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All electrical circuits are subject to energy losses due to the passage of current in real conductors, that is, conductors where there is some equivalent electrical resistance.
The cross-sectional area, length and electrical resistivity of the material that forms the conductor are the parameters that directly influence the circuit's energy loss. The resistance of a conductor can be written as:
R = rx C / A
Where: R is the total resistance of the conductor [ohm]; r is the resistivity of the material [ohm x meter]; C is conductor length [m]; A is the cross-sectional area of the conductor [m2]. The power dissipated in a conductor is given by the equation below:
P = R x I²
Where: P is the power [W]; R is the conductor resistance [ohm]; I is the intensity of the electric current [A]. Calculating the loss in the conductor in a photovoltaic system is not simple to solve manually, as the current that passes through it at each moment depends on the time of day, weather conditions and shading.
Depending on the implementation conditions of a photovoltaic system, it may be possible to choose the position of the inverter in relation to the module arrangement and the AC connection point.
Although the physical process that causes energy losses in conductors is the same for DC and AC cabling, the effect of choosing a longer circuit on the DC side or the AC side can have different implications on the system's power generation.
Case study
To illustrate this study, we will use the system presented below, which has already been covered in another Canal Solar article, which evaluated the issue of voltage drop in conductors on the DC side. A very special feature of the analyzed project is the long distance between the photovoltaic system and the power pole of the consumer unit, as we see in the figure below.
For this case study we can consider two possible options:
- Inverter close to the modules and far from the connection point: less DC cabling and more AC cabling;
- Inverter far from the modules and close to the power input: more DC cabling and less AC cabling.
We could use the formulas presented in the introduction of this article to estimate the total resistance of the circuit and determine the power dissipated at a certain instant. However, as already discussed, the manual calculation of the energy dissipated from the cable resistance is laborious, as the electrical current of the photovoltaic system varies according to the instantaneous operating conditions.
The important thing in a case like this is not to determine the power dissipated in the cable in a particular operating condition. A photovoltaic circuit differs from a circuit that powers a machine or a fixed consumer load.
In this case, when it comes to circuits for photovoltaic systems, the important thing is to know the global losses, considering all operating conditions over a period that is typically one year. In summary, the losses of the photovoltaic system can be evaluated based on its energy generation result in a given period.
The choice of the best cabling must be based on maximizing the overall performance of the photovoltaic system over the period considered. We will use the PVSyst for this study. The software allows you to model and predict the generation behavior of the system as a whole.
System data:
- 240 400 W Mono-Perc modules;
- 1 75 kW inverter with 6 MPPTs;
- DC cabling: 4 mm², NBR 16612 solar cable;
- AC cabling: 50 mm², EPR type cable, copper conductor;
- Location: Campinas (SP).
By reporting the average distances and cable section, PVSyst estimates the resistivity of the circuit. This average resistivity per section and the current information throughout the plant's annual operation translate into energy losses, which are shown below:
With these settings, we then obtain the loss diagram for each of the systems:
Table with summary of information
The analysis of energy losses in DC and AC cabling is not trivial and is not in a tabulated or “ready” form. It is also worth remembering that cabling prioritized in DC will not always generate more energy. Therefore, analysis through software is essential to choose the best solution.
It can be seen then that the system that prioritized the laying of DC cables was able to generate more energy. Assuming a tariff of 0.80 R$/kWh, the system that prioritized DC cabling saved R$ 2,080.00 more in the first year, approximately 2% of the system's financial result.
It is also noted that the voltage drop on the AC side is close to the limit established by standard, 7%. If this drop is also associated with poor connections or other defects, the inverter may shut down.
Prioritization of DC circuits
Despite the study presented in the previous section, there is a recommendation that the plant's cabling be done in DC when possible. To explain the reason for this recommendation, we will use the example in the figure below, where we have a 60 kW system with a 45 kW inverter (with 100% efficiency for example purposes), with 133% overload and identical cabling losses.
The power of the array is commonly denoted in terms of the STC condition, which represents a module receiving a high irradiance of 1000 W/m² and a cell temperature of 25 °C, which would be equivalent to an ambient temperature of 0 °C. These conditions are rarely achieved in the real world, especially in Brazil.
In the example in the figure, the power of the array was determined under NOCT conditions, which represent scenarios most likely to occur (irradiance of 800 W/m² and cell temperature of 45 °C – equivalent to 20 °C ambient). In normal operating conditions, the module arrangement is capable of supplying 45 kW of power to the inverter.
However, due to losses in the DC cabling, the inverter only receives 44 kW. Therefore, we were only able to extract 44 kW from the equipment. The section between the inverter and the measurement point also presents cabling losses of 1 kW, which means that the power delivered from the system at that moment is 43 kW.
Assuming an installation where it is not possible to choose the positioning of the system items and consequently the length of the circuits, we have the option to minimize system cabling losses by increasing the conductor section or increasing the inverter overload (addition of more modules ).
Using the example in the figure, we can add more modules to compensate for the loss in the cabling and deliver 45 kW or more at the inverter input – which would virtually no longer “see” the effects of losses in the DC cabling. As for AC cabling, the only option we have is to increase the conductor section.
Overloading (increasing the number of modules) can, in a certain way, minimize the effects of losses in the cabling on the DC side, which is why it is preferable to prioritize the use of DC cables in photovoltaic systems. Losses on the AC side, on the other hand, cannot be compensated in any other way than by increasing the section or opting to use an inverter with a higher output voltage (consequently with lower AC current).
2 Responses
Great content, congratulations, but I can't deny that I still have some doubts. All verbal content denotes that priority must be given to the DC circuit, however, when analyzing the table with the data in figure 7 and the information contained in figure 9, it seems to me that priority must be given to the AC circuit, as this way, the “Total energy delivered” or “Power at the point of delivery” proved to be more effective compared to the data presented when prioritizing the DC circuit.
Dr. Mateus, it is normal for the cables between the inverter and the energy company meter to heat up, in my case CELPE, I noticed that between 09:00 and 15:00 this connection is always hot, the cable used to connecting the inverter to the meter is the cable that connects the boards to the inverter and the distance from the inverter to the meter is around 20 meters, could you confirm if this situation is normal.