Rigorous Mathematical Steps for Sensitivity Analysis of High Impedance Ground Fault Detection in Power Distribution Systems

Figures & data

Figure 1. Single line representation

Figure 2. Representation of a single-phase to the ground fault of the MV system

Figure 3. Flowchart

Table 1. Total sequence impedances (Z₁, Z₂, Z₀) in a practical system

Total Sequence Impedance	Values
Positive seq. impedance (Z1 S + Z1 t+ Z1 L)	0.969+ j1.778 Ω
Negative seq. impedance (Z2 S + Z2 t+ Z2 L)	0.969+ j1.778 Ω
Zero seq. impedance (Z0 L + Z0 t)	1.671+ j5.154 Ω
Fault impedance (Zf)	0.1 to 1000 Ω

Figure 4. Sensitivity of phase voltage S (V_b) curve for various “Z_n”.

Table 2. Magnitude of the sensitivity of healthy phase voltage S(V_b)

Zf	Zn (Ω)
(Ω)	0.1	63.5	635
0.1	0.01	0.00	0.00
100	0.01	0.19	0.07
1000	0.00	0.05	0.19

Figure 5. Sensitivity of phase voltage S (V_c) curve for various “Z_n”.

Table 3. Magnitude of the sensitivity of healthy phase voltage S(V_c)

Zf	Zn (Ω)
(Ω)	0.1	63.5	635
0.1	0.01	0.00	0.00
100	0.01	0.19	0.07
1000	0.00	0.05	0.19

Note: Sensitivity values of Tables 2 and 3 are identical.

Figure 6. Sensitivity of fault current S (I_fa) and neutral voltage S (V_n) curves for various “Z_n”.

Table 4. Magnitude of the sensitivity of fault current S(I_fa)

Zf	Zn (Ω)
(Ω)	0.1	63.5	635
0.1	− 0.03	0.00	0.00
100	− 0.99	− 0.61	− 0.14
1000	− 1.00	− 0.94	− 0.61

Table 5. Magnitude of the sensitivity of neutral Voltage S(V_n)

Zf	Zn (Ω)
(Ω)	0.1	63.5	635
0.1	− 0.03	0.00	0.00
100	− 0.99	− 0.61	− 0.14
1000	− 1.00	− 0.94	− 0.61

Note: Sensitivity values of Tables 4 and 5 are identical.