# Cable impedance versus mV.A.m method of Vrise

## The Question

With solar the  Australian and New Zealand standards stipulate a max of 2% voltage rise from the POS/POA all the way through to the inverter with the largest run and/or biggest load current.

AS4777 uses the millivolt per A.M method which assumes almost the worst case scenario but there are other methods to calculate Voltage rise and in this presentation we will compare the ‘standard’ method with the cable impedance method.

## What is voltage rise?

• The grid voltage levels  vary throughout the day
• Depending on how much power is being drawn from the grid
• Also how much solar is being sent back.
• For energy to flow, voltage at inverter is higher than at Grid
• Issue can occur when cables haven’t been sized correctly
• If too much resistance then voltage has to rise

## How much can it rise, max 2%

In AS/NZS 4777.1 Volt rise is restricted to 2%

This is from Point of Supply to last inverter and the Distributor requires this information

The installer must assess the existing cable, do the necessary calculations and this determines new cabling specs.

## The solar system example, the basics

Our example solar system consists of the following:

• 3 x 100 kVA inverters
• 1 x PVDB
• PVDB connects to a DB
• DB connects to a MSB
• MSB connects to POS

The cables are installed in the following manner:

• Inverters to PVDB: Cu XLPE 90 deg 4C+E Solid Wiring Enclosure in Air Enclosed, 150mm2
• PVDB connects to a DB: Cu XLPE 90 deg Single Core Solid Touching Unenclosed, 150mm2, 2 cables paralleled per phase
• DB connects to a MSB: Cu XLPE 90 deg Single Core Solid Touching Unenclosed, 150mm2,  2 cables paralleled per phase
• MSB connects to POS: Cu XLPE 90 deg Single Core Solid Touching Unenclosed, 300mm2,  2 cables paralleled per phase

## 3 phase volt drop/rise, which Table and standard

AS/NZS 4777.1 references a table in AS/NZ 3008

This reference is Table 41, column 6

## Now for the maths. . . . . .

So the calculation is  Vd/r* = L x I x Vc/1000 where:

• L   = cable run in metres
• I   = the current,
• Vc = mV/A.m factor for the cable in question
• Vd/r = X amount of  volts
• *Vrise and Vdrop is mathematically the same

## mV/A.m  method, our example

In our example we have 3 x 100 kVA inverters cable to a PVDB to a DB to MSB to the POS.

## Cable selected

We are talking about volt rise here but cables also have to be selected on the CCC ( current carrying capacity ) as well.

In our example some parallel cables have been used. In this case the current is equally distributed between the parallel cables and this is reflected in the Vrise result.

So what are the results?

## mV/A.m  method, our example, the results

• Vrise from POS to MSB is 0.059%
• Vrise from MSB to DB is 1.381%
• Vrise from DB to PVDB is 0.42%
• And the highest Vrise from PVDB to inverter is 0.046%

Resulting in a total Vrise of 1.918% for the total run

## The cable impedance method

According to AS3008: 2017 “A  more accurate assessment can be made of the actual voltage drop (Vd) using the appropriate equation of Clause 4.5, the cable reactance determined from Table 30 to 33, the cable a.c. resistance determined from Table 34 to 39

The calculation is as follows:

Vd = IZc . . . 4.3(1)   where:

• Vd = voltage drop in cable, in volts
• I = current flowing in cable, in amperes
• Zc = impedance of cable, in ohms
• = √(R2c + X2c)

Where:

• Rc = cable resistance, in ohms; a function of the material, size and
• Temperature of the conductors
• Xc = cable reactance, in ohms; a function of the conductor shape and cable spacing

## The cable impedance method continued

Single-phase, two-wire supply system

For a single-phase circuit the impedance of the active and neutral conductors is taken into account. As these conductors are of the same material and generally the same size, the voltage drop on the circuit is twice what it would be for a single cable:

Vd=ILZc/1000

For a balanced three-phase circuit no current is flowing in the neutral conductor and at any given instant the current flowing in one active conductor will be balanced by the currents flowing in the other active conductors. The voltage drop per phase to neutral is the voltage drop in one cable and the voltage drop between phases is:

Vd=√3ILZc/1000

## Impedance method, our example, the results

• Vrise from inverter to PVDB is 0.043%
• Vrise from PVDB to DB is 0.398%
• Vrise from DB to MSB is 1.25%
• Vrise from MSB to POS is 0.050%
• Vrise total is 1.766%

## Conclusion

It can be seen from the two methods outlined that the cable impedance method of determining the Voltage rise gives a lower figure. In most cases use the mV/A.m method will suffice BUT if the result is slightly over 2% then using another more accurate method may be the way to go.

Remember not only does the cable have to satisfy all Vrise stipulations but also it has to be able to safely carry the current that the system imposes on it.

Good luck on your next project.

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