**5. Modeling and simulation of diode rectifiers**

Three-phase AC to DC converters are widely used in many industrial power converters in order to obtain continuous voltage using a classical three-phase AC-line. These converters, when they are used alone or associated for specific applications, can present problems due to their non-linear behaviour. It is then important to be able to model accurately the behaviour of these converters in order to study their influence on the input currents waveforms and their interactions with the loads (classically inverters and AC-motors).

Several studies have shown the importance to have tools to simulate the behaviour of complex power electronics systems (Ladoux et al., 2005), (Qijun et al. 2007), (Zuniga-Haro & Ramirez, 2009) and several methods have been also presented in order to reduce the simulation time or to improve the precision. Although constant topology methods have been developed (Araujo et al., 2002), variable topology methods seem to be very suitable for simulation of power-electronics converters (Terrien et al., 1999).

In this chapter, an original and simple method is developed to model and simulate AC-DC converters taking into account overlap phenomenon with continuous and discontinuous conduction modes using Matlab-Simulink. The diodes are assumed ideal (vd = 0 when the diode is state-on, id = 0 when the diode is state-off)

If the electrical network is considered as ideal (no line inductance) and the conduction is maintained continuous, (id>0), the modelling of the converters can be realised very simply by a functional approach (commutation functions) where the switches are opened or closed. An example is presented in figure 14.

**Figure 14.** Basic model of a single-phase rectifier.

**Figure 13.** Simulation example of a three-phase inverter with PWM control

Three-phase AC to DC converters are widely used in many industrial power converters in order to obtain continuous voltage using a classical three-phase AC-line. These converters, when they are used alone or associated for specific applications, can present problems due to their non-linear behaviour. It is then important to be able to model accurately the behaviour of these converters in order to study their influence on the input currents waveforms and their interactions with the loads (classically inverters and AC-motors).

0 2 4 6 8 10 12 14 16 18 20

Time (ms)

0 2 4 6 8 10 12 14 16 18 20 Time (ms)

i1

Current (A)

vm vt

Several studies have shown the importance to have tools to simulate the behaviour of complex power electronics systems (Ladoux et al., 2005), (Qijun et al. 2007), (Zuniga-Haro & Ramirez, 2009) and several methods have been also presented in order to reduce the simulation time or to improve the precision. Although constant topology methods have been developed (Araujo et al., 2002), variable topology methods seem to be very suitable for

In this chapter, an original and simple method is developed to model and simulate AC-DC converters taking into account overlap phenomenon with continuous and discontinuous conduction modes using Matlab-Simulink. The diodes are assumed ideal (vd = 0 when the

If the electrical network is considered as ideal (no line inductance) and the conduction is maintained continuous, (id>0), the modelling of the converters can be realised very simply by a functional approach (commutation functions) where the switches are opened or closed.

**5. Modeling and simulation of diode rectifiers** 

v10


Voltage (V)

simulation of power-electronics converters (Terrien et al., 1999).

diode is state-on, id = 0 when the diode is state-off)

An example is presented in figure 14.

In this chapter, the proposed approach is completely different from the approach based on commutation functions. It permits to simulate accurately the commutation in the six-pulse AC-DC converter, even under unbalanced supply voltages (the influence of voltages unbalances on AC harmonic magnitudes currents has been demonstrated (de Oliveira & Guimaraes, 2007) or line impedances conditions.

a) Electrical circuit b) Simulink equivalent circuit

The overlap phenomenon and the unbalance of line impedances can be taken into account by modifying the commutation functions to correspond to the real behaviour of the rectifiers in these conditions. Indeed, the commutations are not instantaneous. Several contributions have already been proposed in scientific literature to refine the modelling of rectifiers. Most of these contributions show good simulation results but the analytical models used are complex and not reflecting precisely the real behaviour of the converter (Hu & Morrison, 1997), (Arrillaga et al., 1997). Some methods have been developed in order to model and simulate power factor corrected single-phase AC-DC converters (Pandey et al., 2004).
