Hybrid Ant Colony Robust Genetic Algorithm for Optimal Placement of

Renewable Distributed Generation and Storage units in Distribution

Networks

VASCO SANTOS1,2, EDUARDO GOUVEIA1,2

1CISeD – Research Centre in Digital Services, Polytechnic Institute of Viseu, PORTUGAL

2Electrical Engineering Department, Polytechnic Institute of Viseu, 3504-510 Viseu, PORTUGAL

Abstract: This paper presents a multi-objective algorithm to support sizing and placement of Renewable Distributed

Generation with storage units (RDG&S) in radial distribution networks. Two objectives are considered in the model,

the first one is focused in the minimization of the RDG&S units capital costs and the second one in the minimization

of system losses.

This approach uses a hybrid Ant Colony Genetic Algorithm (ACGA) divided in two steps. At the first step of the

approach an Ant Colony (AC) acts to face with the uncertainty of the problem and to deal with instabilities of the

initial data. This way a good Pareto front, which is used to feed the initial population of da Genetic Algorithm (GA).

At the second step, an Elitist Robust Genetic Algorithm with a secondary population is used, to characterize the non-

dominated Pareto Optimal Frontier. In this algorithm the concept of robustness is operationalized in the computation

of the fitness value assigned to solutions. The results presented in this approach demonstrates the real capabilities of

the proposed algorithm to generate a well-spread and more robust effective non-dominated Pareto Optimal Frontier.

Key-Words: Renewable Distributed Generation, Storage units, Ant Colony optimization, Genetic Algorithms,

Distribution Networks.

Received: June 9, 2021. Revised: June 7, 2022. Accepted: July 2, 2022. Published: July 22, 2022.

1 Introduction

Energy resources in our modern world are running out

very fast, so it is urgent that we find new ways of

generating electricity, which is self-sustaining, easy to

manage and has high efficiency [1]. In this context

DG technologies appear as the natural substitute of

electric generation focused on centralized plants

mitigating many problems, such as the high level of

dependence on imported fossil fuels, the

environmental impact of high concentrations of

greenhouse gases and other pollutants, electric

network transmission losses and the necessity for

continuous upgrading of transmission and distribution

facilities [1, 2]. Using DG, smaller amounts of energy

are produced by, modular energy conversion units,

which are often located close to electricity consumers

avoiding transmission power losses. The development

of new-generation technologies and power electronics

are the key issues that have attracted many investors.

Despite these advantages many issues are however,

still pending concerning the integration of DGs within

the existing power system networks; that require

special attention [3, 4]. Specifically the way how their

integration have changed the system from passive to

active networks and the change with serious impact

on both the reliability and operation of the network as

a whole [2]. In addition to this situation is the non-

optimal placement of DG, which can result in an

increase in the system power losses with consequence

in the voltage profile [5]. However when DG is

strategically sized and placed in the network it can

reduce transmission and distribution losses, fossil fuel

emissions, reduce capital costs and improve

distribution energy quality and security [5, 6].

The DG placement problem has therefore attracted the

interest of many research in the last decade [7], since

it can provide useful input for the derivation of

incentives and regulatory measures for some market

players, DSOs, regulators, and policy makers. This

requires that the models used for planning the future

architecture of electricity systems recognise that high

levels of DG penetration in the distribution network

can no longer be considered as a passive appendage to

the transmission network. The entire system has to be

redesigned and operated in an integrated manner. In

addition, this operation of increased complexity must

be carried out by a system under multiple

management agents and market players.

Many mathematical approaches, such as nonlinear

programming, quadratic programming and linear

programming, have been used solve placement and

sizing of DG problems [2, 5]. Unfortunately, this kind

of problem is a highly nonlinear and a multimodal

optimization problem. Therefore, conventional

optimization methods that makes use of derivatives

and gradients, in general, are not able to locate or

identify the “Optimal solution”.

The best way to deal with the problem of locating and

sizing DG units in a distribution network are usually

stated as multi-objective planning problems. In fact,

most of the real world problems have multiple,

conflicting and incommensurate evaluation aspects so

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if we want to assess good solutions that relate

investment costs vs. power losses it is usual to benefit

one objective and worse another. Multi-objective

models have the capability to better reflect reality,

incorporating objectives of distinct nature that are

weighed by decision-makers (DM) and planning

engineers to select good compromise solutions having

in mind their practical implementation. These models

enable to work with the conflicting nature of the

objectives and the trade-offs in a way to identify

satisfactory compromise solutions providing non-

dominated solutions eliminating most of the

difficulties associated to classical methods [8, 9].

To meet the increasing demands in the design of real

world multi-objective problems, many evolutionary

algorithms, PSO, Genetic Algorithms, Tabu-search,

Ant colony and many others have been used. As can

be see some algorithms are used successfully to mimic

the corresponding natural, or physical, or social

phenomena such as the ant colony optimization [10-

11]. Ant colony optimization (ACO) is a

metaheuristic inspired by the shortest path searching

behaviour of ant colonies in their working day trails.

Since the first usage of this algorithm researchers have

designed ACO algorithms to deal with multi-objective

problems in a way to have a set of solutions that

satisfy both convergence and diversity criteria [11-

12].

The mathematical model proposed in this paper

involves discrete and continuous variables as well as

nonlinear constraints, related to power flow equations.

Therefore, due to the presence of multiple objective

functions, non-linear relations, and its combinatorial

nature the model is hard to solve using classic

mathematical programming algorithms [3, 4].

Therefore, a hybrid Ant Colony algorithm associated

to a Genetic Algorithm has been used to solve the

problem of optimal placement and sizing of RDG&S

units in radial distributed networks where two

objective functions are considered: minimizing

installation costs and minimizing system losses. The

AC uses two colonies to guarantee more diversity.

Associated to the GA an elitist strategy has been

implemented aimed at increasing the performance,

both accelerating the convergence speed towards the

non-dominated frontier and ensuring that the solutions

attained are indeed non-dominated ones and are well-

spread over the frontier. In order to influence the

iterative process and obtain more robust solutions, a

robustness concept is embedded in the fitness with a

non-dominance test [9]. At each non-dominance front,

the more robust solutions are more likely to bring their

contribution to future ant colony generations. This

was the way found to deal with the uncertainty that

surrounds real problems. The greatest motivation and

contribution of this work, shows that this way of

implementing a hybrid ACGA increases both,

performance and convergence speed towards non-

dominated and well-spread solutions, when compared

with other approaches.

In this section the motivation around the problem and

it’s interest for the future networks has been provided.

The problem formulation is presented in section 2. In

section 3, the developed ACGA is presented and

computed solutions obtained are analysed. Section 4

reports results of a case study. Finally, some

conclusions are drawn in section 5.

2 Problem Formulation

The following formulation illustrates the effect of

RDG&S units, on the load demand of radial

distribution network. Here DG technologies are

automatically associated to storage unites (usually

Lithium batteries) to overcome some operational

problems like variability of the renewable resource. In

radial networks, bus voltage decreases as the distance

from the distribution transformer increases, and may

become lower than the minimum voltage allowed by

the utility. Utilities usually solve this problem by

upgrading facilities, increasing the tap ratio of the

distribution transformer, and/or by switching on the

shunt capacitors and reinforcing distributions lines. By

providing a portion of energy on site, RDG&S units

reduce branch current, which in turns leads to the

reduction of power losses and increasing voltage

throughout the feeder.

The proposed approach deals with the location and

sizing of RDG&S units in order to obtain the benefits

associated with lower power loss and lower investment

costs of installation of RDG&S units [9].

Hence, it can be formulated as the following

optimization problem:

   







s.t.

The MO problem is a constrained non-linear

optimization problem with mixed variables (due to the

presence of modular sizes of DG units).

Technology Installation Costs

For installation cost minimization is given by:

   





 (1)

min l

l n m

nm V

r



lnmy

i,,,1 





Vnm MIN

lVnm

lVnm MAX

l,m,n,l

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where Ci represents the installation cost of the RDG&S

unit i with a certain nominal power (kW), installed on

bus l (from the derived feeder n of the main feeder m).

xli nm are the binary decision variables, that defines if a

RDG&S unit (i), is installed.

Active Power System Losses

This objective minimizes the real power losses arising

from line branches.

(2)

where, rlnm is the ohm value of bus l (from the derived

feeder n of the main feeder m), and Plnm and Qlnm are

the corresponding active and reactive power flow.

Constraints

In addition to the constraints of physical nature related

to the load flow equations some other constraints were

considered:

- at most only one kind of defined (RDG&S unit) can be

placed in each bus (avoiding multiple installations).

- related with quality of service, regarding the upper and

lower limit imposed by legislation, 󰇟

󰇟

󰇠,

of voltage in each bus .

- what kind of (RDG&S unit) can be placed in each bus

(pre-defined by local characteristics, son, wind,…).

where 

 is a binary coefficient, if it assumes the

value 0 it means that a specific RDG&S unit cannot be

install in bus l. If the value is 1 it means that the

technology i can be installed at bus l.

3 Proposed Algorithm

This section presents a new hybrid algorithm for

solving the problem of placement and sizing RDG&S

units in distribution networks. The algorithm

optimizes two objective functions; minimizing costs of

installation of RDG&S units and the network losses.

The flowchart of the proposed algorithm is illustrated

in Fig 1.

Fig. 1: The Flowchart of the proposed hybrid

algorithm

The proposed algorithm integrates the merits of both

Ant Colony Optimizations (ACO) [11] and GA [9] and

by enhancing ACO through GA, a strong and robust

algorithm was created. The main steps of the proposed

algorithm are:

1: Colonies. In a multi-objective optimization

problem, because of incommensurability and

confliction among objectives functions need to be

optimized simultaneously. This step starts with the

definition of the number of colonies F with its own

pheromone structure, where F represents the number

of objectives to optimize, in this case F=[f1, f2].

2: Initialization. This step begins with the

initialization of pheromones trails, where a given value

β0α is attributed, known as the pheromone information

in the current iteration, α=(1, 2) assumes the objectives

to optimize. At this stage the Pareto set are initialized

as empty. To know the ant pheromone concentration

min l

l n m

nm V

r



lnmy

i,,,1 





Vnm MIN

lVnm

lVnm MAX

l,m,n,l

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of each path a multi-pheromone ant colony

optimization was implemented to this problem, which

requires a representation of n variables for each ant,

where each variable i has a set of ni options (bus) with

their values lij, where i=1, 2, …, n) and j=1, 2, …, ni)

generating a fully connected graph with the detailed

information about their associated pheromone

concentrations. The process starts by generating x

ants’ position from the population (solutions), these

are generated randomly, meaning that each ant y, y



{1,2, …, x} has a position with a selected value for

each variable according to the associated pheromone

with this value. This process is repeated for each

objective. Consequently the path of each ant represents

the bus and its respective value.

3: Evaluation. The Ant Colony optimization is

parameterized by the number of ant colonies and the

number of associated pheromone structures. For a

matter of consistency of results, all the colonies have

the same number of ants. Each colony tries to optimize

an objective considering the pheromone information

associated to it´s own colony, where each colony is

determined knowing only the relevant part of a

solution. This methodology guaranties that all colonies

search in different regions of the non-dominated front,

creating more diversity of solutions.

4: Trail Update. At the moment that pheromone trails

are updated, a decision has to be made on which of the

constructed solutions laying pheromone to choose.

The quantity of pheromone left behind represents the

past experience of the colony with respect to a chosen

passage. Then, at each sequence every ant constructs a

solution, and pheromone trails are updated.

After all ants have constructed their solutions,

pheromone trails are updated as can be followed by

two steps:

- Step 1, to prevent premature convergence, pheromone

trails are reduced by a constant factor to simulate

evaporation;

- Step 2, in a way to reinforce good solutions, some

pheromone are laid on components of the best

solution. Changing pheromone concentration

associated with each possible route (variable value).

5: Solution Construction. When the pheromone is

updated after one iteration, the next iteration will begin

with the modification of the ants’ paths (this means

with the variable values) in a manner, that respects

pheromone concentration and some heuristic

preference. For each ant and for each dimension new

candidates construct a new group that replaces the

older one. In other words in each colony an ant

changes the value for each variable according to the

transition probability expressed in the following

equation.



󰇛󰇜













󰇛󰇜



󰇛󰇜





Where, pαij(t) is the Probability that option lij is chosen

by ant y for variable i at iteration t.

6: Archived Solutions. The set of non-dominated and

a few dominated solutions are stored in an archive.

During the optimization search, the set of solutions is

updated. At each iteration, the current solutions

obtained are compared to those stored in a Pareto

“ideal” archive; all dominated solutions within a

predefined radius  of domination (a set of about 10%

of the generated solutions)and the non-dominated

ones are added to the set.

7: Genetic Algorithm. An elitist robust GA algorithm

is implemented to use the archived solutions obtained

from the Ant colony optimization. This elitist strategy

ensures, the solutions are indeed non-dominated and

are well spread over the frontier. This strategy uses a

secondary population where each individual (solution)

are only feasible non-dominated solutions.

In order to force the GA process towards more robust

solutions, the degree of robustness in the variable

space was embedded in the fitness.

The details of the GA are shown below.

Genetic Algorithm used

Initialize population P0 (generate the initial population satisfying the problem constraints with NP0 solutions,

resulted from step 6 of the Ant colony algorithm)

Evaluate P0 with real fitness (Compute the fitness of each individual in P0)

Determine PS (initial secondary population obtained from P0)

If NPS > NP0 then

PS = P0 (Copy all solutions from P0 to PS)

Else

ShP0 (Apply sharing mechanism to P0 to select NPS solutions)

Update Population: P(iter) = PS

For Iter=1 to iterMax) (maximum number of iterations is attained)

Begin

Build P(iter+1) (the next generation of NP0 solutions)

Apply elitism: P(iter+1) = E (introduce E solutions from PS in P(iter+1))

Repeat

Selection: ST2 (Select 2 individuals ST4 from P(iter) by tournament)

Crossover and Mutation: GO2 (Apply genetic operators to 2 individuals selected above ST2)

P(iter+1) = GO2

Until (NP(iter+1)



NP0)

Evaluate P(iter+1) with real fitness (Compute the fitness of each individual in P(iter+1))

Determine NPscand (solutions that are candidate to belong to PS)

Update PS(iter+1)

If NPS ≥ NPscand then

PS(iter+1) = NPscand (Copy all NPscand solutions to PS)

Else

ShNPscand (Apply sharing mechanism to all NPscand solutions)

Update Population: P(iter+2) = P(iter+1)

End For

This procedure aims at finding a good compromise

among the different non-dominated solutions for

sizing and sitting of RDG&S units, The goal is to

provide the DM with dedicated information about the

a set of non-dominated solutions and the underlying

trade-offs, which could be used to support the choice

of a satisfactory compromise plan of investment.

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4 Case Study

The methodology described in section 3 to

characterize the optimal Pareto front, and provide

decision support in the multi-objective model

presented in section 4, has been applied to a

distribution network with 86 nodes and 16 lateral

feeders.

Five types of RDG&S units are considered for possible

installation, as in table 1.

Table 1. RDG&S units considered for instalation

RDG&S unit

type

RDG Technology and storage unit

Installed capacity

(kW)

Fotovoltaics + 100kWh Li-ion Bat.

250

Cogeneration (Biomass)

500

Wind Turbine + 20kWh Li-ion Bat.

100

Fotovoltaics + 50kWh Li-ion Bat.

150

Wind Turbine + 100kWh Li-ion Bat.

250

The characteristics of this approach enables the DM to

preform experiments adjusting different sets of

parameter, throughout the process.

The initial parameters used are:

 Initial population size NA (number of Ants) of each Ant

Colony and NP (solutions of the pareto front result from da AC optimization

that will be the initial populations for the GA);

 Set value parameters α, β0α, x, y, i , j and 

󰇛󰇜;

 Set the secondary population size NPS of the GA;

 Set the number of elite individuals E introduced in the

main population of the GA;

 Set the number of generations, Mutation probability

mp and Crossover probability cp.

In Fig. 2, we can see the initial population and the

Pareto front of final population obtained by this hybrid

algorithm. As can be seen the initial population is very

disperse because it is generated randomly. The Pareto

front obtained is the result of the adjustments made to

the algorithm parameters.

Fig. 2: Initial populations and Final population

Fig. 3, shows the Pareto front of the population

evolution at the first stage of the algorithm. Here it’s

possible to verify that the population resulted from the

two colonies (Final Populations AC1 and Final

Populations AC1 ) of the AC algorithm present

nominated and non-dominated solutions in the well-

defined Pareto fronts. When at the second stage, the

GA is applied to these solutions AC1 and AC1 )), the

final very well defined Pareto front with more robust

non-dominated solutions.

Fig. 3: Evolution of the solutions after the ACO and

final front of the GA.

In Table 3 are presented the values of the losses

experienced by the network before the installation of

RDG&S units, for a chosen load scenario.

Table 3. Initial losses of the considered

network

Active losses (kW)

Reactive losses (kVAr)

903,21

1211,30

Final population AC1

x Final population AC2

 Final population (Final pareto front)

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Fig. 4: Final population with 40 solutions

Fig. 4 displays the Pareto front, in the objective

function space (objective function system losses and

installation costs). Since the algorithm has embedded

the robustness concept, the DM has the guarantee that

all solution in the pareto front are very robust

solutions. So this set of solutions on the non-

dominated frontier is used by the DM as the input to

select a final compromise solution with the smallest

uncertainty.

For example, if the DM considers the solutions

identified with the red color in Fig. 4 as good

compromise plans according to the two conflicting

objectives, the results are illustrated in Fig. 5 and 6.

Fig. 5: Instalation costs (103 €) from solutions 2, 3, 20,

22 and 40 marked by the DM.

Fig. 6: Sytem active power losses (kW) from solutions

2, 3, 20, 22 and 40 marked by the DM.

As can be seen in table 5 there is a real reduction of the

active power losses in the network comparing with the

initial situation (before any equipment is installed).

Table 5. Reduction of losses in persentage compared

with the initial condition (without RDG&S units

instaled)

Solution

Active losses

reduction (%)

80,1

98,9

93,1

87,3

99,2

If solution 20 is the chosen one, table 6, shows the

buses where the DG units would be installed.

Table 6. Installed DG in network buses (solution 20).

Bus

14 17 30 23 48 51 54 55 57 58 61 71 73 76 82 83

Type of

RDG&S

unit

installed

3 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1

5 Conclusion

In this paper, the problem of location and sizing of

RDG&S units in distributed networks has been

modeled as a multi-objective problem. Two objective

functions of technical and economical nature are

considered in the model: minimization of total power

losses and minimization of RDG&S unit installation

costs.

The algorithm developed is based on a Hybrid ACGA,

characterizing the optimal Pareto frontier that

represents a set of distributed solutions, which can be

chosen by the DM for practical implementation.

Firstly, aaccording to a set of predefined parameters a

defined number of solutions are generated randomly,

creating two AC. Secondly, an AC algorithm is

applied aimed to deal with the uncertainty and

instabilities of the problem, as a final result we have

strong solutions, which are used to feed the initial

population of da GA. The GA uses an Elitist Robust

Algorithm with a secondary population, to

characterize the non-dominated Pareto Optimal

Frontier. In this algorithm the concept of robustness is

operationalized in the computation of the fitness value

assigned to solutions.

The use of the Ant colony optimization shows its

importance designing effective combinatorial

optimization solutions, and when its combined with

the GA shows that his algorithm is aimed to obtain the

input information (obtained from the output of the

robust Algorithm) necessary to develop a decision

support system. As can be seen in the case study this

decision support system may be integrated in radial

distribution networks, generating very good results. To

summarize we can say that using this kind of approach

we can obtain better performance and more robust

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Volume 17, 2022

solutions using less computing resources. This was a

reality using radial distribution networks, our intention

is to test and adjust this algorithm for more complex

networks using multiple voltage stages and integrating

smart grids.

References:

[1] European Commission, Energy research. Available

online http://europa.eu.int.

[2] Jenkins N., Allan R., Crossley P., Kirschen D.,

Strbac G., “Embedded Generation”, IEEE –

Power and Energy Series 31, 2000.

[3] V. Santos, "A Robust Genetic Algorithm for Sizing

and Placement of Distributed Generation,

Capacitors and Automatic Reclosers in Radial

Distribution Networks", WSEAS Transactions on

Power System, ISSN: 1790-5117, ISBN: 978-960-

474-392-6, pg. 132-139, November 2014.

[4] Deb K., “Multi-Objective Optimization using

Evolutionary Algorithms”, Wiley, 2001.

[5] Hung, D.Q., Mithulananthan, N., “Multiple

distributed generators placement in primary

distribution networks for loss reduction”, IEEE

Trans. Ind. Elect. 60(4):1700-1708, 2013.

[6] Ochoa, L.F., Harrison, G.P., “Minimizing Energy

Losses: Optimal Accommodation and Smart

Operation of Renewable Distributed Generation”,

IEEE Trans. Power Syst., 2011.

[7] Aseem Chandel, D.S. Chauhan, D. Singh.,

“Enriched Technique for DG Placement and

Sizing by GA Optimization”, American-Eurasian

Journal of Scientific Research 12 (5): 260-270,

2017.

[8] Barrico, C. e Antunes, C.H. (2007), “An

Evolutionary Approach for Assessing the Degree

of Robustness of Solutions to Multi-objective

Models”, Studies in Computational Intelligence

(SCI) 51, p. 565-582, Springer, 2007.

[9] Santos V., “Uma Abordagem Multi-objetivo para a

Inclusão de geração Dispersa no Planeamento da

expansão da Produção de Energia Eléctrica”, Ph.D

Dissertation, FCTUC Coimbra Universaty, 2011.

[10] Moradi, M.H., Abedini M., “A combination of

genetic algorithm and particle swarm optimization

for optimal DG location and sizing in distribution

systems”, Int. J. Electr. Power Energy Syst.,

34(1):66-74, 2012.

[11] Abd Allah A. Mousa, “Hybrid ant optimization

system for multiobjective economic emission load

dispatch problem under fuzziness”, Elsevier,

Swarm and Evolutionary Computation 18 (2014).

[12] Sirote Khunkitti, et al, “A Hybrid DA-PSO

Optimization Algorithm for Multiobjective

Optimal Power Flow Problems”, MDPI, Energies

2018.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

This work is funded by National Funds through the FCT -

Foundation for Science and Technology, I.P., within the

scope of the project Refª UIDB/05583/2020. Furthermore,

we would like to thank the Research Centre in Digital

Services (CISeD) and the Polytechnic of Viseu for their

support.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the Creative

Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en_

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