# Test Suite Problem 2.5 - Description

## Power Converter Problem

### References

Power Converter Page

### Origin:

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.

### Problem Size:(see definition of terms)

• Number of continuous design variables: 6

• Number of discrete or integer design variables: none

• Lower bounds on design variables: yes

• Upper bounds on design variables: no

• Number of equality constraints: 0

• Number of inequality constraints: 4

• Number of fixed parameters: 2

• Number of subsystems: 2

• List of disciplines: electrical

### Problem Definition:

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.

### Solution Strategies:

Solution using CONMIN with Quasi-Analytic Gradients
The problem was solved using the method of feasible directions and a line search method as implemented by the CONMIN code. Gradient information was obtained by automatic differentiation of the system analysis code using ADIFOR.

Describe your strategy and computational experience (in HTML form preferably). It will be included here. Send code if you'd like.

### Source Code Availability:

• The source code for the solution of the system described above is available.

• All source code is in FORTRAN.

### References:

• R. B. Ridley, C. Zhou and F. C. Y. Lee, "Application of Nonlinear Design Optimization for Power Converter Components", IEEE Transactions on Power Electronics, Vol.5, No. 1, January 1990.

• G. Kott, G. A. Gabriele and J. Korngold, "Application of Multidisciplinary Design Optimization To The Power Stage Design Of A Power Converter", ASME, Advances In Design Automation, Vol. 2, 1993.

• J. E. Renaud, "Design Driven Concurrent Optimization in System Design Problems Using Second Order Sensitivities", International Conference on Engineering Design , August 1993.