
Physics Physics Forum 
 LinkBack  Thread Tools  Display Modes 
January 30th, 2017, 06:06 AM  #1 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,164 Thanks: 736 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Increase in current as power is transmitted along a cable?
I have a situation where I have some (real) power demand at the end of a transmission line ($\displaystyle P_r$) for a given receivingend voltage ($\displaystyle V_r$). For a line 150km in length the mathematics for calculating the sendingend voltage and current is laid out below: Complex numbers... Impedance: $\displaystyle Z = R + 2\pi f L j$ where R is resistance of the cable, f is frequency of AC current and L is the inductance of the cable. Admittance: $\displaystyle Y = 2\pi f C j$ where C is the shunt capacitance of the cable. Receiving power (including reactive component): $\displaystyle S_r = P_r  P_r \tan \phi j$ where $\displaystyle \cos \phi$ is the receivingend power factor (can be used to obtain $\displaystyle \tan \phi$). Receiving current: $\displaystyle I_r = S_r/V_r$ Define: $\displaystyle A = 1 + \frac{YZ}{2}$ $\displaystyle C = Y\left(1 + \frac{YZ}{4}\right)$ Sending voltage and current: $\displaystyle V_s = A V_r + Z I_r$ $\displaystyle I_s = C*V_r + A I_r$ Sendingpower: $\displaystyle S_s = V_s I_s^*$ $\displaystyle P_s = Re\{S_s\}$ For the following parameter choices... $\displaystyle P_r$ = 1800 MW $\displaystyle V_r$ = 400 kV $\displaystyle \cos \phi = 0.9$, (so $\displaystyle \tan \phi = 0.4843$) $\displaystyle R = 2.55 \Omega$ $\displaystyle L = 0.1289 $ H $\displaystyle C = 5.05 \times 10^{6} $ F ... I get the following results: $\displaystyle I_r = 4500.00  2179.45 j$ $\displaystyle I_s = 4359.15  1475.70 j$ $\displaystyle V_s = 518$ kV $\displaystyle P_s = 1863.75 $ MW The value for $\displaystyle V_s$ is correct according to the textbook problem I am working through (Electric Power Systems 5th edition pp 120121), so I think I've calculated everything correctly. However, the magnitudes of the current are $\displaystyle I_s = 4602.16$ A $\displaystyle I_r = 5000$ A which just doesn't seem right to me... why is the sending current lower in magnitude than the receiving current? That is, why is the current increasing along the line? I would have expected the inductance and capacitance to cause a reduction in both current and voltage as the electrical energy is being transmitted along the cable. Last edited by Benit13; January 30th, 2017 at 06:08 AM. Reason: typos... 
January 30th, 2017, 06:39 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 3,044 Thanks: 1627  
January 30th, 2017, 06:52 AM  #3 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,164 Thanks: 736 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
Haha! According to wikipedia... https://en.wikipedia.org/wiki/Electr...r_transmission "Counterintuitive behaviors of mediumlength transmission lines: a) voltage rise at no load or small current b) receiving end current magnitude can exceed sending end current" So there it is... apparently the model can cause an increase in current. I'm not sure I'd refer to it as "counterintuitive" personally, but hey ho! 
January 30th, 2017, 06:55 AM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 2,590 Thanks: 1434  Quote:
 
January 30th, 2017, 07:08 AM  #5 
Senior Member Joined: Apr 2014 From: UK Posts: 965 Thanks: 342 
DC for the win!


Tags 
cable, current, increase, power, transmitted 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Tension in a cable for a cuboidal block hinged at its top edge on a wall.  Statistics132  Applied Math  2  October 8th, 2015 09:22 AM 
Build the correct cable out of fixed length cables  patrick1984  Art  2  January 5th, 2013 03:23 PM 
Finding Current Changes Without V Or R?  GRNDPNDR  Algebra  2  September 26th, 2011 04:04 AM 