Analysis of Environmental Data (S4 ENVISA Workshop 2009)

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- 1. S4 ENVISA "Intelligent Analysis of Environmental Data" Ant colony search and heuristic techniques for optimal dispatch of energy sources in micro-grids ELEONORA RIVA SANSEVERINO Dipartimento di Ingegneria Elettrica Elettronica e delle Telecomunicazioni Università degli Studi di Palermo JUNE 19th 2009 - PALERMO
- 2. OUTLINE Problem description: microgrids and operational issues Optimization in microgrids Heuristic optimization Recent solution methods: MC-ACOR and NSGA-II
- 3. Problem description: microgrids ‘Small networks of power generators in “microgrids” could transform the electricity network in the way that the net changed distributed communication.’ A microgrid is a small-scale power supply network, designed to provide power to few building or a small community. Features -Large penetration of RES -Load=Generation -Electronics and telecommunication facilities -Accurate Control
- 4. Problem description: microgrids and operational issues Issues: -Protections -Voltage and frequency regulation -Load management -Power generation dispatch -Generation and load forecasting -Islanded operation Aims: -Economical, Secure and Environmentally sustainable operation
- 5. Problem description: microgrids and operational issues
- 6. Problem description: microgrids and operational issues Environmental data optimizer
- 7. Optimization in microgrids Objective function: -production cost and/or C=∑i=1,NDG [ci * Pgi] -environmental impact and/or Equivalent CO2 emissions -technical constraints Losses = ∑j=1,Nbr [Rj Ij] or Voltage drops minimization
- 8. Optimization in microgrids Variables: Pg1, Pg2, ……, PgNDG Pgk
- 9. Heuristic optimization Variables can be: -Too many -Mixed integer A good chance is Objectives can be: heuristic optimization -Multiple -Non linear -Non continuous There may be one or more constraints
- 10. Algorithms for Heuristic optimization - Allow any kind of problem formulation - Require the expert knowledge for faster convergence - Are easy to implement and modify We will see for microgrids optimization: MC_ACOR derived from ACOR NSGAII
- 11. ACO: Ant Colony Optimization "What is it that governs here? What is it that issues orders, foresees the future, elaborates plans and preserves equilibrium?“ (M. Maeterlinck – “The Life of the Ant 1930) A co-ordinated behaviour can be observed in nature so that the system as a whole is able to attain some goals. Such co-ordinated behaviour is unsupervised: -Particle Swarm Optimization [Kennedy, Eberhart 95], birds swarms -Ant Colony Optimization [Dorigo 92], ant colonies
- 12. ACO Ability to identify the shortest path Indirect communication through the pheromone Stigmergy, communication through environment modification
- 13. ACO First used for Traveling Salesman Problem Pheromone information is implemented as a weighted directed graph (matrix) Ants path is constructed step by step (search space is discrete). An intermediate step may be more attractive than another based on pheromone trail intensity and local cost Local search is solution perturbation based on some empirical rule or problem specific knowledge
- 14. ACO for TSP
- 15. ACO Probability to choose one city or another depends on pheromone and cost τandcost Below η is the inverse of cost
- 16. ACO FOR CONTINOUS OPTIMIZATION (ACOR) ACO was created originally for discrete optimization, its extension to continuous domains is the ACOR [Socha, Dorigo 08] . Let’s consider a generic optimization problem as: min f(S) ; f : ℜn → ℜ ; Design variables vector S : S = [ s1, s2, ... , sn ];
- 17. ACO FOR CONTINOUS OPTIMIZATION (ACOR) PROBLEMS: How to implement the solution construction and the probabilistic transition from one state to another? What is pheromone?
- 18. ACO FOR CONTINOUS OPTIMIZATION (ACOR) Step 1: Initialize parameters f(x): Objective function Step 2: Initialize archive xi: Decision Variable For i:=1 To k do N: number of decision variables Randomly generate solution k: number of solution vectors in the archive T ξ: scaling parameter vector Q: elitism parameter Calculate f(x) NI: number of solutions vector generations m: number of ants for each generation Step 3: create new ant Step 4: Update archive(t+1) Choose xi (t) using eqn(9) For j=1 To N Calculate f(bi) bji(t + 1) = xji (t) + gauss(0, σjs) If f(bi) is better than the worst in T then Include bi in archive(t+1) Step 5: check if number of ants m is reached If i=m then go to step6 Step 6: check stopping criteria Else go to step 3 If t=NI then stop else repeat steps 3, 4,5
- 19. ACO FOR CONTINOUS OPTIMIZATION (ACOR) It is based on the construction of an Archive of k solutions. A solution is chosen and all of its parameters are modified using information derived from the archive The pheromone information is in the archive! Each component of the solution vectors in the archive converges to the optimal solution
- 20. ACO FOR CONTINOUS OPTIMIZATION (ACOR) The basic feature of the ACOR is the construction of solutions based on a probabilistic choice, driven by the ‘pheromone’ trace. Each variable of the chosen solution is perturbed by means of a gaussian function centered in the parameter to be perturbed with a standard deviation calculated using the archive of solutions. Iterate 5.Choice of a solution from the archive (better solutions are preferred) 6.Perturbation of all the components considering the information derived from the archive 10.Storage into the Archive if better than the worst solution
- 21. ACO FOR CONTINOUS OPTIMIZATION (ACOR) For the i-th variable, we consider the following probability density function: The vectors standard deviations and weights (σ and ω) are attained from the solutions in the Archive in the following way: ξ and q are algorithm parameters typically in [0÷1].
- 22. ACO FOR CONTINOUS OPTIMIZATION (ACOR) Solutions are chosen using the following probability: The i-th components of the l-th solution is then perturbed using a gaussian function with the following standrad deviation calculated over the archive T: ξ and q are algorithm parameters typically in [0÷1].
- 23. ACOR:from single objective to multiple objectives risK We can’t say that A is better than B, or even that D is better than A. All these solutions are non dominated or A maybe PARETO OPTIMAL. C Comparing C and A we can’t tell which is D better. Comparing C with B or D, we B find that C is ‘worst’. cost 1) The notion of non dominance or PO is given with reference to a set of solutions 2) The solution of a MO problem is linked to the identification of many different solutions
- 24. ACOR:from single objective to multiple objectives Non dominance ordering and ranking of solutions f1 F E A C Rank=2 D B Rank=1 f2 We want low rank uniformly distributed solutions
- 25. ACOR:from single objective to multiple objectives At each iteration, the solution to be perturbed is chosen using one of the criteria (COLONIES) The variables are perturbed The solution is taken if it is not too A dominates B much dominated by other solutions (a probability depending on the amount of domination [Deb et al. 2008] is used for this choice) Solutions from the Archive are ordered for non domination and the best solutions are taken A Simulated Annealing-Based Multiobjective Optimization Algorithm: AMOSA IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 12, NO. 3, JUNE 2008 by S. Bandyopadhyay,S. Saha, U. Maulik, K. Deb
- 26. ACO and ACOR ACO Reference: Ant Colony Optimization: A New Meta Heuristic Dorigo, M.; Di Caro, G. Proc. of IEEE Evolutionary Computation,1999 CEC99 p. 1470-1477 Vol. 2 ACOR Reference: Ant colony optimization for continuous domains Socha, K., and Dorigo, M., 2008 European Journal of Operational Research
- 27. NSGAII Non dominated Sorting GA II: a MO Genetic Algorithm Genetic algorithms: Iterative population based optimization algorithms simulating Darwinian evolution of solutions 1. Parents population initialization 1. Offsprings creation • Selection (RWS, Tournament…) • Crossover • Mutation 3. Parent:= Offspring 4. Best_so_far update
- 28. NSGAII Non dominated Sorting GA II (Deb 2002) It is a Genetic Algorithm, where non domination and crowding are used for solutions ranking and selection. Recombination: Crossover+Mutation Qt+1
- 29. NSGAII Non dominated Sorting GA II (Deb 2000) Reference: A Fast Elitist Multi-Objective Genetic Algorithm: NSGA-II (2000) by Kalyanmoy Deb,Amrit Pratap,Sameer Agarwal,T. Meyarivan IEEE Transactions on Evolutionary Computation Download: http://rick.ucsd.edu/%7Esagarwal/nsga2j.pdf
- 30. The test system: the Island of Lampedusa diesel PV µturbines Fig. 4. Single-line scheme of the MV system supplying the Island of Lampedusa (Italy).
- 31. TEST RESULTS Table III. Data of the 9 DG units connected to the distribution network (m.u. indicates a generic monetary unit). Connection bus and Cost Pmax DG type (m.u./kWh) (kW) 1-diesel 12 11000 7- photovoltaic - 150 10- photovoltaic - 150 20- microturbines 14 50 27- microturbines 14 50 44- microturbines 14 100 46- photovoltaic - 100 52- photovoltaic - 50 58- photovoltaic - 50 63- diesel 12 400
- 32. TEST RESULTS Optimization has been carried out using both algorithms: - With 50 individuals and 100 iterations (NSGAII) - Mutation probability: 0.7 - Crossover probability: 0.7 - With 50 ants and an archive of 50 solutions for 100 iterations (MC ACOR) − ξ:0.6 - q:0.25
- 33. TEST RESULTS: competing objects 105200 6 p.m. 105000 summer day Working day NSGA-II MO ACOR Production Cost [UM] 104800 104600 104400 104200 104000 58 59 60 61 62 63 64 65 66 67 Pow er Losses [kW]
- 34. TEST RESULTS: concurrent objects 0.0126 6 p.m. 0.0124 summer day 0.0122 Working day Voltage drops p.u. 0.012 NSGA-II MO ACOR 0.0118 0.0116 0.0114 0.0112 58 59 60 61 62 63 64 65 66 67 Pow er Losses [kW]
- 35. TEST RESULTS Comparison: Same Complexity (ND Solutions ranking): O(mk2) [m=nr. objectives, k archive size] MC ACOR finds less but better solutions than NSGA II because ACO is intrinsically more elitist than GA
- 36. TEST RESULTS: mathematical test function
- 37. TEST RESULTS 2 0 -25 -20 -15 -10 -5 0 -2 nsgaII MC ACOR -4 4.5 -6 f2 4 3.5 -8 3 -10 2.5 -12 f2 2 NSGA II -14 MC ACOR 1.5 f1 1 0.5 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 f1
- 38. CONCLUSIONS AND FUTURE DEVELOPMENTS The tests carried out show the validity of both approaches for optimized microgrids operations, although MC ACOR is easy to implement and with the same number of objective functions evaluations finds more optimized solutions. Future developments of the present work will include - New formulations with new objectives taking care more specifically of the environmental impact -Work to improve the uniformity of solutions along the output front - Modified approaches to include ‘robustness’ to parametric variations (uncertainty on power production and loads)

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