Henley:Eship

(From Angie's notes)

Definitions

$P: \mbox{Power in kW}$

$pf: \mbox{power factor (value 0-1)}$

$S: \mbox{Apparent Power kVA}$

$V_{ll} : \mbox{line-to-line Voltage}$

$I_{line} : \mbox{line current in Amps}$

$\left | \bar{I} \right | : \mbox{Available Cable Ampacity}$

$\phi : \mbox{phase}$

$f : \mbox{system input frequency in Hz}$

$\bar{Z} : \mbox{Impedance (complex)}$

$r_0 : \mbox{conductor radius in m (inner r)}$

$r_1 : \mbox{conductor + insulation radius in m (inner r + insulation)}$

$r_2 : \mbox{conductor + insulation + sheath radius in m (inner r + insulation + sheath)}$

$\mu_r : 1 \mbox{ (for copper)}$

$\epsilon_r : 2.7 \mbox{ simulink constant (for copper)}$

$tandelta: 0.0016 \mbox{ tangent of } \delta$

$l : \mbox{length of cable}$

$R: \mbox{Resistance}$

$L: \mbox{Inductance}$

$C: \mbox{Capacitance}$

$G: \mbox{Conductance}$

$X: \mbox{Reactance}$

$X_L: \mbox{Inductive Reactance}$

$X_C: \mbox{Capacitive Reactance}$

Equations

$S = \frac{P}{pf}$

$I_{line} = \frac{S * 1000}{\sqrt{3} * V_{ll}}$

Note: For AC, most loads are $3\phi$, thus 3 "lines". For DC, +conductor and -conductor, thus 2 "lines".

$\bar{Z}_\text{per phase} = \frac{\bar{Z}_\text{per cable}}{\frac{cables}{phase}}$

Find Total Cables

1. Compute $I_{line}$ using above equations.
2. From a Look Up Table [or from S3D catalog], Find the cable with closest size $AvailableCableAmpacity$.
3. Compute cables per phase with the formula $\frac{cables}{phase} = \left \lceil \frac{I_{line}}{AvailableCableAmpacity} \right \rceil$
4. Compute $TotalCables = \frac{cables}{phase} * NumberOfPhases$

Find Impedance per cable ($\bar{Z}_\text{per cable})$

1. From cable selected above, use lookup tables [or S3D catalog] to get area in mm^2, insulation thickness in mm, and sheath thickness in mm.
2. Compute $r_0 = \frac{\sqrt{\frac{Area(mm^2)}{\pi}}}{1000}$
3. Compute $r_1 = \frac{Insulation thickness(mm)+\sqrt{\frac{Area(mm^2)}{\pi}}}{1000}$
4. Compute $r_2 = \frac{Sheath thickness(mm)+Insulation thickness(mm)+\sqrt{\frac{Area(mm^2)}{\pi}}}{1000}$
5. Compute $\mu = (\mu_r)(4\pi)(1e^-7)$
6. Compute $\epsilon = (\epsilon_r)(8.854e^-12)$
7. Compute $\omega = 2\pi f$
8. Compute $R = \left( \frac{1}{\sigma\pi} \right) \left( \frac{1}{r_0^2} \right) \left( l \right)$
9. Compute $L = \left( \frac{\mu}{2\pi} \right) \left( \ln \left(\frac{r_1}{r_0} \right) \right) \left( l \right)$
10. Compute $C = \left( \frac{ 2 \pi \epsilon l}{ \ln \left(\frac{r_1}{r_0} \right) } \right)$
11. Compute $G = \left( \frac{2 \pi \omega \epsilon \tan(\delta)}{ \ln \left(\frac{r_1}{r_0} \right)} \right) \left( l \right)$
12. Compute $\bar{Z}_\text{per cable} = \left[ \frac{R}{2} + j \frac{L\omega}{2} \right] + \left[ \frac{1} {\left[ (G + j C\omega) + \frac{1}{\left( \frac{R}{2} + j\frac{L\omega}{2} \right)} \right]} \right]$

Alternatively (if R,L,C are known):

1. Compute $X_L = j \omega L$
2. Compute $X_C = j \frac{1}{\omega C}$
3. Compute $X = X_L - X_C$
4. Compute $\bar{Z}_\text{per cable} = R + jX$

ToDo

• Need to compute bending radius per phase from bending radius per cable. (Angie is going to check with Mike on what to do for this.)