Analytic Hierarchy Process Algorithm Applied to Battery Energy Storage System Selection for Grid Applications

Abstract

The increasing use of energy storage in batteries has been contributing to the electric sector technological advancement, specially to guarantee of continuous supply in periods of intermittence or low production. In this work the problem of selecting batteries for application in the quality of energy supply is addressed. A methodology to size and classify the best battery technology based on the multicriteria decision-making method AHP (Analytic Hierarchy Process) was developed. The opinions of specialists in the area were considered for the avaliation to four types of criteria: environmental, technological, regulatory and financial. Finally, to evaluate the developed approach a problem of classifying four different battery alternatives (Ventilated Stationary Tubular Lead Acid, Lead-Carbon Acid, Ventilated Stationary Lead Acid, and Lithium Ion LFP) was tested and the result pointed to the Ventilated Stationary Lead Acid technology as the best alternative. In addition, analyses using theoretical scenarios with preferences in certain criteria were performed. The methodology proved applicable, considering that with the input data provided by the decision maker, it is possible suggest the best technological alternative for a given purpose. The simulations carried out suggest that the methodology has potential to evolve and act in a real situation.

1. Introduction

The supply of energy, in times of intermittency or low production, can be assured through energy storage systems (ESS). Efficient management of energy storage is crucial in the process of achieving a balance between power quality, efficiency, costs, and environmental constraints [1]. In Brazil, for example, it is estimated that by 2023 its market will use around 95 GWh in energy storage systems, and this number corresponds to 50% of all installed capacity in the world at the end of 2015 [2].

ESS, in particular battery energy storage systems, are the most frequently installed options to facilitate the use of renewable energy [3], and batteries have been maturing for several decades and increasing their reliability and durability. In Germany, the market for stationary battery storage systems is growing rapidly compared to pumped storage systems [4]. Taking into account the expected increase in consumption of this technology for the coming years, it is expected, as a reflection of its large-scale use, a gradual reduction in its acquisition and implementation costs.

The choice of batteries for energy storage is a complex decision, as it needs to take into account several technical, economic, regulatory, and environmental criteria. In this sense, the multicriteria decision-making (MCDM) methods can serve as a decision support tool.

Conventional MCDM methods are frequently used in the energy field [5] in a wide range of problems [6, 7, 8, 9, 10, 11, 12]. In [11], the combination of analytic hierarchy process (AHP) and Vise Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) methods are used to select the best solution for electrical power supply in remote rural locations. The evaluation and classification of renewable energy sources are addressed as an MCDM problem in [10], based on the theory of gray systems. The problem of selecting investment projects for solar thermal power plants addressed in [12] uses the AHP and Analytic Network Process (ANP) methods.

More specifically in the energy storage problem, we also have the applicability of MCDM methods [1, 13, 14, 15, 16]. In [16], an attempt is made to determine the most appropriate among six energy storage alternatives, considering four main criteria and 16 subcriteria. For this, a hybrid methodology is used that combines AHP and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) based on type 2 fuzzy sets. In [15], a decision support tool is proposed for the selection of energy storage alternatives. Considering a multi-objective optimization approach based on the augmented $ϵ$ constraint method meets the technical constraints, economic, and environmental objectives of the problem. The AHP method combined with fuzzy logic is used in [1] for the selection of energy storage considering criteria of efficiency, load management, technical maturity, costs, environmental impact, and energy quality. In [5], five different battery alternatives (lead-acid, lithium-ion, vanadium redox flow battery, sodium-nickel chloride, and sodium-sulfur) are evaluated using Pythagorean Fuzzy sets combined with AHP-TOPSIS.

A literature review of the main MCDM approaches in evaluating ESS is provided in [3]. As seen earlier, among the multicriteria decision-making methods, we have the AHP method created by the mathematician Thomas L. Saaty [17, 18]. This approach consists of evaluating criteria through a measurement scale, organizing them in a hierarchical structure [18]. Since this is a flexible decision support method, which can take into account objective and subjective criteria by comparing pairs of criteria [19], in the subjective criteria we can consider the opinion of specialists in an area of knowledge. Its use in its original form or in hybrid approaches has applications in several problems in the energy sector [8, 20, 21, 22, 23, 24, 25, 26].

Given the growing demand for ESS technologies, especially batteries, here we develop a multicriteria analysis methodology based on the AHP method, which is one of the most traditional MCDM methods used in a wide range of energy field problems. The main objective of this approach through AHP is to help choose the best battery technology for energy storage, considering for this, technical, regulatory, environmental, and economic criteria and subcriteria through the opinions of specialists in the area.

This chapter is organized as follows. In Section 2, we make a brief summary of the AHP method. In Section 3, we present the methodology developed to choose the best battery technology for energy storage using the AHP method. To validate the developed methodology, we performed numerical experiments in Section 4, considering an analysis of a scenario based on expert opinion and another analysis based on theoretical scenarios. Finally, in Section 5, we present our conclusions.

2. Brief review of the AHP method

Decision theory is the set of techniques that help decision-makers to recognize the particularities of a problem and structure it. In this context, MCDM refers to determining the best option in relation to multiple and often conflicting criteria [27].

Among the traditional methods of MCDM, we have the AHP method which has already been applied in various problems in the energy field, such as renewable energy [26, 28, 29, 30], energy storage [3, 13, 21, 31, 32, 33], site selection for wind farms [22, 34, 35, 36], among others [37, 38, 39, 40].

This method was created by the mathematician Thomas L. Saaty in the 70s [17, 18], being a method used to solve problems with multiple criteria and which emphasizes modeling according to the knowledge of specialists in the area. This method considers quantitative and qualitative aspects and can be used both to identify the best possible alternative and also to list the alternatives according to a ranking of priorities.

One of the advantages of using the method is the consideration of the experience of the decision-maker who can intuitively assign weights to the relevant criteria by comparing them pair by pair. Figure 1 describes the steps of this method.

Figure 1.

Steps of the method AHP.

First, the alternative solutions to the problem are listed, and the criteria and subcriteria for choosing the alternatives are listed. Then, based on the judgment of the decision-makers, scores are assigned to each criterion following the Saaty scale [17, 18], as described in Table 1.

Intensity of importance	Description
1	Equal importance
3	Moderate importance of one over another
5	Essential or strong importance
7	Very strong importance
9	Extreme importance
2, 4, 6, 8	Intermediate values between the two adjacent judgments
Reciprocals	If judgment of factor i compared with factor $j$ is $a_{\mathit{ij}}$, then judgment of factor $j$ compared with factor $i$ is $a_{\mathit{ji}}$ $=1=a_{\mathit{ij}}$.

Table 1.

The Saaty rating scale for deciding relative importance of factor i compared to factor j [17].

Each criterion/subcriteria are judged pair by pair, and this judgment is represented through a square decision matrix $A=\left(a_{\mathit{ij}}\right)\in {ℝ}^{n\times n}$, where n is the number of evaluations of criteria/subcriteria. To calculate the consistency of the judgments made, we first normalize the decision matrix, according to Eq. (1):

$$A_{\mathit{norm}}={\overline{a}}_{\mathit{ij}}\in {ℝ}^{n\times n},\text{such that}{\overline{a}}_{\mathit{ij}}=\raisebox{1ex}{$a_{\mathit{ij}}$}\!\left/ \!\raisebox{-1ex}{$\sum _{i=1}^n{a}_{\mathit{ij}}$}\right.$$E1

must satisfy the equation Eq. (2):

$$\mathit{Av}=\mathit{\lambda v}$$E2

where $A$ represents the squared decision matrix, $\lambda$ is the eigenvalue with the largest value of $A$, and $v$ is its corresponding eigenvector.

Then, the consistency ratio $\left(\mathit{CR}\right)$ of each decision-maker’s preferences is calculated, according to the Eq. (3):

$$\mathit{CR}=\frac{\left({\lambda }_{\mathit{max}}-n\right)}{\left(n-1\right)}\bullet \frac{1}{\mathit{RCI}}$$E3

where $\mathit{RCI}$ is the random consistency index, obtained from Table 2, $n$ is the number of evaluated criteria, and ${\lambda }_{\mathit{max}}$ is the maximum eigenvalue of $A$.

$n$	1	2	3	4	5	6	7	8	9	10
$\mathit{RCI}$	0.00	0.00	0.52	0.89	1.11	1.25	1.35	1.40	1.45	1.49

Table 2.

Average random consistency index [41].

If the value of $\mathit{CR}$ is less than 0.1 we say that matrix $A$ is consistent, otherwise the matrix is inconsistent and decision-makers must repeat their evaluations until a satisfactory $\mathit{CR}$ is obtained.

After this brief explanation about the AHP theory, in the next section, we will present the methodology developed for sizing batteries and show the approach developed for the application of the AHP method, which uses some of the information obtained through sizing.

3. Approach developed for the application of the AHP method

In order to fulfill the objective of listing the battery alternatives, the “Input data” stage concerns the collection of essential data for the other calculations, originating from the region where the battery bank will be allocated, the demand, the conditions of use of the application, and the information provided by the manufacturers. In the dimensioning stage, the application data are combined with the data provided by the manufacturers, and the results of this stage alone provide a range of information on the different batteries evaluated, some of which will serve as input for the AHP method. In the “Application of the AHP method” stage, the batteries are classified according to each of the considered criteria and subcriteria. As a result, AHP lists battery alternatives in a priority ranking (Figure 2).

Figure 2.

Overview of the developed methodology.

3.1 Input data of the problem

One of the objectives of this work is the classification of different battery technologies to form a bank that meets a certain demand. Since this ordering is established considering the preference of certain qualification criteria. Therefore, input data are necessary for the development of the methodology, namely:

1. average temperature of the region: provided in C°, being necessary for calculating the time of use of the batteries;

2. energy demand: supplied in kWh, used to calculate the energy of the battery bank in the sizing.

3. operating regime: in this regard, we provide the period considered (hours, days, etc.), number of cycles per period, and the duration of each cycle per hour, and this information is used to determine the time of use of the battery bank.

4. battery database: these are made available by the manufacturers and used in the sizing calculation.

3.2 Battery sizing

In the methodology developed for dimensioning the batteries, the application data entered by the user and the information contained in the database are combined. The variables that make up the sizing are gravimetric density, volumetric density, optimal Depth of Discharge (DOD), battery bank energy, number of containers, and battery usage time. Determining the sizing variables provides the user with a range of information on the different battery alternatives evaluated, and some of this information serves as input for the AHP method.

Therefore, the design calculation was divided into six steps, as shown in the following algorithm. In Step 1, we described the calculation of gravimetric energy density. In Step 2, we present the calculation of the volumetric energy density. In Step 3, we show the methodology adopted to determine the optimal DOD. The calculation for energy from the battery bank is performed in Step 4. In Step 5, we establish the logic for defining the number of containers for storing the battery bank, taking two options for containers with volumes of $33{\mathrm{m}}^3$ and $67{\mathrm{m}}^3$, named type I and type II, respectively. Since, we consider only $60\%$ of the total capacity of the container, since the remaining space is destined for the control and refrigeration systems. Finally, the calculation of the battery usage time is presented in Step 6.

Battery sizing algorithm

Step 1 Gravimetric Energy Density

Require: Capacity (Ah), Voltage (V) and Weight (kg)

  For each type of battery technology do

    G$\text{ravimetric density}\leftarrow \frac{\text{Capacity}\times \text{Voltage}}{\text{Monoblock Weight}}$

  End For

Step 2 Volumetric Energy Density

Require: Capacity (Ah), Voltage (V) and Volume ($m^3$)

  For each type of battery technology do

    $\text{Volumetric density}\leftarrow \frac{\text{Capacity}\times \text{Voltage}}{\text{Monoblock Volume}}$.

  End For

Step 3 DOD great

Require: Energy Throughput (kWh) and DOD (percentage)

  For each type of battery technology do

    Calculate the $\underset{\mathrm{DOD}}{max}\left(\text{Energy Throughput}\right).$

    If you have a maximum then

        $\text{great}\mathrm{DOD}\leftarrow {\mathrm{DOD}}^{\ast }$, where ${\mathrm{DOD}}^{\ast }$ is the solution obtained

    Else

        $\text{great}\mathrm{DOD}\leftarrow {\text{manufacturer}}^{\prime }\mathrm{s}\mathrm{DOD}$.

    End If

  End For

Step 4 Battery bank power

Require: Optimal DOD (percentage) and Demand (kWh)

  For each type of battery technology do

    $\text{Bank Energy}\leftarrow \frac{\text{Demand}}{\text{Optimal}\mathrm{DOD}}$.

  End For

Step 5 Number of containers

Require: Bank Volume ($m^3$) and Effective Container Capacity ($m^3$)

  For each type of battery technology do

    $\text{Type}\mathrm{I}\text{Containers}\leftarrow \left(\frac{\text{Bank Volume}}{0.6\times \text{Type}\mathrm{I}\text{Container Capacity}}\right)$.

    $\text{Type}\mathrm{II}\text{Containers}\leftarrow \left(\frac{\text{Bank Volume}}{0.6\times \text{Type}\mathrm{II}\text{Container Capacity}}\right)$.

    $\text{Optimal number of containers}\leftarrow min\left(\text{Type}\mathrm{I}\text{containers},\text{Type}\mathrm{II}\text{containers}\right)$

  End For

Step 6 Battery usage time

Require: Number of optimal DOD cycles and number of cycles per period

For each type of battery technology do

$\text{Usage time}\leftarrow \frac{\text{Number of optimal}\mathrm{DOD}\text{cycles}}{365\times \text{Number of cycles}\mathrm{per}\text{period}}$.

End For

3.3 Application of AHP

The methodology developed was divided into four phases: (i) definition of alternatives, (ii) definition of criteria and subcriteria, (iii) pairwise comparison and consistency check, and (iv) final classification. The methodology for phases (i) to (iii) is presented in this section. Phase (iv) consists of the calculations for prioritizing the alternatives and final classification, and these results are presented in Chapter 4.

3.3.1 Definition of battery alternatives

For the developed approach, four types of battery technologies were chosen, according to Table 3.

N°	Battery alternatives	Manufacturer	Model
1	Ventilated Stationary Tubular Lead Acid (OPzS)	Fulguris	3OPzs150
2	Lead-Carbon Acid (PbC)	Narada	12RECX120
3	Ventilated Stationary Lead Acid	Moura Clean	12MF175
4	Lithium-Ion LFP (Iron Phosphate)	UniPower	UP-LFP 4875

Table 3.

Battery technology alternatives.

Batteries 1, 2, and 3 are lead-acid, one of the most used and developed technologies in the world. It has a low acquisition, installation, and maintenance cost and competes with lithium-ion batteries when weight and volume are not decisive factors. These batteries have the following characteristics: fast response time, low percentage of self-discharge, fully recyclable, presenting risks of corrosion, exposure to toxic agents, leakage, and potential for contamination. However, there are still limitations such as energy density and malfunction at low temperatures [42].

Battery 4 is iron phosphate lithium ion, and this technology features low weight, good storage capacity, absence of memory effect, high energy density, risk of explosion, exposure to toxic agents, contamination by lithium, phosphorus, and organic solvents [43].

3.3.2 Definition of criteria and subcriteria

Based on previous studies and the experience of the researchers who developed this work, four criteria were defined for choosing battery alternatives, namely: environmental, technological, regulatory and financial, and subcriteria were also defined according to Figure 3. The main idea for these criteria is to consider different aspects that can influence this type of decision-making. Accordingly, a breakdown of the criteria and subcriteria is provided below.

Figure 3.

Hierarchical structure of the problem criteria.

3.3.2.1 EC environmental criteria

EC1. Security: It refers to sporadic environmental risks, whose indicators are associated with potential damage. The risks are classified based on the sum of scores distributed as follows: 1 for the risk of corrosion, 2 for the risk of exposure to toxic agents, and 3 for the risk of explosion and fluid leakage. In this subcriterion, the lower the score obtained, the greater the preference for drums.

EC2. Demobilization: It refers to the recycling of batteries according to the material they are made of and the types of waste generated at the end of the equipment’s useful life.

EC3. Visual Impact: It refers to the visual impact caused by the size of the containers that will be used to support the battery bank, considering that the larger the container, the lesser the importance of the technology.

EC4. Contaminant Potential: It refers to the environmental damage on the biota caused by the chemical components of the batteries. The following damage classes were defined: low when the contaminating elements reduce the quality of fauna and flora and even affect local ecosystems, medium when they can reduce reproduction or biological survival, and high or very high when they cause damage that can lead to death of organisms and the impossibility of reproduction.

3.3.2.2 TC. Technological criteria

TC1. Technological Maturity

TC11. Number of Systems Installed: It refers to the number of systems installed worldwide for each battery technology this information is taken from [44]. In this third-level criterion, the greater the number of projects, the greater the importance of technology.

TC12. Installed Power: It refers to the total amount of installed power in projects deployed in the world for each technology, and the information was taken from [44]. In this subcriterion, the greater the installed capacity, the greater the importance of technology.

TC13. Availability of suppliers: With regard to the number of suppliers available for each type of technology, this information was obtained from [44]. In this subcriterion, the greater the number of suppliers, the greater the importance of technology.

TC14. Time of Commercial Use: The time in which the technology is commercially available is evaluated, that is, the longer the time, the greater the degree of importance of the technology.

TC2. Efficiency: Maximum percentage charge and discharge of stored energy with minimal decrease in battery life. When evaluating this criterion, it is defined that the higher the percentage, the greater the degree of importance.

3.3.2.3 TC3. Density

TC31. Gravimetric Energy Density: Amount of energy stored per unit mass, expressed in $\mathit{Wh}/\mathit{kg}$. For density criteria, the higher the density, the greater the degree of importance. The value is numeric and undergoes a normalization process to generate the score for this subcriterion.

TC32. Volumetric energy density: Amount of electrical charge stored per volume; in this case, the greater the density, the greater the degree of importance, being measured in $\mathit{Wh}/{\mathrm{mm}}^3$ As this criterion is numerical, the values undergo normalization to acquire the score for each technology.

3.3.2.4 RC. Regulatory criteria

RC1. Applicable Environmental Law: It refers to the existence of legal provisions for the analysis of technologies with regard to the operation, since the existence of legislation gives legal certainty to contracts. The adaptability of the legislation can be considered by the absence of specific legal provisions, and the degree of importance is increased as the alternative has valid and applicable legislation.

RC2. Compliance with regulations and certificates: It is evaluated by the existence or not of norms and/or specific laws for a certain type of technology. The degree of importance increases due to the existence of specific norms and laws.

3.3.2.5 FC. Financial criteria

FC1. Average Cost: It refers to the average cost of purchase, installation, and maintenance of the battery system; in this criterion, the higher the average cost, the lesser its importance. If there are exact values obtained through budgets, this value can be used and goes through a normalization process to obtain the score for each technology.

FC2. Manufacturing/Import: It concerns the existence of domestic or foreign battery factories. The degree of importance is increased if the company has a national domicile, as it excludes possible difficulties related to importation.

With the exception of the security and density subcriteria, we can associate ranges of importance to each subcriteria according to Table 4. Note that if the average cost subcriterion does not have a budgeted value, studies can be used to estimate this value, adopting the importance ranges defined in Table 4.

Subcriteria	Feature evaluated	Small	Great	Very large	Absolute
EC2	Recycling	Disposable	Partially recycling	Fully recycling	—
ec3	Number of containers	More than 2 type II containers	2 type II containers	1 type II containers	2 type I containers
EC4	Damage to the biota	Very serious	Serious	Average	Little
TC11	Projects in the world	[0,10[	[10,40[	[40,80[	$\ge 80$
TC12	Energy (MW)	[0,10[	[10,50[	[50,100[	$\ge 100$
TC13	Number of suppliers in the world	[0,5[	[5,20[	[20,40[	$\ge 40$
TC14	Usage time worldwide (years)	[0,10[	[10,30[	[30,60[	$\ge 60$
TC2	Efficiency percentage	[0,0.8[	[0.8,0.9[	[0.9,0.95[	$\ge 0.95$
RC1	Applicability of law	Not applicable	Law can be adapted	Established law but with difficult application	Established and applicable law
RC2	Compliance with regulations and issuing of certificates	There is no norm and law	Is there a rule	There is rule and there is law	—
FC1	Average cost $\left(\text{\$}/\mathrm{MWh}\right)$	> 1000	]500,1000]	]100,500]	$\le 100$
FC2	Domestic or foreign manufacturing	Foreign	Domestic	Foreign	Domestic

Table 4.

Level of importance per characteristic evaluated in each subcriterion.

3.3.3 Pairwise comparison and consistency check

After defining the alternatives and the hierarchical model of the problem, according to the AHP method, the pairwise comparisons begin to determine the level of importance between the criteria and subcriteria. For that, a questionnaire was developed with comparison matrices between the criteria and subcriteria, separated by type and level. For each comparison matrix, a pairwise evaluation must be performed using the Saaty scale (Table 1).

To carry out these evaluations, the questionnaire was sent to 12 professionals with degrees in the areas of Electrical, Environmental, Chemical, Materials, Forestry, in addition to the areas of Biology and Ecology.

From the responses of the questionnaire, the process of normalization and consistency of the scores is assigned by the specialists to validate the interdependence of the criteria and subcriteria (Section 2). The experts’ inconsistent assessments were dismissed. In sequence, to define the final weights to be used, we considered the geometric mean of the normalized scores of the eight specialists with consistent responses.

4. Numerical experiments

We performed numerical experiments for the problem of classifying different battery alternatives for energy storage in a region of Brazil, with an application demand of 50 kWh, two cycles of battery use per day, where each cycle lasts 10 hours, and also a temperature of 25C°.

4.1 Dimensioning of the chosen alternatives

Based on the input data of the problem, on the manufacturer’s catalog and the sizing methodology developed in Section 3, the characteristics of the batteries were obtained and calculated according to Table 5.

Battery alternatives	Gravimetric energy density $\left(\mathrm{Wh}/\mathrm{kg}\right)$	Volumetric energy density $\left(\mathrm{Wh}/{\mathrm{m}}^3\right)$	Optimal DOD (%)	Battery pack energy supplied $\left(\mathrm{kWh}\right)$	Containers number	Battery usage time (years)
1	18.75	3.82E+04	54.43	91.9	1 of type I	3.53
2	23.53	6.27E+04	25	200	1 of type I	13.13
3	35.42	5.55E+04	20	250	1 of type I	2.47
4	87.80	1.15E+05	64	78.12	1 of type I	6.19

Table 5

Result of sizing battery alternatives.

4.2 Evaluation of the batteries according to the criteria

Through the results obtained in the dimensioning phase and also through the manufacturers’ data, in Table 6, we describe the results of each battery in relation to each criterion.

Criteria	Battery 1	Battery 2	Battery 3	Battery 4
EC1	6	6	6	5
EC2	Recyclable	Recyclable	Recyclable	Disposable
EC3	1 container of type I	1 container of type I	1 container of type I	1 container of type I
EC4	Little damage	Serious damage	Average damage	Little damage
TC11	45	3	69	112
TC12 $\left(\mathit{MW}\right)$	61.4	1.0	61.4	174.6
TC13	[40,80[	[5,20[	[40,80[	[40,80[
TC14	$\ge 60$	[10,30[	$\ge 60$	[30,60[
TC2	0.85	0.92	0.85	0.98
TC31 $\left(\mathrm{kWh}/\mathrm{kg}\right)$	0.01875	0.02353	0.03542	0.08780
TC32 $\left(\mathrm{kWh}/{\mathrm{m}}^3\right)$	3.82E+04	6.27E+04	5.55E+04	1.15E+05
RC1	Law enacted and applicable to technology	Law can be adapted	Law enacted and applicable to technology	Law can be adapted
RC2	Standard only	No standard	Standard only	Standard only
FC1 $\left(\text{\$}/\mathrm{MWh}\right)$	]500,1000]	]500,1000]	]500,1000]	$>1000$
FC2	Brazil	Abroad	Brazil	Abroad

Table 6.

Characteristics of each battery regarding the criteria.

4.3 Application of the AHP method

To rank the different battery technologies, we use the AHP method. For this study, we considered two types of analysis. The first considers the view of specialists in the areas of engineering, environment, and chemistry regarding the analyzed criteria. The second considers theoretical cases where scenarios are generated considering the preference in each of the environmental, technological, regulatory, or financial criteria, and even a neutral scenario where all criteria have the same level of importance.

4.3.1 Expert scenario analysis

As presented in section 2, based on the consistent evaluations of the eight experts, the weights for each criterion and subcriteria were defined, according to Table 7. This set of weights was named Expert scenario.

1st level criteria	(%)	2nd level criteria	(%)	3nd level criteria	(%)
EC	24.64	EC1	37.39
		EC2	20.20
		EC3	5.35
		EC4	37.09
TC	29.64	TC1	19.04	TC11	12.92
				TC12	33.28
				TC13	37.07
				TC14	16.72
		TC2	36.90
		TC3	44.04	TC31	54.65
				TC32	45.35
RC	21.07	RC1	51.67
		RC2	48.33
FC	24.64	FC1	61.45
		FC2	38.55

Table 7

Weights for each criterion and subcriteria based on consistent expert responses.

Considering the weights defined by the expert’s answers (Table 7) and the weights defined through the ranges of interest (Table 4) together with the information of the batteries made available (Table 6), the final score of each heat in each criterion is provided in Table 8, and also the final priority of the heats.

Battery	Environmental	Technological	Regulatory	Financial
1	0.2371	0.1700	0.3415	0.3267
2	0.2371	0.1819	0.1186	0.2433
3	0.2527	0.2176	0.3415	0.3267
4	0.2730	0.4305	0.1985	0.1033

Table 8

Notes for each battery against the criteria.

From the perspective of the environmental criterion, the indicated technology is that of lithium ions; however, the difference between the results of the four technologies was not substantial. This alternative is also the most adequate regarding the technological criterion, in this case with a wide advantage in relation to the others. As for the regulatory and financial criteria, lead-acid (OpzS) and vented lead-acid batteries obtained the same results, since the two technologies have exactly the same input data for the associated subcriteria as show in Table 6.

Finally, with the assumptions adopted in this study and the four technologies evaluated, the final results are presented in Table 9. It appears that the overall result pointed to the Ventilated Stationary Lead-Acid technology as the best alternative for this study, that is, 27.92% priority over the others.

Battery		Final priority
1	Ventilated Stationary Tubular Lead Acid (OPzS)	26.13%
2	Lead-Carbon Acid (PbC)	19.73%
3	Ventilated Stationary Lead Acid	27.92%
4	Lithium Ion LFP (Iron Phosphate)	26.22%

Table 9

Final result of the AHP for each battery technology.

The results of the final priorities of technologies 1, 3, and 4 are very similar (around 2% off difference), so they can be considered technically equivalents and small changes in weights may result in different classifications.

4.3.2 Analysis of theoretical scenarios

With the AHP weights established, we can create other scenarios, which can explain different user preferences. For example, assuming a greater preference for a certain criterion and a lower weight for the others, or leaving them all with the same decision-making power, in this way the decision-maker indicates his priority.

To create these scenarios, we changed the weights given to the first-level criteria (Environmental, Technological, Regulatory, and Financial), while the rest of the weights are defined according to the expert’s scenario (Table 7).

In this way, we generate five different scenarios, namely: environmental, technological, regulatory, financial, and neutral. The weights for the criteria of each scenario can be seen below in Table 10, with the criterion with the highest weight highlighted in bold.

		Scenario
		Environmental	Technological	Regulatory	Financial	Neutral
Criteria	EC	0.4000	0.2000	0.2000	0.2000	0.2500
	TC	0.2000	0.4000	0.2000	0.2000	0.2500
	RC	0.2000	0.2000	0.4000	0.2000	0.2500
	FC	0.2000	0.2000	0.2000	0.4000	0.2500

Table 10

Weights for the 1st level criteria in each scenario

Finally, considering the assumptions adopted in this study and the four technologies evaluated, Table 11 shows the final result of the AHP for each scenario. The general result presents the priority ranking of the batteries, with the Stationary Vented Lead-Acid technology being the best alternative for this application, among the four of the five analyzed scenarios. The evaluation of these scenarios is interesting to verify the performance of technologies considering different strategies.

Battery	Scenarios priorities
	Environmental	Technological	Regulatory	Financial	Neutral
1	26.25%	24.90%	28.33%	28.04%	26.88%
2	20.36%	19.26%	17.99%	20.48%	19.52%
3	27.82%	27.12%	29.60%	29.30%	28.46%
4	25.57%	28.72%	24.08%	22.18%	25.14%

Table 11

Final AHP result for each battery technology in each scenario.

5. Conclusions

The Brazilian Power Sector is preparing the introduction of battery energy storage in its distribution lines for energy quality control. The success or failure of this new technology (from a financial and technical standpoint) depends on many factors. Different kinds of battery technologies have advantages and disadvantages depending on the operational systems regimes adopted. Different geographical locations, accessibility, spare parts availability, and other related factors may play a significant role in giving priority to one technology rather than another, and even environmental restrictions and the local regulatory framework can affect the results. The AHP algorithm is designed to take into account all these factors. It should be pointed out that the results depend a great deal on the evaluations of the specialists. In view of this, as many experts as possible must be consulted for each evaluated criteria and subcriteria to overcome this subjectivity.

In this work, we present a methodology to size and classify different battery alternatives, based on the AHP method. For this, considering the opinions of experts in the field, grades were assigned to different criteria and subcriteria, defined from the main characteristics of batteries in the segments: environmental, technological, regulatory, and financial.

Finally, to validate the developed methodology, we approach a problem of classifying four different types of battery technologies (Ventilated Stationary Tubular Lead Acid, Lead-Carbon Acid, Ventilated Stationary Lead Acid, and Lithium Ion LFP). In the study, two types of analysis were performed. The first analysis considered the specialists’ view about the analyzed criteria, and the study pointed out that the best alternative for the application was the Ventilated Stationary Lead-Acid battery.

The second analysis considered theoretical cases, with scenarios generated assuming a preference for each of the first-level criteria, and even a neutral scenario where all criteria have the same level of importance. In the results, the Ventilated Stationary Lead-Acid battery was the best alternative among the four of the five analyzed scenarios.

It is important to note that the useful life of the alternatives was used to calculate the batteries dimensioning; however, it was not considered as a criterion in the AHP method. In the future work, it is expected to use the useful life with the real prices of the technologies to replace the average price subcriteria.

The results of the method must be evaluated by specialists to validate the choice, since they have greater knowledge of the particularities of each technology. The advantage of using AHP for this problem is the consideration of subjective criteria such as environmental and regulatory criteria, which cannot be used directly in the calculation of the cost-benefit of technologies.

Acknowledgments

This research is been funding by R&D project PD-2866-0444/2016 proposed by Parana State Energy Company—Copel, under the auspices of the R&D Program of the Brazilian Electricity Regulatory Agency—ANEEL. The authors are also indebted to National Council for Scientific and Technological Development—CNPq for the subsidies for importation through law 8010/1990, I.I. 17/3098290-0.