Is it possible to have PR > 1?

Disclaimer: if you're looking for ways to improve your Public Relations (which is also called PR) ... Sorry, "but your article is in another castle" :)
Keep looking. And don't settle ;)

Well, the short answer to that question is Yes, it's possible. To give you a slightly longer one - Performance Ratio (PR) of the photovoltaic (PV) system can exceed 1, but only for a short period of time. This phenomenon can occur on specific days when the system operates in cold weather conditions with high irradiation

To understand why, let’s first distinguish between efficiency and performance ratio in a photovoltaic system.

• Efficiency represents the how much solar energy a panel receives to how much of this energy is converted to electricity, typically ranging from 19% to 22% (see more here). It can be defined by this simple equation*:

• On the other hand, performance ratio compares the actual energy fed into the grid to the ideal energy yield of the PV system. It serves as an indicator of system design (i.e. how many losses are there) and is calculated using the equation:

You see the difference, right? While the efficiency is (basically) a ratio between the ideal output of the panel to energy from the sun, performance ratio is ratio between the actual energy yield to the ideal one. Efficiency focuses on comparing solar cells and panels, while performance ratio is used to evaluate solar plants.

Let's delve deeper into understanding the Performance Ratio and its components.

"Dissecting" Performance Ratio

Let's focus on E_Ideal component of the previous equation and what it consists of. The equation for Ideal Energy Yield is simple:

Here:

• P_DC is the nominal power output of a PV panel (in Watts).
• PSH is Peak Sun Hour (in ... hours (duh!)) which is basically how much "clear blue sky" hours of sun (that is 1000 W/m^2) we have per day or year.

Now, how do we get P_DC values? From labs that test each solar panel under Standard Test Conditions (STC). You can read more about STC here, but there is one important thing I want you to keep in mind while you are reading this article: during the test measurements, cell temperature of the PV module must be 25°C. This information will be important for us later.

The performance ratio can only be reliably calculated after the system is built, but it can be estimated during the feasibility phase.  We just need to consider all the possible losses that the PV plant experiences, and "subtract" it from the ideal energy yield.

Losses are inevitable. However, if the system is well designed, PR values usually range between 70% (for regions with desert-like conditions and high ambient temperatures) and 85% (for regions with moderate ambient temperatures).

Now, here is the question: why in the regions with desert-like conditions PR is low? They have more sun hours and should have higher PR, shouldn't they?

The answer lies in temperature!

The Impact of Temperature on Performance Ratio

Solar panels perform worse during the days with high temperature. In fact, each panel has the chart of temperature characteristics/coefficients that show how I_sc, V_oc, and P_max change with temperature, and it can be used to more or less reliably estimate the energy output of the panel during the different temperature conditions**:

And the temperature is the thing that will help us to answer the question of possibility of having PR > 1.

How to get PR > 1

One of the largest losses in PV systems are temperature and shadow losses. Let's assume that we have a small array of PV panels that doesn't experience any shadow losses. In this case, shadow loss is 0%.

As I mentioned earlier, all the panels are tested under STC, where the cell temperature must be 25°C. We also learned about the temperature coefficient of PV panels and if this is higher than 25°C, then the output of the panel is lower. But what if the temperature of the cell gets lower than 25°C? What if we have "clear blue sky" conditions, but it's freezing cold outside? This is the time when you get your energy output higher than during STC conditions! Using the temperature ratings from the example table above, we can observe that for every 1°C deviation from the 25°C cell temperature, the energy output of each PV panel increases by 0.340%. Have a low enough temperature, and you have PV higher than 1.

Simulating the assumption

In order to prove my assumption, I decided to conduct the simulations on PVsyst using the modified meteo data. I used the meteo data from Geneva, Switzerland, and changed the Average Ambient temperature parameter to reflect the lowest possible temperature in that region, while the other parameters stayed the same (more about how realistic this is later). I ran the number and here are the results of the simulation:

Graph:

Diagram:

But of course, these meteorological conditions are not possible in Geneva (citation: needed?). However, we still have days when it's cold outside and have "clear blue sky" conditions. This is more probable in the mountainous areas, where the solar irradiation is high, while the ambient temperatures are low.

Which leads me to the conclusion: PR of the system can reach values higher than 1, but for a short period of time. It can be during the particular days when the system is operated in the cold weather but with the high irradiation. This doesn't mean that PR will be larger than 1 during the entire year, but it will be larger than 1 in particular days, maybe even weeks.

Let me know what you think about this topic. What are other times (or ways) when PR values can be higher than 1? Can we work on other aspects of STC to make it so (like changing Air Mass or irradiance of the Sun)?
Please share your thoughts in the comments

Footnotes:

* Just as a reference: here is more detailed equation for efficiency of the panel is this:

but this is not the ultimate conversion efficiency formula. This is :)

** Temp. coefficients are also useful for estimation of maximum and minimum voltage that string of panels can generate.

Disclaimer: the idea for this article came from the assignment from Certified PV Professional course. If you are currently passing this course, please don't copy the content from this article to your answers. They will still find out about your plagiarism.