# Optimum Battery Model Based on AHP and TOPSIS

Summary

This is a teamwork done by 4 people during the international competition High School Mathematical Contest in Modelling 2021.

Adoption of solar energy for home usage is becoming increasingly popular nowadays, which has led to an increased demand for solar energy storage systems, and consequently various suppliers of such storage systems. An objective evaluation model, which can address the following four problems, is thus needed to provide trustworthy suggestions of solar energy storage systems to numerous households.

For problem 1, to build the battery system, we first identify the energy needs, which are power rating and total energy required. After that, we design storage systems to satisfy such energy needs. When evaluating the energy storage systems designed, we translate the battery factors into ratings from 1 to 9, and then use an analytic hierarchy process to calculate the relative importance, the weight, of each factor. The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) analysis is thereafter used to find the similarity of each battery storage system respective to the worst situations. This helps us select the best solar energy storage system for the 1600-square-foot off-the-grid home that we are planning to build.

For problem 2, we further generalize our model, enabling it to provide suggestions to every household in need. Firstly, we introduce quantitative models of the factors influencing the energy needs: size of the house, number of family members, average temperature, and energy consumption habits. Secondly, we utilize public surveys to obtain individual factors that determine personal preferences. Then we evaluate the model’s strength and weaknesses.

For problem 3, we survey recent research on cement batteries about the operation principles, properties and both advantages and disadvantages. Then we identify what other data is needed to include cement batteries as an alternative in the model for choosing the best battery storage system.

For problem 4, we explain our solar battery storage decision model and discuss the future of a cement battery through a news article.

Key words: Analytic Hierarchy Process, TOPSIS analysis, Normalization of Factors, Quantitative model, Satisfy Individual Needs, Adaptable to Personal Preference, Comprehension and Detailed Evaluation Model