Power System Analysis and Load Flow MCQs 2026

Gauss-Seidel update for PQ bus uses

1. Apower injection equations solved for new voltage estimate✓
2. Bonly real power ignoring reactive✓
3. Conly transformer tap without power✓
4. Donly fault current✓

Admittance matrix Y-bus of a power network relates

1. Aonly real power to angle only without voltage✓
2. Bnodal current injections to nodal voltages via I = YV✓
3. Conly transformer losses to frequency✓
4. Donly cable tan delta to humidity✓

Diagonal element Yii of Y-bus equals

1. Asum of all admittances connected to node i including shunt terms✓
2. Bonly off-diagonal mutual terms✓
3. Czero always✓
4. Dreciprocal of line length only✓

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

1. Apositive sum of all system admittances✓
2. Balways zero in any network✓
3. Cequal to transformer MVA only✓
4. Dnegative of branch admittance between i and j✓

Y-bus of a large transmission network is typically

1. Afully dense with all entries nonzero✓
2. Bdiagonal only always✓
3. Csparse because each node connects to few neighbours✓
4. Didentity matrix✓

Including transformer off-nominal tap in Y-bus requires

1. Aignoring tap completely always✓
2. Bmodifying effective admittance and sometimes phase shift✓
3. Cusing only resistance of conductor✓
4. Dreplacing Y with Z always✓

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

1. Ashunt admittance terms at line terminals✓
2. Bonly series impedance without shunt✓
3. Conly DC resistance✓
4. Donly motor slip✓

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

1. Apositive susceptance on the diagonal of that bus✓
2. Bonly off-diagonal mutual terms✓
3. Cnegative resistance on all buses✓
4. Dzero change✓

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

1. Aonly diagonal elements✓
2. Bno effect in any case✓
3. Coff-diagonal terms between corresponding nodes✓
4. Donly in DC analysis✓

Assembly of Y-bus from branch data is called

1. Aonly Gauss-Seidel iteration✓
2. Bonly per unit conversion of load only✓
3. Conly symmetrical component reduction✓
4. Dbuilding by successive addition of branch stamp contributions✓

Per unit system simplifies Y-bus construction because

1. Aall impedances become zero✓
2. Bbranches on common bases add directly✓
3. Cvoltage angles are eliminated✓
4. Dloads disappear✓

Singular Y-bus (no reference) occurs if

1. Aall lines are lossless✓
2. Ball loads are unity PF✓
3. Cfrequency is exactly 50 Hz✓
4. Dno ground/reference node is specified✓

Z-bus is related to Y-bus by

1. Asimple transposition only✓
2. Bmatrix inversion Z = Y⁻¹ for nonsingular Y✓
3. Cadding identity only✓
4. Dsquaring each element✓

Modified Y-bus for fault studies may insert

1. Afault admittance at faulted node✓
2. Bonly transformer magnetizing branch removal✓
3. Conly solar irradiance data✓
4. Donly train mass✓

Three-phase Y-bus can be built from

1. Aonly single-phase without coupling ever✓
2. Bonly DC battery model✓
3. Cphase network or from sequence networks with coupling✓
4. Donly corona loss formula✓

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

1. Aseries impedance and total shunt admittance of line model✓
2. Bonly tower height✓
3. Conly insulator creepage✓
4. Donly VFD carrier frequency✓

Y-bus symmetry for passive network without phase shifters means

1. AY is always diagonal✓
2. BY is always real✓
3. CY has no diagonal terms✓
4. DYij = Yji for corresponding mutual entries✓

Phase-shifting transformer introduces in Y-bus

1. Aonly real diagonal terms✓
2. Bcomplex mutual admittances with angle shift between buses✓
3. Cno connection between buses✓
4. Donly DC link✓

Load-flow study computes

1. Aonly transformer no-load loss✓
2. Bonly motor starting current peak✓
3. Cvoltage magnitudes and angles at buses for given generation and load✓
4. Donly solar MPP only✓

Weakly meshed distribution feeders may converge with GS when

1. Anever under any condition✓
2. Bonly with no loads✓
3. Conly without slack✓
4. Dsystem is not too stiff and initial guess is reasonable✓

PV bus in load flow specifies

1. Aactive power P and voltage magnitude V✓
2. BP and Q both fixed✓
3. CV and angle both fixed✓
4. DQ and angle only✓

Slack (swing) bus in load flow specifies

1. Aboth P and Q fixed always✓
2. Bonly reactive load✓
3. Czero voltage reference✓
4. Dvoltage magnitude and angle to balance system power✓

PQ bus in load flow specifies

1. Avoltage magnitude and angle✓
2. Bactive and reactive power demand P and Q✓
3. Conly current magnitude✓
4. Donly frequency deviation✓

Gauss-Seidel method solves load flow by

1. Aonly Newton Jacobian inversion each step without iteration structure✓
2. Bsuccessive substitution using updated values immediately✓
3. Conly DC mesh analysis✓
4. Donly symmetrical components only without voltages✓

Acceleration factor in Gauss-Seidel can

1. Aguarantee divergence always✓
2. Beliminate need for slack bus✓
3. Cspeed convergence of voltage iterations✓
4. Dconvert AC to DC✓

Convergence of Gauss-Seidel is generally

1. Aslower than Newton-Raphson for large systems✓
2. Balways faster than NR always✓
3. Cindependent of R/X ratio✓
4. Dguaranteed in one iteration✓

Initial voltage guess for GS load flow often sets

1. Aall voltages zero✓
2. Brandom negative magnitudes✓
3. Conly DC values✓
4. Dflat start: 1.0 pu angle 0° except slack✓

Reactive power limit violation at PV bus during GS iteration requires

1. Aignoring limits always✓
2. Bremoving slack bus✓
3. Cswitching bus type from PV to PQ temporarily✓
4. Dsetting frequency to zero✓

Number of iterations in GS depends on

1. Aonly utility tariff✓
2. Bonly motor poles✓
3. Conly solar STC✓
4. Dtolerance, acceleration and network parameters✓

After GS converges, line flows are computed from

1. Abus voltages and branch admittances✓
2. Bonly nameplate MVA✓
3. Conly rotor resistance✓
4. Donly braking resistor size✓

Gauss-Seidel is attractive for teaching because

1. Ait never requires iteration✓
2. Bit solves nonlinear equations in closed form✓
3. Calgorithm is simple and needs little memory✓
4. Dit eliminates Y-bus✓

Mismatch at a bus in load flow is

1. Aonly voltage magnitude without angle✓
2. Bdifference between specified and calculated power injection✓
3. Conly frequency error✓
4. Donly transformer iron loss✓

Stopping criterion for GS typically checks

1. Aonly one bus voltage exactly✓
2. Bonly number of lines✓
3. Conly solar fill factor✓
4. Dmaximum power mismatch below tolerance✓

Distributed slack shares

1. Aall loss to one bus only always✓
2. Bslack bus responsibility among multiple generators by participation factors✓
3. Cno slack needed ever✓
4. Donly reactive load at slack✓

Newton-Raphson load flow linearizes

1. Aonly DC resistance network without angles✓
2. Bonly single-phase DC battery✓
3. Cpower mismatch equations using Taylor expansion and Jacobian✓
4. Donly corona power loss✓

Jacobian matrix in NR contains partial derivatives of

1. Apower mismatches with respect to voltage angles and magnitudes✓
2. Bonly line resistance✓
3. Conly train mass✓
4. Donly biomass moisture✓

Quadratic convergence of Newton-Raphson near solution means

1. Aerror is constant each step✓
2. Berror squares each iteration when close to root✓
3. Cdivergence always✓
4. Dlinear halving only✓

Fast decoupled load flow approximates Jacobian by

1. Aignoring all reactive power✓
2. Busing only DC analysis forever✓
3. Cdecoupling P-θ and Q-V assuming high X/R lines✓
4. Deliminating slack bus✓

PV bus treatment in NR includes

1. Aequations for P and V with Q within limits✓
2. Bonly Q and θ specified✓
3. Cno reactive power variable✓
4. Dfixed Q always✓

Ill-conditioned cases for NR include

1. Aunloaded open circuit only✓
2. Bheavy loading near voltage collapse and low impedance ties✓
3. Csingle slack only✓
4. Dlossless lines only✓

Rectangular coordinates (e,f) alternative in NR uses

1. Aonly magnitude without angle ever✓
2. Bonly frequency deviation✓
3. Creal and imaginary parts of voltage instead of polar V,θ✓
4. Donly per unit resistance alone✓

Optimal multiplier in NR can

1. Aincrease mismatch intentionally✓
2. Bremove Jacobian✓
3. Cfix all angles at zero✓
4. Ddamp step size to improve global convergence✓

After NR solution, LMP or marginal loss calculations may use

1. Asolved voltages and sensitivity factors✓
2. Bonly guesswork✓
3. Conly motor nameplate✓
4. Donly wind cut-out✓

Continued power flow uses NR with parameterization to trace

1. Aonly transformer OC test✓
2. Bonly cable tan delta✓
3. Conly VFD ramp✓
4. DP-V nose curve toward voltage collapse point✓

NR is preferred in commercial EMS for

1. Asmallest possible 2-bus homework only always✓
2. Breliable fast convergence on large transmission networks✓
3. Csystems without any nonlinearities✓
4. DDC circuits only✓

Symmetric Jacobian structure is not generally symmetric because

1. AY-bus is complex✓
2. Ball loads are zero✓
3. Cmixing of P and Q equations with θ and V variables breaks symmetry✓
4. Dfrequency is variable✓

Updating voltage in polar NR computes

1. Acorrections Δθ and ΔV/ V from solved linear system✓
2. Bonly Δf frequency✓
3. Conly transformer tap without voltage✓
4. Donly DC link current✓

Flat start for NR on stiff EHV system may require

1. Ano iteration at all✓
2. Bbetter initial voltages or damping to avoid early divergence✓
3. Cremoving all loads✓
4. Dsetting all P to zero✓

Transformer regulating tap change during NR may use

1. Acontinuous tap without limits always✓
2. Bno tap model✓
3. Cdiscrete tap steps outer loop around continuous NR✓
4. Donly mechanical brake model✓

Loss allocation after NR can use

1. Aonly guess without voltages✓
2. Bonly solar azimuth angle✓
3. Conly corona RI✓
4. Dincremental loss factors or proportional sharing methods✓

Symmetrical three-phase fault has

1. Aequal fault currents in all phases with zero sequence unaffected if ungrounded✓
2. Bonly single line open✓
3. Conly DC offset in one phase without AC✓
4. Donly negative sequence only✓

Line-to-line fault (LL) contains

1. Aall three sequences always including zero✓
2. Bonly zero sequence✓
3. Cpositive and negative sequence components without zero sequence if ungrounded✓
4. Donly DC component✓

Sequence impedances Z1, Z2, Z0 are used to

1. Aanalyze unbalanced faults via symmetrical components✓
2. Bonly calculate solar fill factor✓
3. Conly VFD carrier✓
4. Donly train adhesion✓

Fault MVA at a bus equals

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

Subtransient reactance Xd″ of synchronous machine governs

1. Aonly steady-state thermal limit✓
2. Bonly governor droop only✓
3. Conly excitation ceiling at steady state✓
4. Dinitial symmetrical short-circuit current contribution✓

Transient reactance Xd′ is relevant for

1. Aonly DC time constant of armature✓
2. Bonly long-term steady state only✓
3. Cfault current decay in first few cycles✓
4. Donly solar Voc✓

DC offset component in fault current arises from

1. Ainductance opposing sudden current change making current asymmetric✓
2. Bonly solar irradiance change✓
3. Conly biomass moisture✓
4. Donly PWM switching✓

Breaker making capacity must withstand

1. Aonly RMS symmetrical value always✓
2. Bpeak asymmetrical fault current including DC offset✓
3. Conly load current✓
4. Donly charging current✓

Percentage DC component for breaker rating considers

1. AX/R ratio at fault point affecting asymmetry✓
2. Bonly cable colour✓
3. Conly tower paint✓
4. Donly motor poles only✓

Thevenin equivalent at fault bus for fault calculation uses

1. Aonly load power factor✓
2. Bonly solar MPP✓
3. Cprefault voltage and equivalent impedance looking into network✓
4. Donly train schedule✓

Solid fault means fault impedance is

1. Ainfinite✓
2. Bequal to surge impedance only✓
3. Cequal to load resistance✓
4. Dzero✓

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

1. Avoltage at remote buses to zero always✓
2. Bfault current magnitude compared with solid fault✓
3. Cneed for any protection✓
4. Dsequence impedance to zero✓

Open conductor fault can cause

1. Aperfect balance always✓
2. Bonly symmetrical fault✓
3. Cno effect on loads✓
4. Dunbalance and abnormal voltages on unaffected phases✓

Distance relay measures

1. Aonly transformer temperature✓
2. Bonly solar azimuth✓
3. Cimpedance to fault to trip appropriate line section✓
4. Donly biogas pressure✓

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

1. Aonly off-diagonal mutual terms✓
2. Bdriving-point impedance at bus i for fault calculations✓
3. Conly shunt capacitance✓
4. Donly motor slip✓

Post-fault voltage sag severity depends on

1. Afault level, impedance to fault and prefault voltage✓
2. Bonly solar panel tilt✓
3. Conly VFD ramp time only✓
4. Donly train pantograph material only✓

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

1. Aimproving conditioning always✓
2. Bmaking equations more ill-conditioned✓
3. Celiminating reactive power✓
4. Dfixing all angles to zero✓

Removing a line from service updates Y-bus by

1. Ainverting Z-bus only without change✓
2. Bmultiplying all elements by zero✓
3. Csubtracting that branch stamp from the matrix✓
4. Dadding random entries✓

Sparsity techniques in NR exploit

1. Adense matrix inversion always✓
2. Bno branch data✓
3. Conly 2-bus systems✓
4. Dfew nonzero Jacobian entries in large networks✓