Power Eng 1st Class cheat sheet

Critical path method: the longest duration path through the network sets minimum project duration; any activity on it has zero total float.

Total float = LS − ES = LF − EF; a negative float indicates the schedule cannot meet the imposed completion date.

Earned value: CPI = EV/AC and SPI = EV/PV; CPI < 1 means cost overrun per unit of work performed.

Estimate at completion (typical variances) EAC = BAC/CPI; atypical variances EAC = AC + (BAC − EV).

Life-cycle cost analysis discounts O&M, fuel, and outage costs to present value; capital cost alone is not a valid comparison.

Reliability: availability = MTBF/(MTBF + MTTR); maintainability improvements reduce MTTR and raise availability without touching failure rate.

A management-of-change review is triggered by any modification to design, procedure, or setpoint affecting a safety-related function; the review precedes implementation.

Root cause analysis distinguishes physical, human, and latent (organizational) causes; correcting only the physical cause leaves recurrence likely.

ASME BPVC Section I governs power boilers; Section VIII Division 1 governs unfired pressure vessels; Section II covers materials, Section IX welding and brazing qualifications.

Maximum allowable working pressure derives from the longitudinal shell formula: t = PR/(SE − 0.6P) + corrosion allowance, with S from Section II Part D at design temperature.

A hydrostatic test is conducted at 1.5 times MAWP (Section I) with the test pressure held and no permanent deformation accepted as the pass criterion.

ASME Section IX qualifies procedures (WPS/PQR) and performance (WPQ); a change in essential variables requires requalification.

National Board NBIC covers in-service inspection, repair, and alteration; an R-stamp holder performs repairs and an AI authorizes return to service.

Jurisdictional authority: the state or provincial boiler code adopts the ASME code by reference and sets inspection intervals and operator licensing.

Code cases and interpretations are not retroactive unless the jurisdiction adopts them; the edition in force at installation governs unless otherwise directed.

Safety valve capacity must equal or exceed maximum generating capacity; the set pressure may not exceed MAWP and the accumulation limit (typically 10%) applies.

Rankine cycle efficiency = (Wturbine − Wpump)/Qin; regenerative feedwater heating raises mean temperature of heat addition and improves cycle efficiency.

Reheat to the original steam temperature increases work output without exceeding throttle temperature limits; double reheat adds a smaller further gain.

Carnot efficiency = 1 − Tc/Th; no real cycle between the same reservoirs can exceed it.

Isentropic efficiency of a turbine = actual enthalpy drop / isentropic enthalpy drop; moisture above roughly 12% at exhaust erodes last-stage blades.

Supercritical steam (above 22.06 MPa, 374 °C critical point) has no latent heat of vaporization; once-through design replaces the drum.

First law for steady flow: q − w = Δh + Δke + Δpe; second law fixes the maximum work and identifies irreversibility as entropy generation.

Heat rate = 3600/thermal efficiency (kJ/kWh basis); a 40% efficient unit uses about 9,000 kJ/kWh.

Throttle conditions and condenser pressure dominate output; a 1 kPa rise in back pressure typically costs on the order of 1% of output.

Fourier's law: q = −kA dT/dx; convection q = hAΔT; radiation q = εσA(Ts⁴ − Tsur⁴).

Overall heat transfer coefficient U combines conduction and convection resistances: 1/UA = 1/hiAi + Rwall + 1/hoAo.

Log mean temperature difference LMTD = (ΔT1 − ΔT2)/ln(ΔT1/ΔT2) for counterflow and parallel flow exchangers.

Reynolds number Re = ρVD/μ; transition near 2,300 in pipe flow, turbulent above roughly 4,000.

Darcy-Weisbach head loss hf = f(L/D)(V²/2g); friction factor rises with roughness and falls with Reynolds number in turbulent flow.

NPSH available = (Patm − Pv)/(ρg) + static head − friction losses; NPSH required must be lower or cavitation occurs.

Bernoulli with losses: P1/ρg + V1²/2g + z1 = P2/ρg + V2²/2g + z2 + hL.

Dittus-Boelter: Nu = 0.023 Re^0.8 Pr^n, n = 0.4 for heating and 0.3 for cooling of the fluid.

Drum material is typically SA-516 Gr 70 carbon steel; superheater and reheater tubing uses SA-213 T91 or TP347H for creep strength at high metal temperature.

Creep becomes design-limiting above roughly 400 °C for carbon steel; the Larson-Miller parameter correlates stress, temperature, and rupture time.

Corrosion fatigue and thermal fatigue crack at attachments and header ligaments; fatigue life is consumed by start-stop and load-change cycles.

Waterwall tube failures commonly trace to short-term overheat (restricted flow), long-term overheat (scale), or hydrogen damage from low-pH corrosion.

Post-weld heat treatment relieves residual stress; Section I mandates it above specified thicknesses and for certain alloys.

Dissimilar metal welds (ferritic to austenitic) require nickel-based filler (e.g., ERNiCr-3) to accommodate differential thermal expansion.

Boiler drum level and drum internals design must accommodate swell and shrinkage during load changes; false level indication is a known trip cause.

Fitness-for-service (API 579/ASME FFS-1) evaluates flaws against remaining strength rather than requiring immediate repair.

Drum level is maintained by a three-element control using steam flow, feedwater flow, and drum level; single-element control is used at low load.

Furnace purge before ignition is mandatory: typically five air changes at not less than 25% of full-load airflow to clear combustible gases.

Loss of flame, loss of all flame scanners, or loss of forced draft trips the fuel supply; a master fuel trip is the final protective action.

Cold start warming rate limits thermal stress in the drum; the drum-to-fluid temperature difference and saturation temperature ramp are the controlling variables.

Sootblower operation reduces gas-side fouling and restores heat transfer; blowing during high load with stable combustion avoids tube damage.

Boiler trip and interlock testing is performed before each startup; bypassing a protective device requires documented management authorization.

Carryover control depends on drum internals, steam purity, and dissolved solids; silica volatility limits steam-side deposition in turbines.

A drum level low-low trip protects against waterwall starvation; a high-high trip protects against carryover and turbine water induction.

Stoichiometric air for natural gas is about 17.2 mass units per unit fuel; for coal it is roughly 11 to 12; excess O2 of 2–3% dry is typical for gas firing.

The three T's - temperature, turbulence, and time - govern complete combustion; CO rises when any is deficient.

NOx control: low-NOx burners, overfire air, flue gas recirculation, and selective catalytic reduction with ammonia or urea reagent.

SCR operates near 300–400 °C with a vanadium-titania catalyst; ammonia slip and catalyst poisoning by sulfur and arsenic are key limits.

SO2 control via wet limestone flue gas desulfurization achieves over 95% removal; the by-product is gypsum.

Particulate control: electrostatic precipitator efficiency depends on resistivity and specific collection area; fabric filters rely on a conditioned filter cake.

Combustion efficiency losses: dry flue gas, moisture in fuel and air, and unburned carbon; stack loss dominates and rises with excess air.

Mercury control uses activated carbon injection or co-benefit capture from SCR plus wet FGD; coal chlorine content affects speciation.

Steam turbine stage types: impulse (pressure drop across nozzles only) and reaction (pressure drop across both fixed and moving blades).

Turbine governor control: droop (typically 4–5%) defines the speed or load change for a frequency deviation; isochronous control holds constant speed.

Overspeed trip is set at 110% of rated speed, independent of the main governor, with a separate mechanical or electronic trip device.

Gas turbine Brayton cycle efficiency rises with pressure ratio and firing temperature; simple cycle is about 35–40%, combined cycle above 60%.

Combined cycle HRSG recovers exhaust heat; duct firing raises output but lowers overall efficiency relative to unfired operation.

Generator synchronization requires matching voltage, frequency, phase sequence, and phase angle before breaker closure.

Reverse power protection prevents a generator from motoring; loss-of-excitation and negative-sequence relays protect the rotor.

Steam turbine water induction causes thermal shock and rotor bowing; drain systems and turbine drains must be verified before rolling.

Centrifugal pump affinity laws: flow ∝ N, head ∝ N², power ∝ N³; throttling wastes energy compared with variable speed control.

Pump operating point is the intersection of the pump curve and the system curve; running two pumps in parallel adds flow, in series adds head.

Best efficiency point (BEP) operation minimizes radial thrust and vibration; sustained operation far from BEP shortens bearing and seal life.

Positive displacement pumps deliver near-constant flow against varying pressure and require a relief valve on the discharge.

Compressor surge is reversed flow at low flow/high pressure ratio; anti-surge control recycles flow to keep the operating point off the surge line.

Safety valve vs relief valve: a safety valve opens fully and pops; a relief valve opens proportionally; a pilot-operated valve uses system pressure to actuate.

Piping expansion loops and hangers absorb thermal growth; a cold spring is installed to offset thermal movement at operating temperature.

Check valve selection affects water hammer; a nonslam or damped check valve limits surge on pump trip.

A control loop is proportional-integral-derivative; proportional action leaves offset, integral removes it, derivative anticipates and amplifies noise.

Loop tuning: increase gain until oscillation, then back off; Ziegler-Nichols open-loop uses the process reaction curve (dead time, time constant, gain).

A distributed control system separates controllers from the human-machine interface; a safety instrumented system is independent of the DCS for protective functions.

Safety integrity level (SIL) is assigned from risk graph or LOPA; SIL 3 requires a probability of failure on demand between 10⁻³ and 10⁻⁴.

Redundant transmitters with voting (2-out-of-3) reduce spurious trips while preserving detection of a failed sensor.

A thermocouple and an RTD differ in principle: thermocouples generate a small voltage from dissimilar metals; RTDs change resistance with temperature.

Calibration traceability requires a documented chain to a national standard; as-found and as-left data are recorded for each instrument.

Alarm rationalization reduces nuisance alarms; the operator response time must exceed the alarm flood interval for the alarm to be meaningful.

Motor starting current for a squirrel-cage induction motor is typically 5–7 times full-load current at direct-on-line start.

A generator breaker must be rated for the system fault level; interrupting rating must exceed the calculated short-circuit current.

Ground fault protection limits damage and touch potential; high-resistance grounding limits fault current while allowing continued operation.

Power factor correction capacitors reduce line current and losses; overcorrection causes leading power factor and possible overvoltage.

Transformer loading: oil-filled units are rated with a top-oil rise and hot-spot limit; loading beyond nameplate shortens insulation life.

Uninterruptible power supply and battery systems support controls and emergency loads; battery capacity is rated in ampere-hours at a specified discharge rate.

Station service and emergency diesel generators must be tested under load; a start-and-run test without load does not prove capacity.

Arc flash hazard analysis defines incident energy and boundary; energized work requires a permit and appropriate personal protective equipment.

Boiler feedwater: oxygen removal by deaeration to ppb levels plus chemical scavenging with hydrazine, carbohydrazide, or DEHA.

Scale control uses phosphate or coordinated phosphate/pH treatment; caustic embrittlement (stress corrosion cracking) is avoided by keeping caustic concentration controlled.

Corrosion control: maintain pH in the range 8.5–10.5 for carbon steel feedwater; copper alloys need lower pH and ammonia limits.

Conductivity and cation conductivity indicate dissolved solids and ionic contamination; cation conductivity is more sensitive to chloride and sulfate.

Cooling water treatment uses biocides, scale inhibitors, and corrosion inhibitors; cycles of concentration are limited by the least soluble salt.

Condensate polishing removes corrosion products and ionic impurities; a rise in cation conductivity signals a condenser tube leak.

Effluent limits cover thermal discharge, pH, metals, and biocides; the Clean Water Act NPDES permit sets the enforceable limits.

Ash handling and landfill leachate are regulated separately from air emissions; coal combustion residual rules govern storage and disposal.

Hazard analysis methods: HAZOP for process deviations, FMEA for component failure modes, and LOPA for independent protection layer counting.

Risk = likelihood × consequence; ALARP requires risk to be reduced as low as reasonably practicable, with documented justification for residual risk.

Permit-to-work and lockout/tagout isolate energy sources; verification of zero energy is required before work begins.

Confined space entry requires atmospheric testing for oxygen, flammables, and toxics, plus a rescue plan and attendant.

Incident investigation: preserve evidence, interview witnesses separately, and distinguish immediate causes from root and latent causes.

Emergency response for a boiler or turbine trip: verify fuel shutoff, maintain auxiliary power, and follow the written emergency procedure rather than improvising.

Hot work near combustible dust or gas requires a gas test and a fire watch with a defined post-work monitoring period.

Management of change, pre-startup safety review, and operating procedures are the process-safety pillars that prevent repeat incidents.