# Boosting voltage from a current source

Hiah all,

I have a beginner question about boost converters. I would like to model a solar cell using the following equivalent circuit: This effectively gives me a current source (constant in the simplest cases but ultimately I want to add variability due to temperature and insolation as well). Now, when I connect a boost converter to the above circuit, I can increase the voltage but not by as much as I would like. Changing the duty cycle makes the input voltage of the converter lower and thus the output doesn't increase... Here's a schematic of the converter:

simulate this circuit – Schematic created using CircuitLab

It also doesn't really make sense (based my limited knowledge of electronics) to join a current source to the boost converter without any modifications as, when the switch is connected vertically (on state), the steady state current over the inductor doesn't change so its voltage is zero. Therefore, the longer the on state (or the greater the duty cycle D), the closer to zero the voltage to be boosted gets before the switch opens again.

How could I easily change my model to overcome this? Can I just smack a capacitor of the right size in parallel between the solar cell and the boost converter? I'm ultimately looking into creating a controller that keeps a steady output voltage with varying load so just choosing a greater resistor as load doesn't really solve the problem.

Any help is greatly appreciated.

• What HatimB says. Simply: While panel acts similar to a CC it does NOT deliver CC at all times - that is rather the max I it will supply if the load demands it. At load currents up to the available current I it is more like a CV. To get "near MPPT" you load it to about 80-85% of Voc. Available current is then approx proportional to insolation. A cap across the panel charges to the level you'd get if you drew the average load current continually.... – Russell McMahon Mar 28 '17 at 12:11
• ... What really happens is you draw I into load when switch is on and cap also feeds load and then when switch is off cap charges from panel and Vcap rises. ... Ccap is made large enough that ripple due to PWM loading is small overall. – Russell McMahon Mar 28 '17 at 12:11
• Thanks for your comments, @Russel. So would high capacitance give better results? I'm going to stick to an ideal current source until I get past my DC-DC conversion problem at least... – Kirjain Mar 28 '17 at 14:03
• "effectively gives me a current source" - no, it effectively gives you a current limited voltage source. samlexsolar.com/learning-center/… – Bruce Abbott Mar 28 '17 at 16:11

I can increase the voltage but not by as much as I would like.

Theoretically a booster can produce as much voltage as you like, but you can't get more power out than what you put in. The solar panel has maximum power output at the point where the product of voltage and current is maximum. If you try to draw more current that this then the voltage and power will drop so your booster's output power must decrease.

So the answer to getting more booster output voltage is to increase the load resistance. It will then drop more voltage when drawing the available power.

I'm ultimately looking into creating a controller that keeps a steady output voltage with varying load so just choosing a greater resistor as load doesn't really solve the problem.

Then your problem cannot be solved because you can't put more power through the resistor than the panel provides. All you can do is reduce power (by lowering the PWM ratio) to regulate voltage when you have more power than you need.

A boost converter is not a transformer - it doesn't boost voltage by any particular ratio - but it will convert power to whatever (higher) voltage you want at lower current.

Can I just smack a capacitor of the right size in parallel between the solar cell and the boost converter?

You can, but you still won't get more power out than what the panel can deliver. Booster input current is continuous, but there will be some ripple due to limited inductance. A capacitor smooths out the ripple and so makes the panel's job a little easier because it only has to deliver the average (not peak) current.

• Thank you for your answer @Bruce. You cleared up some of the confusion around this issue. Would up-vote your answer but I'm afraid I'm not allowed to yet! I'm too new around here. – Kirjain Mar 29 '17 at 14:36

Well, a solar panel is not a perfect current source. If the load has a high impedance value, your solar panel can't generate a high enough voltage to provide $I_{SC}$ otherwise It should be to generate unlimited amount of power.

when the switch is connected vertically (on state), the steady state current over the inductor doesn't change so its voltage is zero.

Assume we're in the boost steady state. Before connecting the inductor to solar panel, the value of the current going through it decreased since it was releasing its energy to the output. When you connect it to the panel, the current has to jump instantaneously to $I_{SC}$ which means the panel has to generate an infinite voltage, not possible. The voltage across the panel (equal to the voltage across the inductor) has a finite value. You calculate $I_{L}$ using integrals until is reaches $I_{SC}$ then it maintains that value.

Can I just smack a capacitor of the right size in parallel between the solar cell and the boost converter?

That's is a good idea to make the panel work in a specific operating point (voltage and current generated by the panel are more stable because of the capacitor charging/discharging) which I'm guessing is the MPP. Otherwise they will be varying a lot and your controller will be struggling if it was able to work at all.

PS: This is quite a simplistic approach I made just to get the point across, if you want precise calculations, be prepared to use a bit more of maths $(e^{f(V)})$ :P

• Thanks @HatimB. If you don't mind elaborating, I'd love to see a bit of maths. I would also love to see how this problem is usually solved, I haven't really found any solid answers on the Internet. Not using the right key words when searching, I suppose. – Kirjain Mar 28 '17 at 13:53
• There is an equation which describes the solar panel behavior $I=f(V)$, I dropped a hint at the end of my answer (the exponential function) which you can use to know the voltage and current that the panel will be able to supply at that specific moment, but first you have to find your panel's parameters to plug them in the equation. From what I can remember it's very difficult to do this by hand, you might want to use a computer for this. The equation looks like this $I_{PV}=I_{SC}-I_0*(e^(qV/KT)-1)$ while neglecting series, parallel resistors and a second parallel diode – HatimB Mar 29 '17 at 8:03