Virtual Prototyping for Power Electronics

Virtual Prototyping for Power Electronics Cross-Theme Project (Design Tools and Modelling) EPSRC Centre for Power Electronics Dr Xibo Yuan 5 th July 2016

Contents Background Challenges and approaches Accuracy and speed T z2 Results and thoughts T x1 T y 2 T y1 T x 2 T z1 T y1 Rx1 R x 2 Tx1 T x 2 T z1 R y1 R x3 R z1 R y2 T y 2 R y3 q C R z3 R z2 T z2

Background What is the ideal layout of the system? Highly-integrated and high-power-density converters Design Optimization Google Little Box Challenge --- Bristol Entry

Background What is the optimal geometry of components? Inductors Capacitors

What do we normally simulate? 500 Two-level Converter Line voltage (V) 0 Control, modulation, voltage, current, etc Starter/Generator Current (A) -500 0.984 0.985 0.986 0.987 0.988 0.989 100 50 0-50 -100 0.984 0.9845 0.985 0.9855 0.986 0.9865 Time (s) MATLAB/Simulink, Pspice, Saber, Simplorer, PLECS, Ansys, etc What we need: A comprehensive modelling and design tool taking into account the physical design optimization in terms of geometry and arrangement of components.

Hardware Prototyping vs. Virtual Prototyping Time-consuming, longer development cycle and higher cost. Incremental development, stemming from prior experience of similar converters (e.g. for geometry and layout). Repetition and iteration are normally required and the design is therefore often sub optimal.

The Importance of Virtual Prototyping Automated process, the converter performance can be predicted and optimised. Quantified and optimized in an early design stage and the cost and time for the final hardware test will be significantly reduced. Allows for measuring the internal signals which are difficult to approach in a highly integrated hardware. The geometry and layout optimization is very important in highfrequency, high-density and highly-integrated design.

Multi-domain Problem Electrical Magnetic Thermal Mechanical

Full Finite Element Analysis (FEA) Time consuming Source: Thermal and electro-thermal modelling of components and systems: A review of the research at the University of PARMA

Speed and Accuracy

Proposed Approach I Combined Physical and Behaviour Models Physical model: The Physical Model defines the physical form and the material properties of the component. A relevant numerical method must be available for each domain which is to be considered. Behaviour model: the physical representation may be limited for example modelling the power semiconductor device physics is not necessary. R Ld R Lg R d = f (T j) C gd = f (V d1g1 ) C gd g L g R g g1 C gs R Ls d1 Ld d1 s1 I ch s L s D1 C ds (E) I ch = f (T j, V d1s1, V g1s1 )

Combination of Physical and Behaviour Models Electrical domain Magnetic domain Thermal domain Other domains Physical Model (geometry, material, boundary) Interface ports Behavior Model may have geometry arameters as input) The behavior model can also contain geometry information.

Physical Model + Numerical methods Physical Model Geometry and Material Info Discretization Techniques MOR Matrix solver

Physical Model + Numerical methods Discretization Techniques There are several numerical approximation methods used to solve Maxwell s equations to model electrical components. Numerical Method Formulation of Maxwell s Equations FDM (Finite Difference Method) Differential equation FEM (Finite Element Method) Differential equation MoM (Method of Moments) Integral equation PEEC (Partial Element Equivalent Circuit) Integral equation Mesh Domain Field Field Circuit Circuit Advantages Easy to use Robust Cell flexibility Sparse system Cell flexibility Circuit & EM cell flexibility Disadvantages Cell inflexibility Large storage requirement Solution of large linear system Dense system matrix, Department computationally of Electrical and heavy Computationally heavy

Physical Model: Numerical Methods in Each Domain PEEC in electro-magnetic domain to analyse, for example, parasitic inductance, capacitance, inductor, etc. Finite difference/lumped parameter in the thermal domain. Pick up the right discretization method in each domain. Pick up the right solver for each problem.

Lumped Parameter Method vs. Finite Difference Method Lumped Parameter Finite Difference elements Tmax Tmin Time 224 103.2 85.6 Seconds 624 102.9 85.7 Seconds 1104 102.8 85.7 Seconds 8832 102.5 85.5 Minutes ANSYS 102.0 85.6 mesh Tmax Tmin time 8832 97.1 85.4 Seconds 70656 102.1 88.2 Minutes 565248 103.6 88.5 Hours ANSYS 102.0 85.6

Analytical Solution.... Partial differential equation for conduction heat transfer: dv x k T x + y k T y + z k T z + qdv = ρcdv T τ Both LPM and FDM assume heat transfer independently in 3 directions, so 1D is analyzed Steady state Assumption: k does not change along x k 2 T x 2 = q q : heat generation density (W/m3) q = 0 q 0 2 T x 2 = 0 T = C 1 x + C 2 Linear 2 T = q k x2 T = q 2k x2 + C 3 x + C 4 Parabolic

Lumped Parameter Model (LPM).... if q = 0 Rx1 T R x x 2 Tx1 T x 2 R x1 = R x2 = l x 2kA Linear 2R thermal network for q=0 if q 0 Parabolic R x1 T R x x2 Tx1 T x 2 R x3 l x T x = 1 q x 2 + l x 2k x 0 q 2k x l x x + T x2 T x1 l x x + T x1 dx = ql x 2 12k + T x1 + T x2 2 Q T x R x3 = T Q R x1//r x2 = l x 6 ka 3R thermal network for q 0 Solution of the circuits: 2 T x = R x1 Q + T x1 + T x2 T x = 1 T x + R x3 Q 2R 3R

Finite Difference Method (FDM).... 2 T x 2 = q k T i 1 R 1 R 2 Q T i T i+1 h 2 T x 2 = T i+1 T i h = T i T i+1 R 1 T i T i 1 h h = Q kah + T i T i 1 R 2 = Q (R = h ka) T KCL i 1 Q T i T i 1 Where, q: heat generation density (W/m3) Q: heat generation (W) FDM is in fact the 2R thermal network for both q=0 and q 0

LPM vs. FDM.... Example: 1D bar with internal heat generation L=10m; Cross section: 0.01m*0.01m; Left end T=20 o C; Right end T=10 o C; Internal heat generation P=100 W/m 3. 1 mesh 5 meshes 2 meshes 10 meshes

PEEC for Inductor Modelling....

SiC MOSFET Behaviour Model d1 R Ld Ld R Lg R d = f (T j ) C gd = f (V d1g1 ) C gd g L g R g g1 C gs R Ls d1 D1 C ds I ch s1 L s I ch = f (T j, V d1s1, V g1s1 ) s

Proposed Approach II Model Order Reduction Physical Model Numerical discretization FEA, FD, PEEC Inputs Full order space High Fidelity Model (n) Outputs Model Order Reduction (MOR) Inputs Reduced order space Reduced Order Model (m) m << n Outputs

MOR Techniques There are two main categories of MOR methods: Krylov (or moment matching) Singular value decomposition (SVD or Gramian based) Krylov (Moment matching) Realization Interpolation Lanczos Arnoldi PRIMA PVL AWE Others MOR Methods SVD ( Gramian based) Balanced Truncation Hankel Approximation Balanced Singular Perturbation Approximation Laguerre Others. Electronic SVD-Krylov Engineering method

MOR--An Example Generating FDM thermal equations Applying MOR MOR results in KLU solver Total time MOR 3008 ms 56 equations 62 ms 3070 ms Execution Time 10434 equations 772ms Without MOR Applying MOR 0 ms 10434 equations KLU solver 30918 ms Department Total time of Electrical 30918 and ms

Component Models Physical Model (Thermal) + Lumped-parameter method Finite difference method Heatsink Behaviour model based on datasheet (Thermal) Physical Model + Finite difference method (Thermal) Power device Behaviour model based on datasheet (Electrical)

Component Models Busbar and interconnection Physical Model + PEEC method (parasitic inductance/capacitance) (Electrical/Magnetic) Physical Model + PEEC method (Electrical/Magnetic) Finite difference method (Thermal) i l Surface of heat sink v l Inductor Behaviour Models (Electrical/Magnetic/Thermal)

What have we achieved so far?

An Exemplar System.... Capacitor Physical model of parasitic inductance Inductor DC 300V 380μH Mosfet1 Mosfet2 Parasitic inductance 2μF 22.47Ω DC 300V Heatsink Physical Model Behavior Model

Electromagnetic and Thermal Analysis.... Physical model Electromagnetic Distance between two MOSFETs Thermal Layout on the heatsink Electrical analysis Parasitic inductance Loss Temperature Voltage overshoot of MOSFET Vds Temperature of the components Thermal analysis

Results.... Electrical results: Voltage of the load R Thermal results: Temperature distribution at one time instant

Position3 Parasitic Effect.... Capacitor M1 M2 Inductor Position1 Position2

Temperature.... 20W Inductor 5W 20W 20W Capacitor M1 M2 Position1 Position2 Position3 T ( o C) T_M1 121 T_M2 121 T_ind 118 T_cap 118 T ( o C) T_M1 122 T_M2 122 T_ind 118 T_cap 117 T ( o C) T_M1 127 T_M2 127 T_ind 117 T_cap 114

The Vision---Compared with PCB design Electrical connection Footprint/ Package Netlist

PCB Design Wire connection (automated/manual routing)--- Rule check---analysis

Virtual Prototyping for Power Electronics

Virtual Prototyping for Power Electronics Load Connections FET 1 Gate Connections L 2 C 2 FET 2 C 1 C 3 Supply Department of Electrical Connections and

Exploitation PECAD Motor-CAD PECAD

Future Work Convection heat transfer, liquid cooling Identify optimal numerical methods (including MOR) in each domain for each component Model order reduction for non-linear systems PEEC method for inductors with various magnetic core types and capacitance analysis with fast multi-pole methods Extend the analysis and optimisation for other domains.

Project Partners Bristol: Dr Xibo Yuan Ms Wenbo Wang Greenwich: Prof. Chris Bailey Dr Catherine Tonry Dr Pushparajah Rajaguru Manchester: Prof. Andrew Forsyth Dr James Scoltock Dr Yiren Wang Nottingham: Dr Paul Evans Dr Ke Li Cross themes: Converters, Components, Devices and Drives Interdisciplinary: EE, Mathematics, Computer Science

Back-up Slides

Lumped Parameter Model (LPM).... if q = 0 T = T x2 T x1 x + T x1 R x1 T R x x2 Tx1 T x 2 Q R x3 l x Rx1 T R x x 2 Tx1 T x 2 R x1 = R x2 = l x 2kA 2R thermal network for q=0 if q 0 T = q x 2 + q l 2k x 2k x x + T x2 T x1 x + T x l x1 x T x l x T x = 1 q x 2 + l x 2k x 0 R x3 = T Q R x1//r x2 = l x 6 ka q T x = T x1 + T x2 2 Linear 2k x l x x + T x2 T x1 l x x + T x1 dx Parabolic = ql x 2 12k + T x1 + T x2 2 3R thermal network for q 0 Solution of the circuits: T x T x1 R x1 + T x T x2 = Q R x2 T x T x = Q R x3 2 T x = R x1 Q + T x1 + T x2 T x = 1 T x + R x3 Q 2R 3R

Finite Difference Method (FDM).... 2 T x 2 = q k T i 1 R 1 R 2 Q T i T i+1 h 2 T x 2 = T i+1 T i h = T i T i+1 R 1 T i T i 1 h h = Q kah + T i T i 1 R 2 = Q (R = h ka) T KCL i 1 Q T i T i 1 Where, q: heat generation density (W/m3) Q: heat generation (W) FDM is in fact the 2R thermal network for both q=0 and q 0