Understanding manually calculating Zs

[Loki]

Hi,

I know that Zs = Ze +(R1+R2) & that you can look in the OSG page 125 to get maximum Zs figures (with the applied 0.8) but I wanted to check if my understanding to calculate it manually is correct?

Example:
16Amp MCB type B
230v


16Amps x 5 (cos of type B) = 80Amps
Ohms law formula: voltage/Current

230/80 = 2.875 Ohms
Rounding off to 1 decimal point = 2.8
So allowing for the 20%
2.8 x 0.8 = 2.2
Maximum Zs = 2.2 Ohms

The final figure seems to match up with the figures in OSG.

Just want to confirm if my understanding is correct?


Thanks

Michael

 

[Richard Burns]

You have the theory correct and the calculations generally accurate.
The MCB must trip within the time limits required for ADS and this occurs when they trip "instantly" i.e within much less than 0.1 seconds thereby complying with all the disconnection times in table 41.1 (0.2s to 5s).
The type of the MCB determines the current at which the MCB will trip "instantly" in accordance with the 60898 standard.
Type B 3 to 5 times rated current
Type C 5 to 10 times rated current
Type D 10 to 20 times rated current

So for a type B 16A MCB the worst case is at 5 times rated current i.e. 80A
These values are shown in the tables on the graphs in appendix 3.

The formula in 411.4.5 can be rearranged to be:
Zs <= (Uo x Cmin)/Ia

Therefore you have Uo as 230V, Cmin as 0.95 and the Ia is calculated as above for the type of breaker.

So Maximum Zs is 230*.95 / 80 = 2.731Ω
When the conductor is at maximum operating temperature (70°C in most cases)

Making corrections for the drop in resistance when the conductor is at room temperature, such as when Zs is measured, means the measured resistance must be lower than the limit specified so that when the conductor is in use the resistance rises to the calculated value.
The accepted correction factor to convert values from 70°C to 20°C is 0.80.

So the maximum measured Zs would be 2.731 * 0.80 = 2.185Ω.

 

[Loki]

You have the theory correct and the calculations generally accurate.
The MCB must trip within the time limits required for ADS and this occurs when they trip "instantly" i.e within much less than 0.1 seconds thereby complying with all the disconnection times in table 41.1 (0.2s to 5s).
The type of the MCB determines the current at which the MCB will trip "instantly" in accordance with the 60898 standard.
Type B 3 to 5 times rated current
Type C 5 to 10 times rated current
Type D 10 to 20 times rated current

So for a type B 16A MCB the worst case is at 5 times rated current i.e. 80A
These values are shown in the tables on the graphs in appendix 3.

The formula in 411.4.5 can be rearranged to be:
Zs <= (Uo x Cmin)/Ia

Therefore you have Uo as 230V, Cmin as 0.95 and the Ia is calculated as above for the type of breaker.

So Maximum Zs is 230*.95 / 80 = 2.731Ω
When the conductor is at maximum operating temperature (70°C in most cases)

Making corrections for the drop in resistance when the conductor is at room temperature, such as when Zs is measured, means the measured resistance must be lower than the limit specified so that when the conductor is in use the resistance rises to the calculated value.
The accepted correction factor to convert values from 70°C to 20°C is 0.80.

So the maximum measured Zs would be 2.731 * 0.80 = 2.185Ω.

Thank you for your reply & explaining all that.
Omg I actually understand it lol

 

[hightower]

As Lee has said don't forget cMin, and not quite sure how 2.875 gets rounded to 2.8...

 

[Loki]

I was just trying to keep it simple so rounding it off.
I will remember cMin now & round off at the end & not in the middle.

2.875 if rounded up to 1 decimal point would be 2.9 & not what I had said 2.8 my mistake

 

[hightower]

I was just trying to keep it simple so rounding it off.
I will remember cMin now & round off at the end & not in the middle.

2.875 if rounded up to 1 decimal point would be 2.9 & not what I had said 2.8 my mistake

Good plan, also, don't round to 1 decimal place, I would argue the standard for most electrical calculations would be 2 decimal places.

 

[davesparks]

Good plan, also, don't round to 1 decimal place, I would argue the standard for most electrical calculations would be 2 decimal places.

there is no standard, you just can't be more accurate than your input data, so you work to the number of decimal places, or significant figures of your least accurate input data.
But you wouldn't necessarily apply this to constants or declared values.

So if you are calculating resistance and are given measured values of 235V and 5.27A to use then the answer should be 45ohms
If the measured values were 235.00V and 5.27A then the answer should be 44.59ohms

 

[ElectroChem]

235V and 5.27A are both to 3 significant figures. You could make the argument that 44.6ohms is consistent with your input precision.