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- 1. MAJOR ASSIGNMENT Buck Boost Converter SECTION: G-2 (MECHANICAL ENGG.) CAREER POINT UNIVERSITY KOTA, RAJASTHAN Prepared by Prepared for Vinit Kumar Chauhan Mr.Somesh Sir Course: B.Tech(6th sem.) UID: K10972
- 2. ABSTRACT A study on the properties and control of a promising circuit topology for a DC-DC buckboost power converter is presented. The circuit contains four transistors operated synchronously in couples. We propose a set of mathematical models to describe this circuit, and an approach to determine the behavior of the losses occurring inside of it. These are then combined in order to achieve a control scheme that drives the circuit while minimizing said losses. The control strategy proposed here is based on a combined feedback (MPC) and feedforward action. Control performance parameters such as disturbances rejection capability have been investigated as well. INTRODUCTION once provided by the diode - i.e. current rectification - is now undertaken by a rectifying transistor, typically a MOSFET. Such rectification improves efficiency, thermal performance, power densities, manufacturability, reliability as well as having typically faster switching transients, and decreases the overall system cost for power supplies (Selders 2003). These performance increases are mainly due to the fact that the on-resistance of MOSFETs, RDS;on, can be reduced either by increasing the size of the die or by paralleling discrete devices, while the forward voltage-drop across diodes cannot be lowered under a certain (physically imposed) limit; this motivates the choice of using synchronous rectifiers in the circuit topology studied for this project. The main objective of this project can now be stated as follows: by exploiting these two degrees of freedom we will be able to affect the state of the circuit; thus, many internal states will lead to the same output voltage, and the main task will be to choose among all these possibilities the one that will lead to the least possible power losses - i.e. to the most efficient way of driving the circuit. This has been achieved as follows: first, different models of the circuit have been developed for different purposes, see next Chapter. After that, a thorough study of the losses inside the circuit has been conducted using some of these models. Based on the study of the losses, the design of a control that drives the circuit while accounting for losses has been done, and conclusive chapter, where possible outlooks will be discussed and a summary of this project will be given.
- 3. Basic Analytical Models: Full-Buck The circuit can be considered equivalent to a synchronous buck converter if the third switch T3 is always turned on, i.e. if d2 = 1. Apreliminary study of the ”buck mode” is useful to show the general approach which is going to be used for more complex modes. It turns out in fact that this version is the most attractive one as a starting point for a study because the differential equations describing the states of the circuit coming from the averaging method are linear by nature. This makes the successive development of a control for this mode of the circuit straight-forward. The procedure is the following: first, consider the case where T1 is on, and T2 is off; applying Kirchhoff Voltage Law (KVL) and Kirchhoff Current Law (KCL) to the circuit depicted in Figure 2.1 leads to the following equations for the states: Then, consider the complementary case where T1 is off, and T2 is on; the same equations hold basically, if vin is taken to be zero. Again, applying KCL and KVL leads to:
- 4. Power Losses Our objective is to drive the circuit while minimizing the losses occurring inside of it. In order to do this, models for the behavior of these losses are necessary; Losses Description There are two different types of losses occurring inside the circuit: Conduction Losses (PConduction) and Switching Losses (PSwitching); in the following, these two types of losses are going to be shortly described. Conduction Losses These are losses of resistive type, and, for the particular circuit that is investigated, they are produced because of current flowing through the following resistive media: MOSFETs’ channel resistance RDS;on MOSFETs’ body diode Capacitance’s ESR (Equivalent Series Resistance) Inductance’s ESR Switching Losses The mechanisms involved in the production of switching losses are more complicated than the previous ones. They are produced by the action of turning on and off active devices on the power’s path, therefore they only happen at discrete times ”tj” (where j indexes all the times at which switchings of a given MOSFET occur) and for a short period; they occur under the following circumstances (Mohanet al. n.d.): switching of power currents (”turning on and off currents in the presence of voltage”) parasitic drain capacitance charge and discharge gate drive losses body diode reverse recovery
- 5. MODELING POWER LOSSES because of this, if the current iL is positive (flowing from the input stage to the output stage), then switching losses will occur only at switches T1 and T4. Conversely, if iL is negative, then switching losses will occur in switches T2 and T3. On a side note, it can be noted that since these losses occur at switching times, the more switchings there are, the higher the switching losses will be (if the same MOSFETs are used), i.e. switching losses grow proportionally to the switching frequency. Therefore, on one hand, switching frequency should not be chosen to be arbitrarily high. But on the other hand, switching frequency should not be chosen too low either because that would cause higher ripples on the output voltage. Also, it is of critical importance to note at this point that during the simulations described further in this chapter, the magnitude of the losses is estimated using these very equations. But since these equations only give results that are proportional to the exact values, their shape will describe the general behavior of the losses properly, but their magnitude will need to be corrected by an adequate multiplicative correction constant. This constant will strongly depend on the choice of components that is going to be made. This aspect is discussed more in detail in the next Section. Controller Design Based on the research done on the models in Chapter 2 and the Losses in Chapter3, it is now possible to start developing an efficient control for the plant. As a reminder, our task is to control the duty cycles of each pair of transistors and their phase, so as to ensure: First and most important: reaching of and stabilizing around a given output voltage demand; reaching the target steady state should happen in the desired manner, i.e. The controller needs to handle transients properly; The controller also needs to be able to reject disturbances (usually encountered on the load and on the input voltage source vin); while doing all this, the controller (in the full buck-boost mode) needs to choose among the infinite possibilities of inputs, that would satisfy the above conditions, those that will cause the least losses.
- 6. Basic Control Strategies Buck, the Simplest Mode As discussed in Chapter 2.3.1, the model obtained with the averaging technique is linear. There is only one variable being controlled (d1) and there is no optimization of controls towards least losses. This is why a simple feedback approach (as opposed to a combined feedforward and feedback approach, as discussed later) is enough to control this scheme. Buck-Boost Operation The buck-boost implementation is similar to the boost one in that non-linearity is still present. Other than that, it turns out that exploiting the possibilities given by the full buck-boost operation requires additional care because: There are now multiple inputs Control actions also need to drive the plant while ensuring least possible losses Results It can be argued that if this precalculated lookup table does indeed contain the best values the plant (circuit) can be driven at steady state, then the contribution from the MPC feedback can be avoided. This is of course not the case: first, it is clear that the contribution from the MPC boosts the performance during the initial transient. Furthermore, a feedback action is always desired in any control scheme, in order to ensure the ability to reject disturbances and model uncertainties. The two contributions to the u signal coming from the feedback and from the feedfoward part can be seen in Figure 4.10. As it can be seen, the MPC supplies the plant with a contribution different than zero only during the transient. As soon as the transient has settled, it contribution goes to zero and stays there; this is always the case as long as no disturbances or other external influences affect the circuit; if disturbances are indeed applied, then the MPC control is going to counter those and its contribution is going to be different than zero. A typical disturbance rejection done by the controller can be seen in the blue bottom curve depicts the perturbation (in percentage) affecting the input voltage vin, while in the upper graph, the red curve shows how this perturbation affects the output voltage if no feedback action is taken, and the green one shows the output if rejections are countered by the MPC.
- 7. The resulting output start-up performance for a set of different output references can be seen in notice that the controller is indeed able to drive the circuit both in its ”buck” mode and ”boost” mode, as specified in the objectives for this project. Further, notice that the control is indeed able to properly drive the plant also towards steady states different than those around which the models were linearized, thus showing its ”well” behavior. Conclusion The present work is a study on the circuit depicted in Figure 1.2 which is used to achieve DC-DC power conversion. In the first part of the work (Chapters 1-3), different models for its behavior have been developed, including a state-space averaged model and an hybrid one. Based on these models simulations have been conducted in order to assess the losses occurring inside of it. These simulations reveal that it is in general not possible to drive the circuit while minimizing simultaneously both conduction and switching losses. Rather, in order to drive the circuit in the most efficent way, an optimizedbalance between these two losses needs to be made. Further, this balance depends on the specific choice of components used. In the second part of the work (Chapter 4), for a specific choice of components, the implementation of a controller for this circuit is discussed. The controller has been designed as working on the combined action of a precalculated look-up table (feedforward action) and a Model Predictive Control (MPC) based feedback action. The abilty to drive the circuit both in its boost as well its buck modes and its noise rejection capabilty are the performance benchmarks for this controller which have been studied. Recommended extensions to this work include the refinement of the models to account for parasitics and non-ideal behaviours, so as to enable a subsequent controller implementation based solely on MPC, and a more accurate evaluation of thecontroller’s stabilization capabilties. Bibliography Cuk, S. and Middlebrooks, R.: n.d., Modeling, analysis and design of switching converters. Erickson, R.: n.d., Dc-dc power converters, Article in Wiley Encyclopedia of Electrical and Electronics Engineering . Frehner, P.: 2007, Control of a buck-boost power converter, Semester Thesis, IFA, ETHZ .
- 8. IfA,W.: n.d., http://control.ee.ethz.ch/ hybrid/control.php, Institut fr AutomatikWebsite, IFA, ETHZ . Lin, Y.-C. and Liaw, D.-C.: 2006, A method using an averaging technique for the analysis and evaluation of real quasi-resonant converters, IEICE TRANS. ELECTGRON. . Mohan, N., Undeland, T. M. and Robbins,W. P.: n.d., Power electronics: Converters, applications, and design. Note, A.: n.d., Synchronous rectification aids low-voltage power supplies. Plesnik, M.: 2006, Use of the state-space averaging technique in fast steady-state simulation algorithms for switching power converters, IEEE CCECE/CCGEI . Selders, R.: 2003, Synchrnous rectification in high-performance power converter design, POWER designer . Torrisi, F. D., Bemporad, A., Bertini, G., Hertach, P., Jost, D. and Mignone, D.: 2002, Hysdel

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