Electronic power processing and conversion have interested researchers and engineers since the 17th century. Nowadays, various electrical apparatuses are used and the consumption of electrical energy is increasing year by year. However, the electrical energy has to be produced somewhere and somehow, and at the same time the amount of produced energy has to be consumed. Between the points of production and consumption different kinds of electronic power processing and conversion methods are needed. Generators, transmission lines, transformers, AC-DC rectifiers and DC-DC converters are the core components in the electric power distribution.
This thesis concentrates on the switched-mode DC-DC converters, which are usually close (in physical and conceptual sense) to the end user or application.
Switched-mode converters have replaced the linear regulators in the modern DC-DC conversion. The history of switched-mode converters dates back to the mid-60s, when the active power switches started to replace the mechanical switches and relays [1].
While the linear regulators are quite simple and have low efficiency, switched-mode converters have a nonlinear nature due to the switching action, and hence, they are more complicated to analyze and model. On the other hand, they are usually smaller,
in modeling and analyzing the dynamics and input-filter interactions are still quite relevant and important, although scientific research has been carried out for more than 30 years. Although the evolution of design and modeling of switched-mode converters, and power electronics in general, have been rapid since the 70s there are still some open questions and misunderstandings waiting for an answer and a correction.
uin
Supply system
48V
Isolated bus converter
8-16V
POL-converters 1-12V IBA
Fig. 1.1. Distributed power system.
In a modern electronic device (e.g. telecom power supply) various DC-voltage and DC-current levels are usually required. To power these devices distributed power systems/architectures (DPSs/DPAs) are widely employed [6]-[9]. An intermediate bus architecture (IBA), shown in Fig. 1.1 inside the dashed line, has become the most used DPA in new applications [10]. The IBA consists of an isolated bus converter, which produces an intermediate bus voltage (8 – 16 V) and several point-of-load (POL) converters. Usually, an EMI filter has to be placed before every power stage and a storage battery may be connected to the system after the front-end rectifier in order to provide energy to the load system during the power outages. It is obvious, that the system shown in Fig. 1.1 is complicated both from a dynamical and design viewpoint. In order to design a stable system with adequate performance margins the functioning of each building block in the system has to be known.
Each DC-DC converter in a DPS, or in any application, is always a part of an interconnected system. This actually means that the source and/or load system may
significantly affect the stability of an individual converter, and hence, the stability of the entire system. Therefore, an important and interesting question arises: How to perform the interaction analysis to ensure stability and adequate performance of the converter and the whole system? The canonical dynamical profile and interaction formalism presented in this thesis will answer this question and provide a powerful facility to analyze the performance and stability of DC-DC converters.
The terms performance, stability and also the crossover frequency or the bandwidth continuously appear in this thesis. Therefore, it is necessary to define the meaning of these terms in the scope of the thesis in order to avoid confusion. The terms performance and stability can be addressed to both the time and frequency domains.
The time domain performance is typically studied by means of a step response (i.e. a transient response in switched-mode converters), where a step change is introduced into the reference signal and the output of the system is monitored. Typical characteristics of the step response are the rise time, over shoot and settling time.
However, the classical step response analysis incorporates the disturbance signal (i.e.
the step) into the reference signal, which is typically constant and even physically unavailable in the modern converters. The transient response analysis of the switched-mode converters is typically done by introducing the step change e.g. into the load current or input voltage and the output voltage is monitored. From a dynamical viewpoint, this approach does not give the same performance characteristics as the classical step response method. The time domain performance is not discussed in this thesis, but the frequency domain performance is often considered. The frequency domain performance relates to the loop gain ( )L s of the converter. The performance of the converter is judged by means of the gain margin (GM) and phase margin (PM).
In the bode plot, the GM can be expressed as the vertical distance of the loop gain magnitude from the unity gain (i.e. 0 dB) at the frequency, where the phase is -180°.
Consequently, the PM is defined as the phase of the loop gain at the unity gain frequency added with 180°. To guarantee adequate performance the GM and PM are typically required to be at least 6 dB and 45°, respectively. The instability occurs if the GM < 0 dB or the PM < 0°. The bandwidth of the system and the (gain) crossover frequency fc are sometimes confusingly defined in power electronics. According to the system theory, the bandwidth is related to the sensitivity or complementary sensitivity function providing two different definitions of the bandwidth. The gain crossover frequency fc is naturally the frequency, where the gain of the system is unity (i.e. 0 dB). In this thesis, the gain crossover frequency fc is used, when
An extensive review of the existing methods to analyze and model the dynamics of a switched-mode converter will be given in Section 1.3. However, it is worth mentioning already at this point that most of the existing modeling and analyzing methods do not reveal the true internal dynamics of a single converter. This is mainly due to the wrong initial modeling with a resistive load, which may hide the internal dynamics of the converter. The internal dynamics for e.g. a voltage-output converter can be derived by using a voltage source at the supply side and a constant-current sink as a load. Illustrative examples of the effect of a wrong initial load will be given later.
New converter topologies and control methods are continuously developed and published in academia and industry, but the focus seems to be only on certain advantages of these new topologies. The dynamical issues and sensitivities for interactions are not usually discussed. So, usually the performance of these new topologies or control methods as a part of an interconnected system, like one shown in Fig. 1.1, is unknown.
It has been found out during the research that the true nature of switched-mode converters relates to the frequency domain. By studying certain frequency responses (i.e. transfer functions) it is easy to conclude the possible sensitivities for the load and/or supply interactions as will be shown e.g. in Chapters 3 and 4. However, only time domain simulations and measurements are usually presented e.g. in converter manufacturers’ datasheets [12]-[15]. If frequency responses are presented like in [12]
only the magnitudes are shown but not the phase plots, which are just as important as the magnitudes. Again, the performance of these commercial converters as a part of an interconnected system, like one shown in Fig. 1.1, remains unknown.
The concept of the dynamical profile of the switched-mode power supply is introduced in this thesis. It provides a straightforward method and a physical insight into the converter internal or the nominal dynamics. By analyzing the dynamical profile, the dynamical properties (i.e. load and supply sensitivities and insensitivities and control-loop stability) can be concluded by analyzing certain transfer functions in the frequency domain. Consequently, the stability and performance of a converter with known and analyzed dynamical profile as a part of the interconnected system can be easily derived. Chapters 2 and 3 will discuss more in detail the concept of dynamical profile and how to derive it.