Find the load dc current and find the rms of the ac current

Question

Project:- Design of an Open-Loop Single Phase Full Wave Rectifier

Design an ac-dc converter that can convert the wall 230 V rms voltage at 60 Hz, to an average dc voltage between 30 V and 35 V across an RL load. The average current in the load must also be between 0.1 A and 0.2 A.

The design specifications are listed in the table below

Table 1: Design Specifications

ac rms voltage	230 V
Frequency	60 Hz
R	200 ohms
L	25 mH

To meet the design goals, you need to add a capacitor in parallel with the load. Also between your ac source and your rectifier circuit you are allowed to add an ideal step down transformer to isolate your circuit and to step down the voltage. A block diagram of the system is shown below

The following design constraints are imposed on the design

Table 2: Design Constraints

C	Less than 5 mF
ΔVload/ Vload ,max imum x 100	Less than 5 %
ΔIload/ Iload ,max imum x 100	Less than 5 %
Number of turns on primary winding	Less than or equal to 100
Number of turns on secondary winding	Less than or equal to 100

Project Phases

Phase 1: Analytically calculate the capacitor and transformer winding turns that will meet the design specifications and constraints. While doing so it is okay to initially ignore the load inductance.

- Find the angles θ₀ and α

- Find ΔV₀

- Find maximum and minimum load voltage

Phase 2: After finding the capacitance and transformer winding turns, simulate the circuit using Simulink for 4 electrical cycles with the inductor included.

- On your Simulink poge, go to "Simulation",then "Model Configuration Parameters", and set your Solver to "ode15s (stiff/NDF)" and the "Max step size" to 1e-5. Leave everything else the same.

- For your diode component, set the on resistance to 0.001 ohms, the on inductance to 0, the forward voltage to 0, and the snubber resistance and capacitance to 1000 ohms and 1 uF, respectively.

- From Simulink, retrieve the following waveforms to MATLAB workspace : rectifier input voltage, rectifier input current waveform, load voltage , load current, voltage across one of the diodes (D2 for example), and simulation time.

Phase 3: - From your Simulink waveforms, find the following

- Average load voltage

- Average load current

- Maximum load voltage (how does it compare to the analytical ? )

- Minimum load voltage (how does it compare to the analytical ? )

- rms load current

- peak to peak load current

- peak to peak load voltage

- rms rectifier input voltage

- rms rectifier input current

- average voltage across diode

- Active power at the load

- Apparent power input at the rectifier

- Power factor

Phase 4: - Plot the Simulink rectifier input voltage and load voltage on the same plot

- Plot the Simulink rectifier input current and load current on the same plot

Phase 5: - Add non-ideal characteristics to the diodes. In particular, set the forward voltage drop to 4 V for each diode and the diode on resistance to 4 ohm.

- Compare your maximum, minimum, and average load voltage drop to the ideal which you calculated in Phase 3.

- Find the load dc current

- Find the rms of the ac current input to the rectifier

- Find the dc power dissipated across the load using Pdc = {i_o (θ)}²(R)

- Find the ac power input to the rectifier using P_ac = 1/2Π ₀∫^2Π v_in,_rec i_in,rec dθ where r_diode is the diode on resistance.

- The rectifier efficiency is defined as the ratio of dc output power to input ac power. Find the rectifier efficiency. Using the same method find the efficiency of your rectifier for the nearly ideal case when forward voltage drop and the diode on resistance where set to 0V and 0.001 ohms respectively. Compare and discuss results.

Phase 6: Write a report to describe what was done in this project and what findings did you encounter. For example, if frequency can be increased can you decrease the size of your capacitor and meet the design requirements. In your report make a table to list all important data such as what was found in Phase 3.

Answer 1

In this task, you have to consider the design specifications illustrated in the problem and design an ac-dc converter which can transform the wall 230 V rms voltage at 60 Hz, to an average dc voltage between 30 V and 35 V across an RL load. The average current in the load should as well be between 0.1 A and 0.2 A. Please follow the phases illustrated below. Phase 1: Analytically compute the capacitor and transformer winding turns which will meet up the design specifications and constraints. While doing so it is okay to at first ignore the load inductance. Phase 2: After finding out the capacitance and transformer winding turns, replicate the circuit by employing Simulink for 4 electrical cycles having inductor included. Phase 3: From Simulink waveforms, find: • Average load voltage • Average load current Phase 4: Write down a report to illustrate what was done in this project and what findings did you meet.