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Energy Engineering - Electric Power Systems

Full exam

Electric Power Systems Exam #1 : 02 /0 7/201 9 1° Part Exercise 1 In the figure bellow (a.) a three -phase induction motor ( IM) is supplied by a external grid (EG) through the electric line L. a. b. The induction motor nameplate specifies the following data: Nominal mechanical power 65 kW Nominal supply voltage 6.0 kV Nominal stator current 8 A Nominal mechanical speed 970 turns/min Number of poles 6 Stator/rotor phases conn ection Y Stator phase resistance 15 Ω The electric line is characterized by ������������= 5 Ω and ������������= 15 Ω. Moreover, the induction motor operating in no -load conditions absorbs from the network a line current of 2.5 A with a power factor of cos ������0= 0.12 - lagging . Neglecting the mechanical losses in the induction motor , considering the iron losses in the induction motor constant and considering the induction motor operating in nominal operating conditions , determine: 1. the iron losses in the induction motor IM ; 2. the Joule losses in the stator and rotor windings of the induction motor IM ; 3. the real and reactive power absorbed by the induction motor from the electrical grid (P M and Q M in Fig a.) ; 4. the real and reactive power supplied by the external grid EG at the sending end of the electric line L (PEG-L and Q EG-L in Fig a. ) and the line to line voltage at the sending end of the electric line L (VEG in Fig a. ); 5. Considering the addition of the synchronous generator SG at the terminals of EG (Fig. b ) and that the EG will supply the entire real power required by the induction motor IM at cos ������������������ = 0.95 – lagging , find the real and reactive power injected by the synchronous generator SG (PSG and Q SG in Fig b. ); 6. knowing that SG is characterized by a synchronous reactance ������������= 21 Ω and that it’s stator windings are D - connected, calculate the emf ������0 and the load angle ( ������) of SG for the operating conditions given at point 5 . Exercise 2 Consider the following electric network Line L [km] xl [/km] Vn [kV] L1 125 0.4 400 L2.1 190 0.4 400 L2 .2 210 0.4 400 L3 125 0.4 400 Generator Vn Real power output: P G Voltage set - point : V G [kV] [MW] [kV] G 400 1800 416 Demand Vn Absorbed real power: PD Power factor [kV] [MW] D1 400 500 0.9 – lagging D2 400 100 0.9 8 – leading Knowing that the External Grid ( Ext Grid ) is modeled as an infinite power generator that imposes at its terminals a voltage of 39 6 kV: 1. determine the bus admittance matrix; 2. identify the bus types for Power Flow (PF) computation; 3. choose the starting profile for the iterative process of PF; 4. perform one PF iteration usin g the Newton -Raphson method (compute the bus voltage phasors); 5. using the results of question 4 , compute the phasors of the currents in the two circuits of line L2, from bus 3 to bus 1. 2° Part Answer only one of the two following questions 1. Enunciate and demonstrate the Galileo Ferraris theorem : (i) describe the structure of the electric machine; (ii) enunciate the hypothesis; (iii) demonstrate the existence of the rotating magnetic field and (iv) show the link between the position of the rotating magnetic field and the AC currents that generate it. 2. Starting from the structure of a round synchronous machine , obtain the equivalent circuit of the synchronous machine operated as a generator . In doing so, descri be the operating conditions of the machine that lead to the definition of the equivalent circuit: hypothesis, physical phenomena, phasor diagrams. Simplifying hypothesis : the magnetic material is linear. Answer only one of the two following questions 1. Using a small electric network as example, demonstrate the construction of the Bus Admittance matrix according to the theory of electric circuits: (i) define the involved physical quantities, vectors and matrices; (ii) define the KC and Ohm laws in matrix form and (iii) obtain the Bus Admittance matrix. 2. Describe the characteristic of the J acobian matrix for transmission networks and comment on the consequences on the network operation. Then, derive the DC power flow method. Equation sheet During the written test the candidate may consult this sheet, which will be delivered in conjunction with the test text. You are not allowed to consult any other material, such as your own notes, handouts or textbooks In t he following equations the subscript m stands for the magnitude (absolute value) of the respective quantity. Power Flow Equations ��= �������� ∙∑ �������� ∙��������� ∙������������� (�������− �������− �������� ) � ��= �������� ∙∑ �������� ∙��������� ∙������������� (�������− �������− �������� ) � Newton -Raphson Method �������� �������������= �������� ∙��������� ∙������������� (�������− �������− �������� ) �������� �������������= ������∙�������� ∙��������� ∙������������� (�������� )+ ∑ �������� ∙��������� ∙������������� (�������− �������− �������� ) �≠� �������� �������������= �������� ∙�������� ∙��������� ∙������������� (�������− �������− �������� ) �������� �������������= −�������� ∙∑ �������� ∙��������� ∙������������� (�������− �������− �������� ) �≠� �������� �������������= �������� ∙��������� ∙������������� (�������− �������− �������� ) �������� �������������= −������∙�������� ∙��������� ∙������������� (�������� )+ ∑ �������� ∙��������� ∙������������� (�������− �������− �������� ) �≠� �������� �������������= −�������� ∙�������� ∙��������� ∙������������� (�������− �������− �������� ) �������� �������������= �������� ∙∑ �������� ∙��������� ∙������������� (�������− �������− �������� ) �≠�