The power converter problem can be considered a multidisciplinary problem comprising the coupling between an electrical subsystem and a loss subsystem. An optimal power stage design is essential to the development of quality power converter. The power stage design dominates the overall efficiency, size, and weight of the power converter. A schematic of the power stage of the power converter is shown in the following figure. The geometry of the transformer core is shown in the following figure.
The objective of the problem is to minimize the weight and yet maintain a high efficiency for the power stage subject to several constraints.
The objective of the power converter problem is to minimize the weight.
The problem consists of six design variables and
twelve state variables of which four define constraints.
The design variables and their lower bounds are:
The state variables are described by the following equations:
There are several constants which complete the description of the power converter.
Name | Description | Value |
EI | Input Voltage (nominal) | 3.25 e2 |
EIMIN | Input Voltage (minimum) | 2.25 e2 |
EIMAX | Input Voltage (maximum) | 4.25 e2 |
EO | Output Voltage | 5.0 |
PO | Output Power | 5.0 e2 |
POMIN | Output Power (minimum) | 0.5 e2 |
VR | Output Ripple Spec. | 5.0 e-2 |
K1 | Aspect Ratio, center leg depth/width | 1.0 |
K2 | Aspect Ratio, window height/width | 2.0 |
XN | Transformer Turns Ratio | 16 |
PXFR | Transformer Related Losses | 0.0 |
FR | Switching Ripple Frequency | 0.1 e6 |
FC | Winding Pitch Factor | 1.9 |
FW | Window Fill Factor | 0.4 |
WBOB | Bobbin Thickness | 2.0 e-3 |
BSP | Maximum Flux Density | 0.3 |
DI | Core Density | 0.78 e4 |
DC | Copper Density | 0.89 e4 |
DK5 | Capacitor Density | 25.0 |
KH | Heat Sink Density | 88.0 |
RO | Copper Resistivity | 1.724 e-8 |
RCK | ESR Time Constant | 0.3 |
CK | ESR Time Constant | 0.1 e-3 |
VD | Diode Conduction Drop | 0.65 |
TND | Diode Turn-on Time | 1.0 e-7 |
TFD | Diode Turn-off Time | 1.0 e-7 |
TRE | Diode Reverse Recovery Time | 0.5 e-7 |
VST | Transistor Saturation Drop | 0. |
VBE | Transistor Base-Emitter Drop | 0. |
GAIN | Transistor Current Gain | 0. |
TSR | Transistor Turn-on Rise Time | 1.0 e-7 |
TSF | Transistor Turn-off Fall Time | 1.0 e-7 |
RDS | MOSFET On Resistance | 0.5 |
CGS | MOSFET Gate-Source Capacitance | 8.0 e-9 |
COSS | MOSFET Output Capacitance | 4.0 e-10 |
VGS | MOSFET Gate-Source Voltage | 10. |