Electrical Power Engineering ELE2019 SECTION A Q1. A four-pole Y-connected, 415 V, 50 Hz, induction motor has phase- equivalent circuit parameters of 1 = 1.5 Ω, 2 = 1.2 Ω, 1 = 2 = 3.0 Ω, and = 80 Ω. Under rated condition, the rotor slip is 4%. (i) What is the rotor speed and rotor electrical frequency under rated conditions [3 Marks] (ii) Calculate the stator input current, power factor, and electromagnetic torque under these conditions. [11 Marks] (iii) What is the maximum torque of this machine [5 Marks] (iv) How much additional resistance (referred to the stator) would it be necessary to add to the rotor to make the maximum torque occur under starting conditions [4 Marks] (v) Suggest how the additional rotor resistance would be added to a wound rotor induction machine, and what effect does the additional rotor resistance have on the starting current. [2 Marks] Electrical Power Engineering ELE2019 Q2. (a) A ferromagnetic core as shown in Figure Q2 has a mean path length l1 of 25 cm. There is a small gap g of 0.1 cm in the structure of the otherwise whole core. The cross-sectional areas of both the core and the air gap are 14 cm2, the relative permeability of the core is 3000 and the coil of wire on the core has 350 turns. If the current flowing to the coil is 1.33 A, what is the flux density in the air gap Note: the permeability for free space is given as H/m104 70 = . [8 Marks] Figure Q2 (b) A 3-phase, 4-pole, 50 Hz alternator has a double-layer winding in 36 slots and produces 415 V when star connected. Each coil has 2 turns and is short-chorded by 60° (i.e. kwc = 0.866), the distribution factor kwd is 0.96, and the specific magnetic and electric loadings are respectively 0.56 T and 38000 Amp Cond/m. Use the voltage and output equations to calculate the length and inside diameter of the stator core if a rating of 200 kVA is to be achieved. [11 marks] (c) Show how short-chording by 60° will eliminate the 3rd harmonic, and explain why the line voltage is affected. [4 marks] (d) Briefly describe what the distribution factor, kwd, is and how it might be derived [2 marks] i g l1 = mean length Electrical Power Engineering ELE2019 Q3. (a) State the various sources of losses in a DC machine and explain, briefly, how they arise. [6 Marks] (b) When DC machines are loaded, armature reaction occurs. What are the causes of armature reaction and explain its consequences. [6 Marks] (c) A shunt DC motor is supplied by 240 V DC. The armature resistance of the motor is Ra = 0.16 , and the field resistance Rf is 50 . The field winding has 600 turns. An adjustable resistance Radj is connected in series to the field and is currently set at 22 . Armature reaction may be ignored in this machine. The magnetization curve for this motor, taken at a speed of 900 rpm, is given in the table below: Ea (V) 95 150 188 212 229 243 mmf (A·turns) 500 1000 1500 2000 2500 3000 (i) What
is the speed of the motor when it is running at an armature current of 50 A [6 Marks] (ii) If the terminal voltage is reduced to 180 V and the armature current stays at 50 A, calculate the required Radj in order to restore the speed of the motor to the value in (i). [7 Marks] END OF SECTION A Electrical Power Engineering ELE2019 SECTION B Q4. (a) Describe the advantages of using per-unit quantities in power system analysis. [5 Marks] (b) Show that the per-unit impedance of a transformer is the same on both the primary and the secondary side. [5 Marks] (c) Using a 100-MVA base, derive an equivalent circuit for the single- line diagram of the 3-phase power system shown as Figure Q4. [5 Marks] (d) Calculate the required voltage at the terminals of the generator, , and the complex power, , delivered by the generator. [10 Marks] Figure Q4 ZL = 100 + j200 20 : 200 kV 200 : 20 kV VR = 18 kV 50 MVA X1 = 0.1 pu 50 MVA X2 = 0.1 pu 45 MVA 0.85 pf, lagging Vt Electrical Power Engineering ELE2019 Q5. (a) Sketch the circuit diagram for the nominal-Π representation of a transmission line and use Kirchhoff’s Laws derive the A, B, C and D parameters of the corresponding 2-port network. [10 Marks] (b) A three-phase, 132–kV, transmission line supplies a load of 49 MW at 0.85 lagging power factor, at rated voltage. The total series impedance and shunt admittance are Z = 20 + j 93 and Y = j 0.001 S respectively. Using the nominal- Π representation, calculate: (i) The A, B, C and D parameters [7 Marks] (ii) The sending-end voltage [2 Marks] (iii) The sending-end current [2 Marks] (iv) The sending-end power factor [2 Marks] (v) The efficiency of transmission. [2 Marks] Electrical Power Engineering ELE2019 Q6. (a) List any two reasons why performing load flow analysis is essential in power systems. [2 Marks] (b) Explain why it is important to be able to control the flow of real and reactive power in a power system. List any four equipment/methods which allow us to implement these controls. [4 Marks] (c) The single-line diagram of a three-bus power system is presented in Figure Q6. All line impedances are marked in per unit (pu) on a 100 MVA base. Line resistances and shunt capacitances are ignored. (i) Using a single iteration of the Gauss Seidel method, calculate the complex voltages (pu) at Buses 2 and 3, i.e., V2 and V3 respectively. [14 Marks] (ii) Determine the losses (MW and Mvar) in line 2–3. Bus 1 (Slack) Bus 2Bus 3 V1 = 1 0° pu |V2| = 1.05 pu P2 = 100 MW P3 = 300 MW Q3 = 120 Mvar Z13 = + j0.05 pu Z23 = + j0.04 pu Z12 = + j0.04 pu Figure Q6 Hint: The voltage of the ith node in a power system consisting of N nodes can be estimated using the following equation (corresponding to iteration cycle p+1): +1 = ( 1 × ) + ( 1 ∑ ( ) =1,≠ ) [5 Marks] END OF EXAMINATION