2020 | Book

# Fundamentals of Power Electronics

Authors: Prof. Robert W. Erickson, Dr. Dragan Maksimović

Publisher: Springer International Publishing

2020 | Book

Authors: Prof. Robert W. Erickson, Dr. Dragan Maksimović

Publisher: Springer International Publishing

Fundamentals of Power Electronics, Third Edition, is an up-to-date and authoritative text and reference book on power electronics. This new edition retains the original objective and philosophy of focusing on the fundamental principles, models, and technical requirements needed for designing practical power electronic systems while adding a wealth of new material. Improved features of this new edition include: new material on switching loss mechanisms and their modeling; wide bandgap semiconductor devices; a more rigorous treatment of averaging; explanation of the Nyquist stability criterion; incorporation of the Tan and Middlebrook model for current programmed control; a new chapter on digital control of switching converters; major new chapters on advanced techniques of design-oriented analysis including feedback and extra-element theorems; average current control; new material on input filter design; new treatment of averaged switch modeling, simulation, and indirect power; and sampling effects in DCM, CPM, and digital control.

Fundamentals of Power Electronics, Third Edition, is intended for use in introductory power electronics courses and related fields for both senior undergraduates and first-year graduate students interested in converter circuits and electronics, control systems, and magnetic and power systems. It will also be an invaluable reference for professionals working in power electronics, power conversion, and analog and digital electronics.

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Abstract

The field of power electronics is concerned with the processing of electrical power using electronic devices [1‐7]. The key element is the switching converter, illustrated in Fig. 1.1. In general, a switching converter contains power input and control input ports, and a power output port. The raw input power is processed as specified by the control input, yielding the conditioned output power.

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Abstract

In the previous chapter, the buck converter was introduced as a means of reducing the dc voltage, using only nondissipative switches, inductors, and capacitors. The switch produces a rectangular waveform v
_{s}(t) as illustrated in Fig. 2.1. The voltage v
_{s}(t) is equal to the dc input voltage V
_{g} when the switch is in position 1, and is equal to zero when the switch is in position 2. In practice, the switch is realized using power semiconductor devices, such as transistors and diodes, which are controlled to turn on and off as required to perform the function of the ideal switch. The switching frequency f
_{s}, equal to the inverse of the switching period T
_{s}, generally lies in the range of 1 kHz–1 MHz, depending on the switching speed of the semiconductor devices. The duty ratio D is the fraction of time that the switch spends in position 1, and is a number between zero and one. The complement of the duty ratio, D
^{′}, is defined as (1 − D).

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Abstract

Let us now consider the basic functions performed by a switching converter, and attempt to represent these functions by a simple equivalent circuit. The designer of a converter power stage must calculate the network voltages and currents, and specify the power components accordingly. Losses and efficiency are of prime importance. The use of equivalent circuits is a physical and intuitive approach which allows the well-known techniques of circuit analysis to be employed. As noted in the previous chapter, it is desirable to ignore the small but complicated switching ripple, and model only the important dc components of the waveforms.

Abstract

We have seen in previous chapters that the switching elements of the buck, boost, and several other dc–dc converters can be implemented using a transistor and diode. One might wonder why this is so, and how to realize semiconductor switches in general. These are worthwhile questions to ask, and switch implementation can depend on the power processing function being performed. The switches of inverters and cycloconverters require more complicated implementations than those of dc–dc converters. Also, the way in which a semiconductor switch is implemented can alter the behavior of a converter in ways not predicted by the ideal-switch analysis of the previous chapters—an example is the discontinuous conduction mode treated in the next chapter. The realization of switches using transistors and diodes is the subject of this chapter.

Abstract

When the ideal switches of a dc–dc converter are implemented using current-unidirectional and/or voltage-unidirectional semiconductor switches, one or more new modes of operation known as discontinuous conduction modes (DCM) can occur. The discontinuous conduction mode arises when the switching ripple in an inductor current or capacitor voltage is large enough to cause the polarity of the applied switch current or voltage to reverse, such that the current- or voltage-unidirectional assumptions made in realizing the switch with semiconductor devices are violated. The DCM is commonly observed in dc–dc converters and rectifiers, and can also sometimes occur in inverters or in other converters containing two-quadrant switches.

Abstract

We have already analyzed the operation of a number of different types of converters: buck, boost, buck–boost, Ćuk, voltage-source inverter, etc. With these converters, a number of different functions can be performed: step-down of voltage, step-up, inversion of polarity, and conversion of dc to ac or vice-versa.

Abstract

Converter systems invariably require feedback. For example, in a typical dc–dc converter application, the output voltage v(t) must be kept constant, regardless of changes in the input voltage v
_{g}(t) or in the effective load resistance R. This is accomplished by building a circuit that varies the converter control input [i.e., the duty cycle d(t)] in such a way that the output voltage v(t) is regulated to be equal to a desired reference value v
_{ref}. In inverter systems, a feedback loop causes the output voltage to follow a sinusoidal reference voltage. In modern low-harmonic rectifier systems, a control system causes the converter input current to be proportional to the input voltage, such that the input port presents a resistive load to the ac source. So feedback is commonly employed.

Abstract

Sections 8.1 to 8.3 discuss techniques for analysis and construction of the Bode plots of the converter transfer functions, input impedance, and output impedance predicted by the equivalent circuit models of Chap. 7. For example, the small-signal equivalent circuit model of the buck–boost converter is illustrated in Fig. 7.18c. This model is reproduced in Fig. 8.1, with the important inputs and terminal impedances identified.

Abstract

In all switching converters, the output voltage v(t) is a function of the input line voltage v
_{g}(t), the duty cycle d(t), and the load current i
_{load}(t), as well as the converter circuit element values. In a dc–dc converter application, it is desired to obtain a constant output voltage v(t) = V , in spite of disturbances in v
_{g}(t) and i
_{load}(t), and in spite of variations in the converter circuit element values.

Abstract

Magnetics are an integral part of every switching converter. Often, the design of the magnetic devices cannot be isolated from the converter design. The power electronics engineer must not only model and design the converter, but must model and design the magnetics as well. Modeling and designing of magnetics for switching converters is the topic of Part III of this book.

Abstract

This chapter treats the design of magnetic elements such as filter inductors, using the geometrical constant (K
_{g}) method. With this method, the maximum flux density B
_{max} is specified in advance, and the element is designed to attain a given copper loss.

Abstract

In the design methods of the previous chapter, copper loss P
_{cu} and maximum flux density B
_{max} are specified, while core loss P
_{fe} is not specifically addressed. This approach is appropriate for a number of applications, such as the filter inductor in which the dominant design constraints are copper loss and saturation flux density. However, in a substantial class of applications, the operating flux density is limited by core loss rather than saturation. For example, in a conventional high-frequency transformer, it is usually necessary to limit the core loss by operating at a reduced value of the peak ac flux density ΔB.

Abstract

Part IV of this text develops analytical tools needed to understand and design larger power electronic systems. It builds on the basic modeling and analysis techniques developed in Part II to analyze and simulate complex feedback circuits, including those having input EMI filters, current-mode control, or digital control.

Abstract

Circuit averaging is another well-known technique for derivation of converter equivalent circuits. Rather than averaging the converter state equations, with the circuit averaging technique we average the converter waveforms directly. All manipulations are performed on the circuit diagram, instead of on its equations, and hence the circuit averaging technique gives a more physical interpretation to the model. Since circuit averaging involves averaging and small-signal linearization, it is equivalent to state-space averaging. However, in many cases circuit averaging is easier to apply, and allows the small-signal ac model to be written almost by inspection. The circuit averaging technique can also be applied directly to a number of different types of converters and switch elements, including phase-controlled rectifiers, PWM converters operated in discontinuous conduction mode or with current programming, and quasi-resonant converters—these are described in later chapters.

Abstract

So far, we have derived equivalent circuit models for dc–dc pulse-width modulation (PWM) converters operating in the continuous conduction mode. As illustrated in Fig. 15.1, the basic dc conversion property is modeled by an effective dc transformer, having a turns ratio equal to the conversion ratio M(D). This model predicts that the converter has a voltage-source output characteristic, such that the output voltage is essentially independent of the load current or load resistance R. We have also seen how to refine this model, to predict losses and efficiency, converter dynamics, and small-signal ac transfer functions. We found that the transfer functions of the buck converter contain two low-frequency poles, owing to the converter filter inductor and capacitor. The control-to-output transfer functions of the boost and buck–boost converters additionally contain a right half-plane zero. Finally, we have seen how to utilize these results in the design of converter control systems.

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Abstract

Middlebrook’s Extra Element Theorem (EET) is a powerful technique of Design-Oriented Analysis that aids in the analysis of complex circuits and systems, with the goal of deriving tractable equations that are useful for design. As with the Feedback Theorem of Chap. 13, it is based on linear superposition and the null double injection analysis technique.

Abstract

It is nearly always required that a filter be added at the power input of a switching converter. By attenuating the switching harmonics that are present in the converter input current waveform, the input filter allows compliance with regulations that limit conducted electromagnetic interference (EMI). The input filter can also protect the converter and its load from transients that in the input voltage v
_{g}(t), thereby improving the system reliability.

Abstract

So far, we have discussed duty ratio control of PWM converters, in which the converter output is controlled by direct choice of the duty ratio d(t). We have therefore developed expressions and small-signal transfer functions that relate the converter waveforms and output voltage to the duty ratio. This direct duty ratio control is sometimes called voltage mode control, because the equilibrium output voltage is approximately proportional to the duty cycle in CCM.

Abstract

Digital control methods and digital controllers based on general-purpose or dedicated microcontrollers, digital signal processors (DSP’s), or programmable logic devices have been widely adopted in power electronics applications at relatively high-power levels, including motor drives or grid-tied three-phase inverters and rectifiers. In these applications, digital control offers clear technical and economic advantages in addressing complex control, management, and monitoring tasks.

Abstract

Rectification used to be a much simpler topic. A textbook could cover the topic simply by discussing the various circuits, such as the peak-detection and inductor-input rectifiers, the phase-controlled bridge, polyphase transformer connections, and perhaps multiplier circuits. But recently, rectifiers have become much more sophisticated, and are now systems rather than mere circuits. They often include pulse-width modulated converters such as the boost converter, with control systems that regulate the ac input current waveform. So modern rectifier technology now incorporates many of the dc–dc converter fundamentals.

Abstract

To obtain low ac line current THD, the passive techniques described in the previous chapter rely on low-frequency transformers and/or reactive elements. The large size and weight of these elements are objectionable in many applications. This chapter covers active techniques that employ converters having switching frequencies much greater than the ac line frequency. The reactive elements and transformers of these converters are small, because their sizes depend on the converter switching frequency rather than the ac line frequency.

Abstract

Part VI of this text deals with a class of converters whose operation differs significantly from the PWM converters covered in Parts I to V. Resonant power converters [272, 295‐329] contain resonant L–C networks whose voltage and current waveforms vary sinusoidally during one or more subintervals of each switching period. These sinusoidal variations are large in magnitude, and hence the small-ripple approximation introduced in Chap. 2 does not apply.

Abstract

In addition to the resonant circuits introduced in Chap. 22, there has been much interest in reducing the switching loss of the PWM converters of the previous chapters. Several of the more popular approaches to obtaining soft switching in buck, boost, and other converters are discussed in this chapter.