blaabjerg pv reliability 201301

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 1, JANUARY 2013 325

Design Optimization of TransformerlessGrid-Connected PV Inverters Including Reliability

Eftichios Koutroulis, Member, IEEE, and Frede Blaabjerg, Fellow, IEEE

AbstractThis paper presents a new methodology for optimaldesign of transformerless photovoltaic (PV) inverters targeting acost-effective deployment of grid-connected PV systems. The opti-mal switching frequency as well as the optimal values and types ofthe PV inverter components is calculated such that the PV inverterLCOE generated during the PV system lifetime period is mini-mized. The LCOE is also calculated considering the failure ratesof the components, which affect the reliability performance andlifetime maintenance cost of the PV inverter. A design example ispresented, demonstrating that compared to the nonoptimized PVinverter structures, the PV inverters designed using the proposedoptimization methodology exhibit lower total manufacturing andlifetime maintenance cost and inject more energy into the electric-grid and by that minimizing LCOE.

Index TermsDCAC power conversion, failure analysis, opti-mization methods, photovoltaic (PV) power systems, reliability.

NOMENCLATURECf LCL-filter capacitor.Cinv (X) Present value of the PV inverter total cost.Ct(X) Total manufacturing cost of the PV inverter.Ei(X) Total energy injected into the electric grid.L Converter-side inductance.LCOE Levelized cost of the electricity generated.Lg Grid-side inductance.Minv Repair cost of the PV inverter.Mt(X) Present value of the total maintenance cost.Nj (X) Average number of failures during the jth year

of operation.Pd,max Maximum power dissipated in the damping

resistor.Pcu Power consumption of the PV inverter control

unit.Pld,i Total power loss of the ith free-wheeling diode.Pl,L (t, y) Power loss of the LCL-filter converter-side

inductor.Pl,Lg Power loss of the LCL-filter grid-side inductor.

Manuscript received February 3, 2012; revised March 30, 2012; acceptedApril 30, 2012. Date of current version September 11, 2012. This paper waspresented at the 27th Annual IEEE Applied Power Electronics Conference andExposition, Orlando, FL, February 59, 2012. Recommended for publicationby Associate Editor P. T. Krein.

E. Koutroulis is with the Department of Electronic and Computer Engi-neering, Technical University of Crete, Chania GR-73100, Greece (e-mail:[email protected]).

F. Blaabjerg is with the Department of Energy Technology, Aalborg Univer-sity, Aalborg DK-9220, Denmark (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2012.2198670

Plps,i Total power loss of the ith power switch.Pl,Rd r Power loss of the LCL-filter damping resistor.PM (t) PV array power production at the maximum

power point during hour t.Pn Nominal output power of the PV inverter.Po Power injected into the electric grid.Ppv Output power of the PV array.PRd r Weighted-average value of the damping resistor

power consumption.Ptot Total power loss of the PV inverter.Rdr LCL-filter damping resistor.RFmax Maximum permissible limit of harmonic current

distortion at the PV inverter output.Rp(X) Reliability (or survival) function.SF Damping resistor oversizing factor.Sl Radiating surface area of case per unit induc-

tance and per unit nominal operating current.TA (t, y) PV inverter ambient temperature at hour t of

year y.TA Weighted-average value of the ambient

temperature.Tjd,i Weighted-average value of the free-wheeling

diodes junction temperature.Tjd,max Maximum permissible junction temperature of

the free-wheeling diodes.Tjnd,i Operating junction temperature of the free-

wheeling diodes.Tjps,i Operating junction temperature of the power

switches.Tjps,i Weighted-average value of the power switches

junction temperature.Tjps,max Maximum permissible junction temperature of

the power switches.TL Weighted-average of the converter-side inductor

operating temperature.TLg Weighted-average of the grid-side inductor op-

erating temperature.TRd r Weighted-average of the damping resistor oper-

ating temperature.VCf Weighted-average of the LCL-filter capacitor

voltage.Vpv Weighted-average of the dc input voltage.Vn Nominal voltage of the electric grid.X Vector of the optimization problem design

variables.cc LCL-filter capacitor cost per unit capacitance.cd Free-wheeling diode cost.chs Cost of the heat sink.

0885-8993/$31.00 2012 IEEE

326 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 1, JANUARY 2013

ci LCL-filter inductor cost per unit inductance andcurrent rating.

cinv Partial manufacturing cost of the PV inverter.cr Filter damping resistor cost per unit resistance

and power.cs Power switch cost.d Annual discount rate.f Nominal frequency of the electric grid.fs Switching frequency.fs,max Maximum switching speed capability of the

power switches.g Annual inflation rate.n Number of years of PV system service lifetime.p Total number of power switches.r() Annual reduction coefficient of the PV modules

output power.t Time number (1 t 8760).y Year number (1 y n).t Simulation time step.ca Thermal resistance of the heat sink.jc,d Thermal resistance from the junction to the case

of the free-wheeling diodes.jc,ps Thermal resistance from the junction to the case

of the power switches.c Total failure rate of the remaining components

and subsystems of the PV inverter.Cf Failure rate of the LCL-filter capacitor.C in Failure rate of the dc-link capacitor.d,i Failure rate of the free-wheeling diodes.inv (X) PV inverter failure rate.L Failure rate of the LCL-filter converter-side

inductor.Lg Failure rate of the LCL-filter grid-side inductor.ps,i Failure rate of the power switches.Rd r Failure rate of the LCL-filter damping resistor.

I. INTRODUCTION

ACCORDING to the European Photovoltaic Industry As-sociation, the growth of the photovoltaic (PV) system ca-pacity seen in the last ten years is expected to continue in thenear future also [1]. Nowadays, the majority of PV systemsare used to supply the generated energy into the electric grid. Ablock diagram of a grid-connected PV system employing a trans-formerless, full-bridge dc/ac inverter (PV inverter) is illustratedin Fig. 1. Compared to the PV inverters with galvanic isolation,the transformerless PV inverters have the advantages of lowercost, higher efficiency, smaller size, and lower weight [2], [3].Using an LCL-type output filter, instead of the traditional L-or LC-type filters, aims toward the reduction of the size of thereactive elements comprising the output filter of the PV in-verter [4], [5].

A cost-effective deployment of grid-connected PV systemscan be achieved by minimizing the initial investment cost re-quired to purchase and install the PV system components (e.g.,PV modules, dc/ac inverters, etc.), maximizing the amount ofenergy injected into the electric grid, and increasing its relia-

Fig. 1. Grid-connected PV system employing a transformerless PV inverter.

bility by minimizing the number of failures of the PV systemcomponents which occur during the operational lifetime pe-riod of the PV installation [6], [7]. The energy injected intothe electric grid can be maximized by applying an effectivemaximum power point tracker (MPPT) control strategy [8] anddesigning the PV inverter such that the PV array output power isefficiently processed by the PV inverter [9]. The reliability char-acteristics of the PV system components are usually expressedusing indices such as the failure rate or the mean time betweenfailures (MTBF) [7]. The duration of grid-connected PV sys-tem investments follows the operational lifetime period of thecommercially available PV modules and it is typically of theorder of 25 years. The components comprising the PV system(i.e., PV modules, dc/ac inverters, and the balance of systemcomponents) are required to operate with high reliability duringthat time interval.

The exploration of the PV system components reliabilitycharacteristics is indispensable in order to accurately predictthe lifetime energy production and total revenues achieved bythe PV energy production system. The commercially availablePV modules are typically offered with a 25-year performancewarranty and constitute the most reliable component of a PVsystem [10]. In contrast, according to the analysis presentedin [11] where both wearout mechanisms of the components (dueto stress factors such as, e.g., the operating temperature) andfailures due to inadequate protection (e.g., from surge voltagesof the electric grid) were taken into account, the PV invertersare considered as the most vulnerable subsystem of a PV plant.Their reliability is affected by the operational characteristics ofthe components they comprise, which also affect the PV inverterpower conversion efficiency and the amount of energy injectedinto the electric grid. A single PV inverter failure may cause asignificant PV power production loss [12], affecting both the PVplant operating and maintenance costs and the energy yield [13].As analyzed in [14], the range of ambient temperature valuesprevailing at the PV inverter installation site, as well as theoperating hours and output power levels, must be consideredduring the PV inverter design stage in order to meet the long-term reliability requirements of the PV inverter. Achieving ahigh reliability of PV inverters is considered as an immediatepriority for the PV industry in order to match the lifetime of PVmodules [15]. According to [16], both cost and reliability shouldbe taken into account in order to design PV power processingsystems, but frequently the impact of reliability is not explicitly

KOUTROULIS AND BLAABJERG: DESIGN OPTIMIZATION OF TRANSFORMERLESS GRID-CONNECTED PV INVERTERS 327

incorporated in the design process of PV inverters (e.g., such asin [17] and [18]).

The failure mechanisms and reliability modeling approachesof power devices used in power converters are analyzed in [19].The development of a simulation tool for determining thecomponent temperature and expected reliability of three-phasedc/ac inverters deployed in hybrid electric vehicles is presentedin [20]. The reliability of parallel-connected dc/ac inverters op-erating under a dynamic power distribution control scheme inan N+X architecture (i.e., the system operates when N of thetotal N+X converters operate) is explored in [21]. The reliabil-ity analysis is then used to determine the optimal values of Nand X such that the total cost of the system is minimized. Aprocedure for reliability assessment, in terms of the mean timeto failure (MTTF) metric, of multiphase dc/dc converters usedin PV applications is proposed in [22].

A methodology based on the design-of-experiment (DOE)technique for the design of a PV inverter such that it exhibitsthe desired MTBF is presented in [23]. The reliability of var-ious topologies for a module-integrated PV inverter is investi-gated in [24] based on the MTBF metric. In [25], a techniqueis presented for the calculation of the MTBF of the dc inputcapacitors employed in a module-integrated PV inverter. Theoperating temperature of the capacitors is predicted by utilizinga heat-flow thermal model of the PV modules. The cost and fail-ure rates of the dc-link capacitor and power MOSFETs used invarious single-phase PV inverter topologies, which are capableof providing reactive power support, are further explored in [26].The reliability estimation of two-stage, three-stage, and boostinverter topologies used in grid-connected PV systems, togetherwith a sensitivity analysis of reliability in terms of the powerswitches type, dc input capacitor voltage rating, and ambienttemperature, is presented in [27].

In [28] the number of failures that the PV inverter is expectedto encounter during its service lifetime period is predicted us-ing a Monte Carlo analysis. The failure rates of the subsystemscorresponding to the PV inverter major failure modes are consid-ered, such as the cooling fans of the power-conditioning unit, theinsulated gate bipolar transistors (IGBTs) comprising the powerstage, and the energy-storage capacitors. It is demonstrated thatthe PV inverter availability can be improved by either increasingthe repair rate in the case of malfunction or reducing the failurerate of the dc-bus capacitors, which constitute the most vulnera-ble components of the PV inverter, by designing the PV inverterusing capacitors of higher quality. A Monte Carlo simulation-based approach is also presented in [12] for the calculation ofthe PV inverter availability. It is based on an analysis of thethermal stress imposed on the PV inverter components due tothe ambient temperature conditions prevailing at the PV systeminstallation site.

A Bayesian estimation technique is analyzed in [29] for pre-dicting the availability of a PV inverter, which is based on treat-ing the failure and repair rates of the PV inverter as randomvariables. The use of Markov reliability models is proposedin [30] for exploring the effect of the PV inverter reliabilitycharacteristics into the resulting energy yield. The analysis isperformed at the PV inverter system level without investigating

the effects of the PV inverter component values and operationalcharacteristics on the PV inverter reliability features.

The methods described previously have been focused on theexploration and improvement of the reliability performance ofthe PV inverters. However, the impact of reliability on the PVinverter lifetime-cost/energy-production tradeoff has not beeninvestigated. Hence, these approaches do not constitute a sys-tematic procedure enabling the optimal selection of the PV in-verter component types and values which will guarantee thedevelopment of the most cost-effective PV inverter configura-tion seen during a lifetime.

In this paper, a new methodology for the optimal design oftransformerless PV inverters is presented taken into accountreliability. The optimal switching frequency as well as the op-timal values and types of the components comprising the PVinverter is calculated such that the PV inverter Levelized CostOf the Electricity (LCOE) generated is minimized. The numberof failures of the components, affecting the PV inverter mainte-nance cost during the PV system operational lifetime period, isalso considered in the LCOE calculation, thus incorporating theimpact of their performance in terms of reliability. In contrastto the past-proposed design methods, the approach presented inthis paper facilitates the optimal design of the PV inverter basedon a systematic process.

In the following sections of this paper, the proposed optimaldesign methodology and PV inverter modeling for optimizationincluding reliability are analyzed. The features of the proposedmethodology are then demonstrated through a design optimiza-tion example.

II. PROPOSED DESIGN OPTIMIZATION METHODOLOGY

With reference to Fig. 1, the target of the proposed designoptimization procedure is to calculate the optimal value of thePV inverter switching frequency fs , the optimal values of theoutput filter components (i.e., L, Lg , Cf , and Rdr), and theoptimal types of the power semiconductors including heat sink.The vector of the optimization problem design variables X is ofthe form X = [L|Lg |Cf |fs ]. The optimal value of the LCL-filterdamping resistor Rdr is calculated using the resulting optimalvalues of L, Lg , and Cf , as analyzed in [5].

A block diagram of the proposed automated optimization pro-cedure is illustrated in Fig. 2. The optimization algorithm inputsprovided by the PV inverter designer are: 1) the inputoutputspecifications, topology, and modulation strategy of the PV in-verter; 2) the technical and economical characteristics of multi-ple alternative types of components (i.e., power semiconductors,heat sinks, inductors, etc.) used to build the PV inverter; 3) thegrid-interconnection specifications (e.g., maximum permittedharmonic current levels, etc.); 4) the operational characteristicsof the PV array connected to the PV inverter; and 5) the 1-haverage solar irradiance and ambient temperature time-seriesduring the year.

During the optimization process, new sets of values of thedesign variables are iteratively produced by the optimizationalgorithm. Then, the objective function is evaluated using theappropriate mathematical model of the PV inverter topology


Fig. 2. Flowchart of the proposed optimization procedure.

under consideration, only for those sets of design variables sat-isfying the PV inverter operational constraints. The reliabilityfeatures of the PV inverter components are also considered dur-ing this stage, as analyzed next. This process is repeated untilthe global optimum of the objective function has been derived.The optimization procedure is implemented using genetic algo-rithms, which are capable to derive the global optimum solutionof the objective function with computational efficiency. ThePV inverter optimal design process described previously is re-peated for all combinations of component types input by thePV inverter designer (e.g., multiple alternative types of powerswitches such as IGBTs and MOSFETs, or IGBT-type powerswitches mounted on alternative heat sink structures available inthe market, each with a different thermal resistance to ambient,etc.). The combination achieving the lowest optimal value of theobjective function and the corresponding values of the designvariables is output as the overall optimal configuration of thePV inverter.

The optimal values of the design variables are calculated suchthat the PV inverter LCOE generated [31], LCOE ( /Wh), is

minimized by

minimizeX

{LCOE (X)}

subject to: design specifications and constraints are met (1)

where

LCOE (X) =Cinv (X)Ei (X)

(2)

with Cinv (X) () being the present value of the PV invertertotal cost during its operational lifetime period, Ei (X) (Wh)being the total energy injected into the electric grid by the PVinverter during its operational lifetime period, and X being thevector of the design variables.

The present value of the PV inverter total cost Cinv (X) iscalculated as the sum of the PV inverter manufacturing costCt (X) () and the present value of the total maintenance costduring the PV inverter operational lifetime period Mt (X) ()

Cinv (X) = Ct (X) + Mt (X). (3)

The total maintenance cost Mt depends on the PV inverterreliability characteristics. The values of Ct , Mt , and Ei in (2)and (3) are calculated according to the PV inverter modelinganalyzed in the following.

III. PV INVERTER MODELING FOR OPTIMIZATIONINCLUDING RELIABILITY

The PV inverter total manufacturing cost Ct is equal to thesum of the prices of the individual components comprising thePV inverter

Ct (X) = cinvPn + chs + p (cs + cd) + ci (L + Lg )PnVn

+ ccCf + SF crRdrPd,max (4)

where cinv ( /W) is the PV inverter manufacturing cost with-out including the cost of the heat sink, power switches, diodes,and output filter components (e.g., control unit, printed circuitboards, enclosure, etc.), chs () is the cost of the heat sink, pis the number of power switches and free-wheeling diodes con-tained in the PV inverter power section, cs and cd () are the costof each power switch and free-wheeling diode, respectively, ci[/ (H A)] is the LCL-filter inductor cost per unit inductanceand current rating, cc ( /F) is the filter capacitor cost per unitcapacitance, cr [/ ( W )] is the filter damping resistor costper unit resistance and power, SF (%) is the damping resistoroversizing factor, and Pd,max (W) is the maximum power dissi-pated in the damping resistor during the PV system operationallifetime period.

The present value of the PV inverter total maintenance costMt depends on the PV inverter reliability performance during itsoperational lifetime period and it is determined by the type andvalues of the individual components comprising the PV inverter.The value of Mt is calculated by reducing the future expensesfor repairing the PV inverter to the corresponding present value,


Fig. 3. PV inverter reliability evaluation procedure.

according to the following equation:

Mt (X) =n

j=1

Nj (X) Minv (1 + g)j

(1 + d)j(5)

where n is the number of years of PV system service lifetime,Nj (X) is the average number of failures that the PV inverteris expected to encounter during the jth year of operation (1 j n), Minv () is the present value of the cost for repairing thePV inverter, g (%) is the annual inflation rate, and d (%) is theannual discount rate.

The values of Nj (X) are calculated for each set of the com-ponent values (i.e., vector X) produced during the GA-basedoptimization process, according to the PV inverter reliabilityevaluation flowchart illustrated in Fig. 3. The failure rate ofa component depends on the value of the component and thestress factor applied to it (e.g., PV inverter dc input voltage, am-bient temperature, etc.) [32]. However, the PV inverter operatesunder stochastically varying solar irradiation and ambient tem-perature conditions during the year, resulting in time-variablevalues of the stress factors. Thus, in the proposed methodologythe average values of the stress factors developed at each com-ponent during the year, weighted by the percentage of operatinghours at each stress level, are initially calculated. This task isaccomplished using the mathematical model of the PV inverter,which is analyzed next, and the 1-h average solar irradiance andambient temperature time-series during the year input by thePV inverter designer. Then, the failure rate of the PV inverteris calculated by applying the weighted-average values of thestress factors in the individual component failure-rate modelsdescribed in [28] and [32]. Using the resulting value of the PVinverter failure rate, the average number of failures during eachyear of operation Nj (X) is calculated by performing a MonteCarlo simulation with 10 000 samples.

The probability that the PV inverter will operate properly be-yond time t is expressed by the reliability (or survival) functionRp (X) which is given by [21], [33]

Rp (X) = ei n v (X)t (6)

where inv (X) (number of failures/106 h) is the PV inverterfailure rate.

The value of inv (X) is calculated for each set of values ofthe design variables X as the sum of the failure rates of theindividual components comprising the PV inverter, as follows:

inv (X) =p

i=1

[ps,i(Tjps,i) + d,i(Tjd,i)

]+ L (TL )

+ Lg (TLg ) + Cf (Cf , VCf , TA ) + Rd r (PRd r , TRd r )

+ C in (Cin , Vpv , TA ) + c (7)

where ps,i , d,i (1 i p), L , Lg , Cf , and Rd r are thefailure rates (number of failures/106 h) of the PV inverter powerswitches, free-wheeling diodes, LCL-type output filter inductors(L and Lg ), capacitor (Cf ), and damping resistor (Rdr), respec-tively, C in is the failure rate of the dc-link capacitor, c is thetotal failure rate of the remaining components and subsystemsof the PV inverter (e.g., FPGA or DSP boards of the control unit,monitoring sensors, etc.), TA is the weighted-average value ofambient temperature, and Vpv , VCf , PRd r , Tjps,i , Tjd,i , TL , TLg ,and TRd r are the weighted-average values of the PV inverter dcinput voltage (i.e., PV array output voltage), LCL-filter capaci-tor voltage, damping resistor power consumption and operatingtemperature levels of the power switches, free-wheeling diodes,and LCL-filter components (i.e., L, Lg , and Rdr), respectively.

Similarly to [28], [34], the total failure rate of the PV invertercomponents not included in the set of the PV inverter designvariables (e.g., FPGA or DSP boards, monitoring sensors, etc.)c is considered to be constant throughout the PV plant lifetimeperiod. The dc-link capacitor and control unit are not includedin the set X of the design variables of the proposed optimizationprocess. The value of the dc-link capacitor is calculated suchthat the voltage ripple at the PV array output is reduced toan acceptable level, using the methodology analyzed in [35].However, the resulting value of dc-link capacitance, as wellas the control unit, affects the reliability performance of thePV inverter. Thus, their failure rates are included in (7) for thecalculation of the total PV inverter failure rate since they affectthe statistical behavior of the PV inverter availability throughoutits operational lifetime period. The junction temperatures of thepower semiconductors, Tjps,i and Tjnd,i (C), respectively, arecalculated assuming that the power switches and diodes aremounted on a common heat sink, using the following equations:

Tjps,i(t, y) = TA (t, y) + jc,ps Plps,i(t, y)

+ ca p

j=1

[Plps,j (t, y) + Pld,j (t, y)] (8)

Tjd,i(t, y) = TA (t, y) + jc,d Pld,i(t, y)

+ ca p

j=1

[Plps,j (t, y) + Pld,j (t, y)] (9)

where TA (t, y) (C) is the PV inverter ambient temperature athour t (1 t 8760) of year y (1 y n), jc,ps and jc,d(C/W) are the thermal resistance from the junction to the case


of the power switches and free-wheeling diodes, respectively,ca (C/W) is the thermal resistance of the heat sink, and Plps,iand Pld,i (W) are the total power loss (including conduction andswitching power losses) of the ith (1 i p) power switch andfree-wheeling diode, respectively.

Additionally, in order to ensure that the junction tempera-ture of the power semiconductors employed in the optimizedPV inverter structure is less than the maximum operating limitspecified by their manufacturer, the proposed optimization pro-cess is performed subject to the following constraints:

Tjps,i(t, y) Tjps,max (10)Tjd,i(t, y) Tjd,max (11)

where Tjps,max and Tjd,max (C) are the maximum permissi-ble junction temperatures of the power switches and diodes,respectively.

The reliability calculation procedure is performed using thecomplete time-series of the hourly average values of solar ir-radiation and ambient temperature during the year (i.e., 8760values for each parameter), input by the PV inverter designer.During the time periods that the PV inverter operation is sus-pended (e.g., during the night hours), the junction temperatureof the power semiconductors is calculated from (8) and (9) tofollow the ambient temperature.

The operating temperature of the LCL-type output filter in-ductors, TL and TLg , respectively, is calculated as [32]

TL (t, y) = TA (t, y) + 1.1 125 Pl,L (t, y) Vn/ (Sl L Pn )(12)

TLg (t, y)=TA (t, y)+1.1 125 Pl,Lg (t, y) Vn/ (Sl Lg Pn )(13)

where Pl,L (t, y) and Pl,Lg (W) are the power losses (includingcopper and core losses) of the inductors L and Lg , respectively,Vn (V) and Pn (W) are the PV inverter nominal output voltageand power levels, respectively, and Sl [m2 /(HA)] is the filterinductors radiating surface area of case per unit inductance andper unit nominal operating current.

In (8)(13), the parameters TA (t, y), jc,ps , jc,d , ca ,Tjps,max , Tjd,max , Vn , Pn , and Sl are provided by the PV in-verter designer, while the values of Plps,i , Pld,i , Pl,L , and Pl,Lgare calculated according to the power loss models describedin [36] and [37] using the operational characteristics of thecomponents available in the device datasheet, provided by theirmanufacturer.

The total energy production, Ei (X) in (2), is calculated as

Ei (X) =n

y=1

8760

t=1

Po(t, y) t (14)

where

Po(t, y) ={

0, during repair

Ppv(t, y) Ptot(t, y), else(15)

and Po , Ppv , and Ptot (W) are the power injected into the electricgrid by the PV inverter, the PV array output power, and the PV

inverter total power loss, respectively, at hour t (1 t 8760)of year y (1 y n) and t = 1 h is the simulation timestep.

As analyzed in [28], the PV inverter repair time dependson the amount of time required to detect the failure, diagnosethe type of malfunction, obtain and install spare parts, test therepair, and reinstall the inverter. In order to calculate the PVarray output power Ppv in (15), it is assumed that an MPPTprocess is performed by the PV inverter control unit, such thatthe maximum PV power is supplied to the PV inverter [8]. ThePV modules output power deterioration during their servicelifetime period is also considered when calculating the PV arrayoutput power, since it affects the values of the stress factorsapplied to the PV inverter components and the resulting failurerates. As stated in [38], the output power degradation of PVmodules tends to be linear with time. Thus, in the proposedmethodology the PV array output power Ppv (W) is calculatedas follows:

Ppv(t, y) = [1 y r(y)] PM (t) (16)

where y is the year number (1 y n), r( ) (%/year) is theannual reduction coefficient of the PV modules output power (ify = 1 then r(y) = 0, while for 1 < y n its value is specifiedby the PV modules manufacturer), and PM (t) is the PV arraypower production at the maximum power point during hour t(1 t 8760).

The value of PM in (16) is calculated using the PV modulesmodel analyzed in [39], based on the solar irradiation and am-bient temperature time-series, and the electrical specificationsof the PV modules and their configuration (i.e., connection inseries and parallel) within the PV array, which are input in theproposed optimization procedure by the PV inverter designer.The total power loss Ptot (W) is equal to the sum of the powerlosses of the components comprising the PV inverter

Ptot(t, y) =p

i=1

[Plps,i(t, y) + Pld,i(t, y)] + Pl,L (t, y)

+ Pl,Lg (t, y) + Pl,Rd r (t, y) + Pcu (17)

where Pl,Rd r (W) is the power loss of the LCL-type output filterdamping resistor and Pcu (W) is the power consumption of thePV inverter control unit (including the digital controller boards,gate drivers, sensors, etc.).

The value of Pl,Rd r in (17) is calculated using the power lossmodel presented in [36], while the value of Pcu is constant and itis input to the proposed optimization process by the PV inverterdesigner.

The power switches of the PV inverter under considerationare controlled according to the sinusoidal pulsewidth modula-tion (SPWM) principle [40]. Thus, the PV inverter switchingfrequency fs (Hz) is constrained to be an integer multiple of thegrid frequency f (Hz) and simultaneously it also holds that

fs fs,max (18)

where fs,max (Hz) is the maximum switching speed capabilityof the power switches, specified by their manufacturer.


The values of the LCL-type output filter components (i.e., L,Lg , Cf , and Rdr in Fig. 1) are calculated by the proposed opti-mization algorithm according to the design principles describedin [5] such that

1) the current ripple at the PV inverter output is less than themaximum permissible limit of harmonic current distortionat the PV inverter output RFmax (%) which is imposed bythe grid regulations and standards;

2) the LCL-filter resonant frequency is between ten timesthe electric grid frequency and one-half of fs , in order toensure that resonance problems are avoided;

3) the total value of the PV inverter output filter inductance(i.e., L + Lg ) is less than 0.1 pu, in order to limit the acvoltage drop during operation; and

4) the reactive power of the LCL-filter capacitor Cf is lessthan 5% of the rated power, in order to limit the powerfactor decrease at rated power.

During the execution of the proposed optimization process,the components considered each time for incorporation in thePV inverter structure are evaluated according to: 1) their cost[i.e., parameters cs , ci , etc., in (4)]; 2) their resulting failure ratesincorporated in (7), which in turn affect the total maintenancecost of the PV inverter according to (5); and iii) their powerlosses which affect the energy production of the PV inverteraccording to (14) and (15).

IV. OPTIMIZATION EXAMPLE

As an optimization example, a 2 kW/220 V transformerless,full-bridge, grid-connected PV inverter, which is illustrated inFig. 1, has been optimally designed using the proposed method-ology. The PV array connected to the PV inverter is comprisedof 12 175 W/35.4 V (under standard test conditions) PV mod-ules connected in series. The PV modules annual output powerreduction coefficient, specified by their manufacturer, is equalto r(y) = 0.6%. The PV system service lifetime considered inthe optimization process is n = 25 years.

As analyzed in Section II, the proposed optimization proce-dure can be performed considering multiple alternative types ofPV inverter components (i.e., power switches, heat sinks, etc.)in order to derive the overall optimum PV inverter configuration.In this design example, the PV inverter power section is builtusing IGBT-type power switches with free-wheeling diodes. Inorder to demonstrate the features of the proposed methodologyand explore the effect of the heat sink type on the PV inverterreliability characteristics during the execution of the proposedoptimal design process, the IGBT-type power switches and free-wheeling diodes have been considered to be mounted on twoalternative types of heat sinks with dissimilar cost and thermalconduction characteristics, expressed by chs and ca in (4), and(8) and (9), respectively. The technical and economical char-acteristics of commercially available components used to buildthe PV inverter power section and output filter (i.e., heat sinks,IGBTs, inductors, etc.), which are input in the optimizationprocess illustrated in Fig. 2, are summarized in Tables I andII, respectively. The technical characteristics of the PV invertercomponents were based on the information provided by their

TABLE ITECHNICAL CHARACTERISTICS OF THE PV INVERTER COMPONENTS

ca

( )oCWjc, ps

( )oCWjps,maxT

( o C )

jc,d

( )oCWjd,maxT

( o C )s,maxf

( k H z )

lS

2m

H A

Type 1: 0.65

1.7 175 2.6 175 30 5.1 Type 2:

0.29

TABLE IIECONOMICAL CHARACTERISTICS OF THE PV INVERTER COMPONENTS

invc

W

hsc

() s dc + c

()

ic

H A

cc

F

rc

W

invM

() g

(%) d

(%)

280.4

Type 1: 27.2

1.5 832 3134 10 -33.6 10 100.0 3.0 5.0 Type 2: 87.5

manufacturers. The economical characteristics of the PV in-verter components considered in the optimization process arebased on the selling prices of the corresponding components inthe international market, also considering that a large volumeof components is expected to be purchased during the industrialconstruction of the PV inverter.

The maximum permissible limit of harmonic current distor-tion at the PV inverter output RFmax has been set equal to4%. The total failure rate of the PV inverter components notincluded in the set of the PV inverter design variables (e.g.,FPGA or DSP boards, monitoring sensors, etc.) has been setequal to c = 17.2 failures/106 h [28], [34]. It is assumed thatthe PV inverter repair time is zero, in order to derive resultsindependent of factors which are not directly related to the PVinverter design process, such as the geographic isolation of thePV system installation site, maintenance personnel and spareparts availability [28], etc.

A software program operating under the MATLAB platformhas been developed for the implementation of the proposed op-timal design method. The global minimum of the PV inverterLCOE (objective) function is calculated using the genetic algo-rithm functions available in the MATLAB Global OptimizationToolbox.

The proposed methodology has been applied for the designoptimization of PV inverters installed at various sites in Europe.The resulting optimal values of the PV inverter design variables(i.e., L, Lg , Cf , Rdr , and fs) and LCOE for both alternativetypes of heat sinks input in the proposed design optimizationprocess are presented in Table III;. A different set of optimalvalues has been derived for each type of heat sink deployed inthe PV inverter structure since different solar irradiation andambient temperature conditions prevail at each installation site,which affect both the total PV energy production and the PV in-verter reliability performance. Thus, the technical and econom-ical characteristics of the heat sink impact the optimal values ofthe LCL-filter components which are required in order to obtainthe minimization of the PV inverter LCOE.


TABLE IIIOPTIMAL VALUES OF THE PV INVERTER DESIGN VARIABLES AND LCOE FOR

VARIOUS INSTALLATION SITES IN EUROPE

Heat sink L (mH) L ( H) C ( F) R ( ) f (kHz) LCOE

MWh

Athens (Greece)

Type 1 1.481 83.086 4.484 4.189 29.95 15.051

Type 2 1.726 54.326 4.112 3.579 29.95 16.400

Murcia (Spain)

Type 1 1.413 52.360 5.065 3.157 29.95 13.249

Type 2 1.481 54.386 4.827 3.297 29.95 14.404

Freiburg (Germany)

Type 1 1.466 49.305 5.125 3.051 29.90 21.910

Type 2 1.463 45.366 5.519 2.824 29.95 23.776

Oslo (Norway)

Type 1 1.573 49.573 4.887 3.136 29.95 22.277

Type 2 1.602 49.438 4.801 3.161 29.95 24.200

For the specific operational and economical characteristicsof the components considered in the optimization example (seeTables I and II), the manufacturing cost per unit power of theoptimized PV inverters presented in Table III using heat sinktype-1 is 30.2930.35 cents of /W, while the correspondingvalues in case that heat sink type-2 is used are in the rangeof 33.3233.42 cents of /W. The manufacturing cost of theoptimized PV inverter can be further reduced in order to achievethe desirable economic targets by building the inverter usingcomponents with lower selling prices.

During the design of a PV inverter, it is not generally known apriori by how much the switching frequency should be increasedsince this also increases the switching losses of the power semi-conductors. The proposed methodology enables us to explorethe impact of the PV inverter component values on the lifetime-cost/power-losses tradeoff in order to derive the overall opti-mal PV inverter configuration providing the minimum LCOE.For the specific operational and economical characteristics ofthe components considered in this optimization example (seeTables I and II), the optimal value of the switching frequency fsin Table III has been calculated to be close to the maximum per-missible switching frequency of the IGBT-type power switchesconsidered, thus aiming toward the reduction of the LCL-filtersize and cost.

According to Table I, the thermal resistance of heat sink type1 is higher compared to that of heat sink type 2, resulting inthe development of higher junction temperatures in the powersemiconductors. Depending on the installation area, the result-ing failure rates of the IGBT power switches and diodes inthe optimized PV inverters presented in Table III, which havebeen built using heat sink type 1, are 146.58146.71 and 99.33104.48 failures/109 h, respectively. These values are higher by0.020.019% and 0.0030.01%, respectively, compared to thecase that heat sink type 2 is used. The failure rates of the opti-mized PV inverters for both heat sink types in each installationsite are depicted in Fig. 4. It is observed that different values ofthe total failure rates of the optimized PV inverters resulted ineach installation site since: 1) a different set of optimal values

Fig. 4. Failure rates of the optimized PV inverters for both heat sink types ineach installation site.

of the PV inverter components (i.e., design variables) has beenderived for each type of heat sink employed in the PV inverterstructure in order to minimize the LCOE of the correspondingPV inverter, as presented in Table III; and 2) different meteoro-logical conditions prevail in each installation area, which affectthe stress factors applied at the individual components of thePV inverter. As analyzed in Section III, the failure rates arecalculated using the average values of the stress factors appliedat each component, weighted by the percentage of operatinghours at each stress level. This process smoothes the impact ofextreme individual values of the stress factors on the resultingfailure rate. Thus, in each installation site the total failure ratesand lifetime maintenance costs which resulted for the PV in-verters using either of the two heat sink types considered do notdiffer significantly. However, the heat sink of type 1 is of muchlower cost compared to the type 2 heat sink, thus constitutingthe optimal heat sink type which provides the minimum LCOEin all installation sites, as illustrated in Table III. The failure rateis a statistical parameter and the number of failures experiencedby the PV inverter under actual operating conditions depends onthe probability that the PV inverter will operate properly beyondtime t, as expressed by (6). Thus, in the proposed optimizationmethodology, the average number of failures during each year ofoperation is calculated by performing a Monte Carlo simulation,as described in Section III.

The optimal values of LCOE and the total energy injectedinto the electric grid during the 25-year operational lifetimeperiod [i.e., Ei in (2) and (14)] of a PV inverter built usingheat sink of type-1, which is the optimal type of heat sink asanalyzed previously, for various installation sites in Europe, aredepicted in Fig. 5(a) and (b), respectively. It is observed that theoverall minimum LCOE and the maximum energy productionare achieved in Murcia, Spain, since that installation site exhibitsthe highest solar irradiation potential.

The optimal values of the MTBF [27] of the PV invertersoptimized for each installation site are presented in Fig. 5(c). Itis observed that although the PV inverter optimized for Murcia,Spain, achieves the overall minimum LCOE, it also exhibits theminimum optimal MTBF among the PV inverters optimized foreach installation site. This is due to the higher solar irradia-tion and ambient temperature operating conditions prevailing atthis installation site, resulting in increased values of the stressfactors, which adversely affect the PV inverter reliability per-formance. The maximum deviation of the calculated optimalMTBF values among the four installation sites is 0.9%.


Fig. 5. Performance of the optimized and nonoptimized PV inverters forvarious installation sites in Europe: (a) LCOE, (b) total energy injected into theelectric grid for 12 PV modules during the 25-year operational lifetime period,and (c) mean time between failures.

The case that the single-phase, full-bridge PV inverter understudy is designed without using the proposed optimization pro-cess, thus forming a nonoptimized PV inverter, has also beenconsidered for comparison purposes. The manufacturing cost,lifetime energy production, and reliability features have not beenconsidered during the design process of the nonoptimized PVinverter. The nonoptimized PV inverter operates at fs = 8 kHz,which is the typical switching frequency value in this powerrange [2], [41]. Also, it is comprised of type-1 heat sink andan LCL output filter, which has been designed as analyzedin [5], with L = 5.65 mH, Lg = 1.09 mH, Cf = 3.29 F, andRdr = 5.6 . The rest of the nonoptimized PV inverter specifi-cations (i.e., power rating, output frequency, etc.) are identicalto those of the PV inverter which has been optimally designedusing the proposed methodology. Comparing the individual val-ues of the design variables in the nonoptimized PV inverterand the corresponding optimal values derived using the pro-posed methodology for a PV inverter comprised of type-1 heatsink, which are presented in Table III, a significant deviationis observed. The average deviations for all installation sites ofthe corresponding values of the L, Lg , Cf , Rdr , and fs de-sign variables in the optimized and nonoptimized PV invertersare 73.75%, 94.63%, 48.64%, 39.58%, and 274.22%, respec-tively, thus demonstrating the strength of the proposed designmethodology to facilitate the optimal design of the PV inverterbased on a systematic process. The LCOE, total energy pro-

Fig. 6. Total cost of the optimized and nonoptimized PV inverters for variousinstallation sites in Europe.

Fig. 7. Efficiency at maximum ac power and European efficiency of PV invert-ers optimized for various installation sites in Europe and of the nonoptimizedPV inverter.

duction, and MTBF of the nonoptimized PV inverter are alsopresented in Fig. 5. As shown in Fig. 5(c), compared to the opti-mized PV inverters designed using the proposed methodology,the nonoptimized PV inverter exhibits slightly higher MTBF inall installation sites considered. However, such a deviation doesnot significantly affect the resulting lifetime maintenance costof the nonoptimized PV inverter. Thus, compared to the nonop-timized PV inverter, the LCOE of the optimized PV inverters islower by 13.417.6% [see Fig. 5(a)] and the total energy injectedinto the electric grid is higher by 915 % [see Fig. 5(b)].

The present value of the PV inverter total cost [i.e., Cinv in(2) and (3)] of the optimized and nonoptimized PV inverters isillustrated in Fig. 6. In all cases considered, the maintenancecost corresponds to approximately 13.9% of the PV inverter to-tal cost. Thus, the variation of the optimal total cost among thefour installation sites is practically due to the different values ofthe components required to build the optimized PV inverter ineach site (see Table III), which affect the corresponding manu-facturing costs. Compared to the nonoptimized PV inverter, thetotal cost of the optimized PV inverters is lower by 5.65.7%.The manufacturing cost per unit power of the nonoptimized PVinverter is 32.31 cents of /W and it is higher than the corre-sponding cost of the optimized PV inverter using heat sink type1 by 6.476.67%.

The efficiency at maximum ac power and European effi-ciency of the optimized and nonoptimized PV inverters, forvarious installation sites in Europe, are presented in Fig. 7.Compared to the nonoptimized PV inverter, the efficiency atmaximum ac power and European efficiency of the PV invertersdesigned using the proposed methodology are higher by 2.522.59% and 7.557.75%, respectively. The PV inverter optimizedfor Murcia, Spain, achieves the highest values of efficiency at


Fig. 8. Variation of the total energy injected into the electric grid by a PVinverter installed in Murcia, Spain, for various values of the design variables Lgand Cf , in the case that L = 1.413 mH and fs = 29.95 kHz.

maximum ac power and European efficiency and simultane-ously, as demonstrated in Fig. 6, exhibits the lowest lifetimecost.

The variation of the total energy injected into the electric grid[i.e., Ei in (2) and (14)] by a PV inverter installed in Murcia,Spain, for various values of the design variables Lg and Cf inthe case that L = 1.413 mH and fs = 29.95 kHz, is illustratedin Fig. 8. It is observed that Ei is a highly nonlinear function ofthe values of the PV inverter components, thus dictating the useof a computationally efficient optimization algorithm, such asGAs, in order to calculate the optimal value of the PV inverterLCOE. The successful detection by the GA-based optimizationprocedure of the global optimum point where the PV inverterLCOE is minimized has been verified by also performing theproposed optimization process using an exhaustive search pro-cedure.

V. CONCLUSION

Targeting at cost-effective deployment of grid-connected PVsystems, a new methodology for the optimal design of trans-formerless PV inverters has been presented in this paper. Theoptimal switching frequency as well as the optimal values andtypes of the components comprising the PV inverter is calcu-lated such that the PV inverter LCOE generated is minimized.The LCOE is calculated also considering the PV inverter com-ponent reliability in terms of the corresponding failure rates,which affect the lifetime maintenance cost of the PV inverter.

The proposed design method facilitates the optimal design ofthe PV inverter based on a systematic process. The design opti-mization results indicate that in contrast to the past-proposed de-sign approaches, the methodology presented in this paper has theadvantage of enabling to explore the impact of the PV invertercomponent values on the lifetime-cost/power-losses tradeoff inorder to derive the overall optimal PV inverter configuration,while simultaneously considering the PV inverter componentsreliability which affects the lifetime maintenance cost of the PVinverter. The optimal values of the PV inverter design param-eters depend also on the meteorological conditions prevailingat the PV system installation site. Compared to the nonopti-mized PV inverter structures, the PV inverters designed using

the proposed methodology exhibit lower total cost (includingthe manufacturing and lifetime maintenance costs) and injectmore energy into the electric grid.

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Eftichios Koutroulis (M10) was born in Chania,Greece, in 1973. He received the B.Sc. and M.Sc.degrees from the Department of Electronic and Com-puter Engineering, Technical University of Crete,Chania, in 1996 and 1999, respectively. He also re-ceived the Ph.D. degree from the Department of Elec-tronic and Computer Engineering, Technical Univer-sity of Crete, in 2002 in the area of power electronicsand renewable energy sources (RES).

He is currently an Assistant Professor at the De-partment of Electronic and Computer Engineering,

Technical University of Crete. His research interests include power electronics(dc/ac inverters, dc/dc converters), the development of microelectronic energymanagement systems for RES, and the design of photovoltaic and wind energyconversion systems.

Frede Blaabjerg (S86M88SM97F03) re-ceived the Ph.D. degree from Aalborg University,Aalborg, Denmark, in 1992.

From 1987 to 1988, he was with ABB-Scandia,Randers. He became an Assistant Professor in 1992,an Associate Professor in 1996, and a Full Profes-sor in power electronics and drives in 1998 at Aal-borg University. He has been a Part-Time ResearchLeader at Research Center Risoe in wind turbines.During 20062010, he was the Dean of the Facultyof Engineering, Science and Medicine and became a

Visiting Professor at Zhejiang University, China, in 2009. His research areas in-clude power electronics and its applications such as wind turbines, PV systems,and adjustable speed drives.

Dr. Blaabjerg has been the Editor-in-Chief of the IEEE TRANSACTIONS ONPOWER ELECTRONICS since 2006. He was a Distinguished Lecturer for the IEEEPower Electronics Society during 20052007 and for the IEEE Industry Appli-cations Society during 20102011. He received the 1995 Angelos Award for hiscontribution in modulation technique and the Annual Teacher prize at AalborgUniversity. He also received the Outstanding Young Power Electronics EngineerAward from the IEEE Power Electronics Society in 1998. He has received tenIEEE Prize paper awards and another prize paper award at PELINCEC Poland2005. He received the IEEE PELS Distinguished Service Award in 2009 andthe EPE-PEMC 2010 Council award.

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