In the present work, three different methods for obtaining the DC response for modeling practical DC-DC buck and boost converters operating in continuous conduction mode (CCM) are demonstrated using MATLAB/Simulink. The method of selection for inductor, diode, and MOSFET for a DC-DC converter is discussed in detail. The governing equations for the non-ideal converters were derived using volt-sec and amp-sec balance equations. Mathematical modeling of basic converters was carried out using ‘commonly used blocks' reducing the dependence on SimPower System tool box in Simulink. The non-ideal parameters in the converter caused a drastic variation in the duty cycle and output voltage which in turn had an adverse effect on the efficiency. The transients in output voltages and inductor currents were observed. In addition, a Li ion polymer battery was mathematically modeled. Accurate battery modeling for pulse charging was proposed. A comparative analysis of 1, 2, …, 5 RC pair/s modeling of the battery was presented.
TopIntroduction
A converter is a device used to transform electrical power from one form to another. Converters can be of various types, such as AC to AC, AC to DC, DC to DC and DC to AC. Among DC-DC converters, switched mode converters and linear regulators are more commonly used. Since the latter has the increased I2R losses, the former is preferred. Among switched mode converters, several types, categorized as isolated and non-isolated can be used as LED-drivers. These converters are differentiated based on voltage levels and isolation at the input. Buck, Boost, Buck-Boost, CUK and SEPIC are some of the non-isolated / Transformerless converters. Isolated converters are further classified as Unidirectional (e.g., flyback and forward) and Bi-directional (e.g., Push-pull, full bridge and half-bridge) Isolated converters possess a transformer at the input side, which offers the advantage of isolation against short circuits and large surges. Hence, the load which is downstream of the transformer would be protected. These transformers operate at high frequencies (typically kHz) and hence the design of such transformers is a challenge. The flyback and forward converters are the isolated versions of buck-boost and buck converters.
The methodology for obtaining the average current control for DC-DC converters in ideal case operating in CCM is shown using State Space Averaging Technique. It was observed from the frequency response of the transfer functions that ideal buck and boost converters showed high stability. The analysis was carried out using MATLAB software and the code is presented. The basics of peak current mode (PCM) control and its advantages are discussed. The importance of estimating core temperature (Tc) in a Battery Management System (BMS) is shown.
DC-DC converters play a vital role in the design of Electric Vehicle (EV) charging systems, LED drivers and power supply units for critical loads like micro-processors. The converters show different behaviors during ideal and non-ideal scenarios.
The analyses for variety of DC –DC converters have been performed in the recent years. In (Canalli, 1996), a generalized approach for obtaining the large signal averaged model for converters is proposed. The behavioral model proposed provides results independent of the operation of the converter (CCM / DCM). The paper provides the modeling using LTSpice and experimental validations for CCM and DCM operations of buck, boost and SEPIC converters. The factor used to differentiate the operations was duty cycle, µ. µ for DCM was higher than that of CCM.
The behavior of the AC response to the converters can be modeled using various methods viz,. (a) State Space Averaging (b) Small signal model and (c) Circuit Averaging Techniques.
In state space averaging technique, the volt sec and amp sec balance equations for inductors and capacitors are used to obtain the open loop transfer function for the converters. In (Moussa & Morris, 1990), the necessary equations required for the modeling are provided for second order converters. The advantage is that the DC response in addition to small signal modeling equations can be obtained.
The small signal model provides the AC equivalent circuit in which the non-linear equations are converted into linear equations. The volt-sec and amp-sec balance equations for the converter are derived and are perturbed. Later, the system is linearized by re-arranging the terms and the transfer functions of output voltage to the duty ratio (Gvd) is derived.
The circuit averaging of any converter involves three major steps viz,. (a) Separate the switch network from the converter and define the ports (b) Sketch the waveform of the switch current and voltage waveforms and average it and (c) Simplification of the equations and draw the equivalent switch network. In (Cuk & Middlebrook, 1979), a generalized method for modeling any three-state (Input voltage, output voltage & duty cycle) switching converter operating in the DCM was presented and the experimental validation for a Buck Boost converter as carried out. This also provided the design of closed loop transfer functions using P, PI, PD and PID controllers for constant voltage, constant current, peak current and average current control techniques for CCM and DCM operations
In reality, the converters possess ESR (Equivalent Series Resistance) for the inductor and capacitor. This causes increase in the conduction losses. To achieve desired voltage at load, increased duty ratio is essential. In (Erickson & Dragon, 2007), the authors showed that the switching losses are much higher than that of the conduction. In (Czarkowski & Kazimierczuk, 1993), Bilinear large-signal, linear, dc, and small-signal circuit models of the PWM buck converter for a buck converter operating in CCM involving switching losses were shown.