ant colony search and heuristic techniques for optimal dispatch of energy sources in micro-grids...

Ant colony search and heuristic techniques for optimal dispatch of energy sources in

micro-grids

ELEONORA RIVA SANSEVERINODipartimento di Ingegneria Elettrica Elettronica e delle Telecomunicazioni

Università degli Studi di Palermo

JUNE 19th 2009 - PALERMO

S4 ENVISA "Intelligent Analysis of Environmental Data"

OUTLINE

Problem description: microgrids and operational issues

Optimization in microgrids

Heuristic optimization

Recent solution methods: MC-ACOR and NSGA-II

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


Issues:-Protections-Voltage and frequency regulation-Load management-Power generation dispatch-Generation and load forecasting-Islanded operation

Aims:-Economical, Secure and Environmentally sustainable operation


optimizerEnvironmental data


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


Variables:

Pg1, Pg2, ……, PgNDG

Pgk

Heuristic optimization

Variables can be:

-Too many-Mixed integer

Objectives can be:

-Multiple-Non linear-Non continuous

There may be one or more constraints

A good chance is heuristic optimization

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

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

ACO

Ability to identify the shortest path

Indirect communication through the pheromone

Stigmergy, communication through environment modification

ACO

First used for Traveling Salesman ProblemPheromone 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 costLocal search is solution perturbation based on some empirical rule or problem specific knowledge

ACO for TSP

ACO

andcost

Probability to choose one city or another depends on pheromone and cost

Below is the inverse of cost

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 ];


PROBLEMS:

How to implement the solution construction and

the probabilistic transition from one state to another?

What is pheromone?


Step 1: Initialize parametersf(x): Objective functionxi: Decision VariableN: number of decision variablesk: number of solution vectors in the archive T: scaling parameterQ: elitism parameter NI: number of solutions vector generationsm: number of ants for each generation

Step 2: Initialize archive For i:=1 To k do

Randomly generate solution vectorCalculate f(x)

Step 3: create new antChoose xi (t) using eqn(9)For j=1 To N bj

i(t + 1) = xji (t) + gauss(0, j

s)

Step 4: Update archive(t+1)

Calculate f(bi)If f(bi) is better than the worst in T thenInclude bi in archive(t+1)

Step 6: check stopping criteriaIf t=NI then stop else repeat steps 3, 4,5

Step 5: check if number of ants m is reached If i=m then go to step6 Else go to step 3


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


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.

Iterate1.Choice of a solution from the archive (better solutions are preferred)2.Perturbation of all the components considering the information derived from the archive

3.Storage into the Archive if better than the worst solution

For the i-th variable, we consider the following probability density function:


The vectors standard deviations and weights ( and ) are attained from the solutions in the Archive in the following way:

and q are algorithm parameters typically in [0÷1].

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:

and q are algorithm parameters typically in [0÷1].

ACOR:from single objective to multiple objectives

cost

risK

A

DB

C

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 maybe PARETO OPTIMAL.

Comparing C and A we can’t tell which is better. Comparing C with B or D, we find that C is ‘worst’.

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


f2

f1

A

DB

Non dominance ordering and ranking of solutions

C

F

E

Rank=1

Rank=2

We want low rank uniformly distributed solutions

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 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 dominates B

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

ACO Reference:Ant Colony Optimization: A New Meta HeuristicDorigo, M.; Di Caro, G.Proc. of IEEE Evolutionary Computation,1999 CEC99p. 1470-1477 Vol. 2

ACOR Reference:Ant colony optimization for continuous domains Socha, K., and Dorigo, M., 2008European Journal of Operational Research

ACO and ACOR

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:= Offspring4. Best_so_far update

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.

Qt+1

Recombination: Crossover+Mutation

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

The test system: the Island of Lampedusa

Fig. 4. Single-line scheme of the MV system supplying the Island of Lampedusa (Italy).

diesel

PVturbines

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 DG type

Cost (m.u./kWh)

Pmax

(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

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) :0.6- q:0.25

TEST RESULTS: competing objects

104000

104200

104400

104600

104800

105000

105200

58 59 60 61 62 63 64 65 66 67

Power Losses [kW]

Pro

ducti

on C

ost

[U

M] NSGA-II MO ACOR

6 p.m. summer day

Working day

TEST RESULTS: concurrent objects

0.0112

0.0114

0.0116

0.0118

0.012

0.0122

0.0124

0.0126

58 59 60 61 62 63 64 65 66 67

Power Losses [kW]

Volt

ag

e d

rop

s p

.u.

NSGA-II MO ACOR

6 p.m. summer day

Working day

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 IIbecause ACO is intrinsically more elitist than GA

TEST RESULTS: mathematical test function

TEST RESULTS

-14

-12

-10

-8

-6

-4

-2

0

2

-25 -20 -15 -10 -5 0

f1

f2

nsgaII

MC ACOR

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

f1

f2

NSGA II

MC ACOR

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)

ant colony search and heuristic techniques for optimal dispatch of energy sources in micro-grids...

Technology

microgrids optimization

discrete optimization

generic optimization

continous optimization

continous optimization

microgrids variables

solution construction

chosen solution