# Ranking of Electricity Accumulation Possibilities: Multicriteria Analysis
## 3 Materials and Methods  
In this study, TOPSIS, multi-criteria decision analysis (MCDA) was used to determine the best solution among electricity storage technologies. The methodological framework applied in this research is retrieved from [23; 24; 25]. The utilization of Multiple Criteria Decision Analysis (MCDA) is prevalent in the process of decision-making and assessment of determined targets. This approach involves the consideration of diverse forms of information and data, including qualitative and quantitative data, data from the physical and social sciences, as well as policy and ethics. The purpose of this method is to evaluate potential solutions to problems. Various Multi-criteria Decision Analysis (MCDA) techniques can be employed to address problems and they can be categorized based on various parameters and their model structure [26]. The TOPSIS method, also known as the Technique for Order of Preference by Similarity to Ideal Solution, is a decision-making approach that involves selecting the best option based on its similarity to an ideal solution. This can be derived from the notion of a shifted ideal point, whereby the solution that involves compromise is characterizedby the minimum distance. TOPSIS offers significant benefits, including the ability to identify an extensive range of criteria and alternatives, while utilizing a straightforward calculation approach. The TOPSIS methodology enables the attainment of viable and comprehensible alternatives for conducting comparisons. Alternatives must be selected for evaluation, which are evaluated according to four criteria: technological, economic, environmental, and social. The first step using the TOPSIS method is the normalization of the decision matrix, followed by the calculation of the best and worst solution of the normalized decision matrix. The best solution corresponds to the theoretical variant of the preferred level of each criterion, while the worst solution corresponds to the theoretical variant of the least desirable level of each criterion. Finally, the distance of each alternative is calculated, which further allows to obtain the proximity coefficient of the ranking alternatives. Alternatives rank from best to worst [25]. The equations of the TOPSIS method used in this study are described below. The derivation of the normalized matrix value can be achieved through the multiplication of the normalized value and weight, as expressed in Equation (1). \[v_{ai}=w_{i}\ \times r_{ia} \tag{1}\]  
where  
\(v_{ai}\) = weighted value;  
\(w_{i}\) = weight, \(w_{i1}+w_{i2}+\dots\) +\(w_{im}\) = 1, \(w_{i}\) = 1 \(\dots\) \(m\);  
\(r_{ia}\) = normalized criterion value. The calculation of distance for both ideal and non-ideal alternatives involves the summation of the squares of weighted criterion values. The calculation is performed by following Equations (2) and (3). \[d_{a}^{+}=\sqrt{\sum_{j=1}^{n}(v_{i}^{+}-v_{ai})^{2}} \tag{2}\]  
where  
\(d_{a}^{+}\) = distance for each action to the ideal solution;  
\(v_{i}^{+}\) = ideal solution;  
\(v_{ai}\) = weighted value. \[d_{a}^{-}=\sqrt{\sum_{j=1}^{n}(v_{i}^{-}-v_{ai})^{2}} \tag{3}\]  
where  
\(d_{a}^{-}\) = distance for each action to the non-ideal solution;  
\(v_{i}^{-}\) = non-ideal solution;  
\(v_{ai}\) = weighted value. Closeness coefficient (Ca) shows the distance to the non-ideal solution, which is determined by Equation (4). \[\text{Ca}=\frac{d_{a}^{-}}{d_{a}^{+}+d_{a}^{-}}, \tag{4}\]  
where  
\(d_{a}^{+}+d_{a}^{-}\) = sum of the distance to the non-ideal solution;  
\(d_{a}^{-}\) = distance to the non-ideal solution [25]. After conducting a literature review, it was concluded that in order to obtain more accurate results, it was necessary to compare energy storage technologies in two groups. Division in groups is determined by considering energy storage scalability and applicability, conducting a comprehensive evaluation of various criteria to facilitate a more suitable comparison between alternatives.