Electrical Power Losses in a DC-DC Converter

Chapter 2

Electrical Power Losses in a DC-DC Converter

In this chapter, the steady state behavior of the devices will be discussed. The converter that will be analyzed, is the bidirectional buck-boost converter, of which the topology is shown in figure 2.1. The switches are Mosfet operating constantly at 100kHz switching frequency f s .

V _b

C

L _ind C

M bd

D bd

D _mu

M mu

D bu

M _bu

D md

M md

Figure 2.1: Topology of the bidirectional buck-boost converter’

This converter topology allows the output voltage to be higher or lower than the input volt- age, and the current direction in the inductance dictates that the converter is in motoring operation, or in braking operation. In practice the power can flow in both direction. In order to reach all operation modes, the converter operates in the follow four modes:

- Brake step-down

3

- Brake step-up - Motor step-up - Motor step-down

The following table explains the states of the switches for every mode.

modes of operation Mmd Mbd Mbu Mmu

motoring step-down switching off off off

motoring step-up on off off switching

braking step-down off switching off off

braking step-up off on switching off

Switching means that the switch operates at the constant frequency f s , on and of f means that the switch is permanently in the on state or in the off state respectively. In either motoring or regenerative braking steady-state of operations the voltage transfer ratio of the converter can be found as the product of the conversion ratios of the two converter stages in cascade. If d md is the duty ratio of the switch M md , and d mu the duty ratio of the switch M mu , then for motoring operations the converter output-to-input voltage conversion ratio can be written as:

V dc

V b

= d md

1 − d ^mu (2.1)

Where it is considered that d mu = 0 if 0 < d md < 1 and d md = 1 if 0 < d mu < 1. Analogous to equation 2.1, for regenerative braking operations the converter voltage transfer ratio can also be found.

2.1 Simulations

Several simulations were run in order to obtain the efficiency maps. They depict the progress

of the efficiency varying the output current (or load current), the voltages at the input and

at the output. Simulations are run separately for every mode of operation and the leg that

was permanently off, was neglected. One significant problem for this kind of simulation

is the speed of the software caused by the high switching-frequency (f s = 100kHz) that

imposes a very small integration step. Moreover, in order to reach the steady-state, a

simulation length larger than 30ms is also needed in the presence of a controller. For this

reason the decision to find a controller was abandoned and the technique to find the initial

values was developed. The software used for simulate the converter, are:

- Matlab simulink - Simplorer Ansoft

For a first approach at the problem the simpowersystems simulink library was used.

Simpowersystems is a library that contains several power electronics and machine models.

Two problems incurred using simpowersystems library:

• speed of the simulation

• lower accuracy of the MOSFET models

The simpowersystems MOSFET model is depicted in figure 2.2 As shown the gate-source

Figure 2.2: Simpowersystems MOSFET model

and gate-drain capacitance are neglected.

Another approach was writing the electrical equations of the circuit, and building block diagrams by simulink library (chapter 3). This method was good for the speed of the simulation, but not for the accuracy. In fact the equations are written considering simply a resistive model of the switch, hence the switching losses are neglected. In any case simulations using simulink were run for comparison and as a first approach at the problem.

Another approach was using the simplorer program. Simplorer is a software package used

to design and analyze complex technical systems. Simulation models can contain electrical

circuit components of different physical domains, block model elements, and state machine

designs. Several accurate models can be used with definable simulation levels. It is possible

to define two simulation levels for the electrical (0-level and 1-level) and three simulation

levels for the thermal behavior. The switch models use an electrical circuit as shown in figure 2.3. Selecting the electrical 0-level, only the static behavior is calculated. The charge at

Figure 2.3: Simplorer MOSFET Model

the capacitors are ignored, hence no switching behavior. In addition to the static behavior, charging and discharging of the junction and diffusion capacitance are calculated. Values of parasitic capacitors at the terminals can be defined.

2.2 Electric Losses

The losses are due to the parasitic elements associated at every electric component: the inductance, the capacitors and the switches. The energy dissipated in the inductors and in the capacitors can be calculated as R

t r·i ² dt, where r represent their leakage resistance, and i the current through them. The losses through the switches are due to the leakage resistance during the on state of the switch and to the switching losses during the turn-on and the turn-off. Figure 2.4 shows an ideal generic switching characteristic of a switch device, i s is the current flowing through it and v s the voltage across it. t ri is the current rise time, t f v

is the voltage falling time their sum is the turn-on crossover time t _c(on) = t f v + t ri . The energy dissipated in the device during t _c(on) is:

W c(on) = V of f ·I ^on ·t ^c(on)

2 (2.2)

t t

i

t

t

t

t

t

t

i

v

v

V

I

Figure 2.4: Generic switch characteristics

As the turn-on, the turn-off is studied. t rv is the voltage rise time, t f v is the current falling time, their sum is the turn-off crossover time t c(of f ) = t rv + t ri .

W _{c(of f )} = V of f ·I ^on ·t ^{c(f f )}

2 (2.3)

Hence switching losses are the sum of the above results and, considering a switching fre- quency f s , the average power can be calculated as:

P s = 1

2·f ^s ·V ^{of f} ·I ^on ·(t ^c(on) + t c(of f ) ) (2.4) Equation 2.4 shows that the switching power loss in a semiconductor switch varies linearly with f s and the switching times. In order to reduce filtering requirements, it is possible to operate at high f s , choosing a switch with short switching times [3].

Metal-oxide-semiconductor-field-effect (MOSFET), are chosen as switches because their

switching times are very short, being in the range of a few ten nanoseconds to a few

hundred nanoseconds, depending on the device type.