A very acceptable first-pass approximation of determining fault current is to use impedance (Z), or more typically per unit (%Z).
However, when two or more impedances are connected in series, the sum of the absolute values of the separate impedances isn't exactly the same as the sum of the real and reactive parts of the impedance. This can be shown graphically.
(http://pps2.com/images/smf/poweranalysis/triangle_2_in_series.jpg)
Here it is visually evident that the sum of the two impedances does not equal the actual series impedance, or mathematically:
(http://pps2.com/images/smf/poweranalysis/Z1_Z1_equ.jpg)
but since:
(http://pps2.com/images/smf/poweranalysis/Z3_equ.jpg)
and:
(http://pps2.com/images/smf/poweranalysis/Z1+Z2_calc.jpg)
then:
(http://pps2.com/images/smf/poweranalysis/Z3_not_equal_Z1_plus_Z2.jpg)
Click on the image of the spreadsheet below to play back a voiced-over narration describing this issue, plus I explain how to use a spreadsheet tool to visualize the results.
Narrated explanation: https://pps2.com/v/1/ZvRX.php (https://pps2.com/v/1/ZvRX.php)
(http://pps2.com/images/smf/poweranalysis/calc_screenshot.png) (https://pps2.com/v/1/ZvRX.php)
Another thing that might be useful from this video is I show how to calculate and draw these stacked vector plots within Excel. For more detail on creating phasor plots, refer to this separate article (Excel Phasor Diagram Builder (http://http://pps2.com/smf/index.php/topic,40.0.html))
Download the spreadsheet from the link below.