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The size of the PV panels

The solar bike with two solar panels
The solar bike with two solar panels

Since May 2014 I have used the solar bike more than 1000km without any problems. But initially, most people find the solar panels to large and awkward. This is because they have never seen the solar bike before. But is my solar bike unmanageable? Here are examples of other large bikes, which often have a length of 260cm.

Pack max duo
Pack max duo
Filibus
Filibus

WorkCycles Cargobike delivery
WorkCycles Cargobike delivery
Madsen bike black
Madsen bike black

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

Solar Fahrrad Frank-Holger Dobbert
Solar Fahrrad Frank-Holger Dobbert

The disadvantages are:

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

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:

Aerodynamic PV panel
Aerodynamic PV panel

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.

Wind gradient graph

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:

KNMI windprofiel
KNMI windprofiel

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:

Radiation diagram
Radiation diagram

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.

The sun's power

Global CO2 emissions have to be drastically reduced within the next few years in order to prevent a disastrous climate change. This is where DESERTEC offers a solution which can be implemented worldwide: Sufficient clean power can be generated in the world's deserts to supply mankind with enough electricity on a sustainable basis.

The total solar collectors surface (for concentrating solar thermal power) needed to provide the electricity for the humankind is 300x300 km², see here:

Desertec
Desertec

Solar power plant in the Nevada desert
Solar power plant in the Nevada desert

Yearly average horizontal solar radiation

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

Yearly average horizontal solar radiation kWh/m2
Yearly average horizontal solar radiation kWh/m2

Interactive map of solar radiation

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

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.

Outstanding solar cells will break
Outstanding solar cells will break
Solar cells packed between plywood and properly stacked
Solar cells packed between plywood and properly stacked

Solar cells packed airtight
Solar cells packed airtight

Solar cell model SPICE 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:

Multisim solar cell model
Multisim solar cell model

Download here the Multisim solar cell model.

This is the solar cell test circuit:

Multisim solar cell dc sweep simulation circuit
Multisim solar cell dc sweep simulation 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:

Multisim solar cell dc sweep simulation output
Multisim solar cell dc sweep 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:

Diode formula
Diode formula

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:

Solar cell diode model test
Solar cell diode model test

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:

Solar cell model graph
Solar cell model graph

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.

Single solar cell powered step-up converters
Single solar cell powered step-up converters

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".

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

Do you have any comments? Please let me know.
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