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

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

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

Problem description: microgrids and operational issues

Problem description: microgrids and operational issues
Environmental data optimizer

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

Optimization in microgrids
Variables:
Pg1, Pg2, ……, PgNDG
Pgk

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

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 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

ACO for TSP

ACO
Probability to choose one city or
another depends on pheromone
and cost
τandcost
Below η 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 ];

ACO FOR CONTINOUS OPTIMIZATION (ACOR)
PROBLEMS:
How to implement the solution construction and
the probabilistic transition from one state to another?
What is pheromone?

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

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

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

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].

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].

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

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

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

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

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

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

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

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

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

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]

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]

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

TEST RESULTS: mathematical test function

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

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)