Answer

This report gives us a brief overview of the batteries, their types and their use in the solar system it also provides us the comparison for investing in the Solar System with different types of batteries. An excel sheet was developed for this purpose which receives several inputs from the user, for example Load profile, selected battery, solar Size, load requirement, location, tariff, extended warranties, interest/ discount rates etc. and provides us a brief output for a choosing a better option for our investment.
By entering such inputs, the excel sheet calculates the requirement by using the predefined profiles and formulas along with its total cost, return on Investment, Payback Period, savings and many more. It also shows us the trend of your investment and the output of the solar system by displaying them on the X-Y axis graphs and pie chart.
By assuming several parameters and by fixing some, we have designed the compatible system for different locations and came to know that the Load profile i.e. time of load use has no impact on the total investment but directly effecting the other parameters like payback period, Grid Import and Export, Return on investment system health and life span.
The total Kwh requirement of the house/area plus the backup required, has to be designed efficiently in order to get the consistent and efficient output for which we should know about the load we have to use on the solar system keeping mind the total cost of the system. As the solar system is still a costly investment but there is no comparison with the other source of energies available. The solar energy provides us the green and clean energy as a result we can help the environment getting greener and cleaner.
The common types of batteries used in the solar systems are as follow [9][10]
1. Lead – Acid Batteries
2. Nickel – Cadmium Batteries
3. Nickel – Metal Hydride Batteries
4. Lithium – Ion Batteries
The most common type of battery used in house is the 1st and the 4th one in the above list. Both have their own pros and cons while having a huge cost difference between them. One has to choose keeping in consideration the clear view of their requirement.  
Working of Model:
The Simple-Solar-Battery Model provides us the comparison between the inputs and outputs in order to design a solar system with or without batteries. The basic use of this model is to get an extensive idea of how to design an effective solar system keeping in consideration the price and quality of product.
Major products in a solar system are the Solar PV, Inverter and the batteries. These products hold the maximum cost from the total capital investment. The developed excel sheet for this purpose has several inputs in the tab named as Assumptions and Inputs which has to be entered by the user in order to get the tabular and pictorial output for the requirement. The results vary for every situation for example the use of day and night is different so is the load consumption, this is directly proportional to the cost. A general rule is that having more complex requirements will lead to a higher capital investment.
The load flow study and the profile have already been entered in the sheet under the name of Load Profile tab in order to fetch the data of load, time, and tariff with respect to the locations. Power Flow tab has all the power data of load, solar, batteries and grid. By interpolating these we can extract the exact information which is required for investing in the Solar system. The output tab has all the output required for a lay man in order to select the exact required system for their need. 
Design Assumptions:
Following assumptions are made in order to conclude the task
1. Load Profile
a. Morning/evening peak
b. Morning/Evening peak with controlled day loads
c. ‘Stay at home’ steady daytime load
2. Solar PV Size
3. Daily House Hold Energy Use
4. Battery Size, model and its type [10]
5. Brand
6. Location
In the above assumptions point 3 and 4 is set as some fixed parameters while the others were changed in order to get the better comparison from the data.
The decisions made is on the following parameters
1. Total Investment
2. Payback period of solar and battery
3. Solar Consumption
4. Grid Consumption

Table 1: Main calculations of the project

Results Analysis:
From the above assumption we have concluded that the optimum designed system having close output requirement with minimum capital investment, minimum payback period and minimum consumption from the grid side, and as a result the electricity bill shall reduce having direct impact on the ROI (Return on Investment).
There are extensive range of products available in the market some are compatible mostly are not for the domestic or house project. The variety of products confuses the individuals as a result the chosen system, without the market analysis fails most of the time. In this particular article someone has assisted by developing an excel formulated sheet which shall provide up to the mark market rates, product varieties, their price comparisons and many more.
For the above particular case study, we have selected 15 Kwh daily load consumption, 14 Kwh Battery and different capacities of solar plants on different locations. Every state has its own tariffs [8] and rate of solar system due to which the total investment and payback period vary. Similarly, different brands have different price ranges but more or less same output and life [3]. Investment should thus be not into too high nor too low in order to serve the cause. Moreover, change in the load consumption time cannot change the total investment but can lead in change of electricity grid import or export as well as the payback period [2].
Among all, 4 Kw solar plant has the best combinations in all aspects and 5 Kw plant went into the oversized system.

Figure 1 Solar+ Battery-Average household day:

Table 2: (Solar +Battery)Output of the Economic Model

Suggestions:
Based on the findings of the model, the following are the recommendations:
1. Practically, the depth of discharge (DOD) [6] of a battery should not be more than 80% whereas there was the option of 100%. Keeping the battery at 100% can drastically decrease the life span of the battery as a result it needs to be replaced [1].
2. The tariffs of the location can be more precise and accurate by linking it with the ecommerce sites [8]
3. Load profiles should be more detailed having the type of load used
4. The solar only pie chart to reformulate by using the solar only profile
5. Annual interpolation can be more system specific
6. The type of batteries should have been added in order to provide a variety