# Engineering principles, electrical networks, three-pahse supplies

THREE-PHASE SUPPLIES

1) Three 80 Ω resistors are connected in a three-wire star configuration across a 415 V, 50Hz supply. Determine

i) the line and phase currents

ii) the total power dissipated by the load

iii) the power dissipated if, due to a fault, one phase of the load went open circuit.

2) A balanced delta-connected load has a power factor of 0.8 lagging and takes a power of 4080W from a 425V, 50Hz three-phase supply.

Calculate:

i) the resistance and reactance of each phase

ii) the line current if the same load was connected in star.

3) A balanced three-phase, 10kW load is connected to a 415V three-wire supply. Determine the load power factor if the line current is 18A.

4) A star-connected 415V, 50Hz induction motor takes a line current of 20 A at a power factor of 0.75. The load power factor is to be improved by connecting a bank of delta-connected capacitors in parallel to the motor. Calculate:

i) the output power of the motor if it is 85% efficient

ii) the value of capacitance required in each phase to improve the power factor to 0.9.

5) The diagram below shows a star-delta connection of an ideal generator to its balanced, purely inductive load.

Draw, to scale, phasor diagrams for the generator and load to show the relative magnitudes and phase relationships of the line and phase voltage and currents. Use the nomenclature for voltages and currents defined in FIGURE 1.

From your phasor diagrams, state the phase relationship between the generator s phase voltage and current.

SEE ATTACHED FIGURE 1 HERE

6) Explain, with the aid of circuit sketches, the principles of measuring power in three-phase systems using the methods listed below. Your answers must be supported by equations, derived from a consideration of the instantaneous line power with respect to a reference point, to show how the instruments measure the total power.

a) the one-wattmeter method

b) the two-wattmeter method

c) the three-wattmeter method

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NOTE TO WRITTER:

Paper to be written as a question paper, not an essay e.g.

1) i) Answer

ii) Answer etc.

Priority formulas to be used where appropriate.

3 phase star connection

Vl √3 Vp

Il Ip

3 phase delta connection

Il √3 Ip

Vl Vp

Power in a single phase of a 3 phase supply

Pp Vp Ip cos θ

Total 3 phase power in a balanced system, whether connected in star or delta

Pt 3Vp Ip cosθ

Or

Pt √3 Vl Il