Steady-state model of a single-phase full-wave rectifier with a constant voltage load operating in discontinuous mode

Rectifiers are essential elements of the electrical circuits that require AC to DC voltage conversion, their operation can occur either in continuous conduction mode (CCM) or discontinuous conduction mode (DCM). When a rectifier operates in discontinuous current conduction mode, the current waveform will have conduction and zero-current intervals describable by current's turn on and turn off angles. This research's main aim is to analyse that behaviour. An analytical model is developed for a single-phase full-wave bridge rectifier having an AC side smoothing inductor and a constant voltage load, operating in discontinuous conduction mode, after making the necessary assumptions for the simplified version of the model to be derived. The model derivation led to a nonlinear equation that describes the relation between the conduction angles of the input current, which was solved numerically using MATLAB, the numerical solution led to an almost linear relation between the conduction angles, which can also be represented by simply using the equation of line. Simulations of the proposed rectifier circuit are carried out using PSpice and MATLAB's Simulink software to analyse the circuit operation and to find the correct parameter adjustments that need to be made to determine the circuit working mode and achieve the desired circuit characteristics, the relation between the conduction angles was also conducted from the simulation results and was plotted to show if it also satisfies the near-linear relation between the conduction angles, it was found that the maximum percentage error between the results gained from the theory compared to the simulation results was 14.4%. The experimental circuit implementation was also done, the utility electricity with its near-sinusoidal voltage waveform was used to supply an autotransformer (variac) with electrical power, which was followed by a step-down isolation transformer, the output of that transformer fed the rest of the system, the reason behind using a variac was to have the ability to adjust the input voltage amplitude to any desired value for the required testing conditions, that will vary the amplitude of the electrical current flowing through the circuit, hence achieving a useful range of conduction angles. Schottky diodes were used for the rectifier circuit, since they have low forward voltage rating. As this research requires a constant voltage load, 12 V, 12 Ah and 9 Ah, rated lead-acid, sealed batteries were used at the output of the rectifier circuit, and it was shown that a lead-acid battery was a good choice to be used as a constant load, and it fulfilled the need behind it in this research, and the rectifier system can also be used as an affordable battery charging system. A Hall effect sensor-based current probe was used to carry out the current measurements. The acquired electrical measurement data was transferred to the personal computer, then processed and plotted properly utilizing an autonomous measurement system, that shows the measurement readings on the computer easily and enables a code-based automated detection of the conduction angles. The relation between the conduction angles acquired from the experimental system was presented and found that the results gained from the theoretical and experimental approaches showed support for each other, where the conduction angles kept having an almost linear relation between them across a wide range of test cases, by making use of maximum tolerable currents of the circuit components. The result of the maximum error calculation between the numerical solution and the experimental findings was 16.65% when the input voltage amplitude was 14.28 V for the 12 Ah battery. The values of the turn off angles (α2) obtained from the simulation and experiment were less than their values obtained from the numerical solution. It is believed that the effect of I*R in the circuit behaves as if a reverse polarized voltage source whose value changes by the effect of the current is connected to the circuit, that's why the effective source voltage magnitude decreases, resulting in decreasing α2 values.