Electrical Engineering

In star (Y) connection, one end of each phase winding is connected to a common neutral point, while in delta connection, windings are connected end-to-end forming a closed loop. For the same line voltage: Star has phase voltage = line voltage/sqrt(3), line current = phase current. Delta has phase voltage = line voltage, line current = sqrt(3) x phase current. Star is used for long-distance transmission (lower current, lower losses), while delta provides more power for motors.

A transformer works on Faraday's law of electromagnetic induction. When AC flows through the primary winding, it creates an alternating magnetic flux in the core. This changing flux links with the secondary winding and induces an EMF. The voltage ratio equals the turns ratio (V1/V2 = N1/N2). Transformers only work with AC since DC doesn't produce changing flux. Core losses (eddy current, hysteresis) and copper losses affect efficiency, which typically exceeds 95% in power transformers.

Power factor is the cosine of the phase angle between voltage and current, representing the ratio of real power (kW) to apparent power (kVA). A power factor of 1 (unity) means all power is useful; lower values indicate reactive power consumption. Low PF causes: higher current for same power (larger cables, transformers), increased losses, voltage drop, and utility penalties. Industries improve PF using capacitor banks, synchronous condensers, or power factor correction circuits.

PID (Proportional-Integral-Derivative) control adjusts output based on error: P responds to present error magnitude, I accumulates past errors eliminating steady-state error, D predicts future error from rate of change. Tuning methods include: Ziegler-Nichols (increase Kp until sustained oscillation, use formulas), trial-and-error (start with P only, add I to remove offset, add D to reduce overshoot), or auto-tuning features in modern controllers. Trade-offs exist between fast response, overshoot, and stability.

Main types: Buck (step-down) - output < input, used in voltage regulators, LED drivers. Boost (step-up) - output > input, used in battery-powered devices, solar MPPT. Buck-Boost - output can be higher or lower, used when input varies widely. Cuk and SEPIC converters offer non-inverted outputs with continuous currents. Isolated converters (flyback, forward, full-bridge) provide galvanic isolation for safety. Key parameters are efficiency, ripple, and transient response.