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Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE) PDF Download

Q1: The three-bus power system shown in the figure has one alternator connected to bus 2 which supplies 200 MW and 40 MV AR power. Bus 3 is infinite bus having a voltage of magnitude ∣V3∣ = 1.0 p.u. and angle of −15°. A variable current source, ∣1∣ ∠ϕ is connected at bus 1 and controlled such that the magnitude of the bus 1 voltage is maintained at 1.05 p.u. and the phase angle of the source current, Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE) where θ1 is the phase angle of the bus 1 voltage. The three buses can be categorized for load flow analysis as        (2023)
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)(a) Bus 1 Slack bus
Bus 2 P − ∣V∣ bus
Bus 3 P − Q bus
(b) Bus 1 P − ∣V∣ bus
Bus 2 P − ∣V∣ bus
Bus 3 Slack bus
(c) Bus 1  P − Q bus
Bus 2 P − Q bus
Bus 3 Slack bus
(d) Bus 1 P − ∣V∣ bus
Bus 2 P − Q bus
Bus 3 Slack bus
Ans: 
(d)
Sol: Concept : Classification of Bus system :
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Now, from given power system network.
Bus-1 ⇒ PV bus
Bus-2 ⇒ PQ (load) bus
Bus-3 ⇒ Slack bus

Q2: Suppose IA, IB and IC are a set of unbalanced current phasors in a three-phase system. The phase-B zero-sequence current IB0 = 0.1∠0° p.u. If phase-A current IA = 1.1∠0° p.u and phase-C current IC = (1 ∠ 120° + 0.1) p.u, then IB in p.u is        (2021)
(a) 1∠240° − 0.1∠0°
(b) 1.12400.101.1∠240°−0.1∠0°
(c) 1.1120+0.101.1∠−120°+0.1∠0°
(d) 1∠−120° + 0.1∠0°
Ans: 
(d)
Sol: Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)
Q3: A 3-Bus network is shown. Consider generators as ideal voltage sources. If rows 1, 2 and 3 of the YBus matrix correspond to Bus 1, 2 and 3, respectively, then YBus of the network is        (2021)
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)(a) Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)(b) Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)(c) Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)(d) Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Ans: 
(c)
Sol: Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)
and V2 = ji1 + 2ji2 + ji3
V3 = ji1 + ji2 + 2ji3 
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)
Q4: Consider a power system consisting of N number of buses. Buses in this power system are categorized into slack bus, PV buses and PQ buses for load flow study. The number of PQ buses is NL. The balanced Newton-Raphson method is used to carry out load flow study in polar form. H, S, M, and R are sub-matrices of the Jacobian matrix J as shown below:
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)The dimension of the sub-matrix M is       (2021)
(a) NL×(N1)N× (N−1)
(b) (N1)×(N1NL)(N − 1) × (N − 1 − NL)
(c) N× (N − 1 + NL)
(d) (N1)×(N1+NL)(N − 1) × (N − 1 + NL)
Ans:
(a)
Sol: Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)For size of M
Row = No. of unknown variables of Q = NL 
Column = No. of variable which has δ = NL+(N − 1 − NL)
= N − 1
So, size of M = N× (N − 1)

Q5: Bus 1 with voltage magnitude V1 = 1.1p.u. is sending reactive power Q12 towards bus 2 with voltage magnitude V2 = 1p.u. through a lossless transmission line of reactance X. Keeping the voltage at bus 2 fixed at 1 p.u., magnitude of voltage at bus 1 is changed, so that the reactive power Q12 sent from bus 1 is increased by 20%. Real power flow through the line under both the conditions is zero. The new value of the voltage magnitude,  V1, in p.u. (rounded off to 2 decimal places) at bus 1 is _______ .      (2020)
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)(a) 0.118
(b) 1.12
(c) 1
(d) 0.82
Ans:
(b)
Sol: With real power zero, load angle δ = 0
with initial values, V1 = 1.1, V2 = 1
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)With increased value of voltage,
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Hence the practical value in per unit V1 = 1.12 p.u.  

Q6: Out of the following options, the most relevant information needed to specify the real power (P) at the PV buses in a load flow analysis is     (2020)
(a) solution of economic load dispatc
(b) rated power output of the generator
(c) rated voltage of the generator
(d) base power of the generator
Ans:
(a)
Sol: Most relevant information needed to specify P at PV buses is solution of economic load dispatch.

Q7: The Ybus matrix of a two-bus power system having two identical parallel lines connected between them in pu is given as
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)The magnitude of the series reactance of each line in pu (round off up to one decimal place) is ______         (2019)
(a) 0.5
(b) 0.1
(c) 0.3
(d) 0.2
Ans: 
(b)
Sol: Y12 = −(y12) = −j20
Series admittance of each line
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Series reaactance of each line Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)

Q8: The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, P = 1.4sinδ + 0.15sin2δ, where δ is the load angle. Newton-Raphson method is used to calculate the value of δ for P = 0.8 pu. If the initial guess is 30°, then its value (in degree) at the end of the first iteration is        (2018)
(a) 15°
(b) 28.48°
(c) 28.74°
(d) 31.20°
Ans:
(c)
Sol: Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)By using Newton Raphson method for single variable,
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)
Q9: A 1000 x 1000 bus admittance matrix for an electric power system has 8000 non-zero elements. The minimum number of branches (transmission lines and transformers) in this system are _____ (up to 2 decimal places).        (2018)
(a) 4000
(b) 6000
(c) 3500
(d) 7000
Ans:
(c)
Sol: Number of buses = 1000
No. of non-zero element = 8000
% sparsity = %x
= Number of zero element/Total number of elements
((106) - 8000)/(106) = 0.992
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)
Q10: In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 x 100. If there are 20 PV buses in addition to PQ buses and a slack bus, the total number of buses in the system is ________.        (SET-2(2017))
(a) 63
(b) 122
(c) 61
(d) 59
Ans:
(c)
Sol: Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Total number of buses = n = 61.

Q11: The figure show the per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where α is a complex number with non-zero real and imaginary parts.
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)For the given circuit, Ybus and Zbus are bus admittance matrix and bus impedance matrix, respectively, each of size 2 x 2. Which one of the following statements is true?       (SET-2(2017))
(a) Both Ybus and Zbus are symmetric
(b) Ybus is symmetric and bus Zbus is unsymmetric
(c) Ybus is unsymmetric and Zbus is symmetric
(d) Both Ybus and Zbus are unsymmetric
Ans:
(d)
Sol: Both YBUS and ZBUS are unsymmetrical with transformer.

Q12: The bus admittance matrix for a power system network is
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)There is a transmission line, connected between buses 1 and 3, which is represented by the circuit shown in figure.
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)If this transmission line is removed from service, What is the modified bus admittance matrix?      (SET-1(2017))
(a) Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)(b) Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)(c) Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)(d) Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Ans:
(c)
Sol: Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Reactance is eliminated in between Bus 1 and 3.
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)So, modified admittance matrix is,
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)
Q13: A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is _______.        (SET-1 (2017))
(a) 18
(b) 20
(c) 14
(d) 10
Ans:
(c)
Sol: Total number of buses ≡ 10
 G1 ≡ slack bus
 G2 ≡  PQ bus (reactive power limit is reached)
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Minimum number of non linear equation to be sloved = Number of unknown bus voltage variables = (2 × 10 − 4 − 2) = 14

Q14: A 3-bus power system is shown in the figure below, where the diagonal elements of Y-bus matrix are Y11 = −j12pu, Y22 = −j15pu  and  Y33 = −j7pu  
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)The per unit values of the line reactances p, q and r shown in the figure are       (SET-1(2017))
(a) p = -0.2, q = -0.1, r = -0.5
(b) p = 0.2, q = 0.1, r = 0.5
(c) p = -5, q = -10, r = -2
(d) p = 5, q = 10, r = 2
Ans: 
(b)
Sol: Given,
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)The p.u. values of line reactances p, q and r are
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)
Q15: A power system has 100 buses including 10 generator buses. For the load flow analysis using Newton-Raphson method in polar coordinates, the size of the Jacobian is       (SET-2 (2016))
(a) 189 x 189
(b) 100 x 100
(c) 90 x 90
(d) 180 x 180
Ans:
(a)
Sol: Size of the Jacobian matrix is, (2n − m − 1) × (2n − m − 1)
Given that 10 generator buses, we need to assume with in the 10 buses one bus as slack bus the,
 (2 × 100 − 10 − 1) × (2 × 100 − 10 − 1) = 189 × 189

Q16: In a 100 bus power system, there are 10 generators. In a particular iteration of Newton Raphson load flow technique (in polar coordinates), two of the PV buses are converted to PQ type. In this iteration,     (SET-1(2016))
(a) the number of unknown voltage angles increases by two and the number of unknown voltage magnitudes increases by two.
(b) the number of unknown voltage angles remains unchanged and the number of unknown voltage magnitudes increases by two
(c) the number of unknown voltage angles increases by two and the number of unknown voltage magnitudes decreases by two.
(d) the number of unknown voltage angles remains unchanged and the number of unknown voltage magnitudes decreases by two.
Ans:
(b)
Sol: The voltage angle is the commom variable for both PV and PQ buses si it remains unchanged. Where as voltage magnitude is specified in PV bus and not specified in PQ bus, so it increases by two.

Q17: A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the uncompensated system is
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)If the shunt capacitance of all transmission lines is 50% compensated, the imaginary part of the 3rd row 3rd column element (in pu) of the bus admittance matrix after compensation is       (SET-2 (2015))
(a) -j7.0
(b) -j8.5
(c) -j7.5
(d) -j9.0
Ans:
(b)
Sol: Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)By comparing for Y33 element
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)After compensating with 50% of shunt capacitance = j1 × 0.5 = j0.5
Hence, new value = −j8 − j0.5 = − j8.5  

Q18: Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].
Assertion: Fast decoupled load flow method gives approximate load flow solution because it uses several assumptions.
Reason: Accuracy depends on the power mismatch vector tolerance.     (SET-1 (2015))
(a) Both [a] and [r] are true and [r] is the correct reason for [a].
(b) Both [a] and [r] are true but [r] is not the correct reason for [a].
(c) Both [a] and [r] are false.
(d) [a] is false and [r] is true.
Ans: 
(d)
Sol: FDLF method gives approximate solution not because it uses several assumption but due to the fixed number of iterations.

Q19: A 183 bus power system has 150 PQ buses and 32 PV buses. In the general case, to obtain the load flow solution using Newton-Raphson method in polar coordinates, the minimum number of simultaneous equations to be solved is _____.       (SET-3 (2014))
(a) 150
(b) 224
(c) 332
(d) 468
Ans: 
(c)
Sol: Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)where,
n = Total number of buses
m = PV bus or reactive power support bus excluding slack bus
One bus already has taken as slack bus.

Q20: A two bus power system shown in the figure supplies load of 1.0 + j0.5 p.u.
Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)The values of Vin p.u. and δ2 respectively are      (SET-1(2014))
(a) 0.95 and 6.00°
(b) 1.05 and -5.44°
(c) 1.1 and -6.00°
(d) 1.1 and -27.12°
Ans:
(b)
Sol: Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE)

The document Previous Year Questions- Load Flow Studies - 1 | Power Systems - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Power Systems.
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FAQs on Previous Year Questions- Load Flow Studies - 1 - Power Systems - Electrical Engineering (EE)

1. What is the purpose of load flow studies in electrical engineering?
Ans.Load flow studies aim to analyze the flow of electric power in a power system. They help determine voltage levels, power flows, and losses in the network under steady-state conditions. This analysis is crucial for planning, operation, and optimization of power systems.
2. What are the common methods used for load flow analysis?
Ans.Common methods for load flow analysis include the Gauss-Seidel method, Newton-Raphson method, and the Fast Decoupled method. Each method has its advantages and is chosen based on the complexity and requirements of the system being analyzed.
3. How does the Newton-Raphson method work in load flow studies?
Ans.The Newton-Raphson method uses iterative calculations to solve nonlinear equations representing the power flow in a network. It starts with an initial guess for voltages and iteratively refines these values until the power balance is achieved within a specified tolerance.
4. What are the main parameters that need to be considered in load flow studies?
Ans.Main parameters include bus voltage levels, power generation and consumption at each bus, line impedances, and transformer ratings. These parameters help in accurately modeling the electrical network and analyzing its performance under various loading conditions.
5. Why is it important to consider reactive power in load flow studies?
Ans.Reactive power is essential for maintaining voltage levels within the power system. Load flow studies that include reactive power help ensure that the system operates efficiently and reliably, preventing voltage instability and ensuring proper operation of electrical equipment.
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