intro
I posed this question to two current AI platforms.
First Google Bard
“According to a study by the Secretariat of the Energy Community, Serbia would need about 100 million solar panels to replace all its thermal power plants with coal. The study found that solar panels can produce enough electricity to meet the current demand for electricity in Serbia and that the price of solar energy is now competitive with the price of coal-fired energy, etc.”
Bard goes on to explain general terms irrelevant to our question.
I posted same question to chat GPT and get this:
“Unfortunately, I do not have access to the latest data after September 2021, so I cannot give an exact answer to your question for the current situation in Serbia in 2023. It is necessary to have access to the latest statistics and data on energy consumption, electricity production, the use of solar panels, and other relevant information in order to calculate how many solar panels would be needed to replace thermal power plants..”
And since I was not satisfied with the answers offered, I started further analysis.
The thermal power plants of Serbia and their capacity
For the analysis, we will use the EPS yearbook for the year 2022. The total power of all six thermal power plants in Serbia is 4079 MW, and if three thermal power plants in Vojvodina are included, the total is 4376 MW. The total production of thermal power plants and heating plants amounted to 22152 GWH (gigawatt hours) in 2022. It is clearly visible in the following table and diagram.
| no | power plant | power [MW] | Production [Gwh] | Coefficient |
|---|---|---|---|---|
| 1 | Nikola Tesla 1 | 1622 | 7824 | 4.82 |
| 2 | Nikola Tesla 2 | 1220 | 6584 | 5.40 |
| 3 | Kolubara | 216 | 309 | 1.43 |
| 4 | Morava | 108 | 560 | 5.19 |
| 5 | Kostolac A | 281 | 1784 | 6.35 |
| 6 | Kostolac B | 632 | 4338 | 6.86 |
| 7 | TO Novi Sad | 208 | 686 | 3.30 |
| 8 | TO Zrenjanin | 75 | 67 | 0.89 |
| 9 | TO Sr. Mitrovica | 14 | 0 |
In order to make some comparisons of the efficiency of thermal power plants, we will introduce an efficiency coefficient that is equal to the annual production divided by the installed power of the power plant. As can be seen from the table, the most efficient thermal power plant is Kostolac2, with an efficiency coefficient of 6.86, and the worst condition is Kolubara, with a coefficient of 1.43.
Calculation of the total required number of solar panels using the SPAC application
Now, with the help of the SPAC application, we will try to calculate how many solar panels are really needed to produce this much energy. The assumption is that the solar panel (PV module) is ideally placed towards the south under an ideal angle of 39 degrees for Belgrade and its surroundings. We will test solar panels of different powers. Entering parameters in the SPAC application for Europe Input parameters… what are parameters? City: Belgrade, Serbia Slope: 39 degrees Orientation: 0 degrees, facing due south Placement option: on the ground (Ground) network m = 1 n = 1 (1 panel in total) We will analyze two types of panels. Canadian Solar CS3N-405 power: 395 W; current price: $290; ZNShine ZXM7 power: 540 W. In order to replace all the production of thermal power plants in Serbia with this solar panel, we will divide the total production of all thermal power plants in Serbia by the production of 1 panel calculated by the SPAC application, and we will get the theoretical results shown in the following table:
| month | Canadian Solar CS3M (395W) | ZN Shine ZXM7 (540W) |
|---|---|---|
| Jan | 11.87 | 16.18 |
| Feb | 18.37 | 25.04 |
| Mar | 29.84 | 40.68 |
| April | 36.73 | 50.07 |
| May | 41.03 | 55.94 |
| June | 44.57 | 60.76 |
| Jully | 49.18 | 67.05 |
| Avgt | 49.28 | 67.19 |
| Sept | 37.44 | 51.05 |
| Oct | 28.76 | 39.21 |
| Novr | 15,48 | 21.11 |
| Dec | 9.36 | 12.77 |
| overall | 59,562,797 | 43,687,999 |
| Investicija | 1.72 bilions $ |
The total investment for the first type of panel is about 1.7 billion dollars.
What is that area ?
The distance between the solar panels, according to the calculation of the SPAC application, should be a minimum of 4.57 m (to avoid the shadow effect). This further implies that for a network of 10×10 = 100 panels, the plot area would be 524 m2. When this is applied to 59,652,767 panels, an area of 312.2 km2 is required. The picture below shows the south England and green square is approximetly same area.
Production and stability of the energy system
Naravno ovo su samo teoretski rezultati dobijeni prostom matematičkom računicom. Glavni problem je neravnomernost proizvodnje i potrošnje = stabilnost sistema. Kao što može logično predpostaviti a i vidi se iz tabele 2 proizvodnja u zimskim mesecima je mala i nedovoljna da pokrije potrošnju, dok je u letnjim mesecima naročito oko podneva prevelika tako da ne znamo šta bi sa proizvedemom strujom. O problemu sa prekomernom proizvodnjom struje možete pročitati ovde.
Inverters - additional costs
Naturally, the results of a straightforward mathematical calculation are only theoretical. The main problem is uneven production and consumption, which means system stability. As can be logically assumed and can be seen from Table 2, the production in the winter months is small and insufficient to cover the consumption, while in the summer months, especially around noon, it is too high, so that we do not know what to do with the produced electricity. You can read about the problem of excessive electricity generation here.
| Inverters | Huawei SUN2000-10KTL-M0 | Solar Edge SE33.3K | Growatt MID 50KTL3-X2 |
|---|---|---|---|
| Power [W] | 14800 | 50000 | 75000 |
| Price $ | 1690 | 2497 | 2962 |
| Total | 1594022 | 471830 | 314554 |
| Total price [$] | 2,693,896,491 | 1,178,160,487 | 931,707,746 |
From the table, it can be seen that the price of the inverter varies. Of course, the most profitable are large industrial inverters, but not all solar power plants have to have a large capacity (a large number of panels). So we can count on the average price of investments in inverters being $1,601,000,000. When total investments in panels and inverters are added up, the sum of $3,328,000,000 is obtained. That’s how much it would cost to replace all thermal power plants in Serbia with solar panels and inverters. Other costs (land, cables, cabinets, etc.) are not taken into account.
Battery and energy storage
It is quite certain that in the future every household will have to invest in batteries for its own power supply needs when the solar panels are not working. There is a high probability that expensive lithium ion batteries will be replaced by sodium ion batteries, which are heavier and larger, in the home version, but this does not play an important role in home installations. Battery life is 6000 cycles (standard), which is about 12 years
Conclusion
This was simple math. The SPAC application proved useful and simple for this calculation. This is not a study but only a demonstration of the application’s capabilities. The problems with the stability of production, that is, with uneven production and consumption, have not yet been resolved. In my opinion, this is currently the biggest challenge for our (and the world’s) engineers. In the case of thermal power plants and heating plants, we will not get rid of them so easily, at least not in the winter months, because the production of solar energy is 3.6 times higher in July than in December.