6.3 Power Electronics & Transmission
Key Takeaways
- A rectifier converts AC to DC and an inverter converts DC to AC; a full-wave bridge of four diodes uses both half-cycles of the AC input.
- A diode conducts in one direction once forward-biased; a thyristor (SCR) blocks until a gate pulse triggers it and stays on until current falls to near zero.
- Transmission lines are modeled as short, medium (nominal-pi), or long lines depending on length, using series resistance and inductance plus shunt capacitance.
- Voltage regulation = (V_no-load - V_full-load) / V_full-load × 100%; lower regulation means a stiffer, better-performing line or transformer.
- Protection uses fuses, circuit breakers, and relays to clear faults quickly and isolate the smallest faulted section (selective coordination).
Rectifiers and inverters
Power electronics uses switching devices to convert between AC and DC. A rectifier converts AC to DC, and an inverter converts DC to AC. Common rectifier circuits:
- Half-wave rectifier: one diode passes only one half-cycle; output is pulsating DC with high ripple.
- Full-wave bridge rectifier: four diodes use both half-cycles, doubling the average output and lowering ripple.
- Center-tapped full-wave: two diodes with a center-tapped transformer achieve full-wave output.
For an ideal full-wave rectified sinusoid of peak V_m, the average (DC) output is V_dc = 2·V_m/pi; for a half-wave it is V_m/pi. A filter capacitor across the load smooths the ripple.
Switching devices: diodes and thyristors
Know the behavior of each device, because FE questions often hinge on conduction conditions rather than calculation.
| Device | Turns on when | Turns off when |
|---|---|---|
| Diode | Forward-biased (anode positive) | Current reverses / reverse-biased |
| Thyristor (SCR) | Forward-biased AND gate pulse applied | Current falls below holding value |
| Transistor (BJT/MOSFET) | Base/gate drive applied | Drive removed |
A diode is uncontrolled: it conducts whenever forward-biased. A thyristor (silicon-controlled rectifier, SCR) is a controlled switch that latches on after a gate trigger and only turns off when its current drops near zero. Controlling the gate firing angle in a phase-controlled rectifier varies the average DC output.
Transmission line models
A transmission line is modeled by lumped elements whose complexity scales with length:
- Short line (under ~80 km / 50 mi): series resistance R and inductance L only; shunt capacitance neglected.
- Medium line (~80 to 250 km): nominal-pi or nominal-T model adds shunt capacitance, usually split half at each end.
- Long line (over ~250 km): distributed-parameter model using hyperbolic functions of the propagation constant.
The series impedance causes voltage drop and real-power loss (I^2·R), while shunt capacitance can raise receiving-end voltage at light load (the Ferranti effect). Choosing the right model for the stated length is the most common exam decision here.
Voltage regulation and protection
Voltage regulation measures how much the output voltage sags from no load to full load:
VR (%) = (V_no-load - V_full-load) / V_full-load × 100
Lower regulation means a stiffer source. The same formula applies to transformers and lines.
Protection keeps faults from damaging equipment and people. Fuses melt to interrupt overcurrent; circuit breakers are resettable mechanical interrupters; protective relays sense abnormal current, voltage, or impedance and command breakers to trip. Good design uses selective coordination so the device closest to the fault clears first, isolating the smallest possible section and keeping the rest of the system energized. Grounding limits touch voltage and provides a return path for fault current.
A full-wave bridge rectifier is built from ideal diodes. How many diodes conduct during each half-cycle of the AC input?
Which statement best distinguishes a thyristor (SCR) from an ordinary diode?
A transformer supplies 240 V at no load and 228 V at full load. What is its voltage regulation?