# avdweb

## Solar panels for the bicycle

Contents

### 1. Intro

Initially, most people find the solar panels to large and awkward. But is my solar bike unmanageable? Here are examples of other large bikes, which often have a length of 260cm.

### 2. World's most efficient silicon solar cells

Per July 2012, these solar cells have the highest efficiency:

### 3. Solar panel roof

Another option is a roof panel. It has some advantages:

• The panel does not suffer from shadow from the rider
• The bike is more manageable
• Larger solar surface area is possible

The disadvantages are:

• High center of gravity
• More wind load
• More weight

### 4. PV panel air drag

In the ideal situation of the absence of side wind and where the panels are horizontal to the wind, the air drag of the two PV panels is quite low. The skin friction drag is negligible with air. The shape should be aerodynamic like this:

With a PV panel width of 100cm and a thickness of 2cm, the air drag per panel is:
P = 1/2 * ρ * A * v3 * Cw = 1W

• Air density ρ = 1.23
• A = 1 * 0.02 = 0.02
• v = 20km/h = 5.55m/s
• The drag coefficient (Cw) of the PV panel is not precisely known but estimated at 0.5.

### 5. Wind force

The higher you go the higher the wind speed. On the ground the wind speed is zero. The wind profile is logarithmic, but close to the earth surface it is linear, see the wind gradient graph:

So it is important to place the solar panels as low as possible. Also, the moment of the wind load on the bike is larger at high mounted solar panels as a roof. The worst case situation is on bridges because here there the distance to the ground is high.

### 6. Wind aspects of concern

The air drag is low for a flat plate that is horizontal to the apparent wind. But when the panels are pitched by just a degree or two, this leads to a significant increase in force. In essence we have two inefficient aircraft wings that will generate some lift. This lift will act at a vector that is perpendicular to the apparent wind, not perpendicular to the surface of the solar panels, so will act to unbalance the bike. It will also create induced drag that is proportional to the lift generated, adding to the form drag we have from the projected frontal area of the panels.

Cross winds are the problem here, or more specifically, the vector sum of the side wind and the apparent wind caused by the motion of the bike. The force needed to unbalance a bike, by taking it outside the range of corrective moments that the rider can provide by shifting body weight is pretty small. The lift force vector will change direction extremely rapidly as the bike rolls, going from a maximum positive to a maximum negative value in a short time interval as the panels go from a positive to negative angle of attack relative to any side wind component. A known issue at racing bicycles, is the severe impairment of the steering that comes from using a disk wheel in a crosswind.

To avoid serious problems, the panels may not exceed a certain size and the wind force may not be too large. Although, the area of the PV panels is not much larger than the cyclist frontal area (0.5m2). So I don't suspect much wind problems anyway.

### 7. PV panel tilt angle mismatch

The PV panels are not pointed into the sun. But in summer, the loss due to the tilt angle mismatch is less than 20%. See this graph:

### 8. Bifacial solar panels

The back side of a bifacial PV panel generates electricity from ambient light reflected by surrounding surfaces; this results in up to 30% higher energy generation in comparison with a unilateral module.

### 9. Yearly average horizontal solar radiation

The annual energy in kWh/m2 from a solar panel depends on the location:

### 10. Interactive map of solar radiation

On SolarGIS iMaps you can get the solar energy values at every location on earth.

### 11. Solar panels electrically

The power from the solar panel depends on:

• Solar cell efficiency. The power of the highest efficiency solar cells is 230W/m2 at standard test conditions (STC).These conditions are: irradiance 1000W/m2, air mass 1.5 and cell temperature 25 °C.
• Panel angle. The angle that the sun hits the panels changes the amount of exposure. Because the solar panels are flat mounted and not faced to the sun, the power is always lower than rated. However, the fact that the sunlight is diffuse, limits this effect.
• Time of day. Because of the sun angle we can only get sufficient power from the solar panels between about 11:00 am to 4:00 pm.
• Time of year. From October to April the sunlight is not strong enough anymore to deliver energy to de bike.
• Solar cell reflection. The power will be reduced by the solar cell reflection. The protective top layer should have a low reflection coefficient
• Clouds. Clouds have such a large affect to solar panels that the solar bike can only be used at almost cloudless weather. Also veil clouds reduce the power to an insufficient value.
• Shadow. To understand the power loss effects of shadow, see the article about bypass diodes.

### 12. Shadow

In practice the PV panel shadow isn't really so bad. The cyclist is sitting somewhat hunched over on the bike, it isn't an up-right bike. I've taken pictures of the shadow at different sun angles. In most cases there is no shade or just a little bit. With a proper design of the PV panel, with bypass diodes, the power loss due to the shade is no serious problem.

### 13. Soldering solar cells

Soldering solar cells requires a soldering tip with a flat surface:

I use 60/40 tin-lead flux-core solder which melts at 370 °F or 188 °C. Note that cheap rejected solar cells (Evergreen) have sometimes a poor metallization which doesn’t allow proper soldering of the cell tabbing wire.

### 14. How to pack solar cells

Solar cells are very fragile, as baubles. Not well packed solar cells will be damaged easily during transport. Note that a stack of 125 solar cells weigh a kilogram. This weight forms a high stress to the solar cells during shipping; it demands a special attention to packaging. Just packaging solar cells in Styrofoam is inadequate.

• The solar cells should be properly stacked, outstanding solar cells will break.
• Pack the cells between solid plywood, not cardboard.
• Seal the package with shrink foil.
• Put the whole package into an exact fitting Styrofoam box.

### 15. Measurements

Measurements are done with the solar cell curve tracer. It is used to get experience and to do practical measurements; what is the influence of time of day, angle to the sun, temperature etc. Further the influence of the solar cell encapsulation etc. can be determined.

### 16. Solar cell model simulation

The solar panel with bypass diodes is simulated in Multisim. The models of the solar cell and bypass diode have to be created by ourselves. Here I describe how to make a solar cell Spice model for Multisim. The solar cell is a hierarchical block which contains a current source and a diode:

Download here the Multisim solar cell model.

This is the solar cell test circuit:

Download here the Multisim solar cell dc sweep simulation circuit.

Do a DC sweep analysis with these settings:

Analysis Parameters:

• Source = ii1
• Start value = 0A
• Stop value = 5A
• Increment = 0.1A

Output:

• Selected variables for analysis = V(1)

This is the Multisim simulation output:

In the Multisim Grapher View window do: Tools > Export to Excel and make a graph in Excel.

The diode parameters can be changed such a way that the model graph equals the solar cell graph. These are the figures of a particular solar cell:

• Open Circuit Voltage: 0.670 V
• Short Circuit Current: 5.9 A
• Maximum Power Voltage: 0.560 V
• Maximum Power Current: 5.54 A

From the solar cell data, the values of the current source and the diode can be determined:

• Current source 5.9A
• Diode 0.67V - 5.9A
• Diode 0.56V - 0.36A (because 5.9A - 5.54A = 0.36A)

This diode formula is used by Multisim and Spice:

Use this Multisim simulation for the solar cell diode and try successively different values for Is (saturation current) and for N (emission coefficient) to get the proper currents of 5.9A and 0.36A:

These values give a good result:

• Emission coefficient N = 1.52
• Saturation current Is = 0.234 μA

Finally, we get a solar cell model graph which equals the solar cell graph. Here is the graph for a current of 5A:

### 17. Single solar cell powered step-up converters

By using special low-voltage step-up converters, a single solar cell is capable to deliver power to electronic circuits.

The PV panel will further be described in three articles:

### 18. Vertical solar panels for indirect sunlight

Although not applied for the solar bike it is interesting to tell something about a different PV panel approach. Usually, solar panels take advantage from direct sunlight and are therefore as much as possible facing the sun. The power is up to 1000W per m2 earth's surface.

Vertical solar panels receives direct sunlight, this is just 200W/m2 or less. But, you can imagine that the higher the vertical solar panel, the greater the power, without increasing the used earth's surface. So, calculated per m2 of earth's surface, a tower of solar panels can generate more power than a usual solar panel. Per watt solar power, a vertically PV panel is a lot more expensive than a usual solar panel because many more solar cells are required. See more at the article "Solar energy generation in three dimensions".

### 19. Lux to Watt conversion

For the specific spectral composition of sunlight: 1 lux ~ 0.0079 W/m2

• Direct sunlight: max 130000 lux = 1030W/m2
• Indirect sunlight: max 25000 lux = 200W/m2