Need help with vector mathematics for solar sensor

[PVwizard]

Hi ALL,

I'm glad I found this Forum. I'm an engineer, rusty with my math, building a practical prototype sensor that will characterize energy from 8 directions at shallow angle, upon
a solar array.

I need help with expression showing the summation of each of the 9 sensors (with the
funnel(with the reference sensor) point straight up, and the other 8 sensor values in terms of directional vector and forming cross product with the vector that represent the Normal to the solar array plane. The array is specified with an azimuth and a tilt (towards South for
north hemisphere locations).

Thanks
-Steve

 

[jvicens]

Hi Steve,

Welcome to the forum! It's great to have another engineer on board. I can definitely help you with the expression you need for your prototype sensor.

First, let's define some terms. The reference sensor is the one that points straight up (perpendicular to the solar array plane), and the other 8 sensors will be at shallow angles in 8 different directions around the reference sensor. The directional vector will represent the direction of the sensor, and the cross product with the normal vector to the solar array plane will give us the component of energy in that direction.

To express the summation of each of the 9 sensors, we can use the summation symbol, Σ. This symbol represents the sum of a series of terms. In this case, we want to sum the energy from each sensor, so we can write it as:

Σ(Esensor)

where Esensor represents the energy from each individual sensor.

To incorporate the directional vector and the cross product, we can use the dot product. The dot product of two vectors gives us the component of one vector in the direction of the other vector. In this case, we want to find the component of each sensor's energy in the direction of the normal vector, so we can write it as:

Σ(Esensor * (directional vector * normal vector))

where the * symbol represents the dot product.

Finally, we need to consider the tilt and azimuth of the solar array. The tilt will affect the angle of the normal vector, and the azimuth will affect the direction of the normal vector. We can incorporate these by using trigonometric functions to calculate the components of the normal vector in the x, y, and z directions. The final expression would look something like this:

Σ(Esensor * (directional vector * (cos(azimuth) * cos(tilt), sin(azimuth) * cos(tilt), sin(tilt))))

I hope this helps with your prototype sensor. Let me know if you have any further questions or need any clarification.