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Energy Engineering - Electric Power Systems

Full exam

Electric Power Systems Exam # 3: 09 /0 9/20 21 1° Part Exercise 1 In the figure bellow a three -phase demand (D) is supplied by a three -phase synchronous generator ( SG ) through the electric line L. The demand absorbs ��= 400 + 20 ∙������ [MW ] with a lagging power factor cos �������= 0.95 . The electric transformer T nameplate specifies the following data: Nominal electrical power 600 MVA Nominal ideal transformer ratio 20/132 kV/kV Short -circuit voltage 10 % The synchronous generator SG nameplate specifies the following data: Nominal electrical power 700 MVA Nominal line -to -line voltage 20 kV Maximum phase -to -ground emf 24 kV Maximum turbine power 650 MW Stator winding resistance 0.2 Ω Synchronous reactance 0.03 Ω Stator phases connection D The demand is supplied at line -to -line voltage of ������������������������������������� = (95 + ������)% of the nominal voltage at the secondary (high) voltage side of the transformer T. Determine: 1. the real and reactive power supplied by the synchronous generator to the grid (�������,�������) and the line -to -line voltage at the synchronous generator’s terminals (������������); 2. the emf ������� and the load angle ( ������) of the synchronous generator; 3. check the capability curve of the synchrono us generator in the given operating conditions; NOTE : In the above data, N is the last number of the student’s Person Code/Codice Persona (e.g. if Person Code is 10 38148 6 then N = 6); Please substitute accordingly. P su P Exercise 2 Consider the following electric network Line xl [p.u.] L1 0.1 L2 0.2 + 0.01 ∙N L3 0.05 Generator Real power output: P G Voltage set - point: V G [p.u] [p.u] G 4.0 1.0 6 Demand Absorbed real power: PD Power factor [p.u] [-] D 5 + 0.2∙N 0.9 3 – lagging Knowing that the inductive reactor I is characterized by a reactance ������������ = 2 p.u. and that the External Grid ( Ext Grid ) is modeled as an infinite power generator that imposes at its terminals a voltage of 1.0 4 p.u.: 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 using the Newton -Raphson method (compute the bus voltage phasors); 5. calculate, without using the previous results, the exact value of the real power injected by the external grid Ext Grid into the studied network. NOTE : In the above all quantities are in p.u. with respect to ��������� = 100 ������������������ and ��������� = 400 ������������ . NOTE : All calculations are to be made in p.u. with respect to the given base. NOTE : In the above data, N is the last number of the student’s Person Code/Codice Persona (e.g. if Person Code is 10 38148 6 then N = 6); Please substitute accordingly. 2 t rid 1 2° Part Answer only one of the two following questions 1. The Galileo Ferraris theorem : a. describe the structure of the electric machine ; b. demonstrate the existence of the rotating magnetic field (main steps : definition of supply currents → mmf at the air gap → superposition and decomposition → field expression and justification of being rotating) ; c. show the link between the angular position of the rotating magnetic field and the values of the AC currents that generate it . 2. The capability curve of a round synchronous machine : a. define the adopted simplifying hypothesis to construct the capability curve regarding machine losses, voltage at machines terminals and their impact on the model of the machine ; b. define and explain the operational limits considered in the capability curve; c. show, while motivating, the procedure to graphically construct the capabilit y curve starting from the voltage phasor -diagram of the machine. Answer only one of the two following questions 1. The DC Power Flow method: a. Describe what the method aim (goal) is and name all the adopted simplifying hypothesis; b. Consider a generic branch connecting bus p to bus q and derive the nodal power flow equations for the generic bus p starting from the complex power flowing in this branch; in doing this, show the impact of the previously introduced simplifying hypotheses; c. Write the DC PF model in matrix form. 2. The Secondary Frequency regulation: a. Explain why , in general, the frequency regulation is required in the electric power systems and what is the goal of secondary frequency regulation . b. Explain how the Secondary Frequency regulation works in a multi -machine power system with the help of the linear f-P regulating characteristics of the machines . 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 the following equations the subscri pt m stands for the magnitude (absolute value) of the respective quantity. Power Flow Equations ��= �������� ∙∑ �������� ∙��������� ∙������������� (�������− �������− �������� ) � ��= �������� ∙∑ �������� ∙��������� ∙������������� (�������− �������− �������� ) � Newton -Raphson Method �������� �������������= �������� ∙��������� ∙������������� (�������− �������− �������� ) �������� �������������= ������∙�������� ∙��������� ∙������������� (�������� )+ ∑ �������� ∙��������� ∙������������� (�������− �������− �������� ) �≠� �������� �������������= �������� ∙�������� ∙��������� ∙������������� (�������− �������− �������� ) �������� �������������= −�������� ∙∑ �������� ∙��������� ∙������������� (�������− �������− �������� ) �≠� �������� �������������= �������� ∙��������� ∙������������� (�������− �������− �������� ) �������� �������������= −������∙�������� ∙��������� ∙������������� (�������� )+ ∑ �������� ∙��������� ∙������������� (�������− �������− �������� ) �≠� �������� �������������= −�������� ∙�������� ∙��������� ∙������������� (�������− �������− �������� ) �������� �������������= �������� ∙∑ �������� ∙��������� ∙������������� (�������− �������− �������� ) �≠�