Hello everybody and welcome to this training

on how to extract power from a solar cell. My name is Stefano Stanzione and I work for

IMEC NL and I’m researching ultra-low power analog IC design. So all of you probably know what a solar cell

looks like. It’s based on the photoelectric principle so in practice it’s a voltage barrier

and when a photon is absorbed in the junction between these two materials, a charge, a hole

and an electron can be separated by the electric field and be pushed towards the electrodes.

In practice, this implies that you will have a current, even when the voltage is zero and

this current is called short circuit current and can be indicated as IL, illumination current

as you can see in this formula. So, actually, the characteristic of a diode, gets translated,

gets shifted up by the illumination current. So, what happens, if you calculate the power,

you multiply the current times the voltage, you get this kind of curve and for low voltages

you have a linear increase of the power because the current is constant and the voltage is

linearly increasing. But, at a certain point the exponential characteristic of the diode

takes the lead and pushes down the characteristic so it will have peaks of the power like shown

in this figure. And, you can see that the peak of the power are not always for the same

voltage of the solar cell but is moving when the illumination level changes. We can define

a characteristic resistance RCH as the resistance you should connect to the solar cell to extract

maximum power out of it. And, this resistance can be easily approximated as the open voltage

over the short circuit current of the solar cell. Now let’s make things a bit more complicated.

We have seen the illumination current, we have seen the diode but there are also some

more things to model like resistive effects. We have a series resistance which is due to

the finite conductance of the material and also to the contact resistances and also we

have a shunt resistance RP which is modeling more or less the impurities in the material

and both will reduce the maximum power you can extract from a solar cell. What happens if we do the simplest thing we

can think about; connect a load circuit directly to a solar cell? From this simple circuit

you can see that if we do that, the voltage across the load will be non-constant because

the illumination level will change, maybe there are some moments in which there is shade

and so you will not have a regulated output voltage. Also, when indeed there is shade,

or there are very low light conditions, the load will not work. And, finally, you have a problem with matching

the load resistance, because the load resistance would in general not be equal to the RCH which

is the optimal resistance that the solar cell wants to see as a load. So, we need something in-between, we need

to put some circuit between the load and the solar cell. And this interfacing circuit can

be simply something like an inductive switching converter or a switched capacitor converter.

Let’s try now to dive into these two circuits and to understand why we would choose one

over the other. An inductive step-up converter is a circuit

like this. What happens is when you turn on this switch, the inductor current starts increasing

linearly like in this plot, and then when you turn off the switch, the inductor current

decreases linearly and flows through the diode to the output capacitance. If you calculate

the energy that you put into the system and the energy that you get out of the system,

you get for ideal switches without any parasitics, parasitic capacitances on the switching nodes,

etc, you get 100% efficiency. So charging an inductance is inherently not a lossy mechanism,

and that’s very nice. Of course when you do something practical,

so you buy a component, then the peak efficiency will not be 100% it will be something like

90, 95%. and you will have a shape like this which is a function of the load current. So,

it will have something dropping down for very low load currents because you have the control

circuits losses, the quiescent current that’s started to weigh. You will also have power

train losses; the switches in reality have a finite value of resistance, the inductor

is not ideal and you have some parasitic capacitances on the switching nodes. So, the characteristic

will have a peak somewhere. What happens with capacitive step up converters?

Their working principle is very easy to understand; you have two capacitances. First, during phase

phi-1, you charge capacitor C1 with voltage VIN and then during phase phi-2, you put capacitor

C1 in series with VIN towards capacitor C2. So, in the end, at steady state, you will

have an output voltage, if there is no load connected equal to twice the input voltage.

What happens is that if you calculate the efficiency, let’s simplify without any load

resistance, you get an efficiency which depends on the voltage, which is completely different

that what we got for the inductive converters, and 100% is achieved at only one point when

the ratio between the input and output is equal to the steady state value that you want

to achieve without any load. And, in-between, you have very low efficiency. So, what typically,

is done to overcome this problem is to make many types of converters all with different

voltage ratios and then select one or the other, selecting always the one which is better

for the voltage where we are operating. And this for example is done in this nice

ISSCC paper of 2014, where they not only optimized the voltage ratio dynamically but they also

optimized the isolation frequency and they have a quiescent current extremely low of

3 nW. So now let’s try to compare these two approaches;

inductive and capacitance conversion. For sure, inductive conversion is very difficult

to integrate, inductances are much more difficult to integrate than capacitors. So if you want

a very small solution, fully integrated, it’s good to go for a capacitive converter. If

you want the highest possible efficiency then it’s good to go for inductive conversion and

in general in terms of output voltage and output current range, inductive conversion

is better but capacitive converters are stepping out more and more as a trend. Now let’s talk about the maximum power transfer.

We said that the input resistance of this interfacing circuit should be equal to the

characteristic resistance of the cell. So, we need some way to tune some parameter for

example the switching frequency, to always get these maximum power points, here. To do

so, there are algorithms, called maximum power point trackers that have the following task,

they have to be fast enough to follow the illumination for example variations and they

need to be highly efficient which means they must precisely match the input resistance

because every error counts as power losses. They have to be stable, because if they oscillate

around the maximum power point, then you lose efficiency. And, they have to be low power

because you don’t want to consume with this algorithm more power than what you get by

using them. So, the simplest types of MPPT algorithms

are the constant voltage and constant current. Constant voltage means that it can be observed

that the optimal point, the maximum power point, happens at a cell voltage which is

a certain fraction of the open voltage. So, simply what you do, you open the cell, measure

the open voltage, calculate this fraction of the open voltage and try to modify the

switching frequency until you get to that voltage and this is very fast and simple.

But, of course, this optimal ratio is something that varies between different types of cells.

So, you are not really creating a generic solution and also it’s inefficient because

always when you disconnect the solar cell from the interface, you are wasting all of

the power that is generated into the solar cell. Constant current is the dual approach,

the optimal current is a fraction of the short circuit current. Also, in this case, it’s

very simple and fast, optimal ratio is dependent on the type of solar cell and it’s inefficient

because you’re going to short circuit the solar cell once in a while. A more generic approach is the perturb and

observe algorithm. In this case what you need is a bit more complexity, to evaluate the

output power of your system and try to maximize it. So, you actually do things step by step,

you monitor the output power and then change a bit the frequency or the cell voltage and

then you detect the power is increased and you continue changing the direction until

the sign of the power variation doesn’t change, and then you return back and you will remain

oscillating around this maximum. What happens in this case is that you have a trade-off

between the speed that you have in reaching the top of this power hill and the oscillations

around the maximum power point. Because if you want to reduce these oscillations, you

need to reduce this step size which means you will spend more time climbing the hill.

So, a better way would be to make this step variable so you would like to go faster when

you are far from the top of the hill and very slow when you are on the top of the hill.

So you would actually like to have a step size which is proportional to the slope, let’s

say the derivative of this curve and this is what is done in the variable step size

perturb and observe algorithms which have all of the advantages, they are fast and stable

and widely applicable but they have one disadvantage, they are complex. An example of this is shown in ISSCC 2013

and this is a fully analog algorithm, using a step size which is proportional to the logarithm

of the power variation. So, in conclusion, we have seen in this short

training, the solar cell characteristics and modeling, and the types of interfacing circuits

which typically are used and why they are used and also the reason behind the use of

maximum power point tracking algorithms and we have given examples of the advantages and

disadvantages of different types of algorithm. I hope you enjoyed.