X and R values
X and R values
(OP)
I have an underground three phase power cable configuration. It consists of three cables laying in a flat position (three cables next to each other). I have the positive, negative, and zero sequence impedance for that given cable configuration. I am not sure from which of the sequence impedance do I select the X and R values to calculate the voltage drop in the system. In addition, I need the X and R values for a cradle cable configuration as well. Is there a way to convert the sequence impedances for the three phase configuration that I do have to different cable configurations. Please advice and thank you in advance.






RE: X and R values
"The more the universe seems comprehensible, the more it also seems pointless." -- Steven Weinberg
RE: X and R values
If all 3 phases current are the same as absolute value and the lag angle between one with respect to another is the same that means is a symmetrical load you need only positive reactance. The problem is also the current harmonics since both resistance and reactance are sensible to frequency. But usually you may neglect this voltage drop due to high value of this
impedance and reduced value of the currents. The conductor resistance depends on distance between the phases due to proximity effect. The reactance also depends on this distance -as mutual inductance does. The impedance stated by manufacturer is calculated based on some assumptions as single conductor cable horizontally spaced [for instance: 8"] on center or for three-core cable instead of or three single-core cables in triangle.
In order to recalculate the reactance you need to know the conductor diameter and the distance -center to center-of cables and using the following:
X=2*pi*f*(0.1404*log10(2*S/dia)+0.0153)/10^3 [ ohm/1000ft]
dia=diameter of conductor [inches]
dist=distance between conductor axes[inches]
f=frequency [50 or 60 Hz]
For three single-core cables side by side arrangement [flat] S= (dist^2)^(1/3)
For three-core cable or three single-core cables in triangle S=dist
In order to recalculate the resistance you need more:
Ro=d.c. resistance of the conductor at 20 oC[ohm/m]
Usually the standard Ro is intabulated as ohm/1000ft.
Ro[ohm/m]=Ro[ohm/1000ft]/304.8
The rated temperature[T=degreesC] usually is the maximum insulation permissible temperature for steady state. For PVC is 70oC, for XLPE or EPR 90oC.
First you calculate Rdctemp=Ro*(234.5+T)/(234.5+20) the d.c resistance at rated T temperature.
Second is to calculate the skin effect. The skin effect is the tendency of an alternating electric current (AC) to distribute itself within a conductor so that the current density near the surface of the conductor is greater than that at its core. That is, the electric current tends to flow at the "skin" of the conductor.
ys=the skin effect factor
ys=xs^4/(192+0.8*xs^4) where :
xs^2=8*pi*f/Rdctemp/10^7*ks
f=supply frequency in Herz [50 -800 HZ]
ks depends on conductor building .But usually ks=1.
Third is to calculate the proximity effect.
When an alternating current(AC) flows through an isolated conductor, it creates an associated alternating magnetic field. The alternating magnetic field induces eddy currents within adjacent conductors, altering the overall distribution of current flowing through them.
The resulting current crowding is termed the proximity effect.
yp=the proximity effect factor
yp=xp^4/(192+0.8*xp^4)*(dia/dist)^2*[0.312*(dia/dist)^2+1.18/(xp^4/(192+.8*xp^4)+.27)]
where :
xp^2=8*pi*f/Rdctemp/10^7*kp [for your application kp=1 then xp=xs]
dia=diameter of conductor [mm]
dist=distance between conductor axes[mm]
Total Resistance[R]=Rdctemp*(1+ys+yp) [ohm/m]
RE: X and R values
xd = 0.2794·(f/60)·log10(GMD/12), ohms per mile
where GMD is the geometric mean distance in inches.
GMD = (dab·dac·dbc)^(1/3)
Calculate xd for the original configuration, subtract it from the reactance to get the self-reactance. Calculate xd for the cradled configuration and add it to the self-reactance to get the new reactance.
If this is MV or HV shielded cable, the resistance changes with spacing as well because of shield losses. That's a bit more complicated and, as they say, beyond the scope of this answer.
RE: X and R values
For three single-core cables side by side arrangement [flat] S= (dist)*2^(1/3) [should be]
[if the distances between cables are the same, of course] instead of S=(dist^2)^(1/3).