A PID (Proportional–Integral–Derivative) Controller is a feedback control mechanism used to minimize the error between a desired setpoint and the actual output of a control system. It combines three actions: the proportional (P) term responds to the present error, the integral (I) term accumulates past errors to reduce or eliminate steady-state error, and the derivative […]
Category: Electrical Fundamentals
Signal Flow Graph
Signal Flow Graph (SFG) is a graphical representation of the relationships among variables in a control system, where system variables are represented by nodes and the mathematical relationships between them are represented by directed branches with associated gains. The direction of each branch indicates the flow of a signal from one node to another, while […]
Line Voltage for a Delta Connected Alternator
In a delta (Δ) connected three-phase alternator, the three phase windings are connected end-to-end to form a closed triangular circuit, and each winding is directly connected between two line conductors. Therefore, the line voltage is equal to the phase voltage, expressed as VL=VphV_L = V_{ph}. Unlike a star-connected alternator, there is no 3\sqrt{3} multiplication between […]
Three Phase EMF of Alternator
A three-phase EMF of an alternator is generated when three identical stator windings are placed 120° electrical apart and a rotating magnetic field induces sinusoidal EMFs in them. The three generated phase EMFs have the same frequency and magnitude but are displaced from each other by 120° electrical. They can be represented as EA=EmsinωtE_A=E_m\sin\omega t, […]
Resonance Parameter
The values of inductance (L) and capacitance (C) determine the natural resonant frequency of an electrical circuit. Resonance occurs when the inductive and capacitive reactances become equal in magnitude, causing them to effectively cancel each other. The resonant frequency is given by fᵣ = 1/(2π√LC). Therefore, changing either the inductance or capacitance changes the resonant […]
Resonance due to Harmonics
Interactive Harmonic Resonance Simulation ⚡ Harmonic Resonance Simulation Demonstration of resonance between harmonic frequency and an LC system natural frequency 1. Simulation Controls Fundamental Frequency 50 Hz Harmonic Order 3rd Harmonic5th Harmonic7th Harmonic11th Harmonic13th Harmonic Natural Resonant Frequency 250 Hz System Damping 0.20 Harmonic Voltage 5% ▶ Start ⏸ Stop ↻ Reset ✓ Apply Detuned […]
11th and 13th harmonics
11th & 13th Harmonics – Effects & Mitigation 11th & 13th Harmonics Interactive simulation of harmonic distortion, equipment effects and mitigation 1. Harmonic Controls 11th Harmonic Amplitude: 10% 11 × 50 Hz = 550 Hz 13th Harmonic Amplitude: 8% 13 × 50 Hz = 650 Hz Fundamental Amplitude: 100% 50 Hz fundamental ▶ Start ■ […]
Triplen Harmonic
9th Harmonic Neutral Current Simulation 9th Harmonic: Triplen Harmonic & Neutral Current Three-phase system demonstration — 9th harmonic currents become in-phase and add in the neutral conductor ▶ Start ⏸ Stop ↻ Reset 9th Harmonic: 10 A Phase A 9th Harmonic 0 A Phase B 9th Harmonic 0 A Phase C 9th Harmonic 0 A […]
13th Harmonics
13th Harmonic – Motor & Transformer Simulation 13th Harmonic Interactive Simulation See how the 13th harmonic can increase motor/transformer heating, vibration and losses — and how mitigation reduces the problem. ▶ Start ⏸ Stop ↻ Reset 13th Harmonic Level: 10% Induction Motor Motor Heating: 40°C Transformer Transformer Heating: 40°C 13th Harmonic 10% Motor Vibration Low […]
9th Harmonics
Neutral Overheating & Transformer Heating Simulation Neutral Overheating & Transformer Heating This simulation demonstrates how nonlinear loads can produce 3rd harmonic current. Unlike the fundamental current, triplen harmonics can add in the neutral conductor, causing neutral overheating and increasing transformer heating. ▶ START ■ STOP ↻ RESET ● Simulation Stopped 3rd Harmonic Level 65% Load […]