1. (a) Using the Murray Loop test, determine the distance to an earth fauh on one of the cores of a uniform three-core underground cable. R_a = 2 ohms, R_b = 1 Ω and the cable length is 300 m.

(b) If the cable measurement is accurate to ±1% what length of excavation would be required to locate the fault?

2. A cable run consists of 100 m of 120 nm² three-core cable jointed to 100 m of 240 nm² cable. The ratio of the potentiometer resistances in a Murray Loop test, R_b (R_b + R_a), is 1/3. For an earth on one core of the cables, determine the location of the fault.

3. A Varley Bridge is connected to a faulty three-core copper cable by two identical copper leads of resistance R₁.

(a) Show that for the initial reading (connection to earth);

2R_x = 2R_c - R_i

where R_c is the resistance of the cable core Ri is the initial reading of the bridge lc is the cable resistance to the fault from the bridge
and for the final reading:

= R_c - 2R_i

where R_c is a lead resistance

R_f is the final reading resistance.

Then by substituting (2) in (1) and rearranging the equation, show:

R_x + R_I = (R_f - R_i)/R_f (R_c+R_l)

(b) By multiplying the rhs brackets and collecting terms, show the effect of the leads is given by:

R_s = (R_f - R_i)/R_f R_c = R_iR_i/R_f

i.e. = effect with no leads - ratio of initial and final readings x lead resistance

(c) Determine the distance to the fault by modifying the expression in (b) and using R_x/R_c = x/L

where x is the cable distance to the fault

and L is the length of a cable core.

Derive an expression for x, the distance to the fault.

(d) Using R = ΡL/A

where Ρ is the resistivity,

L is the length

and A is the cross-sectional area of a cable core

show that R₁ = R_cA_cL₁/A₁L_c   (where L_c = L)

and by substituting for R1 show that the distance to the fauh is given by:

x = [(Rf - R_i)/R_f = R_i/R_f A_cL₁/A_tL]L

(e) Text Box: X =Text Box: LDetermine the distance to a fault on a 200 m, 120 mm² copper cable if copper 10 mm² test leads of length 10 m are used and R_i/R_f = 0.2

4. FIGURE 1 shows a Wheatstone Bridge connection used to determine the location of a fault on a cable in which two cores are of different cross-sectional area (the Murray Fisher method). Ignoring test lead resistance, show that

(a) For the first reading position, the resistance to the fault,Rr is given by

R_x = R_b1/ (R_a1 - R_b1)/R_f (R_c1+R_c2)

(b) For the second reading position and substituting for R_c1, the distance to the fault, x, is given by:

x = R_b1/ (R_a1 + R_b1) x R_f (R_a1+R_b2)/Rb₂ x L

x = R_b1/R_b2 (R_a2 + R_b2)/R_a1+R_b1 + L

(c) If the cable tested is 100 m in length, R_a1 is 1.5 ohms, R_b1 is 1.0 ohm and R_a2 /R_b2 = 0 8 calculate the distance to the fault.

5. Draw the individual and combined impedance (X pu) diagrams to a base of 10 MVA for the units and system shown in FIGURE 1. Determine the system fault MVA and fault currants at the II kV and 3.3 kV busbars. Show all working.

6. For the system shown in FIGURE 2, using a 10 MVA base, calculate the fault MVA levels through each unit and the base "voltage" MVA across each unit for a fault at F. Draw the impedance diagrams the fault levels and the base "voltage" MVA across each unit for:

(a) bus section switch B open and A open

(b) bus section switch B closed and A open.

Other circuit breakers are closed.

The generators have the same rating and characteristics.

7. FIGURE 3 shows part of an electrical supply system. Draw the impedance diagrams reducing to a single impedance. Calculate the fault MVA levels in each unit for a fault on the left 3.3 kV bus with the bus-section switch B open and A closed. Use a base MVA of 10 and show the fault MVA levels on a diagram. Comment on the result and suggest a method of improving the system to limit the fault MVA through T1 to approximately 5 x FL current. (It is not necessary to recalculate.)

8. Given the relationships: MVA base

X pu = MVA base/ MVA fault

= MVA base/ MVA rated x X%/100

fault MVA = √3VI_fault

XΩ = V/√3I_fault

show that  (a) = Fault MVA = MVA rated/x% x100

                   (b) = x pu = MVA base/V² x xΩ

and hence calculate the pu impedance of 100 m of 3 single core 415 V cables in trefoil. Take the cable impedance to be 90 microhms per metre. Use a 1 MVA base. Neglect the resistance of the cables.

9. For the system shown in FIGURE 4, determine the fault level for a fault on the cable at the 33 kV unit shown when the bus section switch is closed. The cable impedance is 90 microhms per metre. Neglect cable resistance and use a base of 10 MVA.

(ii) What would be the effect on the fault level of replacing the unit shown in FIGURE 4 with a running motor?

10. Determine the pu impedance and the reactance of the intrbus reactor for the system shown if generator G_o, is to be used. The switchgear rating is 500 MVA. Use a 10 MVA base and assume all circuit breakers arc closed, except the 11 kV bus section circuit breaker, and the inter bus reactor is in service.