Power Flow Optimization with Energy Storage - Sal Island Case Study

DENIS SANTOS1,2, VASCO SANTOS2,3

1Claranet - Digital Competence Center,

Polytechnic Institute of Viseu,

Campus Politécnico, 3504-510 Viseu,

PORTUGAL

2Electrical Engineering Department,

Polytechnic Institute of Viseu,

Campus Politécnico, 3504-510 Viseu,

PORTUGAL

3CISeD – Research Centre in Digital Services,

Polytechnic Institute of Viseu,

Campus Politécnico, 3504-510 Viseu,

PORTUGAL

Abstract: - The correlation between energy costs and the country's economic competitiveness is an

unquestionable reality also responsible for the improvement of the population's life conditions. In the past Cape

Verdean electric power system (EPS), expansion was based on fossil-fuel power plants, nowadays it shifted to

renewable energy (RE) which is abundant in the Cape Verde archipelago. However, no reduction in the

electricity tariffs occurred, due to renewable curtailment and other pendent questions related to power

transmission losses in the EPS.

This paper presents an approach, that supports an implementation of a distributed electric energy storage

system (ESS) on the Sal Island of Cape Verde archipelago, as a solution to increase the RE integration and

power Transmission congestion relief. Thus, a power flow optimization is only achievable by storing excess RE

as near as possible to consumption buses that can reduce overall transmission losses. The most advantageous

allocation of ESSs along the EPS buses is combinational which faces a maximization of transmission loss

reduction and minimization of ESS investment capital. The proposed tool to manage the “trade-off” between

cost and avoided losses, is based on a genetic algorithm (GA) that is broadly applied to multi-objective

problems like this.

Key-Words: - Distributed Generation, Power Flow, Renewable Energy, Curtailment, Genetic Algorithms,

Energy Storage.

Received: September 12, 2022. Revised: September 2, 2023. Accepted: Ocotber 7, 2023. Published: November 8, 2023.

1 Introduction

The EPS of Sal Island is this paper’s case study

object because it is one of the most expanding

energy systems in the archipelago which also was

followed by a growth of power transmission losses.

Furthermore, a large portion of wind energy

available in the island’s Wind Power Plant is

curtailed since the peak consumption that usually

doesn’t match with the existing Wind Power Plant

peak production, which is unfeasible because the

Diesel Power Plant minimum production must

represent at least 50% of the production mix to

ensure grid stability and spinning reserve.

Electricity production costs on the island depended

on the fossil fuel importation costs, which had led to

high susceptibility and dependence on international

events. After an increase of 30% in energy costs

from 2005 to 2009, following Brent’s increasing

price, the government initiated a baseline plan for

RE in Cape Verde, to obtain Sustainable Energy

from an economic and environmental point of view.

To solve this situation a Solar Power Plant and

Wind Power Plant were installed on the island and

began operating, increasing endogenous production

as defined in a document titled “Plano de Energias

Renováveis de Cabo Verde-2011”, [1].

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When the RE power plants started operating Sal´s

EPS began to have some stability problems and

couldn’t absorb all ER produced, which is why

curtailment started to assume values above 40%,

that’s why this papers case study is focused on the

use of ESS to improve RE integration. At the same

periods of consumption present in the load diagram,

ESS helps reduce power flow between generation

buses and load buses, by providing energy

discharging next to the consumption distribution

buses.

Some advantages of the ESS implementation on the

island are not accounted in this paper, which is

stated as follows:

• Electrical network Investment Deferral (Cables

and transformers);

• Better use of land disposable to RE plant´s

operation;

• Improving RE plants life cycle and producing

energy.

Typically the companies responsible for the sizing

and location of ESS on the grid, do not take into

account reduction in power losses, they usually

locate da ESS nearby the RE source (Wind Power

Plants or Solar Power Plants) or near consumption

as an efficient way of storing energy, but some

researchers look to the grid as an all, trying to

allocate the best size ESS units that guarantee

technical and economic stability of the grid. As

examples we can see the following two articles:

The authors in, [2], have shown that a multi-

objective multiverse optimization method

(MOMVO) is used as a solution tool for optimal

allocation and sizing of ESS in Power Grids to

improve the voltage profiles and minimize the

annual costs, as result a Pareto optimal solution set

is minimized under economic concerns and cost

sensitivity to provide a decision-support for the

utilities. In, [3], is proposed a three multi-objective

algorithms of particle swarm optimization (PSO),

variable constants (VCPSO) and genetic algorithm

(GA), the main objectives of this solution tool are to

detect the optimum size and location of multiple

ESS aiming to reduce active power loss and

improve bus voltage deviations in the distribution

networks.

In this context, this paper presents an approach,

that supports an implementation of a distributed

electric energy storage system (ESS) on the Sal

Island of Cape Verde archipelago, as a solution to

increase the RE integration and power transmission

congestion relief. Thus, a power flow optimization

is only achievable by storing excess RE as near as

possible to consumption buses that can reduce

overall transmission losses. The most advantageous

allocation of ESSs, and selecting their best size

capacity along the EPS buses is combinational

which faces a maximization of achieved

transmission loss reduction and minimization of

ESS investment capital. The mathematical model

herein proposed involves both discrete and

continuous variables as well as nonlinear

constraints, namely 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 mathematical

programming algorithms. This was the motivation

to resort to GAs to compute non-dominated

solutions to the model developed, [4], [5].

2 Sal Island EPS Characterization

Sal Island is located on the Northeast of the

archipelago, with a total area of 220km2. There is

approximately 30.000 inhabitants, distributed along

the four places (Espargos - main local residential

and administrative city, Santa Maria - touristic

center, Palmeira - port and fishing town, Pedra

Lume -fishing village). The electricity needs of Sal

Island is approximately 72GWh per year. This

amount of electricity is provided in 67,4% by the

Diesel Power Plant of Palmeira town and

Wind/Solar Power Plants that represent 27% and

5,6% of the energetic matrix respectively), [6].

Electra a state owned company is the EPS

concessionary, that operates Palmeira´s Diesel

Power Plant whit 12MW of installed power capacity

to provide energy security and required a spinning

reserve to absorb RE intermittency. The

concessionary also operates a Wind Power Plant

with an installed capacity of 3x1,6MW. As

concluded in a RE assessment, it was strategic to

construct a 2,5MW Solar Power Plant on Sal Island

in a strategic place reserved by law as a Renewable

Energy Development Zone (ZDER), [1], [7].

Electra follows energy sector directives defined

by the local State Agency for Energy, which

currently encourages the entry of private initiative

on the EPS, while seeking to solve Electra´s poor

financial performance, caused by elevated technical

and commercial losses and slow technologic

transition influenced by fuel oil (180 to 380 heavy

fuel) volatile prices.

The electricity price is regulated by the

Economic Regulation Agency (ERA), which is

responsible for balancing the interests of consumers

and producers, [8], [9].

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Fig. 1: Yearly wind availability and statistics on Sal

Island, 2018.

The Islands plan morphology concedes a low

spatial variance of wind availability, but still land-

use is environmentally concerning and restricted by

the aeronautic hub. As shown in Figure 1, wind

temporal availability is constant, having a small

seasonal sag from June to November, studies

suggest 2700 equivalent full load hours, [10]. The

highest wind availability is registered between 6PM-

7AM night-time period.

Sal Island´s Wind Power Plant is operated by

Caboéolica a company formed from a public-private

partnership. The energy is bought by Electra at a

cost of 0,14€/kWh in a “take or pay “signed

contract, [11].

Sal Island electricity consumption doesn´t vary

much over a year period, due to a diversification and

expanding tourist market activity, which is levelling

the Island’s energy consumption and due to a very

stable weather factor.

3 Overview of Storage Technologies

The main technologies to store electric energy are

based on converting it into a storable type of energy

(mechanical, thermal, electrochemical), so it can be

used later using a mechanism to reconvert it back on

electricity. The main characteristics that define the

best sights and strategies where a specific type of

ESS can be applied in EPS are: specific

power/energy, volume/density, charge/discharge

rate and life cycle, [8], [12], [13].

Mechanical storage like Reverse Pumping,

Flywheel or Compressed Air Energy Storage

(CAES), is based on converting electric energy into

gravity potential, rotational inertial or elastic

potential energy, respectively, [14]. CAES and

Reversed Pumping are more profitable on large

scale Power solutions where large quantities of

energy can be stored and used for a long period of

time, usually these technologies have geological and

geographic installation restrictions. Flywheels are

more intended for fast power response, commonly

used for energy quality, which is very useful for

stabilizing the start-up of RES.

Electricity can also be stored in an electrostatic

filed between two plates inside a double layer

capacitor (Super Capacitors) or in a magnetic field

in a cryogenically cooled super conducting coil

(SMES-Superconducting magnetic energy storage),

[15]. These two Electric storage technologies are

used in EPS when a huge amount of power is

needed in a very short time period, often used in

research facilities or to compensate large industrial

machinery voltage fluctuation caused by their

operation (ex: cranes, arc forge, etc.).

Thermal energy storage can be done in

cryogenics or heat which are typically associated to

three types of technologies depending on the heated

material, defined as: Sensible Heat, increases

temperature of a mass; Latent Heat, storage takes

advantage of the energy absorbed or released during

a phase change and thermochemical energy storage,

uses the heat absorption of a chemical reaction.

Practical applications of Cryogenics EES are

achieved by liquefying air or cooling water, [16].

Thermal ESS is usually cost-effective when

employed directly on HVAC or when energy is very

cheap like in electricity from nuclear Power Plants

or from RES surplus energy, [17].

Electricity is stored electrochemically in

Batteries whatever their chemistry (aqueous, no

aqueous, Li or Na-based) within the electrode

structure through charge transfer reactions

(oxidation-reduction), [18], [19]. In Other way, Fuel

Cells, store energy in the reactants that are

externally fed to the cells during the discharge

process, [20], [21]. Both of these differ from redox-

flow cells, which store energy in the redox species

that are circulating in a closed circuit through an

electrochemical cell, [20], [22].

Based on this description, different ESS can be

applied to the EPS to improve its operational

parameters caused by the variability of loads and

RES. So according to their characteristics some

technologies are used in:

 Power quality - provides electrical service to

EPS during oscillations or disruptions to the

waveform such as swells/sags, spikes, or

harmonics;

 Power bridge – ESS discharge in a short period

of time while the main source (thermic, hydro

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or nuclear) is rising up or being set in grid

synchronization;

 Energy Management - curtailed price of excess

energy produced at night can be used during

peak demand periods during the day time. This

allows arbitraging the production price of the

two periods and a more uniform/leveled load

factor as exemplified in Figure 2.

Fig. 2: Energy management is done by ESS; A)

peak shaving and B) load leveling.

The ESS technology most used in islands EPS

the size of Sal Island are ESS using lithium

batteries.

Some examples of this kind of implementations, are:

 Canary archipelago - Grand Canary island,

1MW/3MW lithium-ion ESS, [23];

 Azores archipelago – Graciosa Island

7,4MWh/3,2MW lithium oxide titanium

ESS, [24].

In these examples typically to level a 2-hour

peak consumption the ESS size is suited in an

energy/power ratio of 2:1 and the charging is done

at night-time to avoid an increase on power flow

that results from the most abundant renewable

power excess period. Figure 3 presents an ESS

container topology based on lithium-ion batteries.

Fig. 3: Energy Storage System based on a container

string 9 strings 15 modules each, 700V 90Ah whit

63kWh.

Lithium battery ESS are used in these situations

because they have high reliability and low

maintenance and exploitation costs compared with

other batteries (Lead-Acid, NAS Flow, Zinc Air),

they have a bigger life cycle, specific power and

energy (including density), which makes them a

very interesting solution for island located

installations with low technologic Know-how.

4 Multi-objective Problem Optimization

The problem of finding the optimum location and

sizing ESS distributed along the EPS can be stated

as a multi-objective planning problem. In fact the

solution space is large, combinational, and nonlinear

where the fitness of each solution is analyzed to

guarantee that only strong solutions prevail, [25]. A

multi-objective method handles on a Pareto Front

(PF) display where it has the capability to give a

better understanding to the decision-makers (DM)

for selecting good compromise solutions having in

mind their economic and technical implementation.

The PF, in our case study, is a frontier in the

solution space where non-dominated solutions have

the best trade-off between investment cost and

avoided power losses.

Multi-objective problems (MOP) optimization

relies on three classes of methods: enumerative,

deterministic, and stochastic, [26]. The stochastic

methods such as GA have a great computational

performance and accessible implementation. It is a

bio-inspired method, also called an evolutionary

algorithm because its principles are based on

evolutionary theory like cross-over, mutation and

selection, which can be determinants of the survival

of the more fit individuals in the next generation.

Genetic Algorithms basic concepts

Gene - each variable in the solution is designated as

a gene usually coded in a binary, decimal, or grey;

for easier data manipulation, [27].

Chromosome - an array of genes that represents a

solution also designated as an individuum; the

position in the array identifies the variable, [28].

Non-dominance - a non-dominated solution is

defined as not having a solution with a better

performance to optimize the problem. As illustrated

in Figure 4.

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Fig. 4: Example of the dominance concept, used to

define an individuum’s fitness, on an AG

implementation, [29].

Population – is formed as an array of chromosomes,

each genetic operator along it´s

iterations/generations creates a new population.

There are special populations like the initial (P0) that

is created randomly, and the secondary population

(PS) used as an auxiliary place to save non-

dominated solutions (Piter - P.iteration and Pcand -

P.candidate).

Mutation - genetic operator, that depending on the

mutation probability changes a non-dominated

variable randomly. It is correlated to population

diversification but in high probability can decrease

convergence, [29].

Crossover – is the combination between two fit

solutions, creating a descendant that saves partially

a portion of the genes of the two progenitors. The

genes distribution in the new progenitor solution can

be done according one-point, two-point splitting or

another pattern. Crossover type and probability

shape final population convergence performance,

[26], [29], [30].

Elitism - highest performance solutions are subject

to elitism, which prevent them from passing through

other genetic operators (cross-over, mutation,

selection) shielding them from possible degradation.

High elite array increases population stagnation and

can lead to local optimization solutions, [31].

Selection – to select individuum’s to transit to the

next generation/iteration. The used methods of

selection can be: ranking, roulette wheel or

tournament. The AG that uses the tournament

selection, chooses randomly the best pair of

individuum’s to transit to the next generation, [29],

[30].

Tournament selection preserves population’s

diversification and is low computationally

demanding, [25], [32].

Robustness - practical implementation cannot be

done with ideal material or no tolerance on the

performance specification, also they are subject to

external variables non-accounted in the modulation.

A robust solution is defined as having a low

deterioration, when induced to disturbances. The

GA considers a solution with a high degree of

robustness when it is necessary in a distant radius of

simulated disturbance on input variables centered

from the considered solution, to decrease the

solution fitness in a determined radius from the

initial output fitness, [25], [32].

Sharing - it´s applied when NPS>NP, after solutions

with the best values in each objective function (Fn)

are inserted into the elite population then, a dynamic

niche is computed (ds=Maxdistance(F1, F2)/NPs)

and all the solutions at a distance greater then ds

from the ones already belonging to the elite are

inserted. If Ps remains unfilled, it will be

dynamically adjusted until the population has the

predefined size NPs, [25], [29].

A lot of AG variants are presented and

discussed in academic papers, in this paper we

focused on NSGA II (non-dominated sorting genetic

algorithm) as it grants fewer disadvantages than

other approaches, and also it seems to have a great

rated performance on testing MOP, [29]. NSGA II

application is expressed in Figure 5.

Fig. 5: Flowchart of the applied AG on multi-

objective problems, NSGA II, [25].

A – dominates B and C

A – is dominated by D

A – is indifferent to E and F

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5 Distribute ESS Problem

Formulation

This paper presents a problem of optimal placement

and sizing of ESS units on Cape Verde Islands EPS

where two objective functions are considered:

minimizing installation costs and minimizing

system losses. The used constraints are related with

service quality (bus voltage profile), networks

physical laws (obtained by power flow analysis) and

some technical restrictions (impossibility of

installation of certain ESS units at certain buses).

The result of the formulation expressed below,

represents a simplified notion of avoidable losses

that can be obtained by reducing power flow

between production and consumption buses. As

peak consumption increases DM usually increases

the network capacity or invests in distributed

generation to achieve loss reduction.

The major goal of this approach is finding, a

solution based on distributed storage, in order to

reduce transmission losses and at the same time

RES curtailment.

Thus, the implemented layout of the distribution

of ESS on the grid, should be formulated, regarding

to:

Minimize

[Cost installed storage; Power losses]

Subject to (

Power flow Equations

V, I Limits

PT power and space limitations

Installation costs are given by equation (1),

where, represent the binary decision

variables, that determines if a ESS can be installed

in a certain bus and Cγ is its acquisition cost, γ is its

storage capacity, α is the index related to a bus in a

secondary branch, β the branch identification and κ

the index of a bus number in the main branch.

The power losses minimization is given by equation

(2),

where, and are the corresponding active

and reactive power flow between the buses caused

by the resistivity of the power cable.

Power flow (active/reactive) between buses in a

secondary branch is given by equation (3) while

equation (4) refers to power flow on the main

branch, both depend on power generated

locally in the bus.

Equation (5) defines how voltage can be determined

for a given bus, while constrains (6) ensure that

energy quality in EPS is between acceptable

intervals defined by legislation.

In addition to the constraints of physical nature

related to the load flow equations, another

considered constraint (7) is the limitation imposed

that at most one ESS unit can be placed in each bus.

Based in historical electricity data, for this case

study, the peak consumption is assumed as

10,2MW, this value is taken from the most statically

representative month (July) sampled from 2018.

Sal Islands EPS distribution MV grid simplified

diagram is presented in Figure 6, as can be seen

demand peak loads are dispersed over buses as its

corresponding transformer capacity in each

community location, resident population and

touristic places.

= (5)

(6)

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Fig. 6: Sal Island simplified MV network, taking

load distribution formulation using transformer post

capacity and a statistic consumer assumption.

The MV, 20kV, distribution grid is installed

underground in a star/radial topology. The main

branches have their starting point at the Diesel

Power Plant and ends on the RES generation buses.

Mainly, used cables are identified by LXHIOAV

with 120-240-500mm2 depending on the distance

and load. Two parallel cables go to bus 4 (Santa

Maria) which is divide in two but explored as an

open ring topology. All derived buses on the way

have a sectioning station connecting both cables,

guaranteeing the insolating of faults and power flow

transfer to the outer cable, improving reliability.

Being an underground grid, it creates a capacitive

effect (Ferranti effect) so reactive won´t be

accounted, [33].

Peak-hour transmission losses represent about

6-7% of annual losses. The Sal Island EPS annual

power losses are responsible for technical and

commercial losses of about 280.000€ every year;

losses costs are paid by the consumer through a

tariff compensation parcel. Electra undertook yearly

submission of a Loss Reduction Plan to ERA, thus

ESS can be used as well for RES integration.

6 Case Study

Wind energy curtailment is a long-standing issue on

Sal´s Island EPS, yearly it represents an average of

40% of the energy generated in the Wind Power

Plant as shown in Table 1. The curtailment causes

can be summarized by the oversized Wind Power

Plant installed capacity, made to anticipate an

energy consumption growth that didn’t occur;

possibly due to implementation logistics, to dilute

fixed engineering cost and project scale price

influence was greater than the oversizing cost.

Table 1. Wind energy curtailed vs. Wind farm

availability and used energy wind energy, between

2013 -2018 on the Sal Island network.

Also spinning reserve is not sufficient to

integrate all the wind energy available and it isn’t

economically viable for the EPS concessionary to

buy energy from Cabelólica´s high values

contractually defined. Electra tend to minimize

wind energy purchases, exploit low fuel market

prices and maximize its thermal capacity use to

repay its investment.

Regarding the power transmission losses, the

Island´s grid peak hour (19-20h) losses including

only MV cable represent 6-7% (~16k€) of the global

energy losses (~240k€/ 2% of produced energy),

which are accounted to the energy selling price.

Every five years, regulation obligates the

concessionary to reinvest a share of its profit, in an

energy losses mitigation plan which can create a

synergy between losses reduction and wind energy

integration, using an optimal ESS distribution on the

Island, [34].

The GA configuration

The GA methodology, described in section 4,

should receive input from a “.txt” file that describes

the EPS configuration and the available market

solution, so the algorithm can be able to

interactively generate (ESS allocation) and evaluate

(avoided losses/cost) a solution/individuum.

Electric data is stored in a matrix form, in which

columns divide them by types (resistance, start bus,

end bus, number of derivations, loads, generation)

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and lines by a branch or bus index/code. Table 2

exemplifies some ESS solution codes and

characteristics inserted in the GA.

Table 2. Solution ESS power and its acquisition cost

codification used by the GA, arranged in 20kW step

corresponding to 17,7K€ steps.

ESS installation and operation best practice

Regarding the Diesel Power Plant management, it is

relevant that it limits ESS on Sal Island life cycle

between 30-50%, [35], so some suggestions to

overcome this, are:

 inverters need a configuration to avoid batteries

from overheating (eg: outdoor installation);

 use a PID (proportional, Integrative, derivative)

analyzed ratio of stored/colling energy when

curtailed wind energy is greater than storage

capacity;

 use a predictive curtailment forecast

management to avoid charging on nominal

installed power.

To optimal enclosure of ESS in the grid, we

need to take into consideration the best place to

install it, so when feasible, the ESS should be

installed inside a concrete transformer substation

empty space or as close as possible to the substation

LV bus container or concrete building. The LV

integration of the ESS must be supported by a

technical study, which considers, the LV

substation´s empty space, load diagram, and

ventilation upgrade, in order to avoid overload when

the ESS is charging, personal risk, and cost

reduction. ESS allocation on the LV grid can use the

same allocation method as in the MV, not intended

in this paper.

The GA operator parametrization analysis

As a non-deterministic method used in this case

study GA operators are adjusted experimentally.

Being a small multi-objective problem, the

computational power processing required is low

about (15 minutes/100.000 generations). The best

parametrization is shown in Table 3.

Table 3. AG genetic operator, populations, and

iterations, best suited to find optimized ESS

allocation.

Operator adjustment guidelines were based on

papers, which state, [29], [32]:

 Exclude domination and non-feasible

individuum on the initial population;

 Crossover as the main operator since it is less

stochastic;

 Mutation probability in an interval that

avoid random search or population stagnation;

 Elite population enough to protect good

solution degradation.

Crossover method analysis

As mentioned before crossover is the main operator

used by the GA for the optimum solution

convergence. Thus it´s important to analyze the

crossover method’s influence on the optimum

solution convergence.

From Figure 7, we can conclude that Pareto

convergence is influenced by the crossover method.

Meanwhile, uniform cut and 2 cut-off methods

are more likely to distribute genes between the two

halves of the chromosome in the copy of the genes

to the descendant. The distributed copy of the genes

along the chromosome of the descendant, or damage

good solutions or improve the worst solutions, this

means that it increases intermediate solutions.

The possible explanation for the best

convergence of the one point cut-off crossover

method may be that, when copying the chromosome

of the parents from two halves, it guarantees a

greater probability for the descendant to conserve

the genes related to the installation of the ESS

concentrated in the first half of the grid buses [bus

1 to bus 8] in which these buses represent the

majority of the losses of the ESS (80%) and in the

second half buses [bus 9 to bus 15] receiving little

or no ESS installation, which allows a reasonable

performance to the descendant.

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Fig. 7: Crossover method influence analysis over

optimization gains.

RES variability compensation

Since the load distribution across the MV network

was assumed as fixed for modeling purpose based

on a statistic approach, to reflect the variability of

the Wind Power Plant, an energy injection scenario

method in (bus 5) is best suitable, overall it allows

to simplify the ESS gains effect.

Fig. 8: Wind Power Plant production effect on total

MV losses and observed Wind Power Plant hours of

defined production power, in 300kW intervals.

Figure 8 shows the Wind Power Plant’s

influence on power transmission losses. To

summarize all observed Wind Power Plant

production conditions, quartiles are used as

estimators to represent all sampled data, thus they

sum the sampled values in three scenarios with

statistical significance, as shown in Figure 9.

Fig. 9: Observed Wind Power Plant production

quartiles, set on a whisker plot.

Scenario Q1 – 1500kW RES, analysis

As defined, scenario Q1 represents the first quartile

of the sampled Wind Power Plant production

(1500kW), which leads a 28% (37,1kW) losses

reduction. Most of the losses, and decreases occurs

between bus 1-[...]-4 due to the bidirectional feeding

of bus 4 which represents 50,4% of the grid

consumption.

Other branches aren´t affected by RES

distributed production.

As a result, the last population found by the GA

is a Pareto curve formed by a solution with big loss

reduction/ investment cost ratio optimization.

Figure 10 shows the PF solutions obtained in

scenario Q1 and its linear correlation coefficient as

an optimization concavity/convergence optimization

capability index.

Fig. 10: Secondary population PF, computed by

NSGAII for scenario Q1 -1500kW RES, along

linear regression, and correlation.

It is visible that a reverse correlation between

losses/investment costs, is expected in this kind of

multi-objective problem. To notice solution indexes

are rearranged in ascending order, to simplify

analysis.

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Volume 18, 2023

Solution Q1-N1 minimizes cost, where losses

are reduced by 3% (2,9kW), corresponding to the

installation of a 100kW ESS and 89.000€

investment.

In comparation solution Q1-N31 minimizes

losses in 72%, which corresponds to the installation

of a 6,8MW ESS involving 6.000k€.

Optimized individuals have host of the allocated

ESS, on bus 4 which is the most energy-demanding

and farthest from Diesel Power Plant.

Making a population chromosomic analysis

from Table 4, in solution Q1-N16, we can see that

bus 4 cannot alone guarantee both objective

minimizations, so bus 8 turns out to be necessary.

Bus 8 is a large consumption bus connected by a

120mm2 cable, so is intelligible the appearance of

this gene/ESS. The solution Q1-N17 appearance,

may be explained by a similar minimization

performance and/or due to genetic operator effort to

maintain diversity.

Table 4. AG computed PF population chromosome

matrix and performance for scenario Q1- 1500kW

(1-losses kW; 2-cost k€).

Bus

1-3

4

5-7

8

9-10

11

12-15

L1

C2

Solution Index

0

96,9

0

1

0

5

0

94,0

89

2

0

10

0

91,2

178

3

0

19

0

86,3

338

4

0

28

0

81,6

498

5

0

34

0

78,7

605

6

0

39

0

76,3

693

7

0

45

0

73,6

800

8

0

53

0

70,1

942

9

0

60

0

67,2

1067

10

0

67

0

64,4

1191

11

0

77

0

60,8

1369

12

0

89

0

56,8

1582

13

0

101

0

53,2

1796

14

0

113

0

50,1

2009

15

0

122

0

48,1

2169

16

0

130

0

46,4

2311

17

0

131

0

14

0

43,4

2578

18

0

131

0

28

0

40,9

2827

19

0

130

0

41

0

39,0

3040

20

0

147

0

41

0

36,2

3343

21

0

158

0

41

0

34,8

3538

22

0

171

0

41

0

33,7

3769

23

0

144

0

81

0

31,6

4001

24

0

158

0

81

0

29,8

4250

25

0

173

0

81

0

28,6

4516

26

0

188

0

81

0

28,0

4783

27

0

147

0

135

0

27,8

5014

28

0

158

0

135

0

26,5

5210

29

0

173

0

135

0

25,2

5476

30

0

188

0

135

0

24,7

5743

31

0

194

0

145

0

24,4

6028

Now analyzing the PF solutions economic

performance, they correspond to a reduced watt loss

per thousand € (W/k€) interval, between Q1-N1

32,8 W/k€ and Q1-N31, 12,3 W/k€. The middle

solution or nearest to the interval average is solution

Q1-N16, which makes it of course, the best trade-off

on both objectives.

Scenario Q2 – 3000kW RES, analysis

Secondly, scenario Q2 shows an intermediate RES

use situation (3MW), associated with the average of

the sample.

As a result, losses are reduced by 16%, lower

than in the Q1 scenario. Between buses 1-[...]-4

branches losses are lower, while losses between the

Wind Power Plant (bus 5) and bus 4 increases by

60%.

Figure 11, shows the Q2 solutions present at the

PF. After comparing Q1 and Q2, a linear regression

slope coefficient (Q1.m= -76/Q2.m= -118), shows

that the Q2 Pareto curve slope clearly reflects a

lower avoided losses/investment cost ratio in

comparison to scenario Q1. This happens because

most of the losses between buses 4-5 cannot be

reduced, by a distributed peak shaving ESS

dispatch, but through a production leveling

approach.

Fig. 11: Secondary population PF, computed by

NSGAII for scenario Q2 - 3000kW RES, along with

linear regression and correlation.

Incapability to reduce losses by allocating ESS

along the branch 4-5, as shown in Table 5 creates a

tendency to:

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DOI: 10.37394/232016.2023.18.23

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Volume 18, 2023

 Q2 PF starts early to host ESS in a dispersed

approach (Between Q2-10 and Q2-15) on bus

11, also 3rd more responsible in power losses;

 after the Q2-N16 individuum, ESS solutions

are more disperse and larger on bus 8, in

comparison to the same interval from Q1 PF.

Besides technical analysis is important for the

DM, an economic analysis, in this case, has fewer

optimization gains as stated before. The scenario Q2

population have a ratio of W/k€, between 7,84 and

20,7. It is important to note that the reduction of

RES is possible through the installation of larger

ESS’s, not accounted for in this analysis, but it has a

great and positive influence on economic

evaluation. Applying the same methodology to

define the best solution used before, solution Q2-

N14 evidently manages to have similar gains on

both goals, as having a W/k€ nearest from the Q2

last computed population average (13,62W/k€).

Table 5. AG computed PF population chromosome

matrix, Q2-3000kW (1-losses kW; 2-cost k€).

Scenario Q 3 – 3900kW RES, analysis

The last scenario is Q3, which refers to the

upper/third quartile (3,9MW) of the observed wind

energy injection, on bus 5.

In this scenario, losses increase by 7% when

related to wind absence, in contrast to a higher RES

power injection, from the Wind Power Plant,

reducing fossil fuel consumption, reducing

dependence and shortening distance to carbon

neutrality.

Energy transmission losses are lowered,

between bus 1-[...]-4 which before were 55,5% of

total losses now are 5,7%. However, this gain, is

surpassed by the loss increase between the Wind

Power Plant bus 5 and bus 4, now responsible for

76,3% of the grid technical losses.

Fig. 12: Secondary population PF, computed by

NSGAII for scenario Q3 - 3900kW RES, along with

linear regression and correlation.

From Figure 12, we can conclude that the

tendency of avoided losses/investment cost ratio

continues to decrease. Now the linear regression

slope is -137 (Q2.m-118, Q1.m -76,47).

Linear correlation is also an optimization gain

indicator, increases in this scenario Q3.r2 0,957

(Q2.r2 0,926; Q1.r2 0,899) which are responsible

for lower objectives minimizations, because it

reflects a PF with a lower concavity.

For this scenario, it is possible to see in Table 6

that solutions are earlier divided and less centralized

on bus 4. Now bus 8 is the third bus with more

consumption on the EPS receiving more allocation

of ESS, because most of the losses of the branches

Bus

1-3

4

5-7

8

9-10

11-15

L1

C2

Solution Index

0

112,5

0

1

0

6

0

110,3

107

2

0

13

0

107,9

231

3

0

20

0

105,7

356

4

0

24

0

104,4

427

5

0

28

0

103,3

498

6

0

33

0

101,9

587

7

0

39

0

100,3

693

8

0

46

0

98,6

818

9

0

53

0

97,1

942

10

0

53

0

6

95,8

1049

11

0

59

0

6

94,6

1156

12

0

69

0

6

92,8

1334

13

0

59

0

24

91,3

1476

14

0

66

0

24

90,1

1600

15

0

75

0

24

88,7

1760

16

0

64

0

43

0

87,3

1903

17

0

76

0

43

0

85,4

2116

18

0

75

0

54

0

84,0

2294

19

0

84

0

54

0

82,8

2454

20

0

95

0

54

0

81,7

2649

21

0

79

0

77

0

80,8

2774

22

0

87

0

77

0

79,8

2916

23

0

96

0

79

0

78,8

3112

24

0

95

0

91

0

77,8

3307

25

0

92

0

110

0

76,7

3592

26

0

105

0

110

0

75,7

3823

27

0

103

0

121

0

75,3

3983

28

0

108

0

126

0

74,9

4161

29

0

122

0

126

0

74,5

4410

30

0

109

0

154

0

74,3

4676

31

0

122

0

154

0

74,0

4907

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DOI: 10.37394/232016.2023.18.23

Denis Santos, Vasco Santos

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226

Volume 18, 2023

between buses 4-5 cannot be avoided by a peak

shaving dispatch.

In addition, in this scenario using the same

method of economic analysis, we can see that the

population ratio represents a lower gain for the EPS

and a greater demand in investment for the DM. The

scenario Q3 population, avoided losses/investment

cost is between Q3-N31 6,35W/k€ and Q3-N1

13,43W/k€, being solution Q3-N15 the one with the

better balance in both goals (with results in W/k€

near to the Q3 population average).

Table 6. AG computed PF population chromosome

matrix and performance for scenario Q 3- 3900kW

(1-losses Kw; 2-cost k€).

Scenarios (Q1, Q2 and Q3), sensibility analysis

To apply the best solution, the DM should take into

account the following: the EPS dispatch protocols,

funds available for investment, technological

advancement and other aspects.

Making a fast analysis related to the technical-

economic goals, based on data used in this paper

and considering the DM role, can be assumed that:

 Low power ESS, should be avoided, because

they reduce fixed costs compensation

(engineering, construction and logistics) and

negotiating power;

 ESS solutions with installed power between

1MW to 4MW offer an excellent EPS loss

minimization gain, they have a reduced wind

energy curtailment avoidance;

 Above 4MW ESS, solutions have a reduced

effect on EPS losses mitigation, so they must

be excluded.

The analysis should be located between, 1 and

4MW intervals where are the intermediate solutions

Q1-N16, Q2-N14 and Q3-N15.

Typical scenarios were developed by quartile

and interquartile which divides observed wind space

in four. The space above and under the first and

third quartile (25%) is overlapped by the space of

the third or mean quartile, to compensate that Table

6, shows the “weight” used as a coefficient in the

sum of each plot.

Table 6. Coefficient use in Weight Sum, for avoided

losses analysis.

The solution with the best sensibility gain is

solution Q1-N16, as shown in Table 7, using Table

6 coefficient to sum its performance on the

complementary scenarios and its main scenario, it´s

possible to obtain 28kW, or 23% taking into account

the weight sum losses in RES absence that is

119kW.

Table 7. Weight sum and avoided losses sensibility,

for intermediate solutions on original and

complementary scenarios.

7 Economic Internalities

The Identification of all the variables that may affect

the final result is difficult, but it is an aspect that the

DM must have in mind.

Having a projected actualization rate of 3,5%

(obtained by summing the Cape Verdean low-risk

investment interest and inflation) and a 15-year first

phase project lifetime, the expected expenses are:

- ESS acquisition, which includes engineering,

installation and commissioning, with a cost of

450k€ per MW, [36], [37];

Bus

1-3

4

5-7

8

9

10-15

P1

C2

Solution index

0

144,9

0

1

0

6

0

143,5

107

2

0

12

0

142,1

213

3

0

17

0

141,1

302

4

0

23

0

140,0

409

5

0

29

0

139,0

516

6

0

10

0

25

0

137,9

622

7

0

15

0

25

0

136,8

711

8

0

23

0

25

0

135,3

853

9

0

29

0

25

0

134,3

960

10

0

28

0

31

0

133,5

1049

11

0

33

0

31

0

132,7

1138

12

0

34

0

39

0

131,3

1298

13

0

42

0

39

0

130,2

1440

14

0

34

0

54

0

129,2

1565

15

0

38

0

58

0

128,1

1707

16

0

46

0

58

0

127,1

1849

17

0

46

0

65

0

126,3

1974

18

0

41

0

77

0

125,6

2098

19

0

47

0

77

0

124,9

2205

20

0

53

0

77

0

124,3

2311

21

0

46

0

90

0

123,8

2418

22

0

53

0

90

0

123,1

2543

23

0

61

0

90

0

122,5

2685

24

0

62

0

101

0

121,6

2898

25

0

61

0

110

0

121,1

3040

26

0

67

0

112

0

120,7

3183

27

0

77

0

112

0

120,4

3360

28

0

69

0

130

0

119,8

3538

29

0

79

0

130

0

119,6

3716

30

0

74

0

144

0

119,4

3876

31

0

83

0

144

0

119,3

4036

Scenario

Q1

Q2

Q3

Coefficient

0,4

0,2

0,4

Avoided

losses

(kW)

Scenario

Q1

Q2

Q3

Weight Sum

Q1-N16

-50

-22,8

-7,2

28

Q2-N14

-35,5

-23,3

-14,6

25

Q3-N15

-30,2

-21,6

-11,7

21

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Volume 18, 2023

- Maintenance, to achieve the expected lifetime

of the ESS, these should be subject to a maintenance

plane. The maintenance plan is divided into fixed

maintenance costs and variable maintenance costs.

The typical costs are 8,6€/kW and 2,6€/kWh

respectively, [36].

The positive cash-flow of the project is given by

the following subjects:

- Carbon credit, a mechanism that financially

supports sustainable development. Avoided

CO2(Ton/MW), an index which is sold by

Caboéolica for 0,5€/MWh;

- Energy sold, stored energy sold price is the

same used by Caboéolica RES price of 0,15€/kWh.

Yearly it´s expected the usage of 92% of the

storage capacity, based on 2018 wind injection in

the grid, with a total ESS efficiency of 92% in a

complete charge/discharge battery cycle.

In this analysis the DM is Caboeólica, with the

avoided losses of EPS being a counterpart for

Electra to receive stored RES that otherwise would

be curtailed.

The Profitability study, of both phases results is

given in Table 8, using as indicators pay-back time,

internal return rate (IRR) and net present value

(NPV), [38]; which have low expression a the first

investment phase. But in a second phase that relies

only on the battery exchange it has a great gain for

the DM with an investment value of (135,1k€/MW).

Table 8. Economic indicators result, for ESS

investment.

This case study shows how energy tariffs can be

reduced, because the RE yearly tariff actualization

formula, has a reduction effect based on total RES

integration in the archipelago. The ESS based on

RES curtailed energy will decrease by 1,74% fossil

fuel contribution on the energy tariff.

8 Conclusion

The methodology used in this paper, to model RES

curtailment integration, having in mind the

economic and technical limitation, can be used as a

framework for similar EPS. The initial problem of

allocation and sizing ESS on the EPS aims to:

minimize of total power losses and minimize of ESS

costs.

To solve this multi-objective problem, a GA

was applied, whose PF presents a set of distributed

solutions that can be used by the DM for practical

implementation.

Intuitively, it´s possible to say that the highest

consumption buses are the best candidates to

allocate ESS, the GA excludes the existence of a

small dispersion that may have outweighed this

deduction.

Also, the environmental and economic aspect

heavily contributes to all interested players in the

EPS (Electra, Caboeólica and consumers).

Another crucial observation that can be taken

from this paper and case study is the importance of

integrating more RES combined with ESS on the

power grid and its direct relation with its strong

contribution to global "carbon neutrality" and

energy efficiency. These two technologies should be

intrinsically linked because RES are characterized

as being intermittent and not dispatchable. The

symbiosis between RES and ESS allows RES to be

used with better performance, making better use of

the energy generated by them, avoiding wasted

energy, when these technologies are operating in

over power production (excess of production faced

with low load demand). This way it´s possible to

allocate renewable energy production stored in ESS

to be used in periods of greater consumption or

absence of renewable production avoiding the

operation of fossil fuel technologies and all their

economic and Environmental externalities.

This methodology and its implementation in a

real case study, shows how the use of a

mathematical tool can be useful as a decision

support for EPS DM’s. In future this decision

support system may be integrated in in a non-radial

Islands Power Grid or in a wider Grid of a

continental country divided in Virtual Power Plant´s

Active Power Grids.

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Volume 18, 2023

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WSEAS TRANSACTIONS on POWER SYSTEMS

DOI: 10.37394/232016.2023.18.23

Denis Santos, Vasco Santos

E-ISSN: 2224-350X

230

Volume 18, 2023

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The authors equally contributed in the present

research, at all stages from the formulation of the

problem to the final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The authors have no conflicts of interest to declare.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

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WSEAS TRANSACTIONS on POWER SYSTEMS

DOI: 10.37394/232016.2023.18.23

Denis Santos, Vasco Santos

E-ISSN: 2224-350X

231

Volume 18, 2023