Prepare for the PE Power exam by rehearsing complete decision chains rather than isolated formulas: declare per-unit bases, identify the fault type, choose the sequence-network connection, account for transformer phase shift and grounding, then verify devices on a common current basis. Each worked scenario below shows a plausible early mistake, the better decision, and why the difference matters downstream. Use the adaptable sequence and self-check rubric to grade your own work, and confirm registration and format details with NCEES directly.
Per-unit bases: keeping one consistent reference across voltage zones
The per-unit system lets you add impedances across transformers by choosing one MVA base and one voltage base per zone. Convert every impedance to that common base once, and the network collapses into a single consistent model.
An impedance expressed in per-unit is Z_pu = Z_actual × MVA_base / (kV_base)^2. When you change the MVA base, multiply the existing per-unit value by (MVA_new / MVA_old); the voltage base, however, must follow the transformer ratio zone by zone. Handled this way, an impedance on the 480 V side and one on the 13.8 kV side can be added directly, because the transformer ratio is already embedded in the base change rather than in your arithmetic.
Consider a fault study where a generator nameplate lists its subtransient reactance on its own MVA rating, while the utility supply was given on a different MVA base. A plausible mistake is carrying both bases forward and adding the reactances as written. The result can be off by the ratio of the bases, understating or overstating fault duty enough to misjudge a device rating. The better decision is to convert every source and impedance to one declared common base before any addition, and state that base at the top of your work.
Choosing the right sequence-network connection for each fault type
Three-phase faults involve only the positive-sequence network. Unbalanced faults combine networks differently: single-line-to-ground uses all three in series, line-to-line uses positive and negative in parallel, and double-line-to-ground uses a specific parallel arrangement.
Trace the connection before computing anything: for a single-line-to-ground fault, the positive, negative, and zero-sequence networks connect in series, so the fault current depends on the zero-sequence path. That path exists only where a grounded wye winding or grounding source provides it; delta windings trap zero-sequence current. For a line-to-line fault, only positive and negative networks in parallel matter, so grounding has no effect on the magnitude.
Scenario: a single-line-to-ground fault is asked on a bus fed solely through a delta-delta transformer with no grounding source. A plausible mistake is computing a large fault current using only positive-sequence impedance, mirroring the balanced-fault method. The better decision is to notice that no zero-sequence path exists, so the ground-fault current from that source is essentially negligible, and the answer hinges on other grounding sources if any exist. Recognizing the missing path matters because it changes both the magnitude and which equipment the result applies to. Use the table below as a decision check whenever a fault type appears in a problem statement.
| Fault type | Sequence networks used | Network connection | Key check |
|---|---|---|---|
| Three-phase (balanced) | Positive only | Single network | No sequence conversion needed |
| Single line-to-ground | Positive, negative, zero | All three in series | Does a zero-sequence path exist? |
| Line-to-line | Positive, negative | Parallel, zero omitted | Grounding irrelevant to magnitude |
| Double line-to-ground | Positive, negative, zero | Parallel combination with zero branch | Zero-sequence impedance strongly affects result |
Transformer connections: phase shift and grounding you cannot skip
Delta-wye banks introduce a 30-degree phase displacement between high- and low-voltage quantities, and their winding arrangement controls whether zero-sequence current flows. Both facts change fault results and any paralleling decision.
When you parallel two transformer banks, matching voltage ratios and impedance is not enough; the vector groups must produce voltages in phase, or a large circulating current flows between the banks even with no load. Similarly, in fault calculations the winding connection decides the zero-sequence behavior: a grounded-wye winding provides a path, a delta winding provides none but does supply zero-sequence within its own loop, and an ungrounded wye provides none at all.
Scenario: a plan adds a delta-wye transformer in parallel with an existing wye-wye unit of the same kVA and impedance. A plausible mistake is approving the parallel operation because nameplate electrical ratings match. The better decision is to compare the vector displacement of each bank first; the 30-degree shift of the delta-wye unit makes the secondaries out of phase, so closing them together is not acceptable without a matching connection or phase correction. The comparison changes the recommendation from a routine tie-in to a redesign.
Coordination studies: reading time-current curves on a common basis
Coordinating a downstream fuse with an upstream relay means the fuse clears first for faults in its zone, with margin. An analytical error that silently distorts this check is comparing curves plotted on different current bases, which can make devices look miscoordinated or falsely coordinated.
A time-current curve plots operating time against current, but the current axis may be in primary amps, secondary amps, or multiples of a pickup or plug setting. Before comparing two devices, convert every curve to the same current base, usually amps referred to one side of the transformer. Then check two things for faults within the protected zone: the downstream device operates first, and a reasonable time margin separates the curves across the full current range, not just at one fault value.
Scenario: a feeder fuse protects a cable, and an upstream overcurrent relay backs it up. A plausible mistake is reading the relay curve in multiples of pickup while reading the fuse in primary amps, concluding the relay trips first for a cable-end fault and setting the relay faster. The better decision is to convert the relay plot to primary amps, recheck the overlap, and then set the relay slow enough that the fuse clears zone faults while the relay still covers faults the fuse cannot. The distinction determines whether a cable fault opens the whole bus or only the affected feeder.
Feeder voltage drop and power factor correction: sizing and placement
Voltage drop on a feeder follows from the load current and line impedance, and correcting power factor reduces the reactive component of that current. Correcting from measured reactive power, not apparent power, prevents overcorrection into leading conditions.
For a short single-phase feeder, an approximate drop is I × (R cosθ + X sinθ) × length, doubled for the round trip; three-phase versions use the line-to-line base and a sqrt(3) factor. Capacitor banks are sized from the reactive power needed to move the load toward the target power factor, Q = P × (tanθ_initial − tanθ_target). Placement matters: a capacitor at the load end corrects the entire feeder upstream of it, while the same bank at the substation only relieves the substation-side equipment.
Scenario: a plant at 0.75 power factor wants 0.95, and a plausible mistake is sizing capacitors as a fraction of the kVA demand, which sizes the bank from apparent power instead of reactive power and can overshoot into a leading power factor. The better decision is to compute real power first, take the difference of tangent terms between the two power factors, and select the bank from that reactive difference, then place it near the large motor loads so the feeder sees the benefit. The distinction matters because a leading power factor can raise voltage and create problems the correction was meant to solve.
Rotating machines: relating slip, starting current, and torque expectations
An induction motor at starting conditions draws large current while producing only its locked-rotor torque, because slip is near one and rotor frequency is high. Reasoning from slip clarifies starting, pull-out, and full-load behavior without memorizing curves.
Slip s is the difference between synchronous speed and rotor speed, divided by synchronous speed. At start, s = 1, rotor frequency equals supply frequency, and rotor reactance is large, so current is high while power factor and torque are relatively modest. As the machine accelerates, slip falls, rotor reactance shrinks, and torque rises toward its pull-out value before declining again near synchronous speed. Torque varies roughly with slip in the small-slip operating region.
Scenario: a motor must start a high-inertia load, and a plausible mistake is assuming that because starting current is several times full-load current, starting torque is proportionally large. The better decision is to reason through the slip relationship: the high starting current is largely reactive, so the available accelerating torque must be checked against the load's torque requirement, and a reduced-voltage starter, which cuts current further, must still leave torque above the load curve. The reasoning distinguishes current magnitude from torque capability, which drives the starter choice.
An adaptable scenario-first study sequence with a self-check rubric
Build preparation around repeating the same decision chain on new numbers: set bases, pick the fault type, apply the connection, check the device. Rotate through the topics, and grade yourself with a rubric rather than a single score.
A practical sequence you can compress or stretch to fit your schedule: begin with per-unit and three-phase circuit analysis, closing that block with two full fault calculations carried from base-setting to fault current. Move next to symmetrical components and transformer connections, solving at least one unbalanced fault where you must first identify the zero-sequence path. Then cover rotating machines and protection coordination, including two curve-comparison exercises converted to a common current base. Finish with mixed scenarios that chain two or three of these topics together, plus timed self-tests.
Grade every scenario with this rubric and expect observations to improve across attempts: declare the MVA and voltage bases before calculating, identify the fault type and its sequence-network connection before computing, check grounding and phase shift before concluding, convert currents to one base before comparing devices, and state in a final sentence what the number means for the equipment. An exercise to run now: take one feeder with a transformer, a motor load, and a specified fault, and solve it three times on three different MVA bases; the expected observation is that the per-unit impedance values change but the physical fault current does not, which confirms your base mechanics.
Readiness checks before you sit the exam: you can convert an impedance between MVA bases without notes, you can state the sequence-network connection for all four fault types from memory, and you can justify a coordination decision in two sentences. These are learning milestones, not passing predictions. For registration windows, format, and current exam specifications, use the NCEES PE exam page linked below, since administrative details are set by the exam developer.
References and further reading
Use these references to explore the concepts and check the latest information from the relevant organizations.