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BUCK-BOOST CONVERTER 1.1 Introduction: In a large number of industrial applications, it is required to convert a dc voltage to a different dc voltage level, often with a regulated output. To perform this task, a dc-dc converter is needed. A dc-dc converter directly converts a dc voltage of one level to another. It can be used to step-down (buck), or step-up (boost) a dc voltage source. Higher switching frequency would reduce the size of the filter used. 1.2 Basic Principle of Buck-Boost converter: The buck-boost is a popular non-isolated inverting power stage topology, sometimes called a step-up/down power stage. Power supply designers choose the buck-boost power stage because the required output is inverted from the input voltage, and the output voltage can be either higher or lower than the input voltage. The input current for a buck-boost power stage is discontinuous, or pulsating, because of the power switch current that pulses from zero to IL every switching cycle. The output current for a buck-boost power stage is also discontinuous or pulsating because the output diode only conducts during a portion of the switching cycle. Equivalent circuit 1.2.1 Analysis for the Switch Closed: When the switch is closed, the voltage across the inductor is The rate of change of inductor current is a constant, indicating a linearly increasing inductor current. The preceding equation can be expressed as 1.2.2 Analysis for the Switch Open: When the switch is open, the current in the inductor cannot change instantaneously, resulting in a forward-biased diode and current into the resistor and capacitor. In this condition, the voltage across the inductor is Again, the rate of change of inductor current is constant, and the change in current is 1.2.3 Inductor Design Power absorbed by the load must be the same as that supplied by the source. Average source current is related to average inductor current by Substituting for Vo derived above and solving for IL, we find For continuous current, the inductor current must remain positive. To determine the boundary between continuous and discontinuous current, Imin is set to zero resulting in 1.2.4 Output Voltage Ripple: The output voltage ripple for the buck-boost converter is computed from the capacitor current waveform. The converter consists of dc input voltage source VS, controlled switch S, inductor L, diode D, filter capacitor C, and load resistance R. With the switch on, the inductor current increases while the diode is maintained off. When the switch is turned off, the diode provides a path for the inductor current. Note the polarity of the diode that results in its current being drawn from the output. The condition of a zero volt-second product for the inductor in steady state yields VS DT Vo (1 D)T Fig 1.3 Circuit diagram of buck boost converter Hence, the dc voltage transfer function of the buck-boost converter is V D MV o VS 1 D The output voltage VO is negative with respect to the ground. Its magnitude can be either greater or smaller (equal at D = 0.5) than the input voltage as the name of the converter implies. The value of the inductor that determines the boundary between the CCM and DCM is (1 D) 2 R 2f DVo Cmin Vr Rf Lcric DESIGN PROBLEM: Vs = 24 V D = 0.4 R = 5 Ohm L = 20 uH C = 80 uF f = 100 kHz Limitation = 0 V to 36 V(by simulation) Output Voltage: Vo D VS 1 D Vo = -16Volt. Inductor Current: VsD IL = (R∗(1−D)^2 = 5.33 A Ripple current: VsDT IL= L =4.8 A ILmax= IL + ILmin=IL − ∆IL ∆IL 2 2 = 7.33 A = 2.93 A Output voltage ripple: Vo= D RCF = 0.01=1% Inductor Design: Type : Power Inductor Inductance : 20uH Maximum DC current : 7.8Amps Core Material : Powdered Iron Core Maximum DC resistance : 26mOhm OPEN LOOP SIMULATION: Fig 1.4 Open Loop Simulation of buck boost converter Fig 1.5 Simulation results CLOSED LOOP SIMULATION: Fig 1.6 Output Voltage PI CONTROLLER:(Tuning by trial and error method) Kp 0.00022 0.0005 0.0005 0.0009 0.002 0.005 0.009 0.001 0.01 Ki 15 10 1 5 8 10 5 8 5 Peak overshoot -34 -34 -34 -34 -34 -34 -34 -34 -34 Settling time 0.032 0.052 0.093 0.068 0.055 0.053 0.092 0.060 0.089 Thus if Kp, Ki values are increased or decreased Overshoot remains the same. When Ki value is increased and Kp value decreased further Settling time decreases. The above table is achieved by trial and error method. To further decrease the peak overshoot Derivative controller can be added. M-File Coding for Open loop Buck Boost Converter: function my_ode() global A D Cf Lf Vs f = 100000; R = 5; Vo = 16; Io = Vo/R; Vs = 24; D = Vo/(Vo+ Vs); L = 20E-6; C = 80E-6; Lf = L*f; Cf = C*f; A = [0 -1/Lf; 1/Cf -1/(R*Cf)]; x0 = [D*Io; Vo]; tf = 50; tic [t,X] = ode23(@bukboost,[0 tf],x0); toc; IL = X(:,1); VC = X(:,2); subplot(2,1,1),plot(t,IL),grid axis([0 tf 0 20]) title('Inductor Current') subplot(2,1,2),plot(t,VC),grid axis([0 tf 0 120]) title('Output Voltage') xlabel('cycles') end function dx = bukboost(t, x) global A D Cf Lf Vs iL = x(1); vC = x(2); B = [(vC+Vs)/Lf; -iL/Cf]; u = 0.5*(1-sign(t-fix(t)-D)); dx=A*x+B*u; end Fig 1.7 Inductor Current and Capacitor Voltage Tic starts a stopwatch timer to measure performance. The function records the internal time at execution of the tic command. Display the elapsed time with the toc function. APPLICATIONS: Battery-powered systems: In battery powered systems , where the input voltage can vary widely, starting at full charge and gradually decreasing as the battery charge is used up. At full charge, where the battery voltage may be higher than actually needed by the circuit being powered, a buck regulator would be ideal to keep the supply voltage steady. However as the charge diminishes the input voltage falls below the level required by the circuit, and either the battery must be discarded or re-charged; at this point the ideal alternative would be the boost regulator. Hence buck boost converter will be the preferred choice In Solar PV for MPPT: Buck/Boost converters make it possible to efficiently convert a DC voltage to either a lower or higher voltage. Buck/Boost converters are especially useful for PV maximum power tracking purposes, where the objective is to draw maximum possible power from solar panels at all times, regardless of the load.