Panels and power: How to position and what to expect.

This may be a rather technical read for some. But we have done our research and and recorded the data.
The aim of this document was to really dig a little deeper into how solar panels work and how they work with the sun and how that changes year round.

This article Sun Hours and Seasons: How to Angle the Panels — RenewSolar Is a fairly soft read setting out the general principle, but in this article its going to be a little more detailed.
You may also want to take a read How to Position Your Solar Panels for Maximum Energy Output — RenewSolar

If you ventured into the other articles I have linked to above, then you should be well versed in understanding most of this article. But if you have a question that I have not covered in the articles, then drop a note in the comment box below.

Challenge of concept.

For most of use the solar system is a disc of planets rotating around the sun, This is false, the solar system is more a spiral and there are various wobbles and changes to that rotation. No more so that the the earths tilt which gives us the seasons, but for solar that means the sun, from our perspective moves in the sky differently day by day and and hour by hour.
While we think of the sun arching though the sky, this changes. both in height and duration above the horizon and that’s where we are going to start.

Summer and winter and your roof/ panel mount system.

The sun position rises differently over the year which relates to time, but the rise in terms of height also changes. The sun in winter it can be 10 degrees and in summer 61 degrees. (here in England); and you would have heard the term “sun hours” and should know this does not mean day light hours.

Its just Maths.

The sun above the horizon, in relation to your panel angle means how much power you get or not.
We looked at the angle and range that a solar panel works, so we already know that the solar panel has a 70 degree power range, and peak power is in a narrow margin where the panel and sun are at 90 degrees +- 10.
And we did learn that south facing panels were not always the best option, Right?

We know that the panels angle East or West will alter the time of the peak power production and we know an hour is 16 degrees.

On 29th of January 2025 the sun rose to 10 degrees at 09:10 and dropped below 10 degrees at 15:10
the suns peak height was 20.99 degrees at 12:20.

We already know that 90 degrees is our “optimal”, but we have to account for both axis.
lets run with these numbers

The sun duration is 6 hours.
The rise is 10 degrees.
Therefore the pitch needs to be 80 degrees.

Not available Math.

Each panel location, differs in elevation and also the site and surroundings will effect the panel performance. The Field angle also is effected by the ground at steep angles. this is shading and non reflecting in short terms.
Another wide variable is cloud cover, While it is fairly easy to see power yields 30 minutes in advance with good accuracy a day or even just 12 hours can be difficult.
For the purpose of solar, it is all often based on “best case” or clear skys. This would uses STC ratings, but NOCT is more accurate in the real world.

Back to the math.
The time, as the sun sweeps across the sky is only relevant to the panels angle. The panels field angle playing a larger roll in actual production figures. If the angle is negative relative to the sun.

Let me explain that a little more. If the sun is at 10 degrees in height, and the panels 90 degrees, the field angle being 70 degrees. The optimal position would be proportionally toward the ground by 35 degrees. and reduce yield by around 50% at peak time. We also have to consider the duration that the sun is in the best position and for how long over the day.

At any given time of the year, we can look at the “best pitch” of the solar panel, The height of the sun from the horizon is fairly linear each year.
We then need to account for the array angle (pitch) and in this case I will use a roof which is 45 Degrees.
As we know, the sun is at 10 degrees and rises to 20 and drops back to 10 degrees, we can work on the basis that the pitch angle relative to the field is at the extreme. (45p -35f =10s).

We can work currents from the angle and with a round number (10) we could apply some running numbers. The duration here is 6 hours. We will say the panel current is 10 amps MPP.

This drawing show the angle of the panel (80) with the Fh (top of field) and Dawn and Peak of the sun in relation to the solar panel. We could say that 90 degrees to the panel is 10 amps and as we go to the edge of the panels field this is 0 amps. Therefore the power would be limited to 10 amps for 35 degrees.

Here’s the corrected approach for the math:

• Panel’s Reference: The panel’s orientation is the zero point for our power calculations.
• Field of View: -35 to +35 degrees relative to the panel.
• Sun’s Movement: The sun moves from -35 degrees (relative to the panel) at 09:10, peaking at -25 degrees, and then falling back.
• Amps Scaling: -35 degrees = 0.01 amps; 0 degrees = 10 amps. This being the Angle relevant to the panel (or 90 degrees).

Here’s the corrected and simplified approach:

1. Sun’s Angle (relative to panel): This is the angle we need in relation to the panels angle to the sun, you would need to calculate differently for the panels angle.
2. Power Calculation (Linear Scaling): Since we have a linear relationship between the angle and the power, we can use the following:
   • Slope: (10 amps – 0.01 amps) / (0 degrees – (-35 degrees)) = 9.99 / 35 = 0.2854 amps/degree (approximately)
   • Equation: Power = 0.01 + 0.2854 * (35 + Sun’s Angle relative to the panel)
   • OR
   • Power = 10 – 0.2854 * ABS(Sun’s Angle relative to the panel)

Example Simplified:

• Time: 09:10
• Sun’s Angle (relative to panel): -35 degrees
• Power: 0.01 + 0.2854 * (35 + (-35)) = 0.01 amps OR Power = 10 – 0.2854 * |-35| = 0.01 amps.
• Time: Peak (around 12:00, but we don’t need the exact time)
• Sun’s Angle (relative to panel): -25 degrees
• Power: 0.01 + 0.2854 * (35 + (-25)) = 2.864 amps OR Power = 10 – 0.2854 * |-25| = 2.86 amps.

Table :

You’ll need to calculate the sun’s angle relative to the panel for various times between 09:10 and 15:10. Since we’ve established the range on the day to be -35 to -25, you can directly use these angles in the power calculation.

We have covered the vertical in the above chart, but we also have to cover the horizonal.

Sun’s Angle Relative to Panel: This is the only angle we care about in this example.

Calculating Sun’s Angle Relative to Panel:

At Sunrise (08:00): The sun is just rising. We’ll assume it’s at 0 degrees relative to the horizontal. The panel is at 80 degrees relative to the horizontal. Therefore, the sun’s angle relative to the panel is 0 – 80 = -80 degrees.

Throughout the Day: The sun moves at 15 degrees per hour. So, at time t (in decimal hours), the sun’s angle relative to the horizontal is 15 * (t – 8). The sun’s angle relative to the panel is then: Sun’s Angle (relative to panel) = 15 * (t – 8) – 80

Field of View Check (Crucial): IF Sun’s Angle (relative to panel) is within -35 to +35 degrees: THEN calculate power. ELSE: Power = 0.01 amps. This is not always the case, but it makes understanding it more easier.

Power Calculation: Power = 10 – 0.2854 * ABS(Sun’s Angle relative to panel) IF Power < 0.01 THEN Power = 0.01

Example (for 12:10):

1. Decimal Time: 12.167
2. Sun’s Angle (relative to panel): 15 * (12.167 – 8) – 80 = 62.5 – 80 = -17.5 degrees
3. Field of View Check: -17.5 is within -35 to +35.
4. Power: 10 – 0.2854 * |-17.5| = 5.00 amps (approximately)

Table:

* this figure is likely to be much higher than shown in the chart. This relates to field refection’s and also does not account for reflective clouds.

As you can see in this chart the sun does not rise high enough for most of the morning to give effective current to the panel. it is when the sun reaches the vertical climb, together with the horizontal that you make power from solar.

While I have used 10 amps as the peak power, there are other factors that are important. Your Data sheet will contain the performance data of the panel. therefore you will be working at different ranges.
this is worked out as kWm2 and the rated current is at 1000kwm2 where as in winter this could be much lower.

In this example the power peak is 14.3 amps in winter or under cloudy conditions the kWm2 is reduced and this would effect the charts, you could however use math to backward calculate the kWm2 by using the same formulas above. Just don’t forget to use your own figures.

If you understood this information you should be able to calculate your expected power with some degree of accuracy. You will be aware of your sun hours, and how this relates to the suns current on the the solar panel at a given time of day ( duration) and using the sun position (angle).
With the use of the data sheet and live weather data you should be able to model the actual power of your system year round. The notice you have in advance to what power you will get at which time, may not be 100% but this is the closest way to do so.

If you have multi arrays, you can of course shift the peaks and seasonal power delivery to best suit your needs. This can help moderate power and extend power delivery times.

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There are many articles on this website that cover a wide range of “solar subjects” and we are always adding to them.