394 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 28, NO. 2, JUNE 2013 Optimal Design ... ·...

394 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 28, NO. 2, JUNE 2013

Optimal Design of Modern TransformerlessPV Inverter Topologies

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

Abstract—The design optimization of H5, H6, neutral pointclamped, active-neutral point clamped, and conergy-NPC trans-formerless photovoltaic (PV) inverters is presented in this paper.The components reliability in terms of the corresponding malfunc-tions, affecting the PV inverter maintenance cost during the oper-ational lifetime period of the PV installation, is also considered inthe optimization process. According to the results of the proposeddesign method, different optimal values of the PV inverter designvariables are derived for each PV inverter topology and installa-tion site. The H5, H6, neutral point clamped, active-neutral pointclamped and conergy-NPC PV inverters designed using the pro-posed optimization process feature lower levelized cost of generatedelectricity and lifetime cost, longer mean time between failures andinject more PV-generated energy into the electric grid than theirnonoptimized counterparts, thus maximizing the total economicbenefit obtained during the operational time of the PV system.

Index Terms—DC/AC inverter, optimization, photovoltaic (PV)system, reliability, transformerless.

I. INTRODUCTION

THE modern grid-connected PV energy production systemswidely employ transformerless photovoltaic (PV) dc/ac

converters (inverters), since compared to the inverters using gal-vanic isolation they exhibit the advantages of lower cost, higherpower density, and higher efficiency [1]–[3]. The block diagramof a grid-connected transformerless PV inverter is illustrated inFig. 1. The PV array consists of PV modules connected in se-ries and/or parallel [4], [5]. Typically, the power switches (e.g.,IGBTs, SiC-based JFETs, etc.) of the power section of the PVinverter are controlled by a DSP- or FPGA-based microelec-tronic control unit according to pulse width modulation (PWM)techniques (e.g., sinusoidal PWM, space-vector PWM, hystere-sis band control, etc.) [6]–[8]. A sinusoidal current with lowharmonic content is injected into the electric grid by filteringthe high-frequency harmonics of the PWM waveform producedat the output of the PV inverter power section. The use of LCL-type output filters, instead of the L- or LC-type filters, aims toincrease the power density of the PV inverter [9].

Manuscript received September 6, 2012; revised January 28, 2013; acceptedMarch 3, 2013. Date of publication April 3, 2013; date of current version May15, 2013. Paper no. TEC-00466-2012.

S. Saridakis and E. Koutroulis are with the Department of Electronic andComputer Engineering, Technical University of Crete, Chania 73100, Greece(e-mail: [email protected]; [email protected]).

F. Blaabjerg is with the Department of Energy Technology, Aalborg Univer-sity, Aalborg 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/TEC.2013.2252013

Fig. 1. Block diagram of a transformerless PV inverter.

Many alternative topologies have been proposed during thelast few years in order to build the power section of single- andthree-phase transformerless PV inverters in grid-connected PVinstallations [10]–[19]. Among them, the H5, H6, and conergy-neutral point clamped (conergy-NPC) topologies have been in-tegrated in commercially available grid-connected PV inverters.Also, the NPC and Active-NPC (ANPC) transformerless struc-tures are widely used to build the power stage of PV invertersused in distributed generation systems, due to their low-leakage-current and high-efficiency features [20]. The H5, H6, NPC,ANPC, and conergy-NPC topologies are illustrated in Fig. 2.Compared to the H5 and H6 transformerless PV inverters, ahigher dc input voltage is required for the operation of the NPC,ANPC, and conergy-NPC inverters.

In order to maximize the amount of energy injected into theelectric grid and the total economic benefit achieved by a grid-connected PV installation during its operational lifetime periodit is indispensable to maximize the reliability of the individualcomponents and devices comprising the PV system [21], [22].The reliability features are expressed in terms of indices such asthe failure rate or the mean time between failures (MTBF) [23].The design and production of PV power processing systems withhigh efficiency, high reliability and low cost features has beenindicated in [24] as a major challenge. The PV inverters aretypically designed according to iterative trial-and-error meth-ods, which target to maximize the power conversion efficiencyat nominal operating conditions or the “European Efficiency”of the PV inverter [19], [25]–[27]. The design optimization oftransformerless PV inverters employing full-bridge, NPC, orANPC topologies, has been analyzed in [20], [28], without,however, considering the reliability characteristics of the PVinverter. Also, various methods have been presented for theexploration and improvement of the PV inverters reliability per-formance, which are reviewed in [22]. However, these methodshave the disadvantage that the concurrent impact of differentcritical design parameters, such as the PV inverter topology,component values, operational characteristics (e.g., maximum

0885-8969/$31.00 © 2013 IEEE

SARIDAKIS et al.: OPTIMAL DESIGN OF MODERN TRANSFORMERLESS PV INVERTER TOPOLOGIES 395

Fig. 2. Topologies of the power section in transformerless single-phase PVinverters: (a) H5-inverter, (b) H6-inverter, (c) NPC, (d) ANPC, and (e) conergy-NPC.

switching frequency) and reliability performance, on the trade-off between the PV inverter manufacturing cost, maintenancecost, and total power losses, which affect the amount of en-ergy injected into the electric grid by the PV inverter, is notconsidered during the PV inverter design process.

In this paper, the design technique including reliability, whichwas suited to full-bridge PV inverters in [22], is advanced interms of the power-section topology, thus resulting in a newmethodology for the optimal design of transformerless PV in-verters based on the H5, H6, NPC, ANPC, and conergy-NPCstructures. Using the proposed design process, the optimal val-ues of components comprising the H5, H6, NPC, ANPC, andconergy-NPC PV inverters are calculated such that the PV in-verter levelized cost of generated Electricity (LCOE) is mini-mized. The components reliability in terms of the correspond-ing malfunctions, which affect the PV inverter maintenance costduring the PV system operational lifetime period, as well as thelimitations imposed by the electrical grid interconnection reg-ulations and international standards, are also considered in theLCOE calculation. In contrast to the past-proposed approachesapplied to design H5, H6, NPC, ANPC, and conergy-NPC PVinverters, the optimal design process presented in this paper hasthe advantage of taking into account the concurrent influences

of the meteorological conditions prevailing at the installationsite, the PV inverter topology, as well as the cost, operationalcharacteristics and reliability features of the components com-prising the PV inverter, on both the PV inverter lifetime costand total energy injected into the electric grid. The proposeddesign tool accommodates a systematic design flow based onconventional models and circuit-analysis techniques, which en-ables to calculate the optimal structure of H5, H6, NPC, ANPC,and conergy-NPC PV inverters among computationally com-plex alternatives, with minimum effort from the designer of thePV inverter.

This paper is organized as follows: the methodology for opti-mal design of transformerless PV inverters considering reliabil-ity is outlined in Section II; the modeling for optimization of H5,H6, NPC, ANPC, and conergy-NPC transformerless PV invertertopologies is analyzed in Section III, and the design optimizationresults are presented in Section IV. Finally, the topologies arecompared in terms of their performance in various installationsites and conclusions are drawn.

II. OPTIMAL DESIGN METHODOLOGY

INCLUDING RELIABILITY

The proposed design optimization method calculates, for eachof the H5, H6, NPC, ANPC, and conergy-NPC transformerlessPV inverters, the optimal values of the switching frequencyfs(Hz) and the values of the components comprising the outputfilter, i.e., L,Lg , Cf , and Rdr in Fig. 1, such that the PV-inverterLCOE [29], LCOE (C= /Wh), is minimized, while simultaneouslythe PV inverter specifications and the constraints imposed by thegrid codes and international standards are satisfied like

minimizeX

{LCOE(X)}

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

where

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

(2)

with Cinv (X)(C= ) being the present value of the PV inverter totalcost during its operational lifetime period, Ei(X)(Wh) beingthe total energy injected into the electric grid by the PV inverterduring its operational lifetime period, and X = [fs |L|Lg |Cf ]being the vector of the design variables.

The value of the LCL-filter damping resistor Rdr is calcu-lated using the values of X , as analyzed in [30]. The optimalvalue of the decision variables vector X is calculated usinggenetic algorithms (GAs), since they are capable to solve com-plex optimization problems with computational efficiency. Aflowchart of the proposed design procedure, which is executedfor each PV inverter topology, is illustrated in Fig. 3. Initially,the PV inverter designer provides as inputs the specificationsof the PV inverter (e.g., nominal power, output voltage, etc.),the technical and economical characteristics of the componentscomprising the PV inverter, the operational characteristics of thePV array connected to the dc input of the PV inverter and the1-h average values of the solar irradiation and ambient temper-ature conditions during the year at the PV inverter installation


Fig. 3. Flowchart of the proposed optimization process.

site. During the optimization process, multiple design vectorsX composing the population of the GA process chromosomes,are progressively modified for a predefined number of genera-tions. The LCOE objective function in (2) is calculated for eachchromosome. The design vector X providing the lowest valueof LCOE is comprised of the optimal values of the PV inverterdesign parameters.

In (1), the LCOE minimization is performed subject to thefollowing constraints: 1) the ripple of the PV inverter outputcurrent is less than the maximum permissible limit, which isdefined in the grid-interconnection regulations and/or standards(e.g., the IEEE-1547 standard); 2) the resonance-frequency, ca-pacitance, and total inductance of the LCL-filter are constrainedwithin the limits described in [30]; and 3) the value of the switch-ing frequency fs is limited by the maximum possible operatingswitching speed of the power switches and diodes composingthe power section of the PV inverter fs,max (Hz) specified bytheir manufacturer, such that fs ≤ fs,max .

The present value of the PV inverter total cost, Cinv (X) in(2), is calculated as the sum of the PV inverter manufacturingcost, Ct(X)(C= ) and the present value of the total cost for main-taining the PV inverter during its operational lifetime period,Mt(X)(C= ):

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

The manufacturing cost Ct is equal to the sum of the costs ofthe individual components comprising the H5, H6, NPC, ANPC,and conergy-NPC PV inverters

Ct(X) = cinvPn + chs + nscs + ndcd + ncdccd

+ ci(L + Lg)Pn

Vn+ ccCf + crRdr · SF · Pd,max (4)

where cinv (C= /W) is the manufacturing cost of the PV inverterwithout including the cost of the heat sink, power switches,diodes, and LCL-filter components (e.g., control unit, printedcircuit boards, integration, and housing etc.), chs(C= ) is the cost ofthe heat-sink, ns, nd, ncd are the number of power switches, an-tiparallel diodes, and clamping diodes, respectively, contained inthe PV inverter power section (for the H5, ANPC, and conergy-NPC topologies it holds that ncd = 0), cs , cd , ccd (C= ) are thecost of each power switch, antiparallel diode, and the clamping

diode, respectively, ci [C= /(H · A)] is the LCL-filter inductor costper unit inductance and current, cc (C= /F) is the LCL-filter capac-itor cost per unit capacitance, cr [C= /(Ω · W)] is the LCL-filterdamping resistor cost per unit resistance and power, SF(%) isthe oversizing factor of the damping resistor Rdr(see Fig. 1) andPd,max (W) is the maximum power dissipated on the dampingresistor during operation.

The type and values of the individual components comprisingthe PV inverter determine the reliability performance of the PVinverter during its operational lifetime period, which, in turn, de-fines the present value of the PV inverter total maintenance cost,Mt(X) in (3). In the proposed methodology, the value of Mt iscalculated by reducing the PV inverter repair expenses occur-ring during each future year of operation, to the correspondingpresent value, as follows:

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 operational lifetimeperiod, Nj (X) is the average number of PV inverter failureswhich are expected to occur during the jth year of operation(1 ≤ j ≤ n), Minv (C= ) is the present value of the PV inverterrepair cost, g(%) is the annual inflation rate, and d(%) is theannual discount rate.

The values of Nj (X) in (5) are determined by the failurerate of the PV inverter, which in turn depends on the valuesof the individual components comprising the PV inverter andthe stress factor applied to them (e.g., dc input voltage, ambienttemperature, etc.) [31], as analyzed next. The total failure rate ofthe PV inverter, λinv (X) (number of failures/106 h) is a functionof the design variables values X and it is calculated using thefollowing equation:

λinv (X)

=1

MTBF= λC in (Cin , Vpv , TA ) +

ns∑

i=1

λps,i(Tjps,i)

+nd∑

i=1

λd,i(Tjd,i) +nc d∑

i=1

λcd,i(Tjcd,i) + λL (TL ) + λLg (TLg )

+ λC f (Cf , VC f , TA ) + λRd r (PRd r , TRd r ) + λc (6)

where MTBF(h) is the mean time between failures of thePV inverter, λps,i , λd,i , λcd,i , λL , λLg

, λCfand λRd r (number of

failures/106 hours) are the failure rates of the PV inverter powerswitches, free-wheeling diodes, clamping diodes, LCL-type out-put filter inductors L and Lg , capacitor Cf and damping resistorRdr , respectively, λC in is the total failure rate of the dc-linkcapacitor(s), λc is the total failure rate of the remaining compo-nents and subsystems comprising the PV inverter (e.g. digitalcircuits of the control unit, monitoring sensors, etc.), TA is theweighted-average value of ambient temperature, Tjps,i , Tjd,i ,and Tjcd,i are the weighted-average values of the junctiontemperature of the power switches, free-wheeling diodes, andclamping diodes, respectively, and Vpv , VC f , PRd r , TL , TLg ,and TRd r are the weighted-average values of the PV inverter dc


input voltage (i.e., PV array output voltage), LCL-filter capaci-tor voltage, damping resistor power consumption, and operatingtemperature levels of the LCL-filter components (i.e. L,Lg , andRdr), respectively.

The values of λps,i , λd,i , λcd,i , λL , λLg , λC f , λRd r , and λC in

in (6) are calculated using the mathematical model of the PVinverter, the electrical specifications of the components used tobuild the PV inverter and the 1-h average solar irradiance andambient temperature time-series during the year, according tothe failure-rate models described in [31], [32]. The value ofλinv (X) in (6) is calculated for each set of design variablesvalues (i.e., vector X), which are produced during the evolutionof the GA-based optimization process. The total failure rateλinv (X), determines the probability that the PV inverter will notoperate properly, according to the exponential distribution [32].Thus, the total number of failures that the PV inverter encountersduring each year of operation is statistically variable. In theproposed methodology, in order to calculate the present value ofthe PV inverter total maintenance cost in (2) and (5), the averagenumber of failures during each year of operation, Nj (X) in (5),is calculated using the resulting value of λinv (X) and executinga Monte Carlo simulation with 10000 samples.

The total energy production of the PV inverter, Ei in (2),is calculated using the time series of the PV inverter powerproduction during the PV system operational lifetime period, asfollows:

Ei(X) =n∑

y=1

8760∑

t=1

Po(t, y) · Δt (7)

where Po(t, y) is the power injected into the electric grid by thePV inverter at hour t (1 ≤ t ≤ 8760) of year y (1 ≤ y ≤ n) andΔt = 1 h is the simulation time step.

The values of Po(t, y) in (7) are calculated according to thetransformerless PV inverter modeling analyzed next.

III. MODELING OF TRANSFORMERLESS PV INVERTER

TOPOLOGIES FOR OPTIMIZATION

With reference to the block diagram of transformerless PVinverters, which is illustrated in Fig. 1, the power injected intothe electric grid by the PV inverter is calculated in the proposedmethodology from a power-balance equation as follows:

Po(t, y) = Ppv(t, y) − Ptot(t, y) (8)

where Ppv and Ptot(W) are the PV array output power and thePV inverter total power loss, respectively, at hour t (1 ≤ t ≤8760) of year y (1 ≤ y ≤ n).

Typically, the control unit of the PV inverter executes a maxi-mum power point tracking (MPPT) process, such that the maxi-mum possible power is produced by the PV array [33], [34]. Thedeterioration of the PV modules output power capacity duringthe operational lifetime period of the PV inverter affects the val-ues of the stress factors applied to the PV inverter componentsand the values of the resulting failure rates in (6). Consideringthese parameters, the PV array output power, Ppv (W) in (8), is

calculated in the proposed methodology as follows:

Ppv(t, y) = [1 − y × r(y)] · nmppt · PM (t) (9)

where y is the number of year of PV system operation (1 ≤y ≤ n), r(·) (%/year) is the annual reduction coefficient of thePV modules output power (if y = 1, then r(y) = 0, while for1 < y ≤ n its value is specified by the manufacturer of the PVmodules), nmppt(%) is the MPPT efficiency, which expressesthe accuracy of the MPPT process executed by the control unit ofthe PV inverter (typically nmppt > 99.7%) [35] and PM (t)(W)is the power production at the maximum power point of the PVarray during hour t (1 ≤ t ≤ 8760).

The value of PM in (9) is calculated according to the PVmodules model analyzed in [36], using the time series of hourlyvalues of solar irradiation and ambient temperature during theyear, the electrical specifications of the PV modules and theirconfiguration within the PV array (i.e., connection in seriesand parallel), that the designer of the PV inverter inputs in theproposed optimization procedure.

The total power loss of the PV inverter, Ptot in (8), is equalto the sum of the conduction and switching losses of the powersemiconductors (i.e., power switches, free-wheeling diodes, andclamping diodes) comprising the power section of the PV in-verter, Pcond (W) and Psw (W), respectively, the power loss onthe LCL-filter damping resistor Pd (W) the core and windinglosses of the LCL-filter inductors, PL,c (W), and PL,r (W), re-spectively, and the power consumption of the control unit (dueto the circuits of the SPWM modulator, sensors etc.), Pcu (W)

Ptot = Pcond + Psw + Pd + PL,c + PL,r + Pcu . (10)

The values of Pd, PL,c , and PL,r are calculated using the powerloss models presented in [28], while the designer of the PVinverter provides the value of Pcu .

Initially, the PV inverter output current, Io(t, y)(A), at hour t(1 ≤ t ≤ 8760) of year y (1 ≤ y ≤ n) is calculated by solvingnumerically the following power-balance equation:

Ppv(t, y) = Ptot(t, y) + Vn · Io(t, y) (11)

where Vn (V) is the nominal RMS value of the PV inverter outputvoltage.

In the proposed methodology, the power switches and diodes,which constitute the power section of the PV inverter, are mod-eled as voltage sources connected in series with resistors. Thus,the conduction power losses of each power switch and diode(either clamping or free-wheeling), Pcond (W), are given by

Pcond(t, y) = Vd · Iavg + Rd · I2rms (12)

where Vd (V) and Rd (Ω) are the power switch or diode forwardvoltage and resistance, respectively and Iavg , Irms(A) are theaverage and RMS values, respectively, of the power switch ordiode current.


Fig. 4. Conducting devices in relation to the waveforms of Vs,1 and Io forthe H5, H6, NPC, ANPC, and conergy-NPC inverters.

The average and RMS values of the current of each powerswitch or diode are calculated as follows:

Iavg =12π

∫ 2π

0

√2 · Io(t, y) · sin(ωt − θ) · f(ωt) · dωt (13)

Irms =

√12π

∫ 2π

0(√

2 · Io(t, y) · sin(ωt − θ))2 · f(ωt) · dωt

(14)

where f(ωt) is the modulation function [37] of the correspond-ing power semiconductor, Io(t, y)(A) is the RMS output cur-rent of the PV inverter at hour t (1 ≤ t ≤ 8760) of year y(1 ≤ y ≤ n) and θ (◦) is the phase difference between the PVinverter output current (i.e., Io in Figs. 1 and 4) and the funda-mental (i.e., Vs,1 in Fig. 4) of the SPWM voltage generated atthe output terminals of the power section (i.e., Vspwm in Fig. 1).

The power semiconductors which conduct during each timeinterval of the output-current period of the H5, H6, NPC, ANPC,and conergy-NPC PV inverters, respectively, are also presentedin Fig. 4. During the time intervals that a power semiconductoris not conducting, then the corresponding modulation functionin (13) and (14) is set equal to zero [i.e., f(ωt) = 0]. In theproposed methodology, the values of Pcond and Psw in (10) arecalculated by applying equations (11)–(14), which have beenpresented previously, for each of the H5, H6, NPC, ANPC,

TABLE ICONDUCTION INTERVALS AND MODULATION FUNCTIONS

OF THE H5 PV INVERTER

and conergy-NPC topologies, as analyzed in the followingparagraphs.

A. H5 PV inverter

The modulation functions of the H5-inverter power semicon-ductors, during each conduction interval presented in Fig. 4, aresummarized in Table I as a function of the modulation index mα

of the PV inverter SPWM output voltage (i.e., Vspwm in Fig. 1).Considering the symmetrical operation of the H5 inverter topol-ogy and applying the modulation functions displayed in Table Iin (13) and (14), it is derived that

ISi,avg = ISj,avg = IS,avg , IS i,rms = ISj,rms = IS,rms

IDi,avg = IDj,avg = ID,avg , IDi,rms = IDj,rms = ID,rms

(15)

where i, j = 1, . . . , 4.Then, the total conduction loss, Pcond(t, y), at hour t (1 ≤

t ≤ 8760) of year y (1 ≤ y ≤ n) of the H5-inverter is calculatedas the sum of the conduction losses of the power switches anddiodes comprising of the H5 inverter, using (12) and (15), asfollows:

Pcond(t, y) = 4 · (Vs,onIS,avg + I2S,rmsRs,on) + Vs,onIS5,avg

+ I2S5,rmsRs,on + 4 · (VdID,avg + I2

D,rmsRd)

+ VdID5,avg + I2D5,rmsRd. (16)

The total switching energy, E(Joule) of the semiconductordevices in the H5 power section, which switch during the0 ≤ ωt ≤ π time interval depicted in Fig. 4, is calculated asthe sum of the energy consumed by the power semiconductorsduring the corresponding turn-on and turn-off switching actions

E =Vpv(t, y) · Io(t, y) ·

√2 · fs

Vt · It · 2πf· 2 · (EonS1 + EonS4

+ EonS5 + Eoff D1 + Eoff D4 + Eoff D5 + EonD1

+ EonD4 + EonD5 + Eoff S1 + Eoff S4 + Eoff S5) (17)

where fs(Hz) is the switching frequency, Vt(V), It(A) are thetest voltage and current values, respectively, and Eonxi

, Eoff xi


TABLE IICONDUCTION INTERVALS AND MODULATION FUNCTIONS

OF THE H6 PV INVERTER

(Joule) are the turn-on and turn-off energy, respectively, of thepower switch or free-wheeling diode xi .

Since practically, power switches and diodes of the sameoperational characteristics are used to build the PV inverter, itholds that

EonSi = EonSj = EonT , Eoff Si = Eoff Sj = Eoff T

EonDi = EonDj = EonDT , Eoff Di = Eoff Dj = Eoff DT (18)

where i, j = 1 . . . 5, EonT , Eoff T (Joule) are the power switchturn-on and turn-off energy and EonDT ,Eoff DT (Joule) are thefree-wheeling diode turn-on and turn-off energy.

Due to the symmetrical operation of the H5-inverter topology,the total switching loss during the negative half-cycle of theoutput voltage period (i.e., during [π − 2π]) is equal to E in (17).Thus, the total switching losses of the H5-inverter, Psw (t, y), athour t (1 ≤ t ≤ 8760) of year y (1 ≤ y ≤ n) are calculatedusing (17) and (18), as follows:

Psw (t, y) = 2 · f · E =Vpv(t, y) · Io(t, y) ·

√2 · fs

π · Vt · It

· [6 · (EonT + EonDT ) + 6 · (Eoff T + Eoff DT )]

(19)

where f (Hz) is the frequency of the PV inverter output voltage.

B. H6 PV inverter

Due the symmetrical operation of the H6-inverter [seeFig. 2(b)] and applying the modulation functions displayed inTable II in (13) and (14), it results in

ISi,avg = ISj,avg = IS,avg , IS i,rms = ISj,rms = IS,rms

IDi,avg = IDj,avg = ID,avg , IDi,rms = IDj,rms = ID,rms

IS5,avg = IS6,avg , IS5,rms = IS6,rms , ID5,avg = ID6,avg

ID5,rms = ID6,rms , ID+ ,avg = ID−,avg, ID+ ,rms = ID−,rms

(20)

where i, j = 1, ..., 4..

The total conduction losses, Pcond(t, y), at hour t (1 ≤ t ≤8760) of year y (1 ≤ y ≤ n) of the power semiconductors usedto build the H6 inverter are calculated using (12) and (20)

Pcond(t, y) = 4 · (Vs,onIS,avg + I2S,rmsRs,on) + 2

· (Vs,onIS5,avg + I2S5,rmsRs,on) + 4

· (VdID,avg + I2D,rmsRd)

+ 2 · (VdID5,avg + I2D5,rmsRd) + 2

· (VdID+ ,avg + I2D+ ,rmsRd). (21)

Due to the symmetrical operation of the H6 inverter topology,the total switching losses for an H6 PV inverter, Psw (t, y) in(10), are calculated by applying a similar procedure as that forthe H5 topology described previously, resulting in

Psw (t, y) = 2 · f · E =Vpv(t, y) · Io(t, y) ·

√2 · fs

π · Vt · It

· [8 · (EonT + EonDT ) + 8 · (Eoff T + Eoff DT )

+ 4 · (EonD + Eoff D )]. (22)

where EonD and Eoff D (Joule) are the clamping diode turn-onand turn-off energy, respectively.

C. NPC and ANPC PV inverters

The values of Pcond and Psw in (8) for the NPC and ANPCPV inverters [see Fig. 2(c) and (d), respectively] are calculatedusing the power-loss models analyzed in detail in [20].

1) For the NPC PV inverter:

Pcond(t, y) = 2 · (Vs,onIS1,avg + I2S1,rmsRs,on

+ Vs,onIS2,avg + I2S2,rmsRs,on)

+ 4 · (VdID1,avg + I2D1,rmsRd)

+ 2 · (VdID+ ,avg + I2D+ ,rmsRd) (23)

Psw (t, y) =Vpv(t, y) · Io(t, y) ·

√2 · fs

2π · Vt · It

· [4 · (EonT +Eoff T )+2 · (EonD + Eoff D )

+ 2 · (EonDT + Eoff DT ) + 2 · (Eon,T

+ Eoff ,T − Eon,DT − Eoff ,DT ) · cosθ].

(24)

2) For the ANPC PV inverter:

Pcond(t, y) = 2 · (Vs,onIS1,avg + I2S1,rmsRs,on

+ Vs,onIS2,avg + I2S2,rmsRs,on

+ Vs,onIS5,avg + I2S5,rmsRs,on)

+ 2 · (VdID1,avg + I2D1,rmsRd

+ VdID2,avg + I2D2,rmsRd + VdID5,avg

+ I2D5,rmsRd) (25)


TABLE IIICONDUCTION INTERVALS AND MODULATION FUNCTIONS OF THE

CONERGY-NPC PV INVERTER

Psw (t, y) =Vpv(t, y) · Io(t, y) ·

√2 · fs

2π · Vt · It

· [6 · (EonT + EonDT )

+ 12 · (Eoff T + Eoff DT ) + 2 · (Eon,T + 2

· Eoff ,T − Eon,DT − 2 · Eoff ,DT ) · cosθ].

(26)

D. Conergy-NPC PV inverter

The modulation functions of the power semiconductors com-prising a conergy-NPC inverter [see Fig. 2(e)] are summarizedin Table III. They have been derived by applying the on-state ra-tios of power semiconductors in SPWM 3-level inverters, whichhave been calculated in [38], for each of the power semicon-ductors in the corresponding conduction intervals depicted inFig. 4. Considering the symmetrical operation of the conergy-NPC topology and applying the modulation functions displayedin Table III in (13) and (14), it results that

IS1,avg = IS2,avg = IS,avg , IS1,rms = IS2,rms = IS4,rms

ID1,rms = ID2,rms = ID,rms , ID1,avg = ID2,avg = ID,avg

IS+ ,avg = IS−,avg , IS+ ,rms = IS−,rms

ID+ ,avg = ID−,avg , ID+ ,rms = ID−,rms . (27)

The total conduction losses, Pcond(t, y), at hour t (1 ≤ t ≤8760) of year y (1 ≤ y ≤ n) of the power semiconductors em-ployed in the conergy-NPC inverter are calculated using (12)and (27)

Pcond(t, y) = 2 · (Vs,onIS,avg + I2S,rmsRs,on)

+ 2 · (Vs,onIS+ ,avg + I2S+ ,rmsRs,on)

+ 2 · (VdID,avg + I2D,rmsRd)

+ 2 · (VdID+ ,avg + I2D+ ,rmsRd). (28)

The total switching energy, E1 and E2 (Joule) respectively,of the power semiconductor devices, which switch during the0 ≤ ωt ≤ θ and θ ≤ ωt ≤ π time intervals depicted in Fig. 4,are calculated as the sum of the energy consumed during the cor-

responding turn-on and turn-off switching actions, as follows:

E1 =Vpv(t, y)/2

Vt· Io(t, y) ·

√2

It· fs

f· (EonD1 + Eoff S−

+ Eoff D− + EonS− + EonD− + Eoff D1) ·12π

·∫ θ

0sin λ dλ (29)

E2 =Vpv(t, y)/2

Vt· Io(t, y) ·

√2

It· fs

f· (EonS1 + Eoff S+

+ Eoff D+ + Eoff S1 + EonS+ + Eonf D+) · 12π

·∫ π

θ

sin λ dλ. (30)

The total switching losses of the conergy-NPC inverter,Psw (t, y), at hour t (1 ≤ t ≤ 8760) of year y (1 ≤ y ≤ n) arecalculated using (29) and (30), while simultaneously consid-ering the symmetrical operation of the conergy-NPC invertertopology and that practically power switches and diodes of thesame operational characteristics are used to build the PV inverter

Psw (t, y) = 2 · f · (E1 + E2) =Vpv(t, y) ·

√2 · Io(t, y)

2π · Vt · It

· fs · [3(EonT + EonDT ) + 3(Eoff T + Eoff DT )

+ (Eon,T + Eoff ,T − Eon,DT − Eoff ,DT ) · cosθ].

(31)

IV. OPTIMAL SIZING RESULTS

The optimal design of single-phase, grid-connected PV in-verters, which are based on the H5, H6, NPC, ANPC , andconergy-NPC transformerless topologies (Fig. 2) with Pn =2 kW, Vn = 220 V, and f = 50 Hz, has been performed accord-ing to the optimization procedure described in Section II andusing the models in Section III. The PV inverters under studycomprise an LCL-type output filter and are connected to a PVarray composed of PV modules with MPP power and voltageratings, under standard test conditions (STC), equal to 175 Wand 35.4 V, respectively. The service lifetime of the PV systemis n = 25 years. During that time interval, the PV modules ex-hibit an annual reduction coefficient of their output power ratingequal to r(y) = 0.6% in (9), as specified by their manufacturer.

The power section of all PV inverters consists of commer-cially available IGBT-type power switches with integrated free-wheeling diodes. Discrete clamping diodes have been used in theH6- and NPC-based PV-inverters. The technical characteristicsof the PV inverter components are based on the datasheet infor-mation provided by their manufacturers and they are presentedin Table IV. According to the selling prices of the correspondingcomponents in the international market, the economical char-acteristics of the PV inverter components are summarized inTable V. As discussed in Section II, the cost of integrating andhousing the PV inverter subsystems has been included in themanufacturing cost, cinv , which is displayed in Table V.


TABLE IVTECHNICAL CHARACTERISTICS OF THE PV INVERTER COMPONENTS

TABLE VECONOMICAL CHARACTERISTICS OF THE PV INVERTER COMPONENTS

A heat-sink with convection cooling and a θca = 0.65 ◦C/Wthermal resistance has been selected such that the maximumjunction temperature developed at the power semiconductorsduring the year is less than the 175 ◦C limit set by their man-ufacturer. The total failure rate of the PV inverter components,which are not included in the set of the PV inverter designvariables, λc in (6), has been set equal to 17.2 failures/106 h[32], [39]. The maximum permissible output current ripple islimited to RF = 2% in order to conform to the IEEE-1547standard. The damping resistor over-sizing factor has been setequal to SF = 110%. The control unit power consumption isPcu = 5 W. The global minimum of the PV inverter LCOE(objective) function is calculated using a software program de-veloped under the MATLAB platform. In this program, the GAoptimization process has been implemented using the built-ingenetic algorithm functions of the MATLAB global optimiza-tion toolbox and it is executed for 1000 generations, where eachgeneration is comprised of a population of 40 chromosomes.

The optimal values of the PV inverter design variables (i.e.L,Lg , Cf ,Rdr and fs) and Levelized Cost Of the generatedElectricity, LCOEopt , which have been calculated using theproposed optimization process for the H5, H6, NPC, ANPCand conergy-NPC PV inverters installed in Athens (Greece),Oslo (Norway), Murcia (Spain) and Freiburg (Germany), re-spectively, are presented in Table VI. Different set of optimalvalues has been derived in each case, due to the different struc-ture of the power semiconductors comprising each PV invertertopology and the different solar irradiation and ambient temper-ature conditions prevailing at each installation site, which affectthe input voltage and power operating conditions of the PV in-verters during their lifetime period. For the specific operationaland economical characteristics of the components used to buildthe optimized PV inverters (see Tables IV and V) and dependingon the PV inverter topology and installation location, the opti-mal value of the switching frequency, fs in Table VI, has beencalculated to be equal or close to the 30 kHz maximum limit ofthe power semiconductors considered, in order to minimize thecontribution of the LCL-filter cost to the overall cost of the PVinverter [i.e., Cinv (X) in (2) and (3)].

The LCOE values of the non-optimized H5, H6, NPC, ANPCand conergy-NPC PV inverters in each site, LCOEn−o , are alsopresented in Table VI. The nonoptimized PV inverters are com-posed of the same semiconductors as the optimized PV inverters.

Fig. 5. Total cost of the optimized and nonoptimized H5, H6, NPC, ANPC,and conergy-NPC PV inverters for various installation sites in Europe.

The LCL output filter of the nonoptimized PV inverters has beendesigned according to the methodology presented in [30] and itconsists of: L = 5.65 mH, Lg = 1.09 mH, Cf = 3.29 μF, andRdr = 5.6 Ω. The nonoptimized PV inverters operate with aswitching frequency equal to fs = 8 kHz, which is within thetypical range of switching frequency values applied at powerand voltage levels of this order [10], [19], [25]. Thus, in contrastto the procedure followed in the proposed methodology, thenonoptimized PV inverters have been designed using conven-tional techniques, without considering the manufacturing cost,energy production and number of failures in each installationsite. The LCOE of the optimized PV inverters based on the H5,H6, NPC, ANPC and conergy-NPC topologies is lower by 7.02–9.05% compared to that of the corresponding nonoptimized PVinverter structures. At all installation sites, the best performancein terms of LCOE is achieved by the optimized conergy-NPCPV inverters. The optimal LCOE of the conergy-NPC invertersinstalled in Athens, Oslo, Murcia, and Freiburg, respectively, islower than the optimal LCOE of the rest PV inverter topolo-gies in the same installation sites by 0.44–1.67%, 0.45–1.72 %,0.44–1.66%, and 0.45–1.70 %, respectively.

The lifetime cost, Cinv (X) in (2) and (3), of the optimizedand nonoptimized H5, H6, NPC, ANPC, and conergy-NPC PVinverters for various installation sites in Europe is depicted inFig. 5. Compared to the nonoptimized PV inverters, the cost ofthe optimized H5, H6, NPC, ANPC, and conergy-NPC topolo-gies is lower by 2.98–3.47%. At all installation sites, the min-imum cost is achieved by the optimized conergy-NPC inverterand it is lower by 0.16–0.70% compared to that of the optimizedPV inverters based on H5, H6, NPC, and ANPC topologies.

The total energy injected into the electric grid, Ei(X) in (2)and (7), by the nonoptimized and optimized PV inverters invarious installation sites in Europe is illustrated in Fig. 6(a) and(b), respectively. The energy injected into the electric grid by theoptimized H5, H6, NPC, ANPC, and conergy-NPC PV invertersis higher compared to that of the corresponding nonoptimizedstructures in each installation site, by 3.83–6.35%. Among theoptimized PV inverters, the conergy-NPC PV inverters achievethe maximum energy production in all installation sites. The PV-generated energy injected into the electric grid by the optimizedconergy-NPC PV inverters is higher than that of the optimizedPV inverters based on the H5, H6, NPC, and ANPC topologiesby 0.08–0.76%.


TABLE VIOPTIMAL VALUES OF THE DESIGN VARIABLES OF THE H5, H6, NPC, ANPC AND CONERGY-NPC PV INVERTERS AND THE LCOE

OF THE OPTIMIZED AND NONOPTIMIZED PV INVERTERS FOR VARIOUS INSTALLATION SITES IN EUROPE

Fig. 6. Lifetime energy injected into the electric grid by the H5, H6, NPC,ANPC, and conergy-NPC PV inverters for various installation sites in Europe:(a) nonoptimized PV inverter and (b) optimized PV inverter.

The MTBF of the nonoptimized and optimized H5, H6, NPC,ANPC, and conergy-NPC PV inverters for each installation siteare presented in Fig. 7. It is observed that the H6 and ANPCtopologies exhibit equivalent reliability performance. The sameeffect is observed for the NPC and conergy-NPC inverters. TheMTBF of the H5 PV-inverters is close to that of the NPC and

Fig. 7. Mean time between failures (MTBF) of the H5, H6, NPC, ANPC,and conergy-NPC PV inverters for various installation sites in Europe:(a) nonoptimized PV inverter and (b) optimized PV inverter.

conergy-NPC inverters. Also, for all PV inverter topologies un-der study, the PV inverters optimized for Murcia exhibit theworst performance in terms of MTBF, although, as illustrated inTable VI, they exhibit the minimum optimal LCOE. This is dueto the increased values of the stress factors applied to the PVinverter components during operation, since the solar irradia-tion and ambient temperature are higher at this installation site.The MTBF values of the optimized H5, H6, NPC, ANPC, andconergy-NPC PV inverters are higher by 0.03–0.05% compared


to the MTBF of the corresponding nonoptimized PV invertertopologies. Among the PV inverter topologies examined, theoptimized H5 inverters exhibit the best performance in terms ofreliability in Athens and Murcia, where their MTBF is higherby 0.04–1.66% compared to that of the corresponding H6, NPC,ANPC, and conergy-NPC PV inverters which have been opti-mized for the same installation locations. Similarly, the MTBFof the optimized NPC and conergy-NPC inverters in Oslo andFreiburg is higher by 0.04–1.60% compared to the MTBF ofthe optimized H5, H6 and ANPC PV-inverters in these sites.As analyzed in Section II, the MTBF depends on the values ofthe components comprising the PV inverter and the stress fac-tors applied at these components, which are determined by themeteorological conditions prevailing in each installation area.However, since the MTBF is calculated in (6) by weighting thevalues of the stress factors by the percentage of operating hoursat each stress level, the impact of extreme individual values ofthe stress factors on the resulting MTBF is smoothed. Thus,depending on the installation location, the maximum deviationof the MTBF among the optimized PV inverters is 1.62–1.66%.At all installation sites, the H6 and ANPC PV inverters exhibitthe lowest MTBF due to the larger number of components theyconsist of.

The optimal values of L,Lg , Cf , and fs of optimized H5, H6,NPC, ANPC, and conergy-NPC PV inverters with Pn = 10 kWdiffer by 16.87–51.51%, 90.79–94.93%, 14.05–100.02%, and266.25–275.00%, respectively, from the corresponding valuesof the nonoptimized PV inverter (also with Pn = 10 kW). Incase that Pn = 10kW, the value of cinv dominates in the PVinverter total cost [Cinv in (2) and (3)], thus reducing the sensi-tivity of LCOE with respect to the values of the design variables[i.e. vector X in (2)]. The resulting optimal LCOE values arelower than the LCOE of the nonoptimized PV inverters by 0.03–0.74%.

The convergence of the GA-based optimization procedure tothe global minimum of the LCOE objective function has beenverified by also applying an exhaustive-search method, which,however, requires more time in order to be completed than theGA process.

V. CONCLUSION

Among the transformerless PV inverter structures, the H5,H6, NPC, ANPC and conergy-NPC topologies are employedin commercially available grid-connected PV inverters and dis-tributed generation systems. In this paper, a new methodologyhas been presented for calculating the optimal values of thecomponents comprising the H5, H6, NPC, ANPC, and conergy-NPC PV inverters, such that the PV inverter LCOE is minimized.The components reliability in terms of the corresponding mal-functions, which affect the PV inverter maintenance cost duringthe operational lifetime period of the PV installation, is alsoconsidered in the optimization process. The proposed designmethod has the advantage of taking into account the concur-rent influences of the PV inverter topology, the meteorologicalconditions prevailing at the installation site, as well as the PVinverter component cost, operational characteristics and relia-

bility features, on both the PV inverter lifetime cost and totalenergy production.

According to the design optimization results, the optimal val-ues of the PV inverter design variables depend on the topologyof the PV inverter power section (i.e. H5, H6, NPC, ANPC, andconergy-NPC) and the meteorological conditions at the instal-lation site. Compared to the nonoptimized PV inverters, all PVinverter structures, which have been optimally designed usingthe proposed methodology, feature lower LCOE and lifetimecost, longer MTBF and inject more energy into the electric grid.Thus, by using the optimized PV inverters, the total economicbenefit obtained during the lifetime period of the PV system ismaximized.

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Stefanos Saridakis was born in Heraklion, Greece,in 1980. He received the B.Sc. degree in electricalengineering from the Technological Educational In-stitute of Crete, Heraklion, Greece, in 2004, and theDiploma in electrical and computer engineering fromthe Democritus University of Thrace, Xanthi, Greece,in 2011. He is currently working toward the M.Sc.degree from the Department of Electronic and Com-puter Engineering, the Technical University of Crete,Chania, Greece.

His research interests include power electronicsfor renewable energy sources, electric machines, and high-voltage direct-currentpower systems.

Eftichios Koutroulis (M’10) 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, the Technical University of Crete,Chania, Greece, in 1996 and 1999, respectively, andthe Ph.D. degree in the area of power electronics andRenewable Energy Sources (RES) in 2002.

He is currently an Assistant Professor at the De-partment of Electronic and Computer Engineering ofthe Technical University of Crete. His research inter-ests include power electronics (dc/ac inverters, dc/dc

converters), the development of microelectronic energy management systemsfor RES and the design of photovoltaic and wind energy conversion systems.

Frede Blaabjerg (F’03) received the Ph.D. degreefrom the Aalborg University, Aalborg, Denmark, in1992.

He was employed at ABB-Scandia, Randers, from1987–1988. He became an Assistant Professor at Aal-borg University, Aalborg, Denmark in 1992, an Asso-ciate Professor in 1996 and a Full Professor in powerelectronics and drives in 1998. He has been a part-time Research Leader at Research Center Risoe inwind turbines. During 2006—2010, he was the Deanof the faculty of Engineering, Science, and Medicine

and became a Visiting Professor at Zhejiang University, Zhejiang, China in2009. His research areas are in power electronics and its applications like inwind turbines, PV systems, and adjustable speed drives.

He has been an Editor-in-Chief of the IEEE TRANSACTIONS ON POWER

ELECTRONICS from 2006—to 2012. He was a Distinguished Lecturer for theIEEE Power Electronics Society 2005–2007 and for IEEE Industry Applica-tions Society from 2010–2011. He has been the Chairman of EPE’2007 andPEDG’2012—both held in Aalborg. He received the 1995 Angelos Award forhis contribution in modulation technique and the Annual Teacher prize at Aal-borg University. In 1998, he received the Outstanding Young Power ElectronicsEngineer Award from the IEEE Power Electronics Society. He has receivedthirteen IEEE Prize paper awards and another prize paper award at PELINCECPoland 2005. He received the IEEE PELS Distinguished Service Award in 2009and the EPE-PEMC 2010 Council award. Finally he has received a number ofmajor research awards in Denmark.

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