EECE 471 Midterm, Fall 2005

S. KARAKI AMERICAN UNIVERSITY OF BEIRUT FALL 2005/2006 FACULTY OF ENGINEERING AND ARCHITECTURE MIDTERM FUNDAMENTALS OF POWER SYSTEMS ANALYSIS (EECE 471) CLOSED BOOK (2 HOURS) NOVEMBER 14, 2005 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 power station schematic shown in Fig.1 below and give it a specific caption next to the figure number. Fig.1: ___________________________________________ b) What is the most efficient thermal power generation technology used throughout the world nowadays and what is its approximate efficiency? __________________________________________________________________ c) Name two environmental problems associated with fossil-fuel power plants and indicate ways of mitigating them? __________________________________________________________________ EECE 471E MIDTERM - FALL 2005/ 2006 Page 2/ 5 d) Name a renewable energy technology that you believe is most likely to be used and explain the reasons? __________________________________________________________________ e) Why do we raise the voltage to transmit a given amount of power over a long distance? __________________________________________________________________ 2. It is required to design a transmission line of 200 mile length to supply a demand of 300 MW at 0.9 PF lagging considering one of two voltages 220 and 400 kV at a frequency of 50Hz with typical phase-to-phase spacing of 8 m and 12 m, respectively. Note that 1 kcmil= 0.507mm2 and 1 ft= 0.305 m. a) Considering that characteristic impedances of lines vary within a narrow range around 300Ω, calculate the surge impedance loading (P/PSIL) at both voltage levels. Refer to Fig. 2 below and deduce the more economic voltage that would maintain a stability margin such that the phase angle from sending to receiving is smaller than or equal to 45°. b) From Table 1 shown below select the most appropriate conductor size at the selected voltage if the current density is not to exceed 2.5 A/mm2 at the given load conditions and the prevailing 35°C ambient temperature. Consider using bundled conductors in your design and select the appropriate number of bundles in your conductor. c) Calculate the resistance, inductance and capacitance for the line design and determine its actual characteristic impedance and its surge impedance loading at the selected voltage level. d) If at minimum load conditions, the demand drops to about 40% of its peak value, estimate the voltage at the sending end under such conditions. Having reached so far in your design, are you still confident that you have made the correct voltage choice? Explain. 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 2005/ 2006 Page 3/ 5 100 200 300 400 500 600 0 1 2 3 P12 / PSIL Line length (miles) Typical thermal limit Stability limit (θ12= 45°) Fig. 2: Stability limit of lines 3. Consider a generation system supplying a load through a ∆-Y connected transformer and a transmission line, shown in Fig. 3 below. The nominal line-to-line voltages on the transformer are 13.8-66 kV. The transformer rating is 80 MVA with leakage and magnetizing reactance of one set of low-high turns are xl= 0.8Ω and xm= 25Ω, referred to the low voltage side. The load is consumes 50 MW at 0.85 PF lagging when the voltage at the receiving end is nominal. The line length is 100km, its series reactance is 0.4Ω/ km, its resistance is 0.08Ω/ km, and its susceptance is yc= 4 µS/ km. a) Divide the system into regions and select an appropriate base system and indicate the base MVA, base voltage, and base impedance in each region. b) Calculate the per-unit impedances of the load, transmission line and transformer. Draw the per-unit 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 voltage and current at the generator terminal and deduce the active and reactive power supplied by the generator. d) Is this system well designed? If yes, explain in what way it is good, other wise explain what is not good about this design and the possible ways of improving it. Generator Load ∆-Y Transmission Line 1 2 3 Transformer Fig. 3: Small power system for Problem 4 EECE 471E MIDTERM - FALL 2005/ 2006 Page 4/ 5 Fundamentals of Power Systems Analysis (EECE 471) FORMULAE • Ch.2: Basic Principles 3 ZY = Z∆ • Ch.3: Transmission-Line Parameters H m R D l b ln 2*10 −7 = 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 + × = = EECE 471E MIDTERM - FALL 2005/ 2006 Page 5/ 5 12 2 1 2 1 12 cos = θ X V V X V Q − l y Y × = 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 = =