Power Systems on the FE Electrical Exam
Power systems accounts for 7 to 11% of the FE Electrical and Computer exam. This area covers the generation, transmission, and distribution of electrical power. Whether you specialized in power systems or focused on other areas of electrical engineering, a solid understanding of three-phase circuits and transformers is essential for this section.
Three-Phase Systems
Balanced Three-Phase Sources
A balanced three-phase source produces three sinusoidal voltages of equal magnitude, each displaced by 120 degrees. The two common configurations are wye (Y) and delta. In a wye connection, the line voltage equals the square root of 3 times the phase voltage, and the line current equals the phase current. In a delta connection, the line voltage equals the phase voltage, and the line current equals the square root of 3 times the phase current.
Three-Phase Power
For a balanced three-phase system, the total power (real, reactive, or apparent) equals three times the single-phase power. Total real power equals the square root of 3 times the line voltage times the line current times the power factor. This formula works for both wye and delta connections and is one of the most frequently tested formulas on the FE Electrical exam.
Wye-Delta Conversions
Know how to convert impedances between wye and delta configurations. For balanced systems, the delta impedance equals three times the wye impedance. For unbalanced systems, use the general conversion formulas.
Transformers
Ideal Transformer
An ideal transformer has the voltage ratio V1/V2 = N1/N2 (turns ratio) and the current ratio I1/I2 = N2/N1 (inverse of the turns ratio). Power is conserved: V1 times I1 equals V2 times I2. The ideal transformer model is sufficient for many FE exam problems.
Practical Transformer
Real transformers have winding resistances, leakage reactances, core losses (hysteresis and eddy current), and magnetizing current. The equivalent circuit model includes these non-ideal elements referred to either the primary or secondary side. The referred impedance is multiplied by the turns ratio squared when reflecting from secondary to primary.
Transformer Tests
The open-circuit test (secondary open, rated voltage on primary) determines core losses and the magnetizing branch parameters. The short-circuit test (secondary shorted, reduced voltage on primary) determines winding impedances. Know how to extract equivalent circuit parameters from test data.
Per-Unit System
The per-unit system simplifies power system calculations by normalizing all quantities to chosen base values. Select base values for power (S_base) and voltage (V_base), then calculate base current (I_base = S_base / V_base) and base impedance (Z_base = V_base squared / S_base).
In per-unit, transformer turns ratios disappear (the per-unit impedance is the same on both sides of a transformer), which greatly simplifies analysis of systems with multiple voltage levels. Know how to convert between per-unit systems with different bases.
Power Factor Correction
Industrial loads (motors, fluorescent lighting) typically have lagging power factors due to their inductive nature. A low power factor increases the current required to deliver a given real power, increasing line losses and requiring larger conductors. Capacitors added in parallel with the load supply reactive power locally, reducing the reactive power from the source and improving the power factor.
To calculate the required capacitor size, determine the reactive power before and after correction. The capacitor must supply the difference in reactive power. The capacitance equals the reactive power divided by (omega times V squared), where omega is the angular frequency and V is the voltage.
Power Transmission
Basic transmission line concepts include resistance (causes I squared R losses), inductance (causes voltage drop and reactive power consumption), capacitance (causes charging current and reactive power generation), and conductance (usually negligible). For short lines (under 80 km), use the simple series impedance model. For medium lines (80-240 km), use the nominal pi or T model.
Voltage regulation is the percentage change in receiving-end voltage from no load to full load, expressed as a percentage of the full-load voltage. A lower voltage regulation indicates better performance.
Fault Analysis
Symmetrical (three-phase) faults are the simplest to analyze. The fault current equals the source voltage divided by the total impedance to the fault point, usually calculated in per-unit. Know how to set up the per-unit equivalent circuit and calculate the fault current for a bolted three-phase fault.
Exam Tips
Three-phase power calculations and transformer problems are the most commonly tested topics in this section. Master the relationships between line and phase quantities for both wye and delta configurations. Practice per-unit calculations until you can set up and solve them quickly. The FE Reference Handbook provides the key formulas, but speed comes from understanding when and how to apply them.