11 Single-phase Controlled Rectifiers José Rodríguez, Ph.D., Pablo Lezana, Samir Kouro, and Alejandro Weinstein Department of Electronics, Universidad Técnica Federico Santa María, Valparaíso, Chile 11.1 Introduction .......................................................................................... 183 11.2 Line-commutated Single-phase Controlled Rectifiers ..................................... 183 11.2.1 Single-phase Half-wave Rectifier • 11.2.2 Bi-phase Half-wave Rectifier • 11.2.3 Single-phase Bridge Rectifier • 11.2.4 Analysis of the Input Current • 11.2.5 Power Factor of the Rectifier • 11.2.6 The Commutation of the Thyristors • 11.2.7 Operation in the Inverting Mode • 11.2.8 Applications 11.3 Unity Power Factor Single-phase Rectifiers .................................................. 192 11.3.1 The Problem of Power Factor in Single-phase Line-commutated Rectifiers • 11.3.2 Standards for Harmonics in Single-phase Rectifiers • 11.3.3 The Single-phase Boost Rectifier • 11.3.4 Voltage Doubler PWM Rectifier • 11.3.5 The PWM Rectifier in Bridge Connection • 11.3.6 Applications of Unity Power Factor Rectifiers References ............................................................................................. 203 11.1 Introduction This chapter is dedicated to single-phase controlled rectifiers, which are used in a wide range of applications. As shown in Fig. 11.1, single-phase rectifiers can be classified into two big categories: (i) Topologies working with low switching frequency, also known as line commutated or phase controlled rectifiers. (ii) Circuits working with high switching frequency, also known as power factor correctors (PFCs). Line-commutated rectifiers with diodes, covered in a pre- vious chapter of this handbook, do not allow the control of power being converted from ac to dc. This control can be achieved with the use of thyristors. These controlled rectifiers are addressed in the first part of this chapter. In the last years, increasing attention has been paid to the control of current harmonics present at the input side of the rectifiers, originating from a very important development in the so-called PFC. These circuits use power transistors work- ing with high switching frequency to improve the waveform quality of the input current, increasing the power factor. High power factor rectifiers can be classified in regenerative and non-regenerative topologies and they are covered in the second part of this chapter. 11.2 Line-commutated Single-phase Controlled Rectifiers 11.2.1 Single-phase Half-wave Rectifier The single-phase half-wave rectifier uses a single thyristor to control the load voltage as shown in Fig. 11.2. The thyristor will conduct, on-state, when the voltage v T is positive and a firing current pulse i G is applied to the gate terminal. The control of the load voltage is performed by delaying the firing pulse by an angle α. The firing angle α is measured from the position where a diode would naturally conduct. In case of Fig. 11.2 the angle α is measured from the zero-crossing point of the supply voltage v s . The load in Fig. 11.2 is resistive and therefore the current i d has the same waveform of the load voltage. The thyristor goes to the non-conducting condition, off-state, when the load voltage, and consequently the current, reaches a negative value. The load average voltage is given by V d α = 1 2π  π α V max sin(ωt )d (ωt ) = V max 2π (1 + cos α) (11.1) where V max is the supply peak voltage. Hence, it can be seen from Eq. (11.1) that changing the firing angle α controls Copyright © 2007, 2001, Elsevier Inc. All rights reserved. 183 DOI: 10.1016/B978-0-12-382036-5.00011-2