How to calculate voltage rise in a solar pv system?

Voltage rise is the difference between the voltage in the grid, the power system that provides the electricity, and your solar inverter, which produces energy from sunlight. To transmit energy from your solar system into the grid, the voltage at the inverter needs to be just a little higher than the voltage in the grid. This difference, or “push,” is how the energy is transmitted onto the grid.

For example, if the grid voltage is 230V and the solar inverter gives 235V, then the voltage rise is 5V. This is done by subtracting the grid voltage from the output of the inverter:
235V (solar inverter) – 230V (grid) = 5V.

The inverter needs this small voltage rise so that energy can flow from your home to the grid.

Why is Voltage Rise Important?

Voltage rise is necessary in selling energy from your solar system to the grid. When the voltage at your inverter is much higher than that of the grid, the energy will normally try to find its way into the grid. However, over-voltage rise can be problematic, such as to activate protection mechanisms that would shut down the system to protect it from damage.

Factors That Affect Voltage Rise:

  • Cable Resistance: The resistance in the wiring between the solar inverter and the grid plays a huge role in voltage rise. The more resistant the wire, the higher the voltage difference required to force electricity through it. This increases the voltage rise.
  • Distance from Transformer: The distance from your home to the power transformer is one of the factors that determine the voltage rise. The farther the distance, the more the resistance and therefore a higher voltage rise.
  • Size of Wires: The resistance is dependent on the size of the wire. A thin wire has high resistance; therefore the rise in voltage will be high. The bigger wires have low resistance, hence a reduction in the voltage rise.

Voltage Rise and Ohm’s Law

Ohm’s Law is the basic law which describes the relation between voltage, current, and resistance in a circuit. The formula is stated as:
V = I × R
Where:
  • V is the Voltage (the push that drives electricity through the wire),
  • I is the Current (the flow of electricity),
  • R is the Resistance (the opposition to the flow of electricity in the wire).
The inverter must therefore have a higher voltage than the grid, but only by a small amount: typically no more than 2% above the grid’s voltage. For example, in Australia, where the standard grid voltage is 230V, a 2% rise means that the inverter voltage can rise to at least 4.6V above the grid, or to 235.6V.

Voltage Rise and Cable Resistance

There is a need to include resistance between the inverter and the grid in the calculation of voltage rise. This resistance depends on the following factors:
  • Material: Various materials may conduct electricity to varying extents. In this case, copper is superior to aluminum when it comes to electrical conduction.
  • Thickness: A thicker wire has smaller resistance than that of a smaller wire. With an increase in the diameter, the resistance increases, thus resulting in reduced voltage rise.
  • Wire Length: Longer wires have greater resistance. The farther the inverter is from the transformer or grid connection, the greater the resistance and therefore the higher the voltage rise.
Therefore, the length of the cable between the inverter and the grid should be as short as possible, from high-conductivity material, and appropriately sized in order to minimize voltage rise.

Calculating Voltage Rise

To keep the voltage rise within acceptable limits, we need to make a number of calculations based on the scale of the solar system, the wiring, and distance from the grid connection. For voltage rise calculations, the following is the formula in use:
V_r = (1000 × L × I × V_c) / 1000
Where:
  • L is the length of cables, meters,
  • I is the value of current, amps, which also depends on the power rating of an inverter,
  • V_c is the voltage rise factor for the cable (in millivolts per amp per meter).

Example

Let’s take an example of a 100 kVA solar system to understand how the voltage rise is calculated over multiple cable runs.
Step 1: Calculate the Required Current
In a 3-phase system, the current required for a 100 kVA system can be calculated as:
I = 100,000 / (1.73 × 400)
This gives us a current of 144.51 amps per phase.
Step 2: Choosing the Cable Size
We must now make sure that the chosen cable size can carry this current. For example, using 95mm² cable, we check the CCC. According to AS/NZ 3008, a 95mm² cable is capable of carrying 217 amps, so it is more than adequate.
Step 3: Calculating Voltage Rise for Each Cable Section
Now, we work out the rise in each segment of the cable from POS to MSB and then MSB to inverters. For the first one, from POS to MSB, using Table 41, AS/NZ 3008 for the rise in voltage by this cable = 0.449, thus:
V_r = (1000 × 86 × 144.51 × 0.449) / 1000 = 5.58 volts
Resultant voltage rise 5.58V or 1.39%.
Step 4: Voltage Rise Shall Not Exceed Limit
The voltage rise, as stated by the Australian standard, shall not exceed 2%. For the POS to MSB section, 1.39% is well within the limit, and the repetition of the other sections confirms that the voltage rise does not exceed 2%. For the MSB to Inverter section, the voltage rise remains below the allowed limit.

Voltage rise in a solar power system is defined as the difference between the solar inverter voltage and the grid. This increase has to always be within specified limits, as high as 2%, since high voltage would create problems in the protection scheme and may stall the system completely. The influencing factors on the rise in voltage are wire size, separation between the inverter and grid, and current being supplied. All these conditions have to be weighed during design and setup of the power system. Proper calculations and proper selection of the wire are to be done in order to maintain the voltage rise within the standards and ensure the safe and efficient operation of the solar power system.

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