Recent activity in Power Systems

A single-phase voltage source $v_{s}=325 \sin (2 \pi 50 t) \mathrm{V}$ delivers a current, $i=12 \sin (2 \pi 50 t)+9 \sin (2 \pi 150 t)$ A to a load.The load power factor...

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 reac...

For the balanced $3$-phase transmission line shown, consider the following cases:Case-$1:$ $\left|V_{1}\right|=1.1$ p. u.,$\left|V_{2}\right|=0.9$ p. $u ., Z=0.75 \angle ...

A three-phase two-winding transformer has a voltage transformation ratio $\frac{V_{P}}{V_{S}}=0.866+j 0.5$, where $V_{P}$ is the primary side voltage in p.u., and $V_{S}$...

The operating characteristic of a reactance relay is given by $X \leq 1 \Omega$, where $X$ is the reactance calculated by the relay. Its operating characteristic in the a...

A system with two generators $\text{G1}$ and $\text{G2}$ (without generator limits) is shown.The total load on the system is $1184$ MW. The expressions for the cost of ge...

Three single-phase $11 \mathrm{kV} / 3.3 \mathrm{kV}$ transformers are connected to form a three-phase transformer bank with connections as shown.Considering $\mathbf{A B...

The figure shows the single-line diagram of a synchronous generator delivering $P =50 \mathrm{~MW}$ of power at unity power factor to an infinite bus.$I_{S}$ denotes the ...

A certain application requires power at a frequency of $16.67$ Hz, while the available grid frequency is $50$ Hz. A $3$-phase synchronous motor connected to the $50$ Hz, ...

The initial three-phase voltage phasors $\left(\bar{V}_{A}, \bar{V}_{B}\right.$, and $\left.\bar{V}_{C}\right)$ at a bus of a power network are as shown in Case-$1$. Due ...

The fuel cost functions of two power plants are Plant $P_1 : C_1=0.05Pg_1^2+APg_1+B$ Plant $P_2 : C_2=0.10Pg...

A three phase synchronous generator is to be connected to the infinite bus. The lamps are connected as shown in the figure for the synchronization. The phase sequence of ...

The figure shows a two-generator system supplying a load of $P_D = 40$ MW, connected at bus $2$. The fuel cost of generations $G_1$ and $G_2$ are:$C_1(P_{G1})=10,000$ Rs/...

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

Using shunt capacitors, the power factor of a $3$ -phase, $4 \: \mathrm{ kV}$ induction motor (drawing $390 \: \mathrm{kVA}$ at $0.77$ pf lag ) is to be corrected to $0.8...

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 cir...

The transformer connection given in the figure is part of a balanced $3$-phase circuit where the phase sequence is " $a b c$ ". The primary to secondary turns ratio is $2...

A symmetrical fault (through a fault impedance of $j 0.007 \mathrm{pu}$ ) occurs at bus $2$. Neglecting pre-fault loading conditions, the voltage at bus $1$, during the f...

Consider a distribution feeder, with $R / X$ ratio of $5$. At the receiving end, a $350 \: \mathrm{kVA}$ load is connected. The maximum voltage drop will occur from the s...

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 n...

Two generators have cost functions $F_{1}$ and $F_{2}$ . Their incremental-cost characteristics are$\dfrac{dF_{1}}{dP_{1}}=40+0.2P_{1}$$\dfrac{dF_{2}}{dP_{2}}=32+0.4P_{2}...

An alternator with internal voltage of $1\angle \delta _{1}\text{p.u}$ and synchronous reactance of $\text{0.4 p.u}$ is connected by a transmission line of reactance $\te...

A $3$-Bus network is shown. Consider generators as ideal voltage sources. If rows $1,\:2$ and $3$ of the $Y_{Bus}$ matrix correspond to Bus $1,\:2$ and $3$, respectively,...

In the figure shown, self-impedances of the two transmission lines are $1.5j\:p.u$ each, and $Z_{m}=0.5j \:p.u$ is the mutual impedance. Bus voltages shown in the figure ...

Suppose $I_{A},\:I_{B}$ and $I_{C}$ are a set of unbalanced current phasors in a three-phase system. The phase-$B$ zero-sequence current $I_{B0}=0.1\angle 0^{\circ}$ $p.u...

​​​​​The figure shows the single line diagram of a 4-bus power network. Branches $b_{1}$, $b_{2}, b_{3}$, and $b_{4}$ have impedances $4 z, z, 2 z$, and $4 z$ per-unit (p...

The incremental cost curves of two generators (Gen $\text{A}$ and Gen $\text{B}$) in a plant supplying a common load are shown in the figure. If the incremental cost of s...

​​​​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 volta...

​​​​A $3$-phase, $11 \mathrm{kV}, 10 \mathrm{MVA}$ synchronous generator is connected to an inductive load of power factor $(\sqrt{3} / 2)$ via a lossless line with a per...