Power System Analysis and Load Flow MCQs 2026

Removing a line from service updates Y-bus by

1. A inverting Z-bus only without change ✓
2. B multiplying all elements by zero ✓
3. C subtracting that branch stamp from the matrix ✓
4. D adding random entries ✓

Admittance matrix Y-bus of a power network relates

1. A only real power to angle only without voltage ✓
2. B nodal current injections to nodal voltages via I = YV ✓
3. C only transformer losses to frequency ✓
4. D only cable tan delta to humidity ✓

Diagonal element Yii of Y-bus equals

1. A sum of all admittances connected to node i including shunt terms ✓
2. B only off-diagonal mutual terms ✓
3. C zero always ✓
4. D reciprocal of line length only ✓

Off-diagonal element Yij of Y-bus for i ≠ j with direct branch between nodes is

1. A positive sum of all system admittances ✓
2. B always zero in any network ✓
3. C equal to transformer MVA only ✓
4. D negative of branch admittance between i and j ✓

Y-bus of a large transmission network is typically

1. A fully dense with all entries nonzero ✓
2. B diagonal only always ✓
3. C sparse because each node connects to few neighbours ✓
4. D identity matrix ✓

Including transformer off-nominal tap in Y-bus requires

1. A ignoring tap completely always ✓
2. B modifying effective admittance and sometimes phase shift ✓
3. C using only resistance of conductor ✓
4. D replacing Y with Z always ✓

Line charging susceptance in π-model contributes to Y-bus as

1. A shunt admittance terms at line terminals ✓
2. B only series impedance without shunt ✓
3. C only DC resistance ✓
4. D only motor slip ✓

Grounded shunt capacitor bank at a bus adds to Y-bus

1. A positive susceptance on the diagonal of that bus ✓
2. B only off-diagonal mutual terms ✓
3. C negative resistance on all buses ✓
4. D zero change ✓

Mutual coupling between transmission lines on same tower appears in Y-bus as

1. A only diagonal elements ✓
2. B no effect in any case ✓
3. C off-diagonal terms between corresponding nodes ✓
4. D only in DC analysis ✓

Assembly of Y-bus from branch data is called

1. A only Gauss-Seidel iteration ✓
2. B only per unit conversion of load only ✓
3. C only symmetrical component reduction ✓
4. D building by successive addition of branch stamp contributions ✓

Per unit system simplifies Y-bus construction because

1. A all impedances become zero ✓
2. B branches on common bases add directly ✓
3. C voltage angles are eliminated ✓
4. D loads disappear ✓

Singular Y-bus (no reference) occurs if

1. A all lines are lossless ✓
2. B all loads are unity PF ✓
3. C frequency is exactly 50 Hz ✓
4. D no ground/reference node is specified ✓

Z-bus is related to Y-bus by

1. A simple transposition only ✓
2. B matrix inversion Z = Y⁻¹ for nonsingular Y ✓
3. C adding identity only ✓
4. D squaring each element ✓

Modified Y-bus for fault studies may insert

1. A fault admittance at faulted node ✓
2. B only transformer magnetizing branch removal ✓
3. C only solar irradiance data ✓
4. D only train mass ✓

Three-phase Y-bus can be built from

1. A only single-phase without coupling ever ✓
2. B only DC battery model ✓
3. C phase network or from sequence networks with coupling ✓
4. D only corona loss formula ✓

Equivalent π parameters of a line branch for Y-bus come from

1. A series impedance and total shunt admittance of line model ✓
2. B only tower height ✓
3. C only insulator creepage ✓
4. D only VFD carrier frequency ✓

PV bus treatment in NR includes

1. A equations for P and V with Q within limits ✓
2. B only Q and θ specified ✓
3. C no reactive power variable ✓
4. D fixed Q always ✓

Ill-conditioned cases for NR include

1. A unloaded open circuit only ✓
2. B heavy loading near voltage collapse and low impedance ties ✓
3. C single slack only ✓
4. D lossless lines only ✓

Rectangular coordinates (e,f) alternative in NR uses

1. A only magnitude without angle ever ✓
2. B only frequency deviation ✓
3. C real and imaginary parts of voltage instead of polar V,θ ✓
4. D only per unit resistance alone ✓

Optimal multiplier in NR can

1. A increase mismatch intentionally ✓
2. B remove Jacobian ✓
3. C fix all angles at zero ✓
4. D damp step size to improve global convergence ✓

After NR solution, LMP or marginal loss calculations may use

1. A solved voltages and sensitivity factors ✓
2. B only guesswork ✓
3. C only motor nameplate ✓
4. D only wind cut-out ✓

Continued power flow uses NR with parameterization to trace

1. A only transformer OC test ✓
2. B only cable tan delta ✓
3. C only VFD ramp ✓
4. D P-V nose curve toward voltage collapse point ✓

NR is preferred in commercial EMS for

1. A smallest possible 2-bus homework only always ✓
2. B reliable fast convergence on large transmission networks ✓
3. C systems without any nonlinearities ✓
4. D DC circuits only ✓

Symmetric Jacobian structure is not generally symmetric because

1. A Y-bus is complex ✓
2. B all loads are zero ✓
3. C mixing of P and Q equations with θ and V variables breaks symmetry ✓
4. D frequency is variable ✓

Updating voltage in polar NR computes

1. A corrections Δθ and ΔV/ V from solved linear system ✓
2. B only Δf frequency ✓
3. C only transformer tap without voltage ✓
4. D only DC link current ✓

Flat start for NR on stiff EHV system may require

1. A no iteration at all ✓
2. B better initial voltages or damping to avoid early divergence ✓
3. C removing all loads ✓
4. D setting all P to zero ✓

Transformer regulating tap change during NR may use

1. A continuous tap without limits always ✓
2. B no tap model ✓
3. C discrete tap steps outer loop around continuous NR ✓
4. D only mechanical brake model ✓

Loss allocation after NR can use

1. A only guess without voltages ✓
2. B only solar azimuth angle ✓
3. C only corona RI ✓
4. D incremental loss factors or proportional sharing methods ✓

Symmetrical three-phase fault has

1. A equal fault currents in all phases with zero sequence unaffected if ungrounded ✓
2. B only single line open ✓
3. C only DC offset in one phase without AC ✓
4. D only negative sequence only ✓

Line-to-line fault (LL) contains

1. A all three sequences always including zero ✓
2. B only zero sequence ✓
3. C positive and negative sequence components without zero sequence if ungrounded ✓
4. D only DC component ✓

Sequence impedances Z1, Z2, Z0 are used to

1. A analyze unbalanced faults via symmetrical components ✓
2. B only calculate solar fill factor ✓
3. C only VFD carrier ✓
4. D only train adhesion ✓

Fault MVA at a bus equals

1. A only real load MW ✓
2. B √3 × kV_line × kA_fault (three-phase basis) or V²/|Zf| in consistent units ✓
3. C only transformer iron loss ✓
4. D only cable length ✓

Subtransient reactance Xd″ of synchronous machine governs

1. A only steady-state thermal limit ✓
2. B only governor droop only ✓
3. C only excitation ceiling at steady state ✓
4. D initial symmetrical short-circuit current contribution ✓

Transient reactance Xd′ is relevant for

1. A only DC time constant of armature ✓
2. B only long-term steady state only ✓
3. C fault current decay in first few cycles ✓
4. D only solar Voc ✓

DC offset component in fault current arises from

1. A inductance opposing sudden current change making current asymmetric ✓
2. B only solar irradiance change ✓
3. C only biomass moisture ✓
4. D only PWM switching ✓

Breaker making capacity must withstand

1. A only RMS symmetrical value always ✓
2. B peak asymmetrical fault current including DC offset ✓
3. C only load current ✓
4. D only charging current ✓

Percentage DC component for breaker rating considers

1. A X/R ratio at fault point affecting asymmetry ✓
2. B only cable colour ✓
3. C only tower paint ✓
4. D only motor poles only ✓

Thevenin equivalent at fault bus for fault calculation uses

1. A only load power factor ✓
2. B only solar MPP ✓
3. C prefault voltage and equivalent impedance looking into network ✓
4. D only train schedule ✓

Solid fault means fault impedance is

1. A infinite ✓
2. B equal to surge impedance only ✓
3. C equal to load resistance ✓
4. D zero ✓

Post-fault voltage sag severity depends on

1. A fault level, impedance to fault and prefault voltage ✓
2. B only solar panel tilt ✓
3. C only VFD ramp time only ✓
4. D only train pantograph material only ✓

Bus impedance matrix (Z-bus) diagonal element Zii gives

1. A only off-diagonal mutual terms ✓
2. B driving-point impedance at bus i for fault calculations ✓
3. C only shunt capacitance ✓
4. D only motor slip ✓

Distance relay measures

1. A only transformer temperature ✓
2. B only solar azimuth ✓
3. C impedance to fault to trip appropriate line section ✓
4. D only biogas pressure ✓

Open conductor fault can cause

1. A perfect balance always ✓
2. B only symmetrical fault ✓
3. C no effect on loads ✓
4. D unbalance and abnormal voltages on unaffected phases ✓

Fault through impedance (e.g., arc) reduces

1. A voltage at remote buses to zero always ✓
2. B fault current magnitude compared with solid fault ✓
3. C need for any protection ✓
4. D sequence impedance to zero ✓

Fast decoupled load flow approximates Jacobian by

1. A ignoring all reactive power ✓
2. B using only DC analysis forever ✓
3. C decoupling P-θ and Q-V assuming high X/R lines ✓
4. D eliminating slack bus ✓

Quadratic convergence of Newton-Raphson near solution means

1. A error is constant each step ✓
2. B error squares each iteration when close to root ✓
3. C divergence always ✓
4. D linear halving only ✓

Jacobian matrix in NR contains partial derivatives of

1. A power mismatches with respect to voltage angles and magnitudes ✓
2. B only line resistance ✓
3. C only train mass ✓
4. D only biomass moisture ✓

Newton-Raphson load flow linearizes

1. A only DC resistance network without angles ✓
2. B only single-phase DC battery ✓
3. C power mismatch equations using Taylor expansion and Jacobian ✓
4. D only corona power loss ✓

Distributed slack shares

1. A all loss to one bus only always ✓
2. B slack bus responsibility among multiple generators by participation factors ✓
3. C no slack needed ever ✓
4. D only reactive load at slack ✓

Stopping criterion for GS typically checks

1. A only one bus voltage exactly ✓
2. B only number of lines ✓
3. C only solar fill factor ✓
4. D maximum power mismatch below tolerance ✓

Mismatch at a bus in load flow is

1. A only voltage magnitude without angle ✓
2. B difference between specified and calculated power injection ✓
3. C only frequency error ✓
4. D only transformer iron loss ✓

Gauss-Seidel is attractive for teaching because

1. A it never requires iteration ✓
2. B it solves nonlinear equations in closed form ✓
3. C algorithm is simple and needs little memory ✓
4. D it eliminates Y-bus ✓

After GS converges, line flows are computed from

1. A bus voltages and branch admittances ✓
2. B only nameplate MVA ✓
3. C only rotor resistance ✓
4. D only braking resistor size ✓

Number of iterations in GS depends on

1. A only utility tariff ✓
2. B only motor poles ✓
3. C only solar STC ✓
4. D tolerance, acceleration and network parameters ✓

Line charging and high R/X ratio can affect GS convergence by

1. A improving conditioning always ✓
2. B making equations more ill-conditioned ✓
3. C eliminating reactive power ✓
4. D fixing all angles to zero ✓

Weakly meshed distribution feeders may converge with GS when

1. A never under any condition ✓
2. B only with no loads ✓
3. C only without slack ✓
4. D system is not too stiff and initial guess is reasonable ✓

Gauss-Seidel update for PQ bus uses

1. A power injection equations solved for new voltage estimate ✓
2. B only real power ignoring reactive ✓
3. C only transformer tap without power ✓
4. D only fault current ✓

Reactive power limit violation at PV bus during GS iteration requires

1. A ignoring limits always ✓
2. B removing slack bus ✓
3. C switching bus type from PV to PQ temporarily ✓
4. D setting frequency to zero ✓

Initial voltage guess for GS load flow often sets

1. A all voltages zero ✓
2. B random negative magnitudes ✓
3. C only DC values ✓
4. D flat start: 1.0 pu angle 0° except slack ✓

Convergence of Gauss-Seidel is generally

1. A slower than Newton-Raphson for large systems ✓
2. B always faster than NR always ✓
3. C independent of R/X ratio ✓
4. D guaranteed in one iteration ✓

Acceleration factor in Gauss-Seidel can

1. A guarantee divergence always ✓
2. B eliminate need for slack bus ✓
3. C speed convergence of voltage iterations ✓
4. D convert AC to DC ✓

Gauss-Seidel method solves load flow by

1. A only Newton Jacobian inversion each step without iteration structure ✓
2. B successive substitution using updated values immediately ✓
3. C only DC mesh analysis ✓
4. D only symmetrical components only without voltages ✓

PQ bus in load flow specifies

1. A voltage magnitude and angle ✓
2. B active and reactive power demand P and Q ✓
3. C only current magnitude ✓
4. D only frequency deviation ✓

Slack (swing) bus in load flow specifies

1. A both P and Q fixed always ✓
2. B only reactive load ✓
3. C zero voltage reference ✓
4. D voltage magnitude and angle to balance system power ✓

PV bus in load flow specifies

1. A active power P and voltage magnitude V ✓
2. B P and Q both fixed ✓
3. C V and angle both fixed ✓
4. D Q and angle only ✓

Load-flow study computes

1. A only transformer no-load loss ✓
2. B only motor starting current peak ✓
3. C voltage magnitudes and angles at buses for given generation and load ✓
4. D only solar MPP only ✓

Phase-shifting transformer introduces in Y-bus

1. A only real diagonal terms ✓
2. B complex mutual admittances with angle shift between buses ✓
3. C no connection between buses ✓
4. D only DC link ✓

Y-bus symmetry for passive network without phase shifters means

1. A Y is always diagonal ✓
2. B Y is always real ✓
3. C Y has no diagonal terms ✓
4. D Yij = Yji for corresponding mutual entries ✓

Sparsity techniques in NR exploit

1. A dense matrix inversion always ✓
2. B no branch data ✓
3. C only 2-bus systems ✓
4. D few nonzero Jacobian entries in large networks ✓