1Simulation of Renewable Energy Systems

Jost Allmeling, Orhan Toker

Plexim GmbH

2

Overview

Simulation of power electronic systems

Electrical machine modeling

Renewable energy system studiesDoubly-fed induction generator system

Grid-connected PV system

Thermal and loss simulation

Steady-state and small signal analysis

3

Who We Are

Independent company

Spin-off from ETH Zurich in 2002

Privately owned by founders

Software PLECS sold since December 2002Now in Release 2.0.5 July 2008

Customers in more than 40 countries

4

Simulation of Power Electronic SystemsElectrical Machine Modeling

Orhan Toker, Jost Allmeling

Plexim GmbH

5

Simulation of power electronic systems

Simulation of power electronic systemsChallenges

System vs. circuit simulation

Advantages of software PLECSState-space equations

Ideal switches

Control of simulation step sizeVariable vs. fixed time steps

Simulation of parasitic effectsDiode reverse recovery

Electrical Machine Modeling3-phase vs. rotating reference frame

6

Power Electronic Systems

Typically consist ofElectrical power circuit

Analog/digital controls

Both parts strongly interact and determine thermal losses

Powerconverter

Controller

LoadPower input Power output

Controlsignals

Reference

Measurement

vi ii io vo

Heat

7

Why Simulation of Power Electronic Systems

In research & developmentAnalyze behavior of new circuit concepts

Improved understanding of circuitIn product engineering

Study influence of parameters

Optimize circuit design and control

Shorten overall design processSimulation results

Voltage and current waveforms

Dynamic and steady-state system performance

Power losses

Component ratings

8

Challenges with Numerical Simulation

Power semiconductors introduce extreme nonlinearity Program must be able to handle switching

Time constants differ by several orders of magnitudee.g. in electrical drives

Small simulation time steps Long simulation times

Accurate models not always availablee.g. semiconductor devices, magnetic components

Behavioral models with sufficient accuracy requiredController modeled along with electrical circuite.g. digital control

Mixed signal simulation

9

Different Degrees of Simulation Detail

1. Power circuit modelled as linear transfer functionSmall signal behaviour

No switching, no harmonics

Controller design2. Power circuit modelled with ideal components

Large signal behaviour, voltage and current waveforms

Overall system performance

Circuit design and controller verification3. Power circuit with manufacturer specific components

Parasitic effects (magnetic hysteresis)

Switching transitions (diode reverse recovery)

Component stress (electrical or thermal)

Choice of componentsPower

converter

Controller

LoadPower input Power output

Controlsignals

Reference

Measurement

vi ii io vo

10

System vs. Circuit Simulation

System simulators(Simulink, LabVIEW)

Easy set-up of controllers Circuit equations must be

provided

Circuit simulators(Simplorer, PSpice, Saber, PSIM)

Easy set-up of circuit Incorporation of controllers

often difficult

Switch models too detailed

Requirement: Accurate and efficient simulation ofelectrical circuit and control system

PLECS combines the strengths of both types of simulators

11

Different Degrees of Simulation Detail

1. Controls

2. Circuit

3. Component PLE

CS

Saber

& S

pic

e

Psim

Sim

plo

rer

PLEC

S S

imul

ink/

Labvi

ew

12

Example: Drive System with Direct Torque Control

13

High Speed Simulations with Ideal Switches

Conventional continuous diode modeArbitrary static anddynamic characteristic

Snubber often required

Ideal diode model in PLECSInstantaneous on/offcharacteristic

Optional on-resistanceand forward voltage

14

Comparison: Diode Rectifier

Simulation with conventional and ideal switches

Simulation steps:1160 153Computation time:0.6s 0.08s

15

State Space Model: Buck Converter

State space description

Switch conducting Diode conducting

16

Working Principle of PLECS

Circuit transformed into state-variable system

One set of matrices per switch combination

AB C

D

1s

Sw

itch m

anager

PLECS S-function

Simulink

u

g

y

17

Variable Time-Step Simulation: Buck Converter

Transistor conducts

Diode blocks

Li

Li

Di

Du

Du

Di

18

Variable Time-Step Simulation: Buck Converter

Transistor opens

Impulsive voltage acrossinductor

Li

Li

Di

Du

Du

Di

19

Variable Time-Step Simulation: Buck Converter

Impulsive voltage closesdiode

Li

Li

Di

Du

Du

Di

20

Variable Time-Step Simulation: Buck Converter

Transistor open

Diode conducts

Li

Li

Di

Du

Du

Di

21

Variable Time-Step Simulation: Buck Converter

Switch timing Problem:

Diode opens too late

Impulsive voltage acrossinductor

Li

Li

Di

Du

Du

Di

22

Variable Time-Step Simulation: Buck Converter

Zero-Crossing Detection:

Time-step is reduced

Diode opens exactly atthe zero-crossing

Li

Li

Di

Du

Di

Du

23

Variable vs. Fixed Time-Step Simulation

Variable Time-Step

Highest Accuracy Time-step automatically

adapted to time constants

Can get slow for systems withmany independently operatingswitches

Fixed Time-Step

Can speed up simulation forlarge systems

Hardware controls are oftenimplemented in fixed time-step

Non-sampled switching events(diodes, thyristors) requirespecial handling

24

Handling of Non-Sampled Switching Events

Dio

de c

urre

nts

Dio

de v

olta

ge

Non-sampledzero-crossing

Non-sampledzero-crossing

26

Different Diode Models in PLECS

Diode turn-off

Test circuit:

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Dynamic Diode Model with Reverse Recovery

Reverse recovery effect under different blocking conditions

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Dynamic IGBT Model with Limited di/dt

Variation of vCE:tf and tr constant

Variation of iC:tf constanttr proportional iC

29

Different Ways to Model Electrical Machines

Machine modeled in PLECS3-phase model

Equivalent circuit

Stationary or rotating reference frameEquivalent circuit

Explicit differential equations

Machine modeled in SimulinkStationary or rotating reference frame

Explicit differential equations

30

Common Constraints

Differential equations must be provided in explicit form(neither Simulink nor PLECS can solve implicit equations)

Coordinate transforms are based onvoltage controlled current sources

No open machine terminals,e.g. an ideal diode rectifier may not be connected

Possible workarounds:Add internal resistance between machine terminals

Add RC snubbers to converter semiconductors

31

Option 1: 3-phase Equivalent Circuit in PLECS

+ Machine terminals may be open-circuited

+ External inductors may be connected

Only piece-wise linear nonlinearities(e.g. saturation, temperature)

Not discretizable due to nonlinear feedback

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Option 2: Equivalent Circuit in Reference Frame

+ Common representation (easy set-up)

+ Different circuits for d-axis and q-axis(required for synchronous machines)

No open-circuited machine terminals

No connection of external inductors

Not discretizable

33

Option 3: Explicit Differential Equations in PLECS

+ Arbitrary nonlinearities

+ Discretizable thanks to forward Euler integration

Error-prone set-up of equations

No open-circuited machine terminals

No connection of external inductors

34

Option 4: Explicit Differential Equations in Simulink

Same as differential equations in PLECS

+ Use of all Simulink blocks

+ Use of existing models

Schematic less clear due to additional interfacing andconnections between PLECS and Simulink

35

Some of Our Users Today

Aerospace:GoodrichSaab

Automotive:BoschChryslerOpelSkoda

Automation & Drives:DanfossHiltiRockwellWoodward SEG

Electronics:InfineonPanasonicPhilipsTyco

High Power:ABBBombardierConverteamSiemens

GE AviationUS Air Force

36

Renewable Energy System Modeling

Jost Allmeling, John Schnberger

Plexim GmbH

37

Overview

Renewable energy system studies

Doubly-fed induction generator systemStudy: system verification.

Modeling: Wind turbine, induction generator, converter andcontrollers.

Grid-connected PV systemStudy: Max power tracking strategy, system verification,converter interaction.

Modeling: PV source, converter and controllers, systemintegration.

38

Renewable Energy System Studies

ms, usTransient response

Controller design, MPPT

Power electronics

operation

ms, usStability, islanding, harmonics

Fault operationGrid integration

secMachine dynamics

System transient behaviorInstantaneous powerflow

hr, minSystem dimensioning

Scheduling algorithmsLoad flow

years, monthsForecasting

System planningEnergy supply

Time scaleStudy typeCategory

39

Wind Energy Basics

Wind power

Performance coefficient

t must vary with the wind speed in

order to capture maximum wind power

Tip speed ratio:

40

Power Electronic Wind Turbine Interfaces

Power electronics allows variable speed operation.The interface can process all or part of the generator power.A fully rated interface is suitable for a PM or synchronousgenerator.A partially rated interface is suitable for an large inductiongenerator.

Fully-rated

Partially-rated

41

Doubly-fed Induction Generator

Grid side and rotor side converters are independently controlled.Grid side converter regulates DC bus voltage.

Exports or imports power depending on slip direction.Can set the system power factor through Q control.

Rotor side converter controls speed to obtain max power from the wind.

42

Example System

Synchronous speed = 1500rpm.Variable speed operation between 1000 2000 rpm allows MPT.Above Pmax = 22 kW, pitch control is needed.

Max Power:

v = 12 m/s

Optimum speed => 2000 rpm

Pw = 22 kW

Ps = 16.5 kW

Pr = 5.5kW

43

System Parameters

Based on experimental systemTurbine inertia is omitted

Speeds up mechanical dynamics, shortens simulation time.

44

Simulation Options

Grid integrationInternal dynamics of the converter not of interest.

Use a simplified model, include mechanical dynamics, e.g. shaft.

System functionalityUse average PWM model.

Controller tuning.

Maximum power point tracking.

Converter operationNeed a switching model. Ideal switches can be used.

Useful for studying converter interaction, filter design.

Device operationNeed a switching model, accurate device models, parasitic components.

For ascertaining component stresses.

45

Average PWM Model

Verification of converter operation.Includes averaged PWM response and DC bus dynamics.Electrical system can be simulated with limitations.

Operating range limited to Pw < Pmax.Pitch control can be omitted from wind turbine model.Operating range is variable speed.

46

Wind Turbine Model

Approximate model is sufficientSimple wind model: mechanical torque = fn(wind speed, rotational speed).Gearbox neglected, speed and torque referred to generator side.Pitch control ignored => = 0, Pw < Pmax.

Obtain performance coefficient from data or curve fit.

Approximation of performance coefficient

e.g.

Cf: scaling factor

47

Torque Speed Curve

Tm = fn(v, rpm)

48

Induction Machine Model

Electrical: DQ model

Mechanical:

Tm external input

d axis

49

Average PWM Converter Model

Assumes AC voltages are ideally imposedUsed for rotor-side and grid-side converter

50

Maximum Power Tracking

Infers optimal rpm from wind speed (v).Wind turbine characteristics must be known.

51

Design of a Multi-string PV System

PV interface optionsPV source modelingSimulation exampleDC-DC input converter

MPP tracking

DC-AC output converterDC bus controller

52

PV Interface Options

Centralized inverterString diodes neededNon-optimal centralized MPPT

Multi-stringIndividual MPPT for each string

Converter-per-moduleSeparate MPPT allows for optimal operation

CentralizedInverter

Inverter-per-module

Multistringinverter

53

Multi-string PV System

Two-stage approachPower aggregated at DC bus

Easy to expand the system

A single inverter exports power to AC systemEach string is independently controlled

Separate MPPT allows for optimal operation

54

Simulation Example

Single-string system (10 x 60W, 24V)PV source modelIndependently-controlled converters

Circuit modeled in PLECS, controls in Simulink

55

Modeling Approach

Implement and test control strategies for input andoutput converters.

Use a switching model.

Focus is on functionality not switching transients => use idealswitches.

Understand interaction between the converters andcontrollers.

Include DC bus dynamics and controller.

Simulate the entire system as a whole, not just each part.

Implement and test MPPT control.Need an accurate PV model.

56

PV Module Modeling

Simple model: voltage source with series resistanceSufficient for static operation

Exact model: accounts for non-linear behaviourNeed when implementing MPPT control

Example characteristics of ten 24V,60W arrays connected in series.Insolation = 1000W/m2.MPP occurs at 172V

57

PV Module Electrical Model

Current = fn(voltage, insolation,temp)Cell model

Shockley diode eq.

Reference:

I

58

PV Look-up Table

Current = fn(voltage, insolation)

59

PV Look-up Table Implementation

Voltage-controlled current sourceCapacitor included to add a state and avoid an algebraicloop

60

DC-DC Input Converter

Based on boost topology (isolation not required).

Steps up PV voltage to DC bus level - 170 to 400V.

Responsible for maximum power point tracking.

Challenge: Pulsing power causes voltage fluctuations onDC bus.

Decouple using a large bus capacitor or

Average current mode control (ACMC).

Vo is an AC quantity. If d is controlledusing a PI controller, tracking error will exist.=> degraded MPPT.Use an inner ACM control loop todecouple effect of Vo.

61

Maximum Power Point Tracking

Uses incremental conductance.At the maximum power point, conductance and incremental conductance areequal.

A PI controller adjusts the current reference based on the error.Allows for a dynamic step size => faster tracking.

MPPT using incremental conductance

62

Maximum Power Point Tracking Options

Hill climbing

dP/dV = 0

Incremental conductance

Others:Fractional open circuit voltage

Load current maximization

Reference:

63

Incremental Conductance

At MPP, I/V = -dI/dV

Conductance/incremental conductanceCurrent and power output

PV string characteristics for insolation = 1000 W/m2

64

MPPT Implementation

Executed every 1ms

MPPT controller implementation in Simulink

65

DC-AC Output Converter

Single-phase full-bridge inverter.

PR controller eliminates steady-state AC tracking error that is normallypresent when using PI control.

66

DC Bus Controller

Provides reference for output current controller.Simulation example based on deadbeat control.

Iref calculated to restore Vbus to ref value by end of mains cycle.Iref update once every mains cycle to eliminate dc content at ac output.

Power

Energy

Current reference

67

Thermal Modeling andAdvanced Circuit Analysis

Jost Allmeling

Plexim GmbH

68

Sources of Thermal Losses

Passive componentsResistive power loss: ploss(t) = vR(t) iR(t)

Loads e.g. break resistors

Filters

Winding resistance

Magnetic hysteresis

Power semiconductorsConduction loss

Switching loss

69

Conventional: Switching Losses from Transients

Turn-on energy calculated from:Blocking voltage and Devicecurrent during turn-on

Eon = f(vblock(t, Tj), ion(t, Tj),)

Turn-off energy depending on:Device current and Blockingvoltage during turn-off

Eoff = f(ion(t, Tj), vblock(t, Tj),)

70

Problems with Switching Losses from Transients

Accuracy:

Behavioral models not suited to predict losses

Physical device models required

Physical parameters often unknown

Losses depend on external circuit configuration(Ls, RG, ...)

Simulation speed:

Small simulation steps during transients=> Large computation times

71

Example IGCT Turn-off: Varying Stray Inductance

Courtesy ABB

0.0

1.5

3.0

4.5kV

0.0

1.0

2.0

3.0kA

VPK = 3800V

VDC = 2 kV

TJ = 125C

5 10 15 s

300 nH (10.5 Ws)

800 nH (12 Ws)

1500 nH (13.5 Ws)

tf 2.5s, ttail 7s

72

Switching Losses in PLECS

Turn-on energy depending on:Junction temperature

Blocking voltage before turn-on

Device current after turn-on

Eon = f(Tj, vblock, ion)

Turn-off energy depending on:Junction temperature

Device current before turn-off

Blocking voltage after turn-off

Eoff = f(Tj, ion, vblock)

Losses in PLECS are read from a database

73

Example: IGBT Turn-off Energy

Turn-off loss depending on:

Current before switching

Voltage after switching

Temperature at switching

Linear interpolation between andextrapolation out of range !

74

Semiconductor Conduction Losses

On-state lossVoltage drop represented bynonlinear function:von = f(ion, Tj)

Loss power:ploss(t) = von(t) ion(t)

Off-state lossLeakage current:ileak = f(vblock, Tj)

Loss power usually negligible

75

Losses in IGBT Module

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Application Example: Efficiency Comparison

Project at ABB

Air-cooled MVdrive system

Measurement oflosses difficult

PLECS used forsimulation of

Switching losses

Filter losses

Harmonics

Source: Y. Suh, J. Steinke, P. Steimer: Efficiencycomparison of voltage source and current source drivesystems for medium voltage applications, EPE 2005 Photo: ABB

77

Thermal Circuit

Losses, heatsink, ambient temperature.

How are these represented using PLECS?

78

Thermal Domain

Thermal circuit analogous to electrical circuit.

Thermal and electrical circuits solved simultaneously.

79

Thermal Modeling in PLECS

Heat sink: Isotherm group of componentsAbsorbs loss energy from passives and semiconductors

Propagates temperature back to components

Heat transfer modeled with lumped RC elements

80

Thermal Simulation in PLECS

Electric Circuit

Component Datasheet orMeasurement

Electric Simulation

Switching Conditions

Thermal Calculation

Output

Time

IIGBT

TIGBT

81

Hierarchical Modeling of Thermal Structures

Junctions

Dual IGBTmodule

Heatsink

IGBT Plate

82

Different Thermal Equivalent Networks

Cauer equivalentPhysics based thermal equivalentcircuit

Rth and Cth elements correspond tostructure elements and can directly bedetermined from material parameters

Defined thermal nodes allow for:

Section-wise parameterisation ofthe network

Easy extension

Access to inner temperatures

Foster equivalentNo correspondence between Rth,nresp. Cth,n and the physical structure!

Inner nodes without physical meaning

Any modification of the systemrequires recalculation of all values

Easily applicable since Zth can beexpressed in closed form

Parameters can easily be extractedfrom heating-up and cooling-downcharacteristics

83

Constraints Due to Use of Ideal Switches

Zero transition time when switching=> Dissipation of switching energy not possible in electrical circuit

Loss energy generated by thermal model Energy conservation (electrical thermal) can be achieved

with extra feedback

Efficiency calculation must include thermal losses

Multi-stage converters may need an iteration todetermine exact losses

84

Challenge: Large Thermal Time Constants

Thermal time constants: 0.1 10 s

Switching frequency: 1 100 kHz

Long simulation time until thermal steady-state is reached

Example

85

Solution: Steady-State Analysis

Iterative extrapolation method

Typically converges after

86

Steady-State Analysis

f (x) = x FT (x)

Iterative solution:

Jacobian J calculated numerically,requires n+1 simulation runs (for n state variables)

xk+1 = xk Jk1 f (xk ), Jk =fx xk

FT (x)x

Newton iteration

Broydens Update for Jk-1 Jk

Approach: Finding the roots of

: initial state vector : final state vector after a time T

87

Steady-State Analysis

Convergence criterion

Algorithm1. Find circular topology

(initial switch positions = final switch positions)2. Calculate Jacobian J0 for initial state3. Iterate until convergence criterion is satisfied

(if necessary, go back to step 1)

LimitationsHidden state variables in Simulink (e.g. Memory block)State variable windup

fi (x)

max xi ( )< rtol for all i =1,...,n

88

AC Analysis

ObjectivesOpen-loop transfer function, e.g.

Control-to-output transfer function

Output impedance

Closed-loop gain of feedback system

TechniquesFrequency sweep

Small signal analysis

State variable averaging

89

Frequency Sweep

Algorithm:For each frequency:

1. Apply sinusoidal perturbation

2. Run steady-state analysis

3. Extract system response using Fourier analysis

Caveats:Period length: least common multiple of system period andperturbation period

Computationally expensive

90

Alternative: Impulse Response Analysis

Numerical computation of Laplace transform of impulseresponse

Extremely fast

Ratio between system period and analyzed frequenciesirrelevant

91

Impulse Response Analysis

Impulse responseof a buck converter

)(~

)(~

)(sU

sYsG =Transfer function:

=

0

)(~)(~

dtetysY st

=

0

)(~)(~

dtetusUst

92

Impulse Response Analysis

( ) TT

T

sT

T

stst xedtetdtetysY ~1)()(~)(~

1

0 0

+=

=

0

)(~)(~

dtetysY st

=

+

+=

T

k

Tk

kT

stst dtetydtetysY0 1

)1(

)(~)(~)(~

T

k

T xkTtty~)()(~ 1 =

The original Laplace transform:

Apply some math

+=

=

T

T

k

skTk

T

T

stst xedtetdtetysY0 1

1

0

~)()(~)(~

Reference: D.Maksimovic, Computer-Aided Small-Signal Analysis Based on Impulse Response of DC/DCSwitching Power Converters, IEEE Trans. On Power Electronics, Vol. 15, No. 6, Nov. 2000, pp. 1183-1191

93

AC Analysis: Open-loop Transfer Function

Load voltage as a function of the modulation index

94

AC Analysis: Open-loop Output Impedance

Load voltage as a function of load current

95

AC Analysis: PID Compensator

Limits for output and integrator required to preventwindup problems

96

AC Analysis: Closed-Loop Gain

Load voltage as a function of reference voltage

97

Extraction of State-space Matrices

System matrices accessible for every circuit topology(combination of switch positions)

Useful for:State-space averaging

Eigenvalue analysis

Real-time applications

98

Thank you

Plexim GmbH

Technoparkstrasse 1CH-8005 Zurich

Phone +41 44 445 24 10Email info@plexim.comWeb www.plexim.com