The positive, negative and zero sequence impedances of a 125 MVA, three-phase, 15.5 kV, star-grounded, 50 Hz generator are j0.1 pu, j0.05 pu and j0.01 pu respectively on the machine rating base. The machine is unloaded and working at the rated terminal voltage. If the grounding impedance of the generator is j0.01 pu, then the magnitude of fault current for a b-phase to ground fault (in kA) is __________ (up to 2 decimal places).
The positive, negative, and zero sequence reactances of a wye-connected synchronous generator are 0.2 pu, 0.2 pu, and 0.1 pu, respectively. The generator is on open circuit with a terminal voltage of 1 pu. The minimum value of the inductive reactance, in pu, required to be connected between neutral and ground so that the faults current does not exceed 3.75 pu if a single line to ground fault occurs at the terminals is ___________ (assume fault impedance to be zero).(Give the answer up to one decimal place.)
A sustained three-phase fault occurs in the power system shown in the figure. The current and voltage phasors during the fault (on a common reference), after the natural transients have died down, are also shown. Where is the fault located?
Three-phase to ground fault takes place at locations F_{1} and F_{2} in the system shown in the figure
If the fault takes place at location F_{1}, then the voltage and the current at bus A are V_{F1} and I_{F1} respectively. If the fault takes place at location F_{2}, then the voltage and the current at bus A are V_{F2} and I_{F2} respectively. The correct statement about voltages and currents during faults at F_{1} and F_{2} is
A 2-bus system and corresponding zero sequence network are shown in the figure.
The transformers T_{1} and T_{2} are connected as
In an unbalanced three phase system, phase current I_{a} =1∠(-90^{o}) pu, negative sequence current I_{b2}= 4∠(150^{o}) pu, zero sequence current I_{c0 }3∠90^{o} pu. The magnitude of phase current I_{b} in pu is
A three phase, 100 MVA, 25 kV generator has solidly grounded neutral. The positive, negative, and the zero sequence reactances of the generator are 0.2 pu, 0.2 pu, and 0.05 pu, respectively, at the machine base quantities. If a bolted single phase to ground fault occurs at the terminal of the unloaded generator, the fault current in amperes immediately after the fault is _______
The figure shows the single line diagram of a single machine infinite bus system.
The inertia constant of the synchronous generator H=5 MW-s/MVA. Frequency is 50 Hz. Mechanical power is 1 pu. The system is operating at the stable equilibrium point with rotor angle δ equal to 30^{o}. A three phase short circuit fault occurs at a certain location on one of the circuits of the double circuit transmission line. During fault, electrical power in pu is P_{max} sinδ. If the values of δ and $\raisebox{1ex}{$d\delta $}\!\left/ \!\raisebox{-1ex}{$dt$}\right.$ at the instant of fault clearing are 45^{o} and 3.762 radian/s respectively, then P_{max} (in pu) is _______.
The sequence components of the fault current are as follows: I_{positive} = j1.5 pu, I_{negative} = –j0.5 pu, I_{zero} = –j1 pu. The type of fault in the system is
Two generator units G1 and G2 are connected by 15 kV line with a bus at the midpoint as shown below
G1 = 250MVA, 15 kV, positive sequence reactance X=25% on its own base
G_{2} = 100MVA, 15 kV, positive sequence reactance X=10% on its own base L_{1} and L_{2} = 10 km, positive sequence reactance X = 0.225 Ω/km
For the above system,positive sequence diagram with p.u values on the 100 MVA common base is
In the above system, the three-phase fault MVA at the bus 3 is
The zero-sequence circuit of the three phase transformer shown in the figure is
A 3-phase transmission line is shown in figure :
Voltage drop across the transmission line is given by the following equation :
$\left[\begin{array}{c}\Delta {V}_{a}\\ \Delta {V}_{b}\\ \Delta {V}_{c}\end{array}\right]=\left[\begin{array}{ccc}{Z}_{s}& {Z}_{m}& {Z}_{m}\\ {Z}_{m}& {Z}_{s}& {Z}_{m}\\ {Z}_{m}& {Z}_{m}& {Z}_{s}\end{array}\right]\left[\begin{array}{c}{I}_{a}\\ {I}_{b}\\ {I}_{c}\end{array}\right]$ Shunt capacitance of the line can be neglected. If the has positive sequence impedance of 15 Ω and zero sequence impedance of 48 Ω, then the values of Z_{s} and Z_{m} will be
Consider a power system shown below:
Given that:
${V}_{s1}={V}_{s2}=1.0+j0.0\mathrm{pu}$;
The positive sequence impedences are ${Z}_{s1}={Z}_{s2}=0.001+j0.01\mathrm{pu}$ and ${Z}_{L}=0.006+j0.06\mathrm{pu}$.
3-phase Base MVA=100
Voltage base=400kV (Line to Line)
Nominal system frequency = 50Hz
The reference coltage for phase 'a' is defined as $v\left(\mathrm{t}\right)\mathit{=}{V}_{\mathit{m}}\mathrm{cos}\left(\mathit{\omega}\mathit{t}\right)$.
A symmetrical three phase fault occurs at centre of the line., i.e. point 'F' at time t_{0}. The positive sequence impedance from source S_{1} to point 'F' equals $\mathit{0}\mathit{.}\mathit{004}\mathit{+}j\mathit{0}\mathit{.}\mathit{04}\mathit{}\mathrm{pu}$. The waveform corresponding to phase 'a' fault current from bus X reveals that decayinf dc offset current is negative and in magnitude at its maximum initial value. Assume that the negative sequence impedances are equal to positive sequence impedances, and the zero sequence impedances are three times positive sequence impedances.
The instant (t_{0}) of the fault will be
The rms value of the component of fault current (I_{f} ) will be
Instead of the three phase fault, if a single line to ground fault occurs on phase ‘a’ at point ‘F’ with zero fault impedance, then the rms of the ac component of fault current (Ix) for phase ‘a’ will be
A three phase balanced star connected voltage source with frequency $\omega $ rad/s is connected to a star connected balanced load which is purely inductive. The instantaneous line currents and phase to neutral voltages are denoted by (i_{a}, i_{b}, i_{c}) and (v_{an}, v_{bn}, v_{cn}) respectively, and their rms values are denoted by V and I.
If $\mathrm{R}=\left[\begin{array}{ccc}{v}_{an}& {v}_{bn}& {v}_{cn}\end{array}\right]\left[\begin{array}{ccc}0& \frac{1}{\sqrt{3}}& -\frac{1}{\sqrt{3}}\\ -\frac{1}{\sqrt{3}}& 0& \frac{1}{\sqrt{3}}\\ \frac{1}{\sqrt{3}}& -\frac{1}{\sqrt{3}}& 0\end{array}\right]\left[\begin{array}{c}{i}_{a}\\ {i}_{b}\\ {i}_{c}\end{array}\right]$, then the magnitude of R is
Suppose we define a sequence transformation between ‘‘a-b-c’’ and ‘‘p-n-o’’ variables as follows:
$\left[\begin{array}{c}{f}_{a}\\ {f}_{b}\\ {f}_{c}\end{array}\right]=k\left[\begin{array}{ccc}1& 1& 1\\ {\alpha}^{2}& \alpha & 1\\ \alpha & {\alpha}^{2}& 1\end{array}\right]\left[\begin{array}{c}{f}_{p}\\ {f}_{n}\\ {f}_{o}\end{array}\right]$ where $\alpha ={e}^{j\frac{2\pi}{3}}$ and k is constant.
Now, if it is given that: $\left[\begin{array}{c}{V}_{p}\\ {V}_{n}\\ {V}_{o}\end{array}\right]=\left[\begin{array}{ccc}0.5& 0& 0\\ 0& 0.5& 0\\ 0& 0& 2.0\end{array}\right]\left[\begin{array}{c}{i}_{p}\\ {i}_{n}\\ {i}_{o}\end{array}\right]$ and $\left[\begin{array}{c}{V}_{a}\\ {V}_{b}\\ {V}_{c}\end{array}\right]=Z\left[\begin{array}{c}{i}_{a}\\ {i}_{b}\\ {i}_{c}\end{array}\right]$ then,