Project 2
SOLUTION)
The max heat generation of the battery
There are 2 heat sources for the battery heat generation
- Joules heat
- Entropy heat
Heat generated = Joules Heat + Entropy Heat
Joules Heat :
From ohms law, we know that
V = IR
when a current flowing through a resistance, there is a heat dissipated in the resistor. This heat dissipation is called Joule heating. Joule heating is also known as ohmic heating.
Power,
P = V*I = I*I*R = I^2*R
Heat,
H = ∫P.dt with the limits of time 0 to t
H = I^2*R*t
Joule heat,
H = I^2*R*t
where. p = Power
V = Voltage
I = Current
R = Resistance
H = Heat
t = Time
The heat Generated in the Resistor is-
- Directly proportion to the square of the current flowing through it
- Directly proportion to the resistance
- Directly proportion to the time for which the current flows through it.
Entropy Heat:
The heat generation due to entropy change inside a battery occurs when electro chemical reactions are performed. The entropy heat is reversible heat resulting from change in open circuit voltage with respect to temperature at two Electrodes.
Given parameters are,
Battery resistance is 0.5m ohm
Delta time is 0.1
Entropic factor is 2
Maximum current is -0.896
As we know ,
Total heat = joules heat + Entropic heat
Joules heat = I^2*R*T
Joules heat =(-0.896)^2*0.5m*120sec
Joules heat = 48.16m joules
Entropic heat = 2
Total heat = joules heat + Entropic heat
Total heat = 48.16mA + 2
Total heat = 50.16m Joules
Total power loss is I^2*R
Total power loss = (48.16m)^2*0.5m
Total power loss = 1159.7 m^2 Joules
2) The SOC of the battery at 2 *104second of the battery operation:
The SoC refers to the State of Charge of the battery, which is the capacity percent left in the battery which can be used. It a very important thing which tells about the battery status which helps in using the battery in a proper manner.
The SoC can be measured in different ways. Some of them are listed below
- Voltage Translation Method (VT)
- Coulomb counting method (CC)
- Combination of VT and CC
The VT and CC has its own advantages ad disadvantages so to get accurate value we have to use the Combination of VT and CC.
Voltage Translation Method (VT):
It is measured by Open Circuit Voltage of the battery and compared it with the Data sheet of the battery and SoC is estimated. It cannot used while the battery is in operation.
Coulomb counting method (CC):
It is calculated by the formula
SoC = total charge input / Max capacity of the battery
Total charge input = charge current * time (H)
Or
Z(t) = Z(0) - 1/Cn ∫ Ni*i(t) dt with the limits of 0 to t
where, Cn = Battery Nominal Capacity
Z(t) = State of charge
i(t) = Instantaneous cell current
t = time
Ni = coulomb efficiency
Z(0) = initial state of charge
+ for discharging
- for charging
SIMULINK MODEL:
Result and Conclusion:
1. The max heat generation of the battery
The Max heat generated in which the current flowing in and out i.e., charge and discharge due to internal resistance and chemical reaction during charging and discharging of the battery the heat is generates of 50.16m Joules
