EECE 471 Midterm, Fall 2003

S. KARAKI AMERICAN UNIVERSITY OF BEIRUT FALL 2003/2004 FACULTY OF ENGINEERING AND ARCHITECTURE MIDTERM FUNDAMENTALS OF POWER SYSTEMS ANALYSIS (EECE 471) CLOSED BOOK (2 HOURS) DECEMBER 4, 2003 PROGRAMMABLE CALCULATORS ARE NOT ALLOWED THIS QUESTION SHEET MUST BE RETURNED WITH THE ANSWER BOOKLET. NAME: _________________________ ID#: _________________________ 1. Answer the following questions in the space provided for each on this question sheet: a) Label the various components of the oil-fired power station schematic shown in Fig.1 below: Fig.1: Oil-fired power station schematic b) What is the thermal power generation technology most widely used throughout the world and what is its approximate efficiency? __________________________________________________________________ c) Name two environmental problems associated with fossil-fuel power plants? __________________________________________________________________ EECE 471E MIDTERM - FALL 2003/ 2004 Page 2/ 6 d) Why would the world with current technologies and resources face an energy crisis in the next 50 to 150 years? __________________________________________________________________ e) Name three types of renewable energy technologies? __________________________________________________________________ f) Why do we raise the voltage to transmit a given amount of power over a long distance? __________________________________________________________________ g) When we design generators with higher rating which dimension is usually increased, the diameter or the length of the generator and why? __________________________________________________________________ h) What is the relationship between ac and dc resistances and why are they different? __________________________________________________________________ i) For a given line, how do the shunt capacitive susceptance and the series inductive reactance in per unit change as we increase its operating voltage? __________________________________________________________________ j) What is the surge impedance loading of a line? __________________________________________________________________ 2. A three-phase load draws 500 kW at a PF of 0.707 lagging from a 440 V line. It is required to compensate the load and bring the PF of the compensation equipment and load up to 0.9. a) Determine the line current and reactive power supplied before compensation. b) Determine the line current and reactive power supplied after compensation. c) What is the kind of compensation equipment used and what is its size? d) Draw a phasor diagram showing voltage and current before and after compensation and comment on the effect of compensation on the system. EECE 471E MIDTERM - FALL 2003/ 2004 Page 3/ 6 3. It is required to design a transmission line of 150 mile length to transmit 400 MW of power considering one of two voltages 220 and 400 kV at a frequency of 50Hz. The tower configurations and dimensions of the proposed line designs are given in Fig. 2 below. Note that 1 kcmil= 0.507mm2 and 1 ft= 0.305 m. a) From Table 1 shown below select the most appropriate conductor sizes if the current density at given load conditions is not to exceed 2 A/mm2. b) Calculate line resistance, inductance and capacitance for both line designs. c) Calculate the characteristic impedance, propagation constant and surge impedance loading for both voltage levels. d) Select a voltage to maintain a stability margin such that the phase angle from sending to receiving is smaller than or equal to 45°. Refer to Fig. 3 below. 12m (a) 0.3m 7.6m 7.6m 20m (b) 0.3m 10.7m 10.7m Fig. 2: Tower configurations of a 220 kV (a) and 400 kV (b) transmission lines Table 1: Main Properties of Selected ACSR Bare Wires Name Size (kcmil) Resistance at 60Hz (Ω/mile) GMR (ft) Partridge 266.8 0.411 0.0217 Linnet 336.4 0.327 0.0244 Ibis 397.5 0.277 0.0265 Hawk 477.0 0.231 0.0290 Dove 556.5 0.198 0.0313 Grosbeak 636.0 0.173 0.0335 Drake 795.0 0.139 0.0375 EECE 471E MIDTERM - FALL 2003/ 2004 Page 4/ 6 100 200 300 400 500 600 0 1 2 3 P12 / PSIL Line length (miles) Typical thermal limit Stability limit (θ12= 45°) Fig. 3: Stability limit of lines 4. Consider the generation system supplying a load through a ∆-Y connected transformer and a transmission line, shown in Fig. 4 below. The nominal line-to-line voltages on the transformer are 12.7-220 kV. The leakage and magnetizing reactance of one set of low-high turns are xl= 0.6Ω and xm= 24Ω, referred to the low voltage side. The load is Y-connected and consumes 150 MW at 0.9 PF when the voltage at the receiving end is nominal. The line length is 100km, its series reactance is xl= 0.375Ω/ km, its resistance is 0.075Ω/ km, and its susceptance is yc= 3.8 µS/ km. a) Determine the per-phase equivalent load impedance. b) Draw the per-phase equivalent circuit of the system and show the values of all impedances. c) If power to the load is delivered at nominal voltage determine the phase currents on the transformer primary (low voltage) and secondary sides. d) Determine the voltage at the generator terminal and the active and reactive power supplied by the generator. e) Draw the phasor diagram of the transmission line showing currents and voltages at the sending and receiving, and the voltage drop across the line. Generator Load ∆-Y Transmission Line 1 2 3 Transformer Fig. 4: Small power system for Problem 4 EECE 471E MIDTERM - FALL 2003/ 2004 Page 5/ 6 Fundamentals of Power Systems Analysis (EECE 471) FORMULAE • Ch.2: Basic Principles 3 ZY = Z∆ • Ch.3: Transmission-Line Parameters m H b 7 R ln D 2*10 − λ = D: geometric mean distance between phases Rb: geometric mean radius of bundle 3 bc ac ab D D D D = 4 14 ' 12 13 r d d d Rb = c b R D c ln = 2πε F / m .8 854*10 −12 ε = 4 14 12 13 r d d d R c b = • Ch.4: Transmission Line Modeling � m j l r z Ω / + = ω S m j c y / = ω � yz γ = y z Z c = � 2 2 2 2 1 sinh cosh BI AV l Z I l V V c + = + = γ γ 2 2 2 2 1 sinh cosh DI CV l Z V l I I c + = + = γ γ T= ⎥⎦ ⎤ ⎢⎣ ⎡ D C B A and ⎥⎦ ⎤ ⎢⎣ ⎡ − − − = A C B D T 1 � Complex Power Flow on Medium Line: 12 * 2 1 * 2 1 2 1 * 12 2 jθ e Z V V Z V V Y S − + = For S21 exchange indices 1 and 2 in above equation � Power Flow on a short loss-less line: 12 2 1 21 12 sinθ X V V P P = = − jX R l z Z + × = = 12 2 1 2 1 12 cos = θ X V V X V Q − l y Y × = EECE 471E MIDTERM - FALL 2003/ 2004 Page 6/ 6 12 2 1 2 2 21 cos = Q θ X V V X V − l: length of line � Power Circle Diagram C1 C2 S12 -S21 θ12 θ12 Both circles have a radius: Z V V B 2 1 = Z Z V ∠ 2 1 C1 = Z Z V ∠ 2 2 2 - = C � Power transmission capability: l P l Z V P SIL c β θ β θ sin sin sin sin = 12 12 2 1 12 = ( ) γ β = Im • ∗Ch.5: Transformers and the Per-Unit System an a n K V V ′ ′ = and an a n I K I * 1 ′ ′ = 6 3 : jπ n e K Y = ∆ − 6 3 : jπ e n K Y = − ∆ 1 2 N n = N B B B ll B B S V S V Z 2 3 2 = = Φ B pu actual Z Z Z = n B o B o pu n B actual n pu Z Z Z Z Z Z = =