Project 2

Question 1)Using MATLAB/simulink and  the drive cycle from the attached excel sheet, find-

1. The max heat generation of the battery 
2. The SOC of the battery at 2 *104second of the battery operation.

Soluation: The heat generated by the battery is calculated using Joule's heat and entropy heat. Joule's heat is the result of current flowing through the resistance of the batterry

   The maximum heat generation of the battery can be calculated by finding the maximum current during the drive cycle and using the resistance and time values.

To find the maximum heat generation of the battery, we first need to calculate the maximum current (Imax) during the drive cycle. We can use the given data for time, time step, and battery current to find the maximum current.

To find the maximum heat generation of the battery, we first need to calculate the maximum current (Imax) during the drive cycle. We can use the given data for time, time step, and battery current to find the maximum current.

Using the formula for power (P = VI^2R), we can calculate the Joule heat generated by the battery during the drive cycle. Then, we can calculate the maximum Joule heat generated and the maximum heat generation, which includes the entropy heat

a. Calculation of Maximum Heat Generation:

From the given data, we can find the maximum current (Imax) during the drive cycle:

Imax = -0.896 A

Time (t) at which Imax occurs = 1.7 s

Resistance (R) of battery = 0.0005 Ohms

Using the formula for Joule heat generated (H = I^2Rt), we can calculate the maximum Joule heat generated:

Maximum Joule Heat = (Imax)^2 * R * tmax

= (-0.896)^2 * 0.0005 * 1.7

= 0.0006823936 J

To find the maximum heat generation, we need to add the entropy heat:

Maximum Heat Generation = Maximum Joule Heat + 2 * Maximum Joule Heat

= 0.0006823936 J + 2 * 0.0006823936 J

= 0.0020471808 J

Therefore, the maximum heat generation of the battery during the drive cycle is 0.0020471808 J.

The SOC of the battery is defined as the ratio of the charge stored in the battery (Q) to the maximum charge it can store (Qmax). Therefore, we need to calculate Q and Qmax at 208 s.

Since the drive cycle data is given for a time step of 0.1 s, we can find the battery current at 208 s by selecting the value at index 2080 (since 1 s = 10 time steps). Then, we can integrate the battery current over time to find the charge stored in the battery (Q) at 208 s:

Q = ∫(Battery Current) dt from 0 to 208 s

= Δt * ∑(Battery Current) from 0 to 2080

= 0.1 * ∑(Battery Current) from 0 to 2080

Similarly, we can find the maximum charge the battery can store (Qmax) by multiplying the battery capacity (in Ah) with the nominal voltage (in V) of the battery:

Qmax = Battery Capacity * Nominal Voltage

Assuming the battery capacity is 10 Ah and the nominal voltage is 12 V, we get:

Qmax = 10 Ah * 12 V

= 120 Wh.