Power Systems

Consider a power system with N buses, of which P are generator buses and the remaining Q are load buses (where there is no generation). Assume that there are no reactive power-limi...

The initial three-phase voltage phasors ($\bar{V}_A$, $\bar{V}_B$, and $\bar{V}_C$) at a bus of a power network are as shown in Case-1. Due to a disturbance, the bus voltage phasor...

In the circuit shown, the phase currents are $I_A = 572.812+ j50.115 A$ $I_B = -254.525- j459.175 A$ $I_C = -207.083+ j444.091 A$ Given that the CTs are ideal with no saturation, a...

For the balanced 3-phase transmission line shown, consider the following cases: Case-1: |V1| = 1.1 p. u., |V2| = 0.9 p. u., Z = 0.75∠0° p. u. and θ12 = θ1 - θ2 = 0° Case-2: |V1| =...

In a power system, following a sudden increase in load, the frequency will settle at a lower steady-state value if

In the system shown below, the generator was initially supplying power to the grid. A temporary LLLG bolted fault occurs at F very close to circuit breaker 1. The circuit breakers...

Two units, rated at 100 MW and 150 MW , are enabled for economic load dispatch. When the overall incremental cost is $10,000 \mathrm{Rs}$./MWh, the units are dispatched to 50 MW an...

The incremental cost curves of two generators (Gen A and Gen B) in a plant supplying a common load are shown in the figure. If the incremental cost of supplying the common load is...

A 3-phase, 11 kV, 10 MVA synchronous generator is connected to an inductive load of power factor (√3/2) via a lossless line with a per-phase inductive reactance of 5 Ω. The per-pha...

For the three-bus lossless power network shown in the figure, the voltage magnitudes at all the buses are equal to 1 per unit (pu), and the differences of the voltage phase angles...

Which of the following options is/are correct for the Automatic Generation Control (AGC) and Automatic Voltage Regulator (AVR) installed with synchronous generators?

For the three-bus power system shown in the figure, the trip signals to the circuit breakers B1 to B9 are provided by overcurrent relays R1 to R9, respectively, some of which have...

The expressions of fuel cost of two thermal generating units as a function of the respective power generation PG1 and PG2 are given as F1(PG1) = 0.1aP^2_G1 + 40 PG1 + 120 Rs/hour 0...

A 50 Hz, 275 kV line of length 400 km has the following parameters: Resistance, R = 0.035 Ω/km; Inductance, L = 1 mH/km; Capacitance, C = 0.01 µF/km; The line is represented by the...

The three-bus power system shown in the figure has one alternator connected to bus 2 which supplies 200 MW and 40 MVAr power. Bus 3 is infinite bus having a voltage of magnitude |V...

The two-bus power system shown in figure (i) has one alternator supplying a synchronous motor load through a Y-Δ transformer. The positive, negative and zero-sequence diagrams of t...

The expressions of fuel cost of two thermal generating units as a function of the respective power generation $${P_{G1}}$$ and $${P_{G2}}$$ are given as $$\matrix{ {{F_1}({P_{G1}})...

Two generating units rated for 250 MW and 400 MW have governor speed regulations of 6% and 6.4%, respectively, from no load to full load. Both the generating units are operating in...

Two generators have cost functions $F_1$ and $F_2$. Their incremental-cost characteristics are $$ \frac{d F_1}{d P_1}=40+0.2 P_1 \text { and } \frac{d F_2}{d P_2}=32+0.4 P_2 $$ The...

Consider a power system consisting of $N$ number of buses. Buses in this power system are categorized into slack bus. $P V$ buses and $P Q$ buses for load flow study. The number of...

The Ybus matrix of a two-bus power system having two identical parallel lines connected between them in pu is given as Ybus = [-j8 j20] [j20 -j8] The magnitude of the series reacta...

A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are $v_{an} = 220 \sin (100\pi...

A 3-bus power system is shown in the figure below, where the diagonal elements of Y-bus matrix are: $Y_{11} = -j12$ pu, $Y_{22} = -j15$ pu and $Y_{33} = -j7$ pu. The per unit value...

The figure shows 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. F...

Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator G1 a...

The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, P = 1.4 sin δ + 0.15 sin 2δ, where δ is the load angle. New...

The bus admittance matrix for a power system network is $[-j39.9 \quad j20 \quad j20 \\ j20 \quad -j39.9 \quad j20 \text{ pu.} \\ j20 \quad j20 \quad -j39.9]$ There is a transmissi...

Consider an overhead transmission line with 3-phase, 50 Hz balanced system with conductors located at the vertices of an equilateral triangle of length Dab = Dbc = Dca = 1m as show...

A 3-phase, 50 Hz generator supplies power of 3MW at 17.32 kV to a balanced 3-phase inductive load through an overhead line. The per phase line resistance and reactance are 0.25$\Om...

Two generating units rated 300 MW and 400 MW have governor speed regulation of 6% and 4% respectively from no load to full load. Both the generating units are operating in parallel...

The positive, negative and zero sequence impedances of a three phase generator are Z 1 , Z 2 and Z 0 respectively. For a line-to-line fault with fault impedance Z f , the fault cur...

In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is $$\,100\,\, \times \,\,100.$$ If there are $$20$$ PV buses in addition to...

A $$3$$-bus power system network consists of $$3$$ transmission lines. The bus admittance matrix of the uncompensated system is $$\left[ {\matrix{ { - j6} & {j3} & {j4} \cr {j3} &...

The incremental costs (in rupees/$$MWh$$) of operating two generating units are functions of their respective powers $${P_1}$$ and $${P_2}$$ in $$MW,$$ and are given by $$${{d{C_1}...

The fuel cost functions of two power plants are Plant $${P_1}:\,{C_1} = 0.05\,Pg_1^2 + AP{g_1} + B$$ Plant $${P_2}:\,{C_2} = 0.10\,Pg_2^2 + 3AP{g_2} + 2B$$ Where, $$P{g_1}$$ and $$...

The horizontally placed conductors of a single phase line operating at $$50$$ $$Hz$$ are having outside diameter of $$1.6$$ cm, and the spacing between centers of the conductors is...

The sequence components of the fault current are as follows: $${{\rm I}_{positive}} = j1.5\,pu,\,\,{{\rm I}_{negative}} = - j0.5\,\,pu,$$ $${{\rm I}_{zero}} = - j1\,\,pu.$$ The typ...

A cylindrical rotor generator delivers $$0.5$$ pu power in the steady-state to an infinite bus through a transmission line of reactance $$0.5$$ pu. The generator no-load voltage is...

For the $${Y_{bus}}$$ matrix of a $$4$$-bus system given in per unit, the buses having shunt elements are $$${Y_{BUS}} = j\left[ {\matrix{ { - 5} & 2 & {2.5} & 0 \cr 2 & { - 10} &...

A lossless power system has to serve a load of $$250$$ $$MW.$$ There are two generators ($$G1$$ and $$G2$$) in the system with cost curves $${C_1}$$ and $${C_2}$$ respectively defi...

Given that: $$\,{V_{s1}} = {V_{s2}} = 1 + j0\,\,p.u,\,\, + ve\,\,$$ sequence impedance are $$\,{Z_{s1}} = {Z_{s2}} = 0.001 + j0.01\,\,p.u\,\,$$ and $${Z_L} = 0.006 + j\,0.06\,\,p.u...

Suppose we define a sequence transformation between ''a-b-c'' and ''p-n-0''' variables as follows: $$\left[ {\matrix{ {{f_a}} \cr {{f_b}} \cr {{f_c}} \cr } } \right] = k\left[ {\ma...

A $$110$$ $$kV,$$ single core coaxial, XLPE insulated power cable delivering power at $$50$$ $$Hz,$$ has a capacitance of $$125$$ $$nF/km.$$ If the dielectric loss tangent of XLPE...

A list of relays and the power system components protected by the relays are given in List-$${\rm I}$$ and List-$${\rm II}$$ respectively. Choose the correct match from the four ch...

A surge of 20 kV magnitude travels along a lossless cable towards its junction with two identical lossless overhead transmission lines. The inductance and the capacitance of the ca...

A power system has two generators with the following cost curves Generator $$1:$$ $${C_1}\left( {{P_{G1}}} \right) = 0.006\,P_{G1}^2 + 8{P_{G1}} + 350$$ (Thousand Rupees/Hour) Gene...

For the $$Y$$-$$bus$$ matrix given in per unit values, where the first, second, third and fourth row refers to bus $$1, 2, 3$$ and $$4$$ respectively, draw the reactance diagram. $...

The conductors of a $$10$$ km long, single phase, two wire line are separated by a distance of $$1.5$$ m. The diameter of each conductor is $$1$$ cm. If the conductors are of coppe...

The incremental cost characteristic of two generators delivering $$200$$ $$MW$$ are as follows $$\,\,\,{{d{F_1}} \over {d{P_1}}} = 20 + 0.1{P_1},\,\,{{d{F_2}} \over {d{P_2}}} = 16...

An industrial consumer has a daily load pattern of $$2000$$ $$kW$$, $$0.8$$ lag for $$12$$ Hrs. and $$1000$$ $$kW$$ $$UPF$$ for $$12$$ Hrs. The load factor is

An overhead line having a surge impedance of $$400$$$$\Omega $$ is connected in series with an underground cable having a surge impedance of $$100$$$$\Omega $$. If a surge of $$50$...

Each conductor of a $$33$$ $$kV,$$ $$3$$ phase system is suspended by a string of three similar insulators. The ratio of shunt capacitance to mutual capacitance is $$0.1.$$ Calcula...

For an unbalanced fault, with paths for zero sequence currents, at the point of fault

The insulation resistance of a cable of length $$10$$ km is $$1$$ $$M\Omega $$. For a length of $$100$$ km of the same cable, the insulation resistance will be

The positive sequence component of the voltage at the point of fault in a power system is zero for a _________fault.

In load flow analysis, the load connected at a bus is represented as