Single phase half wave controlled rectifier with an rl load formula

A single-phase half-wave controlled rectifier with an RL load is a circuit that utilizes a thyristor to control the phase relationship between the load current and the supply voltage during the positive half-cycle. By adjusting the firing angle, denoted as α, the rectifier can manipulate the initiation of load current. In this detailed exploration, we will delve into the circuit diagram, working principles, and key parameters such as average load voltage, average load current, and RMS load voltage.

Circuit Diagram

The fundamental components of the circuit include a thyristor (T), a voltage source (Vs), and an RL load. The output voltage (Vo) is measured across the load, and the output current (io) flows through the load.

Working Principle

The source voltage, load voltage, load current, and thyristor voltage waveforms play a crucial role in understanding the rectifier's operation. The firing angle α determines when the thyristor is triggered.

When the thyristor is triggered at ωt = α, the load voltage instantaneously aligns with the source voltage. This occurs because the thyristor becomes forward biased between ωt = 0 to α, allowing conduction to start.

However, due to the inductive nature of the load, the output current does not immediately commence at ωt = α. Instead, it gradually increases, reaching a maximum before decreasing. Notably, this behavior is absent in purely resistive loads.

At ωt = π, the load voltage drops to zero, but the load current persists due to inductance. The thyristor continues to conduct until ωt = β, where the load current becomes zero. This natural commutation leads to thyristor turn-off.

The angle (β-α) defines the conduction angle, representing the period during which the thyristor is ON. The angle β, where the load current becomes zero, is termed the extinction angle.

Observing the voltage across the thyristor, it is crucial to note that the thyristor is reverse biased from ωt = β to ωt = 2π. The circuit turn-off time (tc) is calculated as [(2π – β) / ω], emphasizing the necessity for this time to exceed the thyristor turn-off time to prevent undesired commutation failure.

control-uncontrolled-rectifier

Calculation of Steady Load Current

This webpage provides information on the calculation of steady load current for a Single Phase Half Wave Controlled Rectifier with RL Load.

Calculation Formula

The steady load current (I_o) can be calculated using the following formula:

Is=Io = (Vm / √(square R + square X) *(sinωt- φ)

Where: φ = arctan(X/R) Here φ is the angle by which rms current Is lags Vs.

• Io: Steady Load Current
• Vm: Maximum voltage across the load
• R: Load resistance
• α: Firing angle

Calculation of Average Load Voltage and Current

This webpage provides information on the calculation of average load voltage and current for a Single Phase Half Wave Controlled Rectifier with RL Load.

Calculation Formulas

The average load voltage (V_{o_avg}) and average load current (I_{o_avg}) can be calculated using the following formulas:

Vo_avg = (Vm / 2π) * (cosα - cos(β)) Io_avg = (Vm / (2πR)) * (cosα - cos(β))

Where:

• Vo_avg: Average Load Voltage
• Io_avg: Average Load Current
• Vm: Maximum voltage across the load
• R: Load resistance
• α: Firing angle

Calculation of RMS Load Voltage

This webpage provides information on the calculation of RMS load voltage for a Single Phase Half Wave Controlled Rectifier with RL Load.

Calculation Formula

The RMS load voltage (V_{o_rms}) can be calculated using the following formula:

Vo_rms = Vm / (2√π) * √[(β-α)-0.5{sin2β-sin2α}]

Where:

• Vo_rms: RMS Load Voltage
• Vm: Maximum voltage across the load
• α: Firing angle