Robustness Analysis of PV inverters - Kiel · 2013-12-18 · December18,2013. 45 Robustness...

Robustness Analysis of PV inverters

Faculty of EngineringChristian-Albrechts-University of Kiel

Kiel, Germany

[email protected]://grupos.unican.es/taccp/index.htm

December 18, 2013

mailto:[email protected]

http://grupos.unican.es/taccp/index.htm

45

Robustnessanalysis

Introduction

Robustness of PVinverters: Anexample

Conclusion

Outline

University of CantabriaIEEE COMPEL 2014

IntroductionWhy robustness?Robustness evaluation

Robustness of PV inverters: An exampleAnalysis of parametersSimulation analysis

Impact on µη and σηComparison of parametersEU Efficiency

Experimental results

Conclusion

45

Robustnessanalysis

3 University ofCantabria

IEEE COMPEL 2014

Introduction


Conclusion

Cantabria 1/2 (Spain)

45

Robustnessanalysis


IEEE COMPEL 2014

Introduction


Conclusion

Cantabria 2/2 (Spain)

45

Robustnessanalysis


IEEE COMPEL 2014

Introduction


Conclusion

University of Cantabria (Santander)

I Sciences, Social Sciences and Technical StudiesI Sudents ≈ 10900, Researchers & Professors ≈ 1100I Website: www.unican.es/en

45

Robustnessanalysis


IEEE COMPEL 2014

Introduction


Conclusion

Dept. of Electronics and ComputersUniversity of Cantabria

I Full professors: 5, associate: 14, assistant: 4, other: 14,Researching assistants: 14.

I Researching groups:I Computers and Real-TimeI Computers ArchitectureI Design and Verification of Integrated CircuitsI Electronic InstrumentationI Advanced Control Techniques in Power Converters

I website: http://grupos.unican.es/taccp/EN/index.htmI Electrical power qualityI Active power filtersI Detection of the islanding condition in grid connected power

convertersI Reliability and robustness of PV inverters

http://grupos.unican.es/taccp/EN/index.htm

45

Robustnessanalysis

University ofCantabria

7 IEEE COMPEL 2014

Introduction


Conclusion

15th IEEE Workshop on Control and Modeling forPower Electronics - Santander, June 22-25

I Submission deadline: March 3, 2014.I Some topics:

I Modeling & Simulation: Devices, circuits, and systems; multi-domain andmultilevel modeling; model fidelity & compatibility; electro-thermal, EMI,reliability prediction, failure mechanisms.

I Control of Power Electronics: Advances in smart power control and powermanagement techniques; control algorithms, design methods, implementationtechniques (DSP, microcontroller, FPGA, hardware-in-loop, custom ICs).

I System Power Management: Analysis, modeling and control of powerelectronics in energy efficiency and renewable energy systems: energy harvesting,processors, lighting, data centers, hybrid/electric vehicles, micro grids, renewablesources.

I Design & Simulation Tools: Synthesis, visualization, and verification tools;monitoring, built-in test, diagnosis, adaptation, virtual prototyping.

I Education: Virtual laboratories, multimedia tools, interactive simulation,symbolic analysis tools.

I website: http://compel2014.teisa.unican.es/

http://compel2014.teisa.unican.es/

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Robustnessanalysis

8 IntroductionWhy robustness?

Robustnessevaluation


Conclusion

Robustness analysis of PV inverters

45

Robustnessanalysis

Introduction9 Why robustness?



Conclusion

Why robustness in PV inverters?Some researching topics during the last decade...

H-bridge

dc

dc

Linv Rinv Lgrid

Rgrid

iinv

Rdamp

Cf

vgrid

PWM

P+ResController

MPPT andDC voltagecontroller

Referencecurrent

+ −

Grid syn-chronization

OUV/OUF

PVarray

iinv (t) fgrid ,Vgrid

vgrid(t)

trip

sinωt

I

I sinωt

I Efficiency: Topologies, characteristics of components

I Controller functionalities

45

Robustnessanalysis




Conclusion

Why robustness in PV inverters?Some researching topics during the last decade...

H-bridge

dc

dc

Linv Rinv Lgrid

Rgrid

iinv

Rdamp

Cf

vgrid

PWM

P+ResController


Referencecurrent

+ −


OUV/OUF

PVarray


vgrid(t)

trip

sinωt

I

I sinωt

I Efficiency: Topologies, characteristics of componentsI Controller functionalities

45

Robustnessanalysis




Conclusion

Why robustness in PV inverters?Reliability & Robustness

Reliability

Robustness

I Mission profilesI Design toolsI Accelerated testsI Condition monitoringI Physics of FailureI Component physics

Reliable and Robust PE:More reliable and cost-effectivepower electronics in case ofemerging & critical applicationsand/or harsh environments

H. Wang, M. Liserre and F. Blaabjerg,“Toward Reliable Power Electronics,” IEEEIndustrial Electronics Magazine, june 2013.pp. 17-26.

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Robustnessanalysis




Conclusion

Why robustness in PV inverters?Researching is moving on...

on

failurereparing

uptime

timebetweenfailures

failure

downtime

reparing

From:I MTTF, MTBF =∑

(down time−up time)

No of failuresI FITI Handbook data

94.5 95 95.5 96 96.50

0.5

1

Time

Freq

uenc

y

To:I Probability distribution

functionsI Physics of FailureI 6σ and Design of Experiments

(DoE )

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Robustnessanalysis




Conclusion

Why robustness in PV invertersFailures in PV systems

Unscheduled maintenance costs

59%

6%14%

12%

9%

InverterPV modulesData Acq. SystemAC Disc.Other

L. M. Moore and H. N. Post, “Five years ofoperating experience at a large, utility-scalephotovoltaic generating plant,” Progress inPhotovoltaics: Research and Applications,vol. 16, no. 3, 2008. pp. 249-259.

Failures per subsystem

51%

11%

7%31%

InverterCommunicationsWeather stn.Other

T. Golnas, “Owner/Operator perspective onreliability: customer needs and field data,”

Utility-Scale Grid-Tied PV Inverter ReliabilityTechnical Workshop, january 2011.

Lifetime of PV inverters ≈ 10 years

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Conclusion

Why robustness in PV inverters?Increase the lifetime

UE strategic research agenda for PV technology, 2011:2025: Increased inverter reliability and lifetime to achieve >30 yearsof full operation

Some approaches:

Redundancy

An Efficient, Low Cost DC-AC Inverter for Photovoltaic Systems with Increased Reliability

Rohit Tirumala, Paul Imbertson and Ned Mohan Chris Henze Russ Bonn

~

I Yo/rage F D C

Regulator Source

Department of Electrical Engineering, University of Minnesota, Minneapolis, MN 55455 USA

[email protected], [email protected], mohon@ecc. umn. edu

Abstract -This paper presents a topology for photovoltaic inverters to convert the DC voltage to single phase or split- single-phase AC. The proposed modular approach helps to increase the reliability of the system by introducing redundancy while lowering cost by having identical modules in parallel to achieve different output power levels.

d I

I High 120/240V,

==I I Freauenc PWM ~

-!

1. INTRODUCTION

In recent years, there has been an increase in the use of renewable energy due to the growing concern for the pollution caused by fossil-fuel-based energy. This growing emphasis on renewable energy combined with utility deregulation has increased the possibilities for distributed generation. On-site power generation using sources like photovoltaic (PV) arrays and fuel cells can be used to reduce the dependence on energy from the grid as well as provide back up power for critical systems during grid outages.

The above mentioned sources are, in general, DC sources. A DC-AC inverter system is required to convert the DC voltage to the standard system used in United States at 1 IOV AC single-phase and 220V AC split-single-phase systems. A major component of the cost of the system is the inverter. In order to make the entire system cost effective, the cost of the inverter has to be reduced. The inverter systems that are currently available in the market are built specifically for the source (PV arrays or fuel cells) and cost anywhere between $1.7/watt for low power applications (I kVA) to $O.X/watt for high power applications (10 kVA) [l]. Additionally, the inverter is also the least reliable component of the system with a mean time to first failure of less than five years [2].

In order to achieve a lower cost for the inverter, it will be necessary to design an inverter which can work with different input sources (PV arrays, fuel cells and batteries) and can be used in different applications (grid-tied, off-grid, backup). The broad market for this inverter will ensure a large volume of production and thereby a lower cost per watt.

The reliability of the inverter can be improved by introducing redundancy using paralleled modules, so that the failure of one module does not affect the performance of the system.

This paper discusses a possible topology which can be used to convert the DC voltage of PV arrays and fuel cells to 110/22OV, 60Hz split-single-phase AC. The features of the proposed topology are:

Analog Power Devices, Inc. Lakeville, MN 55044 USA Albuquerque,

Sandia Laboratories

NM 87185 USA

[email protected] [email protected]

Modular: By paralleling inverter systems (both at the input and output) which are designed for a specific power rating (2kW), the system can be configured for output power ratings in the range of 2kW to IOkW. This will also lead to larger volume, which means more failure mode feedback and better reliability. Flexible: The inverter can be easily wired to obtain either single phase of split-single-phase output, utilizing the maximum VA rating of the system. Adaptable: A smart controller using DSP would allow the controller to adjust to the power rating and the type of output. It would also provide all the protection features required to ensure safe operation of the system. Efficient: The proposed system has low conduction and switching losses and can thus achieve high efficiencies. Reliable: The modular design increases the reliability of the system by providing redundancy.

Section 11 describes the power stage of one module of the system rated for 2kW. Section 111 discusses the controller design for each stage of the system. The maximum power point control for the system is described in section IV. Section V discusses the possibility of using the proposed converter with fuel cells. Section VI discusses paralleling of 2kW modules to obtain output power levels between 2kW and IOkW. Simulations carried out on SABER are used to verify the proposed design. Conclusions and summary are provided in section VII.

11. PROPOSED TOPOLOGY

The block diagram of the proposed inverter system is

The first stage is a boost converter, which acts as a voltage shown in Fig. I .

I

Fig. 1 Proposed Inverter System

0-7803-7474-61021161 7.00 02002 IEEE 1095

R. Tirumala, P. Imbertson, N. Mohan, C.Henze, and R. Bonn, “An efficient, low costDC-AC inverter for photovoltaic systems withincreased reliability,” IEEE 28th Annu. Conf.

Ind. Electron. Soc., 2002, vol. 2, pp.1095–1100.

Less electrolitic capacitors2594 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 7, JULY 2008

Fig. 1. PCU.

well known that aluminum electrolytic capacitors, among oth-ers, are the weakest links in power electronic designs. Becausethe ac-module inverter operates at high temperatures, the prob-lem is further intensified. Consequently, one of the design goalsof the inverter presented here was to remove all aluminum elec-trolytic capacitors in the system. In addition to this, other unreli-able components, such as optocouplers and monolithic isolateddc-to-dc power supplies, were also obviated from the finaldesign. Failure-rate analysis shows a theoretical lifetime of theproposed inverter of ten years, whereas an inverter with a singleelectrolytic capacitor would have a lifetime of only five years.

A detailed description of the inverter is presented in thefollowing sections. First, the power electronic topology is in-troduced. A soft-switching full-bridge voltage amplifier is usedto step up the voltage of the PV panel up to 475 V. Then,a current shaping stage is used in series with an unfoldingbridge that works as a current-source inverter. The voltageamplification stage is controlled by using voltage mode thatimproves stability of the power transfer and simultaneouslyallows the use of very little capacitance, enabling the use offilm capacitors. The full bridge is controlled by a phase-shiftpulsewidth-modulation (PWM) controller whose duty cyclevaries in order to keep constant the PV voltage. The currentshaping stage uses current-mode control to generate the sine-wave injection. Power balance is achieved through an energycontrol method used to define the amplitude of the current.In addition, by allowing a large voltage ripple in the dc-linkreservoir, a small film capacitor is sufficient to buffer energymismatches resulting from the difference between the dc inputpower and the fluctuating output power.

The peak efficiency of the system is measured to be 89%,with a European efficiency of 85%. The total harmonic dis-tortion of the current is under 5% above 50 W of powerrating. Moreover, the inverter conforms to the internationalrecommendation IEC-61727 [13].

Finally, reliability analysis is presented that shows the theo-retical long life of the inverter. The calculations are based onfailure-rate statistics at 70 C, either using manufacturers’ dataor the military handbook standard 217F [14]. For this analysisto be valid, the temperature of all devices must be kept below70 C at all times. Special thermal layout was put in practice tohave very little thermal resistance between all components andthe enclosure. Tests carried out in our laboratory show that theinverter works fine at full power rating, 150 W, at an enclosure

temperature of 80 C, and withstands thermal transients from−20 C to +80 C.

II. VOLTAGE-FED AMPLIFIER AND

CURRENT-SOURCE INVERTER

A PV ac-module inverter must comprise two functions inorder to transfer power from the PV panel to the electricitysupply: voltage amplification and grid interaction. Althoughthere have been one-conversion-stage solutions (see, for in-stance, [8]), more practical inverters use two conversion stages.Some of the commercially available low-power inverters usethe concept of a pseudo dc link [9]. These inverters consistof a transformer-based amplifier that is used to transfer high-frequency current pulses with a sinusoidal distribution acrossfrom the PV side to the pseudo dc link and an unfoldingbridge to create a full-wave sinusoidal injection. In this fashion,high efficiency is attained because the unfolding and ampli-fication stages have efficiencies of 98%–99% and 90%–94%,respectively. However, this approach suffers from poor current-injection quality.

Amplification stages using current-fed topologies have beenreported in the literature (see, for example, [15] and [16]).The advantages outlined for these topologies include currentbalancing in the transformer that prevents saturation, easierelectromagnetic-interference control given that the current fromthe PV has less ripple, and available soft-switching techniques.In the inverter presented here, the amplification stage is voltagefed. However, because its purpose is solely to amplify the PVvoltage, any of the two could be utilized.

The power electronic topology presented here uses threeconversion stages: a voltage amplifier, a current shaper, and anunfolding bridge. As opposed to the pseudo-dc-link approach,the soft-switched voltage amplifier can operate at efficienciesas high as 96%, with the current shaper operating between 94%and 96% efficiency. The advantage of this topology lies on thecontrol method and the potential reliability, as will be explainedin Sections III and IV, respectively. The power conditioningunit (PCU) of the system is shown in Fig. 1.

A. Voltage Amplifier

The voltage amplification stage consists of transistorsQ1–Q4 (STB60NF06), resonant inductor Lr (2.2 µH),

C. Rodríguez and G. A. J. Amaratunga,“Long-lifetime power inverter for photovoltaic

AC modules,” IEEE Transactions onIndustrial Electronics, vol. 55, no. 7, july

2008. pp. 2593-2601.

Active thermal control

45

Robustnessanalysis

IntroductionWhy robustness?

14 Robustnessevaluation


Conclusion

Robustness evaluationRobustness Validation - ZVEI

A Robust component:is able to maintain all the required characteristics under theconditions of use over the lifecycle without degradation toout-of-spec values

Requires kwnowledge of:I Mission profiles.I Failure mechanisms and failure modes, and interactions between

failure mechanisms.I Acceleration models for the failure mechanisms → define and

asses accelerated tests.ZVEI, Handbook for Robustness Validation of Semiconductor Devices in AutomotiveApplications, German Electrical and Electronic Manufacturers’ Association, February 2013.ZVEI, How to measure lifetime for Robustness Validation. Step by step, German Electricaland Electronic Manufacturers’ Association, November 2012.

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Robustnessanalysis




Conclusion

Robustness evaluationCommodity Robustness Diagram

Target:Can the mission profile requirements be achieved by using a certaindevice?

13

4.3 Robustness Diagrams

Results of RV can be represented by the use of Robustness Diagrams.

The Commodity Component Robustness Dia-gram, shown in Figure 4.2, represents the first use of a robustness diagram, and is initiated at the conclusion of the finalization of the Mis-sion Profile. At this point, the Semiconductor Component Supplier investigates whether the Mission Profile requirement can be achieved by using the relevant commodity device.

Figure 4.2 provides such a pictorial representa-tion for two parameters, A and B, which have a certain relationship, such as voltage and temperature. Many parameters may be simple enough to plot one-dimensionally. The red box represents the area of the application’s specification, which the commodity compo-nent must meet or exceed. The light blue area represents the commodity components actual performance. The Robustness Margin is the distance between any point of application specification and the point of failure of the commodity component, taking into account

all variations of the product and the applica-tion’s environment. The failure could result in different failure modes X, Y, Z, depending on the values of the parameters A and B. A robust component is a component that is able to maintain all the required characteristics under the conditions of use over the lifecycle without degradation to out-of-spec values.

The Commodity Component Robustness Dia-gram should be reviewed with the customer to demonstrate the actual robustness of the component when developing the application FMEA.

The Application-Specific Component Robust-ness Diagram, shown in Figure 4.3, represents the second use of a robustness diagram and is initiated at the conclusion of the RV Stress Test. At this point, the Component Supplier demonstrates to his customer the robustness of the semiconductor component to exceed the application specification requirement.

Para

met

er B

Parameter A

Component CapabilityRobustness Margin

SemiconductorComponent Specification

CustomerApplication Spec

ICFailureMode Y

ICFa

ilure

Mod

e X

ICFailureMode Z

Figure 4.2 Robustness Diagram for a Commodity Semiconductor Component.I Lifetime vs

supply voltageI Max. current

density vs max.junctiontemperature

I Lifetime vsnumber oftemperaturecycles

I ...

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Robustnessanalysis




Conclusion

Robustness evaluationMission Profile

Mission profile:Collection of all relevant environmental load/stress and conditions ofuse to which a component/system will be exposed during its full lifecycle.

RequiresI Accurate, synchronized and long-term measurements of relevant

system and environmental variables.I Appropriate sampling rate, compression formats and storage

systems.I Signal processing techniques to extract relevant info.

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Conclusion

Robustness evaluationEnvironmental conditions and stress/load factors

I Thermal conditionsI Ambient temperatureI Temperature inside the

equipmentI Junction temperature

I Electrical conditionsI VoltageI CurrentI EnergyI Electric/Magnetic fields

Failures in PETemperature

55%

Vibration& Shock

20%

Humidity& Moisture

19%

Contaminants& Dust6%

I Mechanical conditionsI VibrationI ShockI External load (pressure,

tensile forces...)

I Other conditionsI Chemical reactionsI HumidityI RadiationI Electromagnetic radiationI Particle radiation

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Robustnessanalysis

Introduction

18 Robustness of PVinverters: AnexampleAnalysis ofparameters

Simulation analysis

Impact on µη andση

Comparison ofparameters

EU Efficiency


Conclusion

Robustness of ηEU in PV invertersAnalyzed system

H-bridge

dc

dc

Linv Rinv Lgrid

Rgrid

iinv

Rdamp

Cf

vgrid

PWM

P+ResController


Referencecurrent

+ −


OUV/OUF

PVarray


vgrid(t)

trip

sinωt

I

I sinωt

I Do the selected components have any effect on ηEU?I Which are the best and the worst parameters?

45

Robustnessanalysis

Introduction

19 Robustness of PVinverters: AnexampleAnalysis ofparameters

Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersAnalyzed system model

H-bridge Linv Rinv Lgrid

Rgrid

iinv

Rdamp

Cf

vgridVdc

idc

PWM

P+ResController

Referencecurrent

+ −


OUV/OUF


vgrid(t)

trip

sinωt

PMPPV rmsac

√2

I sinωt

I IGBT param.: Ron, Lon, VCE ,sat , Tr and TfI Diode param.: Ron, If , Vf , ∂If∂t , Irrm, Qrr and TrrI LCL-filter param.: Linv , Rinv , Cf , Rdamp, Lgrid and Rgrid

45

Robustnessanalysis

Introduction


20 Analysis ofparameters

Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersProcedure

Parameterssubjected tovariations

Statisticalanalysis

MonteCarlo (MC)simulations

Statisticalanalysis

I Selection of parameters to be analyzed

I Statistics:I MC require propper simulation points →

Lating Hypercube Sampling (LHS) → Bestfitting of distributions’ parameters →Maximum Likelihood Estimates (MLE) &Goodness tests

I Fitting problems? yes→ Decoupling ofparameters & re-start fitting

I MC:Accurate model of the PV inverter and itscontroller

I Statistics: Does ηEU change? What about theweight of different parameters variations?

45

Robustnessanalysis

Introduction



Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersProcedure

Parameterssubjected tovariations

Statisticalanalysis

MonteCarlo (MC)simulations

Statisticalanalysis

I Selection of parameters to be analyzedI Statistics:

I MC require propper simulation points →Lating Hypercube Sampling (LHS) → Bestfitting of distributions’ parameters →Maximum Likelihood Estimates (MLE) &Goodness tests

I Fitting problems? yes→ Decoupling ofparameters & re-start fitting

I MC:Accurate model of the PV inverter and itscontroller

I Statistics: Does ηEU change? What about theweight of different parameters variations?

45

Robustnessanalysis

Introduction



Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersAnalysis of parameters - IGBT modules

Selected modules:I 54 modules (Semikron and Infineon)I Ratings: Vdc ∈ [600V , 1.2kV ] and Idc ∈ [30A, 100A]

I Technologies: NPT, IGBT2, IGBT3, IGBT4, SPT, V-IGBT

1st Step:Find the best fit of distributions for each parameter

45

Robustnessanalysis

Introduction



Simulation analysis



EU Efficiency


Conclusion


Methodology (using MatLab):1. Graphically (> dfittool)

1.1 Test the available distribution candidates1.2 Select the most suitable ones

2. Numerically (> kstesst and > kstest2)

2.1 Beginning → low confidence level2.2 Run the tests2.3 Increase the confidence level up to reach only one (best fit)

3. Graphically (> qqplot)

3.1 Check the fit3.2 Detect dependencies from other parameters (i.e. module W)3.3 Repeat, if necessary, all steps up to obtain a good fit

45

Robustnessanalysis

Introduction



Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersAnalysis of parameters - IGBT modules - Ron,T=25C mΩ (>dfittool)

Rejected:Extreme value, Rayleigh, Normal, Logistic, Weibull, Gamma, ExtremeValue, Exponential

45

Robustnessanalysis

Introduction



Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersAnalysis of parameters - IGBT modules - Ron,T=25C mΩ

Remaining distributions

and now?Goodness of fit tests

45

Robustnessanalysis

Introduction



Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersAnalysis of parameters - IGBT modules - Ron,T=25C mΩ (>kstest, >kstest2 and>qqplot)

goodness of fit?Bad → groups ofpoints deviate fromline maintaining theslope → otherdistribution shadesthe fitting

45

Robustnessanalysis

Introduction



Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersAnalysis of parameters - IGBT modules - Ron,T=25C/Prated mΩ/W

New fit:Ron = f (module power)→ let’s try Ron,T=25C/Prated

45

Robustnessanalysis

Introduction



Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersAnalysis of parameters - IGBT modules - Ron,T=25C/Prated mΩ/W

Remaining distributions

45

Robustnessanalysis

Introduction



Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersAnalysis of parameters - IGBT modules - Ron,T=25C/Prated mΩ/W (>kstest,>kstest2 and >qqplot)

goodness of fit?OK → Only 5 farpoints

Look at the confidenceAt a confidence level of 81.91% other fit candidates are discarted !!!

45

Robustnessanalysis

Introduction



Simulation analysis



EU Efficiency


Conclusion


Parameter Distribution µ σ ModeIGBT Ron lognormal -3.9858 0.57921 13.3 mΩIGBT Lon

V ·I lognormal -28.6911 0.54508 0.2574 nH/kVAIGBT Tf

V ·I lognormal -25.7833 0.49124 4.9848 ns/kVAIGBT Tr

V ·I lognormal -27.0598 0.46334 1.4284 ns/kVAIGBT VCE,sat

I lognormal -3.4942 0.46530 0.0245 V /ADiode Ron lognormal -4.1475 0.61616 10.8 mΩ

Diode IfV normal 0.075149 0.038791 75.149 mA/V

Diode VfIfV

lognormal 3.2832 0.65968 17.254 V 2/A

Diode dIfdt lognormal 20.9285 0.74512 −704.71 A/µs

Diode Irrm lognormal 3.7343 0.45796 33.9393 ADiode Qrr

IfV

lognormal -9.469 0.75808 43.459 µF · V /A

Diode Trr lognormal -15.7293 0.52236 112.29 nsMode for normal and lognormal distributions are µ and eµ−σ2 respectively.

45

Robustnessanalysis

Introduction



Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersAnalysis of parameters - LCL filter

Parameter Typ. Min. (-5%) Max. (+5%)LCL Rinv 0.4 Ω 0.38 Ω 0.42 ΩLCL Linv 4.5 mH 4.27 mH 4.72 mHLCL Rgrid 0.1 Ω 0.095 Ω 0.105 ΩLCL Lgrid 1 mH 0.95 mH 1.05 mH

LCL Rdamp 5 Ω 4.75 Ω 5.25 ΩLCL Cf 4.5 µF 4.27 µF 4.72 µF

M. Liserre, F. Blaabjerg and S. Hansen, “Design and Control of an LCL-Filter-BasedThree-Phase Active Rectifier”, IEEE Trans. on Industry Applications, vol. 41, no. 5,sept.-oct. 2005. pp. 1281-1291.

45

Robustnessanalysis

Introduction



Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersSelecting the simulation points for MC - Latin Hypercube Sampling (LHS)

10 samples - Ron,T=25/Prated

Why?Allows the MCsamples to bereduced to a 33%-> Simulation time

45

Robustnessanalysis

Introduction



Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersSelecting the simulation points for MC - Latin Hypercube Sampling (LHS) - Allvariables & N sampling points

Procedure:The combination of regions is random. The point selected in eachregion is also random.

Parameter Sample setsRon,T=25Prated

S01

S05 S06 S02 S08 S10 S03 S04 S09 S07

VCE,T=25Ron,T=25Prated

S03

S07 S09 S01 S05 S02 S08 S06 S04 S10

45

Robustnessanalysis

Introduction



Simulation analysis



EU Efficiency


Conclusion




S01 S05

S06 S02 S08 S10 S03 S04 S09 S07

VCE,T=25Ron,T=25Prated

S03 S07

S09 S01 S05 S02 S08 S06 S04 S10

45

Robustnessanalysis

Introduction



Simulation analysis



EU Efficiency


Conclusion




S01 S05 S06 S02 S08 S10 S03 S04 S09 S07VCE,T=25Ron,T=25Prated

S03 S07 S09 S01 S05 S02 S08 S06 S04 S10

45

Robustnessanalysis

Introduction

Robustness of PVinverters: AnexampleAnalysis ofparameters

33 Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersSimulation model (MatLab+PLECS)

45

Robustnessanalysis

Introduction


34 Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersModel parameters & study cases

I Nominal power: 4 kWI Grid: 230 V rms , 50 HzI V ref

dc = 600 VI fsw = 6 kHzI Current controller: Kp = 7, K50Hz = 2000I Study cases:

I Variations of all parameters: 500 simulations per power levelI Variations of parameters within a subsystem: 400 simulations

per power levelI Individual parameter variations: 360 simulations per power level

45

Robustnessanalysis

Introduction


Simulation analysis

35 Impact on µη andση


EU Efficiency


Conclusion

Robustness of ηEU in PV invertersVariations of all parameters - η

0.7 0.8 0.9 10

20

40

60

80D

ensity

η200W

(pu). Fit: µ=0.9393,σ=0.021

P=200 W

Data

Fit

0.9 0.92 0.94 0.960

50

100

150

200

Density

η400W

(pu). Fit: µ=0.9499,σ=0.0037

P=400 W

Data

Fit

0.944 0.946 0.948 0.95 0.952 0.9540

100

200

300

Density

η800W

(pu). Fit: µ=0.9477,σ=0.0015

P=800 W

Data

Fit

0.945 0.95 0.9550

100

200

300

Density

η1200W

(pu). Fit: µ=0.9493,σ=0.0017

P=1200 W

Data

Fit

0.945 0.95 0.9550

100

200

300

400

Density

η2000W

(pu). Fit: µ=0.9517,σ=0.0015

P=2000 W

Data

Fit

0.95 0.952 0.954 0.956 0.9580

100

200

300

400D

ensity

η4000W

(pu). Fit: µ=0.9539,σ=0.0013

P=4000 W

Data

Fit

I µη ∈ [93.93%, 95.39%] y ση ∈ [0.13%, 2.1%]

I If P ↑→ ση ↓ and µη ↑ ( LCL and IGBT parameters have beenselected for operation at the nominal power)

45

Robustnessanalysis

Introduction


Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersVariations of parameters within a subsystem - η

0.93 0.94 0.95 0.960

50

100

150

De

nsity

η200W

(pu). Fit: µ=0.946,σ=0.0033

P=200 W

Data

Fit

0.946 0.948 0.95 0.952 0.954 0.956 0.9580

100

200

300

De

nsity

η400W

(pu). Fit: µ=0.951,σ=0.0017

P=400 W

Data

Fit

0.946 0.948 0.95 0.952 0.9540

100

200

300

400

De

nsity

η800W

(pu). Fit: µ=0.9489,σ=0.0011

P=800 W

Data

Fit

0.948 0.95 0.952 0.9540

100

200

300

400D

en

sity

η1200W

(pu). Fit: µ=0.9504,σ=0.0011

P=1200 W

Data

Fit

0.951 0.952 0.953 0.954 0.955 0.9560

200

400

600

800

De

nsity

η2000W

(pu). Fit: µ=0.9529,σ=0.0006

P=2000 W

Data

Fit

0.954 0.955 0.956 0.9570

200

400

600

800

De

nsity

η4000W

(pu). Fit: µ=0.9551,σ=0.0005

P=4000 W

Data

Fit

0.6 0.7 0.8 0.9 10

20

40

60

80

Density

η200W

(pu). Fit: µ=0.9409,σ=0.0228

P=200 W

Data

Fit

0.935 0.94 0.945 0.95 0.9550

100

200

300

400

Density

η400W

(pu). Fit: µ=0.9501,σ=0.0017

P=400 W

Data

Fit

0.94 0.945 0.950

200

400

600

Density

η800W

(pu). Fit: µ=0.9475,σ=0.0014

P=800 W

Data

Fit

0.946 0.948 0.95 0.9520

100

200

300

400

Density

η1200W

(pu). Fit: µ=0.949,σ=0.0012

P=1200 W

Data

Fit

0.948 0.95 0.952 0.954 0.9560

200

400

600

Density

η2000W

(pu). Fit: µ=0.9518,σ=0.0012

P=2000 W

Data

Fit

0.95 0.952 0.954 0.956 0.9580

100

200

300

400

Density

η4000W

(pu). Fit: µ=0.954,σ=0.001

P=4000 W

Data

Fit

I σηI LCL filter: ∈ [0.05%, 0.33%]I IGBT module: ∈ [0.1%, 2.28%]

I µηI LCL filter: ∈ [94.6%, 95.51%]I IGBT module: ∈ [94.09%, 95.4%]

I The characteristics of the IGBT subsystem impact the most on theoverall performance

45

Robustnessanalysis

Introduction


Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersIndividual parameter variations - µη

variability of H-bridge parameters affects most of the overallperformance.

C. Individual parameter variations

A further analysis can be carried out by considering varia-tions of only one parameter and maintaining other parametersto the mode of their distributions. These results are summarizedin Fig. 5.a, where the mean value of ην at each power levelis plotted. These values increase from 94.55 %, at 200 W ,to 95.51 %, at the nominal power (4 kW ). Deviations fromthese mean values, due to the behaviour of each individualparameter, are shown in Fig. 5.b, 5.c and 5.d, which correspondto IGBT, Diode and LCL parameters respectively. From Fig.5.b, and in the case of variations applied to IGBT parameters,the variation resulting in the worst efficiency, at all powerlevels, is Ron, which reduces the value of µη up to 0.19 % at200 W . The efficiency is also reduced by variations of V sat

CE ,which reduces the value of µη up to 0.03 % at 200 W . As it canbe seen, the importance of changes µη reduces with increasingpower levels and are maintained above 1 kW . In the case ofvariations of diode parameters (Fig. 5.c), variations of Irrm

reduces µη the most at low power levels (below 1 kW ). Asin the case of IGBT parameters, Ron reduces the values ofµη up to 0.015 %. Other parameters decreasing µη are Trr

and dIf/dt. Fig. 5.d shows that the smallest reduction of µη

occurs in the case of LCL-filter parameters variations.

The effect of individual parameter variations on the ef-ficiency variance is shown in Fig. 6.a. As it can be seen,increasing the power level of the PV inverter reduces therelative variance (ση/µη), which reaches its lowest level atthe nominal power. Fig. 6.b shows that, in the case of IGBTparameters, the greatest variances are due to Ron and V sat

CE , lowvalues are obtained when Lon and Tr variations are applied.It is also shown that the variability is greater at 200 W . In thecase of diode variations (Fig. 6.c), the variance of η increases,at low power, due to Irrm variances. The figure shows that theeffect of Trr and dIf/dt is very important at 2 kW . From Fig.6.d, the effect of the variance of LCL-filter parameters is thelowest one on the overall variances. The variance is reduced atlow power levels and increases at the nominal power of the PVinverter. It must be noted that, the values of ση/µη increases,at low powers, due to the variance of Linv and, around thenominal power, due to Rinv variance.

D. Comparison of parameters resulting in the best and worstperformances

The process of manufacturing the power converter topologydepicted in Fig. 1, requires a set of engineering decisions tobe adopted, among them, the selection of the most appropriatecomponents. This section provides a statistical based approachin order to simplify this process. From Fig. 2, the efficiencyof the analyzed topology changes depending on the set ofparameters applied to the simulation model. In order to selectthe most appropriate parameters for implementation purposes,the parameters of the simulation points, which resuls on better(µη + ση) and worst (µη − ση) performances in Fig. 2 canbe compared. This comparison can be carried out by means ofthe two-sample Kolmogorov-Smirnov test applied to these setsof parameters. Increasing the Significance Level (SL) from a

0 1 2 3 4

94.5

95

95.5

Power (kW)

mea

n(µ

η)

(%)

(a) Mean efficiency

0 1 2 3 4−0.2

−0.1

0

0.1

0.2

Power (kW)

µη

-m

ean(µ

η)

(%) Ron

Lon

Tf

Tr

VsatCE

(b) IGBT parameters

0 1 2 3 4

−0.4

−0.2

0

0.2

Power (kW)

µη

-m

ean(µ

η)

(%) Ron

If

Vf

dIr/dt

Irrm

Qrr

Trr

(c) Diode parameters

0 1 2 3 4

−5 · 10−2

0

5 · 10−2

0.1

Power (kW)

µη

-m

ean(µ

η)

(%) Rinv

Linv

Rgrid

Lgrid

Rdamp

Cf

(d) LCL-filter parameters

Fig. 5. Effect of individual parameter variations on the efficiency mode (µη )at 200 W , 400 W , 800 W , 1.2 kW , 2 kW and 4 kW . a) Mean efficiency,b) IGBT parameters, c) diode parameters and d) LCL-filter parameters.

low value and, considering a certain power level, will showthe parameters which are changing the most from worst to thebest performance. Fig. 7.a shows that the mean value of theSL decreases when the power level increases, which impliesthat the differences among the best and worst simulation pointsincreases with power. Further analysis are shown Fig. 7.b, 7.cand 7.d, corresponding to IGBT, diode and LCL parameters.From Fig. 7.b, Tr, for the best and worst simulation points,changes at low and high powers, but it is not very relevantat intermediate power levels. In the case of Lon, its relevanceis higher at low powers and lower at higher power levels. Tf

only changes at 400 W and 1.2 kW , not being relevant atother power levels. In the case of diode parameters (Fig. 7.c),Trr does not change a lot at low power but, increasing thepower, results on a higher effect on the performance variances.dIf/dt changes, in simulation points with worst and bestperformances, only at medium powers (from 1.2 kW to 2 kW )while Ron and Irrm change at almost all power levels. Fig.7.d shows the SL for LCL-filter parameters. As it is shown,at power levels from 400 W to 4 kW , Rinv changes morethan Rgrid. In the case of Linv and Lgrid, at low powers Linv

I Averaged performance: η increases withhigher power levels

I IGBT parameters:I Ron reduces the efficiency the most

(up to 0.19% at 200 W ).I Tr and V sat

CE reduce the efficiency atlow and nominal power levelsrespectively.

I Impact of parameters is maintained inthe range [1.2kW , 4kW ]

I Diode parameters:I Above 1 kW , their impact is lower

than IGBT parametersI Irrm has a higher impact at lower

power levels

I LCL filter parameters:I Low impact on the overall

performance

45

Robustnessanalysis

Introduction


Simulation analysis



EU Efficiency


Conclusion

Robustness of ηEU in PV invertersIndividual parameter variations - ση

0 1 2 3 40

0.1

0.2

0.3

0.4

Power (kW)

mea

n(σ

η/µ

η)

(%)

(a) Mean relative variance

0 1 2 3 4−0.2

−0.1

0

0.1

Power (kW)

ση

/µη

-m

ean(σ

η/µ

η)

(%)

Ron

Lon

Tf

Tr

VsatCE

(b) IGBT parameters

0 1 2 3 4

0

1

2

Power (kW)

ση

/µη

-m

ean(σ

η/µ

η)

(%)

Ron

If

Vf

dIr/dt

Irrm

Qrr

Trr


0 1 2 3 4−0.2

−0.1

0

Power (kW)

ση

/µη

-m

ean(σ

η/µ

η)

(%)

Rinv

Linv

Rgrid

Lgrid

Rdamp

Cf


Fig. 6. Effect of individual parameter variations on the efficiency relativevariances (ση/µη ) at 4 kW , 2 kW , 1.2 kW , 800 W , 400 W and 200 W .a) Mean relative variance, b) IGBT parameters, c) diode parameters and d)LCL-filter parameters.

changes more than Lgrid and, at power levels above 2 kW , thechanges in Lgrid are greater than the changes in Linv and. Asa consequence, the statistic comparison of the MC simulationresults can be employed by the designers in order to focus on,and balance the critical parameters in a certain power range.

E. Effect on the European Efficiency

The European Efficiency of the PV inverter has beenanalyzed in the case of variations within the analyzed ranges.The European Efficiency can be evaluated by means of

ηEU = 0.03 · η5% + 0.06 · η10% + 0.13 · η20%

+0.1 · η30% + 0.48 · η50% + 0.2 · η100%(1)

which, considering µ values in Fig. 2, results on ηEU = 95.09%. This value does not provide information about σ and onlyconsiders mean performances of the PV system at each powerlevel. Fig. 8 shows the evaluated European Efficiency, from (1),

0 1 2 3 4

40

50

60

Power (kW)

mea

n(m

ax(S

L))

(%)

(a) Mean of Max. SL of fittings

0 1 2 3 40

20

40

60

80

100

Power (kW)m

ax(S

L)

(%)

Ron

Lon

Tf

Tr

VsatCE

(b) IGBT parameters

0 1 2 3 40

20

40

60

80

100

Power (kW)

max

(SL

)(%

)

Ron

If

Vf

dIr/dt

Irrm

Qrr

Trr


0 1 2 3 40

20

40

60

80

100

Power (kW)

max

(SL

)(%

)

Rinv

Linv

Rgrid

Lgrid

Rdamp

Cf


Fig. 7. Significance Level (SL) of two-samples K-S tests applied to simulationparameters resulting on best and worst efficiencies at 200 W , 400 W , 800W , 1.2 kW , 1.6 kW , 2 kW , 2.4 kW and 4 kW . a) Mean of the significancelevel, b) IGBT parameters, c) diode parameters and d) LCL-filter parameters.

but considering efficiency distributions at each power level. Asit can be seen, the variance of ηEU is 0.52 % and a maximumprobability of 64.31 % is reached for efficiencies of 95.25 %.Moreover, considering the applied parameter variances thereis a probability of 2.61 % of having low efficiencies, equal orbelow 94.57 %, and a probability of 4.26 % for efficienciesover 95.61 %. It can also be found in Fig. 8 that there isa no null probability (4.4 · 10−3 %) of having very lowefficiencies (< 64 %). As a consequence, by applying theconventional approach for ηEU , information about the qualityof the PV system is missed (σ and distribution of efficiencies)and the effect of parameter variations, due to the involvedmanufacturing processes, on the overall performance are notconsidered.

F. Experimental Results

The general scheme depicted in Fig. 1 has been tested usingtwo modified motor drives operated as inverters. The nominalpower of the laboratory setup is Pn = 1.1 kW , six 1φ H-bridge

I Averaged performance: σ/µ decreases withhigher power levels

I IGBT parameters:I Ron, V sat

CE and Tr variations result ongreater σ/µ variations

I Diode parameters:I Irrm and Qrr have a higher impact at

lower power levels.I Trr and dIf /dt change σ/µ values

around 2 kW .

I LCL filter parameters:I Lower impact on the overall

performanceI Linv and Rinv variations have a greater

impact at low and nominal powersrespectively.

45

Robustnessanalysis

Introduction


Simulation analysis


39 Comparison ofparameters

EU Efficiency


Conclusion

Robustness of ηEU in PV invertersComparison of parameters resulting in the best and worst performances

Comparisson:Best (η > µ + σ) vs worst (η < µ− σ) points.

94.5 95 95.5 96 96.50

0.5

1

η(%)

Den

sity

Which are the changing parameters?KS tests, increasing the significance level (SL), detect the parameterswhich change the most

45

Robustnessanalysis

Introduction


Simulation analysis


40 Comparison ofparameters

EU Efficiency


Conclusion

Robustness of ηEU in PV invertersComparison of parameters resulting in the best and worst performances

0 1 2 3 40

0.1

0.2

0.3

0.4

Power (kW)

mea

n(σ

η/µ

η)

(%)

(a) Mean relative variance

0 1 2 3 4−0.2

−0.1

0

0.1

Power (kW)

ση

/µη

-m

ean(σ

η/µ

η)

(%)

Ron

Lon

Tf

Tr

VsatCE

(b) IGBT parameters

0 1 2 3 4

0

1

2

Power (kW)

ση

/µη

-m

ean(σ

η/µ

η)

(%)

Ron

If

Vf

dIr/dt

Irrm

Qrr

Trr


0 1 2 3 4−0.2

−0.1

0

Power (kW)

ση

/µη

-m

ean(σ

η/µ

η)

(%)

Rinv

Linv

Rgrid

Lgrid

Rdamp

Cf


Fig. 6. Effect of individual parameter variations on the efficiency relativevariances (ση/µη ) at 4 kW , 2 kW , 1.2 kW , 800 W , 400 W and 200 W .a) Mean relative variance, b) IGBT parameters, c) diode parameters and d)LCL-filter parameters.

changes more than Lgrid and, at power levels above 2 kW , thechanges in Lgrid are greater than the changes in Linv and. Asa consequence, the statistic comparison of the MC simulationresults can be employed by the designers in order to focus on,and balance the critical parameters in a certain power range.

E. Effect on the European Efficiency

The European Efficiency of the PV inverter has beenanalyzed in the case of variations within the analyzed ranges.The European Efficiency can be evaluated by means of

ηEU = 0.03 · η5% + 0.06 · η10% + 0.13 · η20%

+0.1 · η30% + 0.48 · η50% + 0.2 · η100%(1)

which, considering µ values in Fig. 2, results on ηEU = 95.09%. This value does not provide information about σ and onlyconsiders mean performances of the PV system at each powerlevel. Fig. 8 shows the evaluated European Efficiency, from (1),

0 1 2 3 4

40

50

60

Power (kW)

mea

n(m

ax(S

L))

(%)

(a) Mean of Max. SL of fittings

0 1 2 3 40

20

40

60

80

100

Power (kW)

max

(SL

)(%

)

Ron

Lon

Tf

Tr

VsatCE

(b) IGBT parameters

0 1 2 3 40

20

40

60

80

100

Power (kW)

max

(SL

)(%

)

Ron

If

Vf

dIr/dt

Irrm

Qrr

Trr


0 1 2 3 40

20

40

60

80

100

Power (kW)

max

(SL

)(%

)

Rinv

Linv

Rgrid

Lgrid

Rdamp

Cf


Fig. 7. Significance Level (SL) of two-samples K-S tests applied to simulationparameters resulting on best and worst efficiencies at 200 W , 400 W , 800W , 1.2 kW , 1.6 kW , 2 kW , 2.4 kW and 4 kW . a) Mean of the significancelevel, b) IGBT parameters, c) diode parameters and d) LCL-filter parameters.

but considering efficiency distributions at each power level. Asit can be seen, the variance of ηEU is 0.52 % and a maximumprobability of 64.31 % is reached for efficiencies of 95.25 %.Moreover, considering the applied parameter variances thereis a probability of 2.61 % of having low efficiencies, equal orbelow 94.57 %, and a probability of 4.26 % for efficienciesover 95.61 %. It can also be found in Fig. 8 that there isa no null probability (4.4 · 10−3 %) of having very lowefficiencies (< 64 %). As a consequence, by applying theconventional approach for ηEU , information about the qualityof the PV system is missed (σ and distribution of efficiencies)and the effect of parameter variations, due to the involvedmanufacturing processes, on the overall performance are notconsidered.

F. Experimental Results

The general scheme depicted in Fig. 1 has been tested usingtwo modified motor drives operated as inverters. The nominalpower of the laboratory setup is Pn = 1.1 kW , six 1φ H-bridge

I Averaged performance: SL decreases withincreasing power → differences inparameters increase with power.

I IGBT parameters:I Differences in Tr are relevant at

intermediate power levelsI Lon has a higher relevance at low

powers

I Diode parameters:I Differences in dIf /dt are relevant at

intermediate power levelsI Trr has a higher relevance at nominal

power.I Ron and Irrm keep on changing at all

power levels.

I LCL filter parameters:I Rinv changes have more impact than

Rgrid ones.I Relevance of Lgrid and Linv depends

on the power level.

45

Robustnessanalysis

Introduction


Simulation analysis



41 EU Efficiency


Conclusion

Robustness of ηEU in PV invertersEuropean Efficiency

60 70 80 90 1000

20

40

60

80

ηEU (%)

Pro

bab

ilit

y(%

)

Fig. 8. European Efficiency evaluated from the efficiency distributions.

60 70 80 90 1000

20

40

60

80

ηEU (%)

Pro

bab

ilit

y(%

)

Fig. 9. European Efficiency evaluated from the experimental efficiencydistributions and applying variations of the H-bridge.

configurations (UV, UW and VW for each drive) have beentested and the efficiency has been measured at diverse timeintervals by means of a Yokogawa WT3000 power analyzer.The European Efficiency has been evaluated according to theproposed approach, based on effciency distributions, resultingon Fig. 9. The obtained mean value is 93.12%, with ση =3.2%, and there is a probability of 2.5% of having EuropeanEfficiencies in the range [78, 81]%. The probability of havingEuropean Efficiencies in the range [93, 96]%, considering theemployed drive series and the analyzed configuration, is 74.13%.

IV. CONCLUSIONS

This paper presents a statistical approach for analysis ofPV inverters and evaluation of their performance subjectedto physical variations due to the manufacturing process. Theperformance of the PV inverter, and the impact of thesephysical variations, are analyzed in simulation at diverse levels(whole system, subsystem and individual components). Fromthis analysis, variations of IGBT Ron and V sat

CE and diode Ron

reduces the PV inverter efficiency. These variations reduce the

PV inverter robustness due to the variance of its performance

which reaches mean(

ση

µη

)= 0.35% at 200W (the obtained

value at the nominal power is 0.02%). It is proposed amechanism for selection of the most suitable componentsby comparing quartiles of the distribution at different powerlevels. Finally, it is also proposed to change the definitionof European Efficiency of PV inverters to an statistical basedapproach, where µη and ση values allow the performance ofPV inverters to be evaluated considering a 6σ methodology.

REFERENCES

[1] F. Blaabjerg, A. Consoli, J. A. Ferreira and J. D. van Wyk, The futureof electronic power processing and conversion, IEEE Trans. on PowerElectronics, vol. 20, no. 3, March 2005. pp. 715-720.

[2] J. M. Carrasco, L. Garcıa Franquelo, J. T. Bialasiewicz, E. Galvan, R.C. Portillo Guisado, Ma A. Martın Prats, J. I. Leon, and N. Moreno-Alfonso, The future of electronic power processing and conversion, IEEETrans. on Industrial Electronics, vol. 53. no. 4, April 2006. pp. 1002-1016.

[3] M. Glinkowski, J. Hou and G. Rackliffe, Advances in wind energy

technologies in the context of smart grid, Proceedings of the IEEE, vol.99, no. 6, June 2011. pp. 1083-1097.

[4] G. Spagnuolo, G. Petrone, S. Vasconcelos Araujo, C. Cecati, E. Friis-Madsen, E. Gubıa, D. Hissel, M. Jasinski, W. Knapp, M. Liserre, P.J. Rodrıguez, R. E. Teodorescu and P. Zacharias, Renewable Energy

Operation and Conversion Schemes: A Summary of Discussions During

the Seminar on Renewable Energy Systems, IEEE Industrial ElectronicsMagazine, vol. 4, no. 1, 2010. pp. 38-51.

[5] R. Teodorescu, M. Liserre and P. Rodrıguez, Grid converters for photo-

voltaic and wind power systems, Wiley 2010. ISBN: 978-0-470-05751-3.

[6] D. G. Holmes and T. A. Lipo, Pulse width modulation for power

converters: Principles and practice, Wiley & Sons, 2003. ISBN: 978-0-471-20814-3

[7] H. Zhang and L. M. Tolbert, Efficiency Impact of Silicon Carbide Power

Electronics for Modern Wind Turbine Full Scale Frequency Converter,IEEE Trans. on Industrial Electronics, vol. 58, no. 1, January 2011. pp.21-28.

[8] S. Shina, Six Sigma for Electronics Design and Manufacturing, McGraw-Hill, 2002. ISBN: 978-0-071-39511-3.

[9] H. Wang, “A Review of Six Sigma Approach: Methodology, Implemen-tation and Future Research,” in Proc. of the 4th International Confer-ence on Wireless Communications, Networking and Mobile Computing

(WiCOM’08), pp. 1-4. 2008.

[10] H. S. Krishnamoorthy, P. Mazumdar, I. Manickam, R. S. Balog andP. N. Enjeti, “Decision making framework for solar photovoltaic powerconditioning unit topologies using Six Sigma,” in Proc. of the 38th IEEE

Photovoltaic Specialists Conference (PVSC’12), pp. 1352-1356. 2012.

[11] J.-S. Hwang, K.-H. Kim, Y.-T. Kim and S.-M. Baek, “Parameteroptimization of field oriented control with 6 sigma tool,” in Proc. ofthe 2001 IEEE International Symposium on Industrial Electronics, vol.3, pp. 1866-1870. 2001.

[12] J.-F. Normand and R. E. Draper, “Resolution of insulation related manu-facturing problems using the Six Sigma methodology and tools,” Proc. ofthe 1997 Electrical Insulation Conference and Electrical Manufacturing

& Coild Winding Conference, pp. 769-774. 1997.

[13] M. Liserre, F. Blaabjerg and S. Hansen, “Design and Control of an LCL-Filter-Based Three-Phase Active Rectifier”, IEEE Trans. on Industry

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[14] J. Allmeling and W. Hammer, PLECS User Manual, v.3.3. 2012.

[15] P. O’Connor and A. Kleyner, Practical Reliability Engineering, 5th Ed.Wiley, January 2012. ISBN: 978-0-470-97981-5.

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ternational Midwest Symposium on Circuits and Systems, vol. 1, no. 8,Aug. 1999. pp. 367370.

I ηEU = 0.03 · η5% + 0.06 · η10% + 0.13 · η20%

+0.1 · η30% + 0.48 · η50% + 0.2 · η100%→ 95.09%

I Statistical approach (distributions): µη = 95.09% and ση = 0.52%

45

Robustnessanalysis

Introduction


Simulation analysis



EU Efficiency

42 Experimental results

Conclusion

Robustness of ηEU in PV invertersExperimental results - European Efficiency

94.6

94.8

95

95.2

95.4

H1 H2 H3 H4 H5 H6

η1

.1kW

(%

)

94

94.5

95

H1 H2 H3 H4 H5 H6

η0

.55

kW

(%

)

92.8

93

93.2

93.4

93.6

H1 H2 H3 H4 H5 H6

η0

.33

kW

(%

)

91

91.5

92

H1 H2 H3 H4 H5 H6

η0

.22

kW

(%

)

86

86.5

87

87.5

H1 H2 H3 H4 H5 H6

η0

.11

kW

(%

)

76

77

78

H1 H2 H3 H4 H5 H6

η0

.05

5kW

(%

)

I Nominal power: 1.1 kWI Six 1φ H-bridge

configurationsI Efficiency

measurements:Yokogawa WT3000

45

Robustnessanalysis

Introduction


Simulation analysis



EU Efficiency

43 Experimental results

Conclusion

Robustness of ηEU in PV invertersExperimental results - European Efficiency

60 70 80 90 1000

20

40

60

80

ηEU (%)

Pro

bab

ilit

y(%

)

Fig. 8. European Efficiency evaluated from the efficiency distributions.

60 70 80 90 1000

20

40

60

80

ηEU (%)

Pro

bab

ilit

y(%

)

Fig. 9. European Efficiency evaluated from the experimental efficiencydistributions and applying variations of the H-bridge.

configurations (UV, UW and VW for each drive) have beentested and the efficiency has been measured at diverse timeintervals by means of a Yokogawa WT3000 power analyzer.The European Efficiency has been evaluated according to theproposed approach, based on effciency distributions, resultingon Fig. 9. The obtained mean value is 93.12%, with ση =3.2%, and there is a probability of 2.5% of having EuropeanEfficiencies in the range [78, 81]%. The probability of havingEuropean Efficiencies in the range [93, 96]%, considering theemployed drive series and the analyzed configuration, is 74.13%.

IV. CONCLUSIONS

This paper presents a statistical approach for analysis ofPV inverters and evaluation of their performance subjectedto physical variations due to the manufacturing process. Theperformance of the PV inverter, and the impact of thesephysical variations, are analyzed in simulation at diverse levels(whole system, subsystem and individual components). Fromthis analysis, variations of IGBT Ron and V sat

CE and diode Ron

reduces the PV inverter efficiency. These variations reduce the

PV inverter robustness due to the variance of its performance

which reaches mean(

ση

µη

)= 0.35% at 200W (the obtained

value at the nominal power is 0.02%). It is proposed amechanism for selection of the most suitable componentsby comparing quartiles of the distribution at different powerlevels. Finally, it is also proposed to change the definitionof European Efficiency of PV inverters to an statistical basedapproach, where µη and ση values allow the performance ofPV inverters to be evaluated considering a 6σ methodology.

REFERENCES

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µη = 93.12%, ση = 3.2%

45

Robustnessanalysis

Introduction


44 Conclusion

Conclusion

I Physical variations in PV inverters have an impact on itsperformance at i) whole system, ii) subsystem and iii)component levels

I The proposed statistical approach allows the most suitablecomponents to be selected once the topology, the operatingranges and the controller have been established.

I The European Efficiency of PV inverters must be defined usingan statistical based approach in order to provide more info aboutthe inverter performance.

45

Robustnessanalysis

Introduction


Conclusion

Thank you very much for your attention.

Robustness Analysis of PV inverters - Kiel · 2013-12-18 · December18,2013. 45 Robustness...

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