Energy losses in cables: What is the ohmic loss?

[Suziii]

having 2 cables of 790 mm^2 cross sectional area and voltage of 450 kV. the maximum power is 700 MW and the length of cables 580 km. Assuming the resistivity of the conductor is 1.67microohmcm. then what is the ohmic lose?

Thanks in advance

 

[tiny-tim]

Welcome to PF!

Hi Suziii! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[Suziii]

Thanks a lot.

I tried to find the ohmic power by the following formula: P(ohmic)=R (cable) x I^2 where R is the resistance and I the current.Then I divided the value for P (ohmic) and for P (max). however the problem is that by doing this I am getting higher value for P (ohmic) than for P (max) which should not be the case.

 

[tiny-tim]

Hi Suziii!

(have an ohm: Ω and a mu: µ and try using the X² icon just above the Reply box )

I tried to find the ohmic power by the following formula: P(ohmic)=R (cable) x I^2 where R is the resistance and I the current.Then I divided the value for P (ohmic) and for P (max). however the problem is that by doing this I am getting higher value for P (ohmic) than for P (max) which should not be the case.

I don't understand … I isn't given in the question

(did you use V²R instead of V²/R ?)

anyway, please show your actual calculations in future ​

 

[pmacias]

Ohmic loss, also known as resistive loss, is the energy lost in a cable due to the resistance of the conductor. In other words, as electricity flows through the cable, some of the energy is converted into heat due to the resistance of the material.

In this scenario, the ohmic loss can be calculated using the formula P=I^2R, where P is the power loss, I is the current, and R is the resistance. To find the resistance, we can use the formula R=rho*L/A, where rho is the resistivity of the conductor, L is the length of the cable, and A is the cross-sectional area.

So, for our given values, the resistance of each cable would be:

R = (1.67 x 10^-6 ohm-cm) * (580,000 m) / (790 mm^2 * 10^-6 m^2/mm^2) = 0.0123 ohm

Now, we can calculate the current flowing through each cable using the power and voltage values:

I = P/V = 700 MW / (450 kV * 1000) = 1,556 A

Finally, we can plug these values into the formula for power loss to find the ohmic loss for each cable:

P = (1,556 A)^2 * 0.0123 ohm = 29,893 W or 29.9 kW

Therefore, the total ohmic loss for the two cables would be 59.8 kW. This means that about 59.8 kW of energy is lost as heat due to the resistance of the cables, resulting in a slightly lower amount of power reaching the intended destination. This loss can be minimized by using materials with lower resistivity and by keeping the length and cross-sectional area of the cables as low as possible.