# Charging a Li-Po with a solar panel

I'm looking to setup my e-bike touring bicycle with a solar outfit so that it can charge on the road, but am unsure of the electronics. I appreciate the size of the panel will be huge, but this can either go over the bike or on a trailer being towed.

The battery is a 36v, 17.5Ah lithium ion, with the following spec -

Maximum Charge Voltage: 42V
Discharge Cut-off Voltage: 28V
Standard Charge Current: 2A (3A maximum)
Charge Method: CC/CV

Bike motor is 450 watts.

What would be a recommended setup to provide an almost constant power (about average 2/3rds of maximum motor pull) stream in say perfect sunlight? What management electronics would I need?

Thanks.

I will caveat the following by saying the sizing will depend on your riding patterns. It's unlikely you draw a full 450 watts at all times while riding. If you did, you would kill the battery in under an hour and a half. So, you might want to build an estimate if your "average" consumption by thinking about how long the battery usually lasts when you're riding the bike.

In terms of providing 2/3rds of the rated motor power, that's just:

$$\frac{2}{3}\times450W = 300W$$

How much power you get out of a solar panel can be approximated by:

$$P = \eta E_e A \,\textrm{cos}\,\theta$$

Where $$\P\$$ is the power output in watts, $$\\eta\$$ is the efficiency of the solar panel, $$\E_e\$$ is the solar irradiance in W/m^2, $$\A\$$ is the panel area in square meters, and $$\\theta\$$ is the angle between the vector normal to the surface of the panel and the sun vector.

Rearranging to solve for area, we find that the surface area of the array needed to generate a specific amount of power is: $$A = \frac{P}{\eta E_e \,\textrm{cos}\,\theta}$$

We know that $$\P\$$ is 300 watts. $$\\eta\$$ is also easy to estimate: commercial solar panels have efficiencies in the 15-20% range, so we'll lean on the optimistic side and go with 20% (special multijunction cells are available that go up to 30-35% efficiency, but these are very expensive to produce and are mainly limited to the aerospace market).

The $$\ E_e \,\textrm{cos}\,\theta \$$ term is a little trickier. Solar irradiance at the Earth's surface is around 1050 W/m^2, but that's only true on a clear day: cloud cover and atmospheric aerosols can diminish that number, sometimes drastically. Likewise, unless your solar array is mounted on a sun tracker, the angle from the panel to the sun is going to vary depending on time of day and your latitude.

Thankfully, there is a lot of data out there about the average expected amount of energy that can be absorbed by a panel on a particular day or a particular location. This is called insolation. For example, if I choose to compute the insolation figures for a flat non-tracked panel in Minneapolis using this calculator, I get the following table:

As you can see, the amount of energy you get varies significantly over the year for a given location. Let's assume you are riding in the summer, so we'll take the figure for June, 5.89. The numbers the calculator gives us are in kWh/m^2/day, so we need to do some quick math to convert it into an "average" W/m^2 throughout a typical day:

$$E_{e(eff)} = Insolation \times 1000 \frac{W}{kW} \times \frac{1}{\textrm{# of Daylight Hours}}$$

We will say that daylight is roughly 15 hours in June in Minneapolis. Putting this together, we get $$\ E_{e(eff)} \$$ is roughly 393 W/m^2.

Since the insolation calculation accounts for panel orientation (in this case, flat on the ground), we can drop the $$\ \textrm{cos}\,\theta \$$ from our calculation. We are just left with:

$$A = \frac{P}{\eta E_{e(eff)}} = \frac{350W}{0.20 \times 393 \frac{W}{m^2}} = 4.5 {m^2}$$

So, you'd need a 4.5 square meter array to solar-propel your E-bike in Minneapolis from sunrise to sunset on a typical June day. Of course, this is only average - due to weather conditions, some days you'll have excess energy, other days you'll have a deficit. An array this size is probably a little too big: if you towed this array behind you, it'd look something like a four foot by twelve foot trailer.

You will probably want to run this analysis for different permutations to see where it might start to look feasible. A spreadsheet is a great what-if tool. Threads to pull on would be power consumption (we assumed your motor needed 300 watts, if it needs less, that's a smaller array), weather (maybe you intend to ride in an exceptionally sunny place), and number of hours on the road (I assumed you ride from dawn to dusk - if you only ride for a few hours a day, things start to look better).

As for electronics, you would need something like a MPPT solar charge controller specifically designed for lithium ion batteries. There should be some available on the market.

• Peter, many thanks for your insight. That's very helpful and interesting to understand. I was aware that the panel would have to be considerable, but that gives me a better idea of the sort of size I'm looking for. – Alex Thomson Jun 11 '19 at 22:40
• Just another question David. I see many panels are 12v. So to achieve the 36v for the battery, would you suggest wiring 3 say 120w 12v panels in series? Or is it best to charge at a slightly higher voltage? Or will the MPPT sort this out? – Alex Thomson Jun 12 '19 at 15:19

A couple of things to consider:

1) Yes, the panel would be rather massive. You may find that the extra weight causes extra battery drain and thus get some pretty serious diminishing returns as you increase in size. You also need to consider air resistance in how you mount it, since again the extra drag could cause some problems if you ride at any decent speed.

2) Since I assume you are riding in the day, most of your charging would be happening at the same time as your discharging. I strongly doubt you can mount a system that would keep the battery charged while in use.

3) Your bike has a maximum weight capacity, which after your body weight (depending on how lite you are) may not leave much room for extra stuff. I'm not sure how a trailer works with that in conjunction with the e-bike, but the motor is probably rated for some maximum weight. It may be higher than the maximum weight you can put on the frame, but a trailer could exceed it.

With all that in mind, I think you should be looking at a slightly smaller system. Maybe keep it under the maximum frame weight (you + solar array). See what kind of size panel(s) come under that weight.

Solar wants to use MPPT (max power point tracking). There is almost certainly an integrated MPPT+Li-Ion charger combo that would fit your needs.

I'm imaging you end up with something that while unable to keep your battery charged, would extend the useful duration and allow some recharging between motor use.

• Thanks for your thoughts hekete. Interesting that you mention about the battery charging and discharging at the same point - will look into that. I'll have to look into light weight panels also – Alex Thomson Jun 11 '19 at 22:42