Power Loss Analysis for Single Phase Grid­Connected PV Inverters

Chee Lim Nge 1,2, Ole-Morten Midtgard1

, Lars Norum", Tor Oskar Sretre'1 University of Agder, Faculty of Engineering and Science, Grooseveien 36, 4876 Grimstad, Norway

2 Norwegian University of Science and Technology, Department of Electric Power Engineering, 7491 Trondheim, NorwayE-mail: chee.l.nge@uia.no

Fig. 1. Single phase full-bridge inverter with LCL filter

(2)

(3)

( J

2

1 maVdc 3 2 8 1 2- -- -m --m +- +112 f,L

j(8 a .,fj a 2) rms.g

( J2

I1 Vdc 3 4 2 2. . = - -- -m -m +1 +1

bi.rmsli 38fs Lj (8 a a ) rms.g

Iuni,nns,li =

Qj03

~~A~~~A3VDC~

• \/GRID

Cf :---U2 ~Lf2

..................... .....................

Qj02

For natural sampling modulation scheme, where referencesignal is compared directly with saw tooth carrier signal, theinverter always operates at continuous conduction mode. Inregion I of Fig. 2, inductor current is bidirectional i.e. itchanges direction within one switching cycle. Thiscomplicates transistor power loss analysis as shown in Fig. 3.Current flows through Dl and D2 in region A, Ql and Q2 inregion B, D3 and D4 in region C and then Q3 and Q4 inregion D. On the other hand, in region II, only Ql, Q2, D3 andD4 conduct. Up to switching angle rc/2, regions I and II areseparated by /31 and /32, The conduction losses of transistor anddiode need to be calculated separately unless they have

II. OVERVIEW OF ANALYSIS ApPROACH

Figure 2 is the typical inductor current waveforms of fullbridge inverter where section (a) is unipolar, and (b) is bipolarSPWM. Both waveforms are plotted with identical operatingparameters. The inverter-side inductor instantaneous current islL while the average current is l svc- The peak and valley of thecurrent ripple is lpK and lVL respectively, which form theenvelope of the inductor current ripple. For a properlydesigned inverter, voltage across the filter capacitor, Cf andcurrent flowing through grid side inductor, Lf consist of onlyfundamental frequency component. With such assumptions,we arrive at simple RMS current estimation for unipolar in (2)and bipolar SPWM in (3) as provided in [4]. The first termsare current ripple and they are independent of the magnitudeof grid current, 19.

Abstract - This paper presents a method for power lossanalysis applied on single-phase grid-connected PV inverter. Theoften neglected current ripple effects are included in powerdevice switching and conduction losses. The relationshipsamongst component losses, output inductance, switchingfrequency and de-link voltage are investigated. It is shown thatcurrent ripple effect is important to power loss analysis due tovarying irradiation. The closed form solutions of componentlosses are proposed and verified with SPICE simulation results.

PV inverter topology considered in this paper is thepopular single phase full-bridge inverter as illustrated in Fig. 1.This topology is also widely used in uninterruptible powersupply (UPS) and single-phase motor drive applications. Thepower loss analysis is presented in [1-3] but neglects thecurrent ripple effects on semiconductor valve devices. This isdeemed sufficient if the application has relatively large outputinductance and the design goal is to meet the thermallimitation at full load. For grid-connected PV inverter, LCLfilter is typically used in order to reduce weight and obtaingood harmonic current filtering. Comparing the equations ofinductor current ripple in [4] with duty-cycle to inductorcurrent transfer function in [5], we notice that both arefunctions of inverter-side inductor, L; and de-link voltage, Vdc'

Reference [5] also shows that L, does not affect the attenuationof grid harmonic current. Hence the lower boundary of L, isdetermined by the level of inductor current ripple where theaspect of component power loss is addressed in this paper.

This paper shows the complexity of including current rippleeffect into component loss analysis. Nevertheless, grid­connected PV inverter typically operates at unity power factorand the analysis can be considerably simplified.

I. INTRODUCTION

The overall efficiency of photovoltaic (PV) inverter is animportant design criterion because it determines the systempayback period. However, due to variation of irradiation, PVinverters seldom operate at the maximum rated power. This isevident from the European efficiency, 17euro in (1) that basedon typical Central European irradiation conditions. It has 80%weight below half of the maximum rated power. The overallefficiency of PV inverter is as a result not only for thermalconsideration at full load but across the power range. Thecurrent ripple effect on component power losses at light loadcondition is significant enough that it should not be neglectedfor satisfactory estimation.

This work is supported by Research Council of Norway and Elkem Solar.

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identical turn-on voltage drop. Similarly, P1 and P2 need to beincluded in the turn-on losses of the Ql and Q2, and turn-offlosses of Q3 and Q4.

2.50

2.00

1.50

1.00

~ 0.50

0.00

.{).5cP

-1.00

-1.50

I

----- ----

-------'------ ::: ...

II.i .. ·1.·.·.·.·.·.· ... ," .

. i. . " .

·-- ·l'~ll~Ir.. , ~.

. .

, 'j • r.-M}!~:t;. - - - • .:.~·~·-• .:..-·":"·- • .:..-·I':'·-• .:..-·":"·- • .:..-·r •• ," •••••

{ .i. .'.: .i "I.

IGBT and MOSFET. Firstly, both devices have ohmicresistance of the channel during on-state but the IGBT has anadditional forward-bias voltage. Secondly, the switchingdynamic characteristics of both devices are identical exceptthat IGBT has tail current at the end of turn-off transientperiod [6]. Hence this paper presents only the IGBTcalculations.

A. Conduction losses

IGBT and diode on-state losses have similar expression in(4). They consist of the voltage drop across the pn junctionand the ohmic resistance, in the function of device RMScurrent.

(4a)

(4b)

o.k [radian]

(b)Fig. 2. Single phase full-bridge inverter with LCL filter

.·,·.·.·.·.·.·.·1.·.·.·.·.·.·,,·.·.·.·.·.·.0.' ..... " .... 0.0 .....·.i.·.·.·.·.·.· ..·.·.·.·.·.·.·,.·.·.·.·.·.·• I ••••• 0.0 ..... '" .....

I I I I .·,·.·.·.·.·.·.·1.·.·.·.·.·.·,,·.·.·.·.·.·.- - - - - - - - ~ - - - - - - - -1- - - - - - - - ., - - - - - - - - ., - - - - - - - --, - - - - - - - - ., - - - - - - - - r- - - - - - - -

- ~- ~- ~- - ~ -~ : - :~:::::::::::::~::::::::::::~::::::::::::I ••• ':'".'~' • :._" ••••••••• ", ••••••••••••

II- fl-tl-' H-ll-ill- fl-tt-R fI .. . .J J ~ ~ -: ~ J.7~

(6)

(5)

It is assumed that the switching frequency is high enoughhence symmetrical waveform up to switching angle 1t/2.Equation (5) is the duty cycle of Ql while (6) is the peak-to­peak current ripple.

If the grid current, Ig is large enough, Ql only operates atregion I. The RMS current of transistor Ql (7a) is the sum ofthe familiar RMS equation of saw tooth waveform of eachswitching cycle. The first term is the instantaneous gridcurrent, I g and we assume that it is relatively constant withinone switching cycle. Equations (5) and (6) are substituted into(7a) and arrived at closed form equation in (7b).

II

o.k [radian]

(a)

I

~. 1.00::::::1.20 :::::1.40 :::::~; 0-"_____ _ ...... J_ ..... J .. ..... ..,,_ ......... _ ....... _ .....

I ·.i.·.·.·.·.·.· ..·.·.·.·.·.·.·•.·.·.·.·.·.·. . •......•...... , .

- -- _~ --- ----~:---f32~--j -'-I~~~········~·:~~~·~~~·I~~····I>;--: : : --------Ivl --IL ::::. . . .......................

4.00

3.00

2.00

~1.00

0.00

o.-1.00

-2.00

-3.00

(8)

ma [2/ Pk'/ +o.s(VdC.ma J2(~m 2.i; Jl'+iJ] (7b)

Jl' 3 L,is 15 a 4 a 3

. Vdcma sin ak [1- ma sin ak ]

Iv- k = I pk..g SIn a, - 2/ L.s 1

=k, sin ak [ sin ak + kn ]

I nns,ql =

I nns,ql =

Diode Dl conducts at region A of Fig. 3 up to Pl. Twocoefficients, k, and k; are introduced in the equation of valleyof current ripple, I v-k (8). Hence the equation of cross-overswitching angle, P1 is simplified to (9). The duty-ratio ofregion A over the switching period, 4-k is simply obtainedfrom the geometry and is given in (lOa). Using Taylor seriesexpansion, (IDa) is simplified to (1Db). Substituting (8-9) and(lOb) into (lla), we arrive at the closed form RMS current ofDl in (lIb).

I( )1Ts =1/fs o.k [radian]

Fig. 3. Details of inductor current at bidirectional region

-3.00 .L-__~ ~ ~_==========!.--.J

1.00~

-2.00

2.00

3.00

III. COMPONENT POWER Loss ESTIMATION

The inverter power loss analysis for unipolar SPWM ispresented here. Similar approach can be applied to bipolarSPWM and it is skipped for this paper. For modern PVinverters, the popular semiconductor valve devices areMOSFET and IGBT. The physical structure of IGBT issimilar to MOSFET but with an extra p+ layer that forms thedrain terminal. This results in only slight differences between

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(9)(13b)

The RMS current of the freewheeling diode D4compliments those of Ql as given in (12a). The transistor Q4provides return path during the negative half-cycle and theRMS current is (12b). It is assumed that region A in Fig. 3 isnegligible and we shall see in section IV that this does notresult in significant discrepancy.

(15)

(16b)

(14a)

(16a)

(14b)

Y fmjl4

P = de ton s ~ {k' [ . k]} E fon,ql L..J e SIn a k sIn a k + n + rr s

mf k=Plmj 12K

p = ma2Ydc2ton [1! +sin-1(k )+k ~]+E fon,ql 81!L

i2 n n n rr s

Contradicts to Ql, Q4 turns off at the valley of currentripple up to switching angle P1 as given in (17).

Similarly, coefficient kf is introduced in the peak of currentripple, I p -k in (15) and it is substituted in (13b) to arrive at(16a). The closed form solution for Ql turn-off switching lossis given in (16b).

Similar to the curve-fitting model approach proposed in [9],this paper further simplifies the switching loss functions tofirst order polynomials. As a result, the parameters tom toff' Err

and E, are constants that can be extracted from IGBTdatasheet. This is shown in an example in section IV. It shouldbe note that Err and E t can be functions of I c and VCE' Suchsurface response model requires tedious regression analysishence it is avoided here. As long as the switching energymodel is first order polynomial function of collector current,closed form solutions as presented below are applicable.

The switching energy is a function of IGBT Ql turns on atthe valley of current ripple and turns off at the peak currentripple. The power loss is calculated from the switching energyof each switching cycle and divided over the switching period.Equation (8) is substituted into (13a) and arrives at (14a) forthe power loss. The IGBTs block de-link voltage during turn­off hence VCE is substituted with Vdc. Referring to Fig. 2, theturn-on switching losses of Ql occur only at region II wherethe instantaneous inductor current is positive. The closed formsolution for Ql turn-on switching loss is arrived at (14b).

(12b)

(lOa)

(lOb)

(lIb)

(lla)

(12a)

Irms,dl = 1/---'------

I 2I = rms,li _ I 2

rms,d4 2 rms,qI

I I'I =~

rms,q4 J2

Amj l 2K

L i.. 2I n- kk=l

»r».t.: dl Z make 1{~[~1- kn 2 (2kn

4 + 11kn 2 +32)+, 6 ~ l Oz

45k. sin-I(k. )- 8(5k.2 +4 )>>

B. Switching losses

The transistor switching energy is the time integral of theproduct of collector current, I C and voltage across collector­emitter, VCEo The voltage and current switching waveformscan be approximated using piece-wise linear functions. Thegeneral form of IGBT switching loss is given in (13). Theterm Err is loss due to diode reverse recovery current while E,is loss due to tail current. As previously mentioned, IGBT andMOSFET have identical dynamic characteristics. Advancedanalytical switching loss model of MOSFET presented in [7,8] are readily applicable to solve for switching transition time,ton and toff. It is shown that ton and toff are non-linear functionsof Ic- transconductance, gfs, threshold voltage, VTH, gateresistance, RG, gate drive voltage, Vdd, input capacitance, Ciss,

reverse transfer capacitance, Crss and parasitic inductances, LE•

The complexity is compounded since gfs is a function of I c andoperating temperature. Also, VTH is a function of operatingtemperature while Ciss and Crss are non-linear functions of VGE

and VCE' Obviously, these analytical models are useful toidentify the deterministic parameters but they are verycomplex. The closed form solutions for ton and toff are notpractical for the loss estimation of inverter unless muchaccuracy is to compromise.

(13a)IV. RESULTS

Due to the complexity of the inverter current waveform, theloss functions are considerably simplified in this paper. The

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higher order curve-fit functions from the datasheet. Equation(18) is second order polynomial switching loss model ofIKB06N60NT. Referring to Fig. 5, the instantaneousswitching current of Ql measured from SPICE is substitutedinto (18) and denoted "sim". They are compared with curveslabeled "cal" obtained from (16b), (17b).

approximations of those closed form solutions are verifiedusing a 2 kW SPICE model. The de-link voltage and switchingfrequency are fixed at 400V and 19.75kHz. Fig. 4 compares(7b), (l l b) and (12) with the RMS current measurementresults of SPICE. It is shown that the proposed closed formsolutions for device RMS current correlate with the simulationresults. The RMS current are evaluated between inverter-sideinductance, L; equals to O.3mH and 1.2mH. This confirms thecurrent ripple effects on conduction losses, which is moresignificant at the range of low grid current, I g or lowirradiati on.

Pon-k = (0.00056IVl_k 2 + 0.018Ivl_k + 0.025 )!s

PDf! -k =(-0.00014 I pk-k 2 + 0.027 I pk-k + 0.021)!s

(18a)

(18b)

6.00 -,-----...,....----~-----,.....------,

864

19 [A]

2

1

1 I

- ~ ~ - - 1 ~ ~ - - ~ - - 1- - -

1 I

I

2.50

3.00

0.00 +--.a::;:;;::..;,.,;..-li--~~::I:II=------+-------1

o

0.50

3.50 -,-----...,....----.....,.....------,--------,

[ 2.00

~a. 1.50

1.00

864

19 [A]

2

0.00 +--~~~---....---....,...---_iIio

5.00

4.00~en 3.00=:~

2.00

I

I I I~ - -t - - - ~ ~ ~ ~I- - - - ~ ~ - ~ ~ - ~ - ~

1 1 I

I I 1_ ~ ~ ~ ~ ~ -l ~ __ 1_ ~ __ ~ _

I I

I 1

_~ i __ ~ _1

I

1.00

--lq1 @O.3mH (sim)

---El-·- Iq1 @O.3mH (cal)

--lq1 @1.2mH(sim)

- - -El- - - Iq1 @ 1.2mH (cal)

(a)

--ld1 @O.3mH (sim)

- - -El- - - Id1 @ O.3mH (cal)

--ld1 @1.2mH (sim)

- - -El- - - Id1 @ 1.2mH (cal)

--Pon @ O.3mH (sim)

- - -El- - - Pon @ O.3mH (cal)

--Pon@1.2mH (sim)

- - -El- - - Pon @ 1.2mH (cal)

--Poff@O.3mH(sim)

- - -El- - - Poff@ O.3mH (cal)

--Poff@ 1.2mH (sim)

- --El- - - Poff@ 1.2mH (cal)

(b)Fig. 4. RMS current of 1GBTs and diodes

8

--Poff@O.3mH (sirn)

- - -El- - - Poff@ O.3mH (cal)

--Poff@ 1.2mH (sim)

---El--- Poff@1.2mH(cal)

4 6

19 [A]

(a)

I

____ ~~J ~_~~~~~ ~l ~~ __1 I

I

4.00 -,-----...,....----.....,.....------,--------,

3.50

3.00

1.00

0.50

0.00 +--.;p:;::..:.;;.....-~~~=--------+-------1

o 2

--Pon@O.3mH (sim)

- - -El- - - Pon @ O.3mH (cal)

--Pon@ 1.2mH (sim)

- - -El- - - Pon @ 1.2mH (cal)

1[ 2.50

== 2.00rna. 1.50

8

--id4@O.3mH(sim)

- - -El- - - id4 @O.3mH (cal)

--id4@1.2mH(sim)

- - -El- - - id4 @ 1.2mH (cal)

4 6

19 [A]

1

I~ __ ~ ~I_ ~ _ ~ __ ~ L ~_

I 1

I I

2

1

1~-----~------

I

--lq4@O.3mH(sim)

- - -El- - - iq4 @ O.3mH (cal)

--iq4@1.2mH(sim)

- - -El- - - iq4 @ 1.2mH (cal)

7.00 -,-----...,....----~-----,.....------,

6.00

5.00

~ 4.00en~ 3.00

2.00

1.00

0.00 +-----+------+-----+------1

o

"DuoPack" IGBT with 6A current rating from Infineon,IKB06N60NT is selected for switching loss analysis. It isassumed that the setup is similar to test circuit illustrated in thedatasheet. The coefficients in (16b) and (17b) can be extractedby referring to the switching energy loss diagram in thedatasheet. If we pick the curve-fitting points at collectorcurrent 3A and 6A, we get Err = O.005mJ, E, = O.025mJ whileboth ton and toff are equal to O.125ns. In order to obtain betteraccuracy, method of least squares can be utilized to derive

(b)Fig. 5. IGBT Ql switching losses at (a)/s =I5.75kHz, (b) I9.75kHz

The closed form solutions correlate with the simulationresults. This can be expected from (18) where the coefficientscorresponding to I v1_k

2 and I pk_k2 are relatively smaller. Fig. 5

compares between switching frequency 15.75kHz and19.75kHz. It is shown that switching frequency effect on

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current ripple as given in (8) and (15) is not evident for thiscase.

V. CONCLUSIONS

This paper demonstrates that it is viable to express thecomplex loss functions of inverter in closed form equations.The current ripple effects are simplified in the proposedequations based on the assumption of grid-tied PV inverteroperation. The approximations made are verified andcorrelated with SPICE simulation results. The main advantageof expressing the losses in close form functions is to enabletop-down design procedure. One possibility is todeterministically select power devices based on the transistor'sfigure-of-merit [10].

The results in section IV confirm the current ripple effectson the power device conduction and switching losses. It isshown that current ripple effects on PV inverter efficiency aremore significant at low load range. Hence it is important toinclude such consideration for PV inverter design due tovarying irradiation. The design of inverter-side inductance, dc­link voltage and switching frequency is a compromisebetween component power loss, as presented in this paper andtransient response, as shown in [5].

Despite the focus of semiconductor devices in this paperinductor losses should not be neglected in inverter power lossanalysis. The inductor coil loss can be calculated from theRMS current provided in (2). The inductor core loss isdependent on current ripple and switching frequency hence itshould be investigated carefully together with the transistorlosses. It is typically expressed in the Steinmetz equation,which is in fact high order polynomial function of currentripple. Transistor gate drive loss should also be considered butit is not affected by current ripple effect.

REFERENCES

[1] Ikeda, Y.; Itsumi, J.; Funato, H., "The power loss of the PWM voltage­fed inverter," Power Electronics Specialists Conference, 1988. PESC '88Record., 19th Annual IEEE, vol., no., pp.277-283 vol.1, 11-14 April1988

[2] Kolar, J.W.; Ertl, H.; Zach, F.C., "Influence of the modulation methodon the conduction and switching losses of a PWM converter system,"Industry Applications, IEEE Transactions on , vol.27, no.6, pp.1063­1075, Nov/Dec 1991

[3] Blaabjerg, F.; Jaeger, U.; Munk-Nielsen, S., "Power losses in PWM-VSIinverter using NPT or PT IGBT devices," Power Electronics, IEEETransactions on, vol. 10, no.3, pp.358-367, May 1995

[4] Hyosung Kim; Kyoung-Hwan Kim, "Filter design for grid connected PVinverters," Sustainable Energy Technologies, 2008. ICSET 2008. IEEEInternational Conference on ,vol., no., pp.1070-1075, 24-27 Nov. 2008

[5] R.Teodorescu, F.Blaabjerg, U.Borup and M.Liserre, "A New ControlStructure for Grid-connected LCL PV Inverters with Zero Steady-stateError" Applied Power Electronics Conference and Exposition, 2004.APEC '04. Nineteenth Annual IEEE, pp 580- 586 Vol. 1

[6] N. Mohan, T. Undeland, and W. Robbins, Power Electronics:Converters, Applications, and Design, third edition, New York: JohnWiley & Sons, 2003.

[7] Xiao, Y.; Shah, H.; Chow, T.P.; Gutmann, R.J., "Analytical modelingand experimental evaluation of interconnect parasitic inductance onMOSFET switching characteristics," Applied Power ElectronicsConference and Exposition, 2004. APEC '04. Nineteenth Annual IEEE,vol. 1, no., pp. 516-521 Vol. 1, 2004.

[8] Yuancheng Ren; Ming Xu; Jinghai Zhou; Lee, F.C., "Analytical lossmodel of power MOSFET," Power Electronics, IEEE Transactions on ,vol.21 , no.2, pp. 310-319, March 2006

[9] S. Clemente, "Application characterization of IGBT's," InternationalRectifier Application Note, AN-990.

[10] B. J. Baliga, "Power semiconductor device figure of merit for highfrequency applications," IEEE Electron Device Lett., vol. 10, p. 455,Oct. 1989.

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