800M 32mm SWA - could this cause increased electricity bills due to voltage loss

Perhaps I'm being rather slow here, but  assuming a constant 230 V at the origin of 800 m of 35 mm2 with a 30 A load at the end you'd end up with about 203 V at the end. Power in = 6900 W, power at end = 6090 W so there is 810 W loss in the cable.

If the magic box receives 203 V and ups it to the desired 230 V from the delivered 6090 W, we get 26.5 A at 100% efficiency. At 98% declared we get 26 A 

But we want 30 A at 230 V so to get this 6900 W we have to supply more than 30 A at the origin.

Let's try 34 A at the origin.

Voltage at end 200 V. Power in = 7820 W. power at end = 6800 W so there is a 1020 W loss in the cable.

Again with receiving 200 V and ups it to the desired 230 V from the delivered 6800 W, we get 29.6 A at 100% efficiency. At 98% declared we get 29 A. Getting closer.

Try 35 A at origin. Voltage at end 199 V. Power in = 8050 W. power at end = 6965 W so there is a 1085 W loss in the cable.

Again with receiving 199 V and ups it to the desired 230 V from the delivered 6965 W, we get 30.3 A at 100% efficiency. At 98% declared we get 29.7 A.

There must be an easier iterative way but to get our 30 A supply at 230 V, we must supply 35 A at the origin. A true efficiency of around 86%. 17 p/kWh at origin becomes 20p/kWh..............


Anyone care to do the calcs for the installed 20 kVA?


It is past my bedtime so EOE and I welcome your replies and corrections!


Regards


BED

Perhaps I'm being rather slow here, but  assuming a constant 230 V at the origin of 800 m of 35 mm2 with a 30 A load at the end you'd end up with about 203 V at the end. Power in = 6900 W, power at end = 6090 W so there is 810 W loss in the cable.

If the magic box receives 203 V and ups it to the desired 230 V from the delivered 6090 W, we get 26.5 A at 100% efficiency. At 98% declared we get 26 A 

But we want 30 A at 230 V so to get this 6900 W we have to supply more than 30 A at the origin.

Let's try 34 A at the origin.

Voltage at end 200 V. Power in = 7820 W. power at end = 6800 W so there is a 1020 W loss in the cable.

Again with receiving 200 V and ups it to the desired 230 V from the delivered 6800 W, we get 29.6 A at 100% efficiency. At 98% declared we get 29 A. Getting closer.

Try 35 A at origin. Voltage at end 199 V. Power in = 8050 W. power at end = 6965 W so there is a 1085 W loss in the cable.

Again with receiving 199 V and ups it to the desired 230 V from the delivered 6965 W, we get 30.3 A at 100% efficiency. At 98% declared we get 29.7 A.

There must be an easier iterative way but to get our 30 A supply at 230 V, we must supply 35 A at the origin. A true efficiency of around 86%. 17 p/kWh at origin becomes 20p/kWh..............


Anyone care to do the calcs for the installed 20 kVA?


It is past my bedtime so EOE and I welcome your replies and corrections!


Regards


BED