EV REFRESHER

Project-1: Loss calculation for a DC_DC converter-MATLAB

Aim: - Calculating the loss that occurred in the components of the DC-DC converter [Buck converter] including the power switching device, diode, etc, and calculating the efficiency of the converter.

Non-ideal Buck Converter:

The circuit is composed of the internal resistance of the supply battery, Switching device & Diode, and low pass filter with resistive load.

Parameters for designing of Model:

Vin=50;%input vtg

Vout=25;%output vtg

L=400e-6;%Filter Inductance

C=500e-6;%Filter Capacitance

R=10;%Resistive Load

kp=0;%proportional gain

ki=0.338661;%integral gain

rL=10e-3;% LPF Inductive Resistance

rC=2e-3;%LPF Capacitive Resistance

rb=8e-3;% Battery Internal Resistance

fsw=20e3;%Switching Frequency

All the parameters were initialized in Model Properties.

Procedure:

The DC voltage source is connected to the MOSFET in series and parallel to the diode then connected to the low pass filter (RL in series and RC in parallel to the load resistance). The voltage Measurement is taken at the resistance load given to the Summation block which will generate the error with the reference of Vout. The error is fed to the PI controller and improves the duty cycle that can be fed to the Pulse generator, which will generate the pulse for the turn-on and turn-off of the MOSFET.

The duty cycle of the converter is given by: d = Vout/Vin.

The output power, that is, the product of the output voltage and current, is also the input power, by the law of conservation of energy but the loss will generate by the components in the circuit such as:

Conduction loss:

The power loss in the MOSFET is due to parasitic components (resistance, inductance, capacitance) which were in the flow of DC current in the circuit. It can be estimated from the output current, On- resistance, and on-duty cycle.

P_cond = Iout*R*d

Switching Loss:

When the MOSFET is turned ON and OFF alternately, a loss is generated during the transition of the switching. It can be estimated by

P_sw =1/2*Vin*Iout*(tr*f_sw)

Diode Loss:

When the MOSFET is a turn-off, the diode is determined by the forward direction voltage of the diode and its value becomes large. Since the diode conducts the current when the high-side MOSFET is OFF, the loss can be estimated with the following equation.

Pd = Iout × 𝑉f × (1 − d).

Loss in the capacitor:

The capacitor―including series resistance, leakage, and dielectric loss―these losses are simplified into a general loss model as equivalent series resistance (ESR). The power loss in the capacitor is calculated by multiplying the ESR by the square of the RMS value of the AC current flowing through the capacitor.

P_cap(ESR)= (I_C)²*ESR

The RMS current in the input capacitor is complex, but it can be estimated with the following equation

I_C(RMS) = I_out*sqrt[(V_in-V_out)*V_out/V_in]

Conduction loss in the inductor

The conduction loss is generated by the DC resistance (DCR) of the winding that forms the inductor. The DCR increases as the wire length increases; on the other hand, it decreases as the wire cross-section increases. If this trend is applied to the inductor parts, the DCR increases as the inductance value increases and decreases as the case size increases.

The conduction loss of the inductor can be estimated as

P_L(DCR)=I_OUT² *DCR

𝐼_𝑂𝑈𝑇: Output current [𝐴]

𝐷𝐶𝑅: Inductor direct current resistance [Ω]

The Simulation Model of Non-ideal Buck Converter:

Blocks used for modeling

1. DC Voltage source
2. MOSFET
3. Diode
4. series RLC branch (Rb, RL, RC, R_load)
5. Voltage and current measurement block
6. PWM generator
7. Display & Scope
8. Bus selector
9. Power-gui
10. Constant
11. Sum
12. PI controller
13. Pulse Generator DC-DC

V&I_OUT: -

Vout=25V, Iout=2.5A

Diode Forward Voltage (Vf): -

Vf=3.242 V

Duty Cycle(d):

d=0.5107

Rise Time(tr): -

Tr=tr2-tr1 = = (1.0005048-1.0005) *10^-3= 4.8e-09

Losses and Performance Calculations: -

Losses and Performance Calculator	Loss In watts			Measurements	Values
Conduction loss in MOSFET P_cond = Iout*R*d	12.7675			Vin	50
Switching Loss: P_sw =1/2*Vin*Iout*(tr*f_sw)	6.00			Vout	25
Diode Loss: Pd = Iout × Vf × (1 − d).	4.183515			Iout	2.5
Loss in the capacitor: P_cap(ESR)= (I_C)^2*ESR	0.16			F_sw	2.00E+07
IC(RMS) = Iout*sqrt[(Vin-Vout)*Vout/Vin] in (A)		8.838835		Tr	4.80E-09
Conduction loss in the inductor: PL(DCR)=IOUT^2 *DCR	0.06			d	0.5107
Power_Loss= P_cond+P_sw+Pd+P_cap(ESR)+PL_DCR	23.17			Vf	3.42
Power_ Out Vout*Iout	62.5			ESR	2.00E-03
Power_In= Power_out+Power_loss	85.67			DCR	1.00E-02
Efficency	72.95%			R	10

Conclusion:

The designed Non-Ideal buck converter produced 23.17 W of power loss with 72.95% performance efficency.

Note:-

Excel calculator and model file attached.