So the simulation is now complete and the code on

this slide shows you how you can

plot some results from the simulation.

We begin by creating a time vector having correct length

against which we can plot the voltage and

current and power and state of charge.

Then in figure one,

we plot the state of charge of

the cell in percent versus time,

in figure two we plot the terminal voltage versus time,

in figure three we plot the input current versus time,

and finally, in figure four we plot

the cell power versus time.

The figures on this slide show you

some example results from the simulator.

In the top left plot,

you see state of charge versus time,

on the top right you see terminal voltage versus time,

in the bottom left,

you see cell input current versus time,

and finally, on the bottom right,

you can see cell power versus time.

If we look first at the top right figure,

you can easily see that

the voltage is increasing as the cell is

being charged under

the constant current part of the profile.

Then when the voltage achieves

its maximum value of 4.15 volts,

you can see that the voltage is held constant

and steady until the end of the simulation.

This is exactly what we would hope to see.

In the bottom left figure,

you can see that the input current

is indeed held constant at

the constant current value until

the maximum voltage is achieved

around time 1,500 seconds,

after that the magnitude of current decreases

towards zero as the terminal voltage is held constant.

By the way, this is exactly what we see

when we're charging real battery cells also,

this is not an artifact of simulation.

While the simulation uses a model that

is not completely precise,

the trends that you see and the basic idea that you see

here is exactly what we see when we're

charging a battery cell in the laboratory.

In the top left figure, you can see state of

charge and how it increases

linearly over time during

the constant current portion of the test.

Then you see that when we switch to

the constant voltage portion of the test,

the state of charge

still increases but not as rapidly and so

the slope becomes non-constant as

state of charge slowly

approaches the desired final values.

By the way, this is a demonstration

of one reason why it's possible

for many systems to charge quickly up

to about 80 or 90 percent state of charge.

But then why it takes so much longer

to charge up to the final state of charge,

the full state of charge of a battery pack.

The reason is if we charged

quickly all the way up to a 100 percent state of charge,

we would exceed the

manufacturer voltage ratings of the cell.

But we can get maybe 80 percent of

the way quite quickly without

exceeding those voltage limits.

Finally, the bottom right figure shows power versus time.

For the first interval,

we know that current remains constant but voltage is

increasing and so the magnitude of

power is actually increasing.

Then for the second interval,

the magnitude of current is

decreasing while voltage is held constant

and therefore the magnitude of power decreases over time.

Notice I've been careful talking about

magnitude of current and magnitude of power.

When we're charging both of

these quantities are negative,

so I am talking about the size decaying,

perhaps, towards zero where you can see that

the signed value is actually

increasing but the magnitude is decreasing.