A Novel Design Methodology Maximizing the Weighted- Efficiency of Flyback Inverter for AC Photovoltaic Modules

Anastasios Ch. Nanakos1, Emmanuel C. Tatakis1, Georgios S. Dimitrakakis1, Nick P.

Papanikolaou2 and Anastasios Ch. Kyritsis3

1UNIVERSITY OF PATRAS, Department of Electrical and Computer Engineering 26504, Rion-Patras, Greece

Tel.: +30 / (261) 099.64.14, Fax: +30 / (261) 099.73.62 E-Mails: tnanakos@ece.upatras.gr, e.c.tatakis@ece.upatras.gr, jimakakis@ece.upatras.gr

URL: http://www.lemec.ece.upatras.gr 2T.E.I. OF LAMIA, Department of Electrical Engineering

T.E.I. of Lamia Campus, 35100, Lamia, Greece Tel.: +30 / (223) - 106.02.54, Fax: +30 / (223) - 103.39.45.

E-Mail: npapanikolaou@teilam.gr URL: http://www.teilam.gr

3CENTRE FOR RENEWABLE ENERGY SOURCES AND SAVING (CRES) 19th km Marathonos Ave, 19009, Pikermi Attiki, Greece

Tel.: +30 / (210) 660.33.71, Fax: +30 / (210) 660.33.18. E-Mail: kyritsis@cres.gr

URL: http://www.cres.gr/kape/contact_uk.htm

Keywords Photovoltaic, Current Source Inverter (CSI), Efficiency, MOSFET

Abstract A new design methodology that optimizes the weighted efficiency of a single-phase, single-stage flyback inverter for AC-PV module applications is proposed. This novel approach combines the essential advantages of the flyback topology with high efficiency in the direction of a reliable, cost-effective and high performance photovoltaic system. The proposed methodology focuses exclusively on choosing the inverter design parameters, taking into consideration the PV module characteristics. In order to meet this goal an analytical losses calculation should be performed. Since the problem is complicated special effort is given to manipulate the equations and variables in such a way to minimize the number of parameters taking into consideration the operation constraints. The proposed methodology is also verified experimentally.

Introduction In the last two decades it becomes more and more obvious, that the rapid climate changes and the energy dead-end of fossil fuel dependence accelerate the large scale adoption of clean energy sources. Towards this aim, the higher interest is concentrated in solar and wind energy exploitation. Nowadays, Photovoltaic power injection to the utility grid is gaining more and more admittance [1, 2]. The latest technology on decentralized grid connected PV systems is the AC-PV module [2, 3] which is the integration of the PV module and the inverter into a single unit that operates as an AC generator. This configuration promises optimum MPPT operation unaffected of shadows that can decrease remarkably the total power generation. The AC PV module can be easily installed to any rooftop without any special technical knowledge or extreme safety precautions. Also, its modular layout assures effortless enlargement of the installations when desired.

The power converter unit of an AC PV module is usually a single-phase inverter, ranging from 50W to 400W. There are many single or multi-stage topologies about grid connected inverters for photovoltaic

modules in the international bibliography [2]. In any case, all topologies must be characterized by high efficiency, high power density, low volume and extreme reliability.

The flyback topology [4-6] concentrates the above mentioned demands and many more advantages, forming an attractive selection for the AC-PV module converter. Therefore, a lot of effort has been given to improve its reliability, cost and efficiency by adopting different control techniques and/or design parameter selection [4-6]. In fact, by selecting judiciously the switching frequency, the transformer ratio, the semiconductor characteristics etc. it is possible to maximize the converter efficiency. In the international bibliography, except some well-known and widely used common practices and empirical rules [4], there are no specific directions or analytically verified guidelines to clarify the relation between this parameters selection and efficiency.

In this paper a special effort was given to comprehend this correlation and form a methodology that clearly defines, always in accordance with the required specifications, the values of the design parameters in order to maximize an objective function that is the weighted efficiency. To perform this task the flyback inverter is analyzed, power losses on each component are estimated and an algorithm is established to define accurately the appropriate parameters.

Flyback converter in DCM operation as a grid-connected CSI The flyback inverter, as shown in Fig. 1, consists of four basic parts a) the main switch, P, located on the primary side of the transformer b) the multi-winding transformer, c) the two semiconductor switches, S1 and S2, located on the secondary side and finally d) the output L-C filter. The converter operates in DCM due to its simplicity of control.

Fig. 1: Flyback inverter topology diagram Fig. 2: Switching sequence diagram As it is shown in Fig. 1 this inverter performs energy flow from the dc to the ac side, by using two identical secondary windings. Each of them is able to transfer energy to the ac side during a utility grid half cycle. For this reason, two switches are placed between these windings and the mains side and they are appropriately controlled by the mains voltage, so as each to conduct during a line half cycle. So, while the main semiconductor, P, is modulated in high frequency (20kHz-200kHz) the switches of the secondary winding are modulated in 50Hz or 60Hz. The switching sequence of each semiconductor can be observed in figure 2. A thorough analysis of the flyback inverter operation under Discontinuous Conduction Mode is described in [4].

The transferred power is expressed by equation: 2 2PV dc L p1P V g d4

= (1)

where L 1 sg 1 L f= (2)

Design methodology and performance optimization The AC-PV module has to ensure the maximum exploitation of the solar energy. So the efficiency of the inverter has to be high, not only for the nominal power, but also for other power values corresponding to various irradiance levels. To overcome this obstacle, the European-weighted, given

by equation (3), and the American-weighted, given by equation (4), efficiencies can be used. These factors, depending on the PV installation location, integrate in one quantity the efficiency at various power levels.

EU 5% 10% 20% 30% 50% 100%0.03 0.06 0.13 0.10 0.48 0.20 = + + + + + (3) 10% 20% 30% 50% 75% 100%0.04 0.05 0.12 0.21 0.53 0.05 = + + + + + (4)

The basic aim of the present paper is to establish a methodology based on the weighted efficiency optimization to accurately define all the design parameters of the topology. The weighted-efficiencies require various power levels, eq. (5), so different power loss ratios, eq. (6) must be calculated.

PV,ww

nom

PP

= (5)

loss,wr,loss,w

PV,w

PP

P= (6)

where Pnom is the PV module nominal power and w is the percentage of the nominal power.

However, power losses depend on many parameters that correlate directly to the topology components as well as to various operational variables. In order to establish the optimization algorithm it is necessary to clearly define the design parameters and the dependent variables. For this reason, all system parameters are reported in table I and classified in three different categories, namely the input specifications, the component parameters and the operational parameters.

Table I: Parameters of the system

Input Specifications Pnom[W], Vdcmin[V], Vdcmax[V], Vacp[V]

input and output electrical characteristics of the inverter

Com

pone

nt P

aram

eter

s

Sem

icon

duct

ors

Para

met

ers

Primarys Mosfet

Rds1[], tf1[sec], tr1[sec], VDSBD1[V] on-resistance, rise and fall time,

breakdown voltage Secondarys Mosfets

Rds2[], tf2[sec], tr2[sec], VDSBD2[V]

Secondarys Diode Vd[V], Rd[]

forward voltage drop, series resistance of the diode

Tran

sfor

mer

par

amet

ers

Core Type W[mm2], Ve[mm3], Ac[mm2], le[mm],

Rt[oC/W]

window area, volume, cross sectional area, effective length, external thermal

resistance

Core Material , , k, Bsat[T]

material coefficients from material datasheet, saturation flux density

Winding Parameters

r[mm], str1, str2, J[A/mm2], NDC, n,

Cff=Aw/W

wire radius, strands of the primary and secondary winding, current density,

turns ratio, copper fill factor

Operational Parameters

fs[Hz], DCM

the converter switching frequency, MMF mode

parameters independent of the specific component selection

Objective Function EU=f(n,fs,J,Bmax) function under optimization

Constraints DT, dpeak,max,

Vmax,sec , Bmax, Cffmax

constraints that ensure feasibility and proper operation of the design

Design Parameters n, fs, J, Bmax independent variables that define the maximum weighted efficiency

As it is shown in Table I the system parameters are numerous so, special manipulations must be conducted in order to make specific and proper conclusions.

At the first step of the optimization procedure the input characteristics have to be assigned. These parameters are determined by the PV module output. At the second step, the packages and the technology of the main and the secondary switches can be selected. According to these selections the following parameters should be specified: tf1, Vd, as well as the relation between Rds and VDSBD. Due to the operation of the inverter (DCM) the variables tr1, tr2, tf2 and Rd can be neglected. Afterwards, the type and the material of the transformer core should be selected so, all corresponding variables are defined.

The independent variables are now reduced to only four that are reported in Table I as design parameters. The specific semiconductor parameters and the winding parameters will be defined by the optimization procedure. Furthermore, the optimization procedure has to ensure the feasibility and the proper operation of the proposed design. In order to fulfill such a task the constraints presented in Table I should be applied. These limitations consist of: the maximum voltage on the secondary switches, eq. (7), the temperature rise of the magnetic component, eq. (8), the copper fill factor of the core window, eq. (9), the duty cycle limitation, eq. (10) to ensure DCM operation and the maximum flux density in order to avoid saturation.

dcmaxmax,sec acp DSBD2

acp

VV (n) 2 V 150% VnV

= +

(7)

( ) ( ) ( )dc s max t CRL dc s max CPL dc s max maxDT n,V ,f ,B ,J,r R P n,V ,f ,B P n,V ,f ,B ,J,r DT= + (8) ( ) ( )dc s maxff dc s max ff maxAw n,V ,f ,B ,J, rC n,V ,f ,B ,J, r CW= (9)

1 1

dcmin dcmin dcminp pmax

dc acp acp

ww dc

V V Vd (n, ) 1P

d 1V nV n

P ,VV

= + = +

(10)

max satB B (11)

So, by reducing the multidimensional parameter space the design procedure becomes the optimization of an objective function the weighted efficiency - that depends on only four variables, the design parameters. Furthermore, the constraints limit even more the possible configurations. To resolve this mathematical problem a numerical algorithm for constrained nonlinear optimization is adopted and implemented on a software platform. In order to formulate the equations to predict the converter losses, the rms and average value of both input and output currents should be calculated. The adequate equations are presented in the following paragraphs.

Input and output current calculation At first, the current of the primary winding is examined and the necessary equations are presented. In [4] the average current is described as:

2DCavg dc L p

1I V g d4

= (12)

The rms current of the primary winding can be found from the following equation:

( )

shl hl

s

2iTT T w

2 2 2 2DC,rms DC DC DC

i 1hl hl hl0 0 i 1 T

1 1 1I i (t)dt i (t)dt i (t)dt QT T T

=

= = = + (13)

where w is the integer part of hl sT T and Q is the rest part of the integral referring to the beginning or to the ending of a line cycle and so it can be neglected. After some mathematical manipulations we can conclude that:

2 3 3 2 2 3ws p DC s p2 3DC

DC,rms 2i 1hl 1 1

t d V T dV1 4I sin ( i)T L 3 w 9 L

=

= = (14)

In order to define the current value of the secondary winding the same procedure can be executed. The average and rms value of this current are:

2 2 2 2wDC s p DC s p

sec,avg 2 2i 1acp 1 acp 1

V T d V T dI sin( i)

2wV L w V L

=

= = (15) 3 2 3 3 2 3wDC s p DC s p2

sec,rms 2 2i 1acp 1 acp 1

nV T d nV T dI sin ( i)

3wV L w 6V L

=

= = (16) Losses estimation of the flyback inverter in DCM operation The loss calculation procedure of the individual components will be presented. This analysis is divided into two categories: a) the transformer losses calculation and b) the semiconductor losses calculation.

The transformer loss calculation The losses on the magnetic element are highly related not only to the parameters of its construction but also to the waveform of the flowing current. There are many different approaches to predict the magnetic losses but the most fundamental step is the discrimination between core and copper losses. The core losses deal with the material and size of the core, temperature, frequency and form of the flux waveforms. On the other hand the copper losses consist of rms, skin and proximity losses of the windings.

Core loss estimation for arbitrary waveforms The most common empirical equation exclusively used for sinusoidal excitation is the well-known Steinmetz equation. Furthermore, the data provided by the manufacturers of magnetic materials are valid only for sinusoidal excitations fact that prevent their use in topologies with different excitation waveforms and thus to the flyback transformer. The excitation of the flyback transformer under discontinuous conduction mode is described by equation (17) and presented in figure 3.

When P switch conducts, the voltage on the transformer is Vdc and by the time it switches off the voltage on the transformer is that of the grid.

V , , t tdc i on,iV (t ) nVac( t ) , t t ti on,i i off ,itrans,i i

0 , t t toff ,i i offz,i

f1 1

kk1.70612 0.2761

1.354

+

= + +

(19)

The core loss of each switching cycle, eq. (20), was calculated according to eq. (18). For a time interval equal to Thl a series of successive core losses takes place. The total power core loss ratio, eq. (22), is estimated by analytically computing a series of losses, eq. (21), over the weighted input power given by eq. (6).

( )1

1 1 1f dcCRL,i e s p dc acp dc

c

k VP V T d V sin( i) V n V sin( i) 0w wNA

+

+

= + + (20)

w

CRL CRL,ii 1hl

1P PT

=

= (21) ( )

( )11

s pCRL dc s max f dce 11 1 1

PV,w DC c dc acp PV

w

,w

w dc(T dP n, ,V ,f ,B k VVP N A V 0.51762 V n 0.46 P

n,P ,V )P

+ +

= + (22)

It can be easily understood that the core loss ratio depends on the turns ratio n, input power level Pw, input voltage Vdc, switching frequency fs and maximum flux density Bmax.

Copper losses estimation of the multi-winding high frequency transformer The copper losses that increase the magnetic component temperature and winding resistance lead to special operation conditions and decrease the overall performance. Proximity, skin and rms effects are the main causes for copper losses. A semiempirical model to determine HF copper losses for non-layered coils is presented in [11]. The HF current through the flyback transformer obligates the use of significantly low diameter copper wire, fact that proves the implementation of a layered winding, practically impossible. The model presented in [11] is based on the statistical treatment of simulation results performed by FEA software and verified by experimental measurements. The common practice in calculating HF copper losses is to calculate two different loss components given by eq. (23) and eq. (24). The resistance factor Frj=Rac/Rdc of the winding j is calculated by equations presented in [11].

2ac, j j dc, j rms, jP Fr R I= (23)

2dc, j dc1 dc, jP R I= (24)

So, the final power loss ratio is:

( )CPL w dc s maxPV,w

P f n,P ,V ,f ,B ,J, rP

= (25)

Calculation of semiconductor losses The semiconductor losses can be distinguished in switching and conduction losses.

Switching losses Due to the DCM operation there are switching losses only during the turn off transition. The switching losses for a specific switching cycle can be approximated as shown in eq. (26), where usp(t), iip(t) are the voltage and current values during the transition. The switching losses on the mosfets on secondary windings can be neglected.

f1SL1 sp ip s

t(t) = u (t)i (t) f

2P (26)

In order to compute the total switching losses firstly, we calculated the energy lost in each switching cycle by the following equation:

i ii f

V IE t2

= (27)

where i DC AC DC ac,iV V nV (t) V nV= + = + (28) After the series computation, eq. (29), the total switching power loss ratio is given by eq. (30).

w w2DCf

s p DC ACpi 1 i 11

VtE T d V sin( i) nV sin ( i)2 L w w

= =

= + (29)

acps f

SL1 w dc s dc

PV,w p w dc

nV 4f t ( )P (n,P ,V ,f ) V

P d (n,P ,V )

+

= (30)

In eq. (30) the parasitic output capacitor loss is absent because latest research presented in [12] proved that, this kind of loss is already integrated in eq. (26).

Conduction losses

As it concerns the conduction losses (PCL1 and PCL2 on the switches in primary and secondary windings respectively), they can be described as follows:

2CL1 rms DS1DC,P I R= (31)

2CL2 rms DS2sec,P I R= (32)

The problem that came up was the selection criteria of the appropriate mosfet. As the transformer ratio rises, the maximum voltage on the primary Mosfet is getting higher while the maximum voltage on the secondary switches is decreased. In order to compromise the selection between transformer ratio, on-resistance and breakdown voltage on both switches we used the relationship between the on-resistance and the junction breakdown voltage mentioned in [13]. To meet our requirements this relationship was adjusted to match the datasheet characteristics of a single mosfet manufacturer. The curve fitting was conducted for various packages and two different voltage levels since depending on voltage (high or low) and junction surface (package) the mosfet characteristics are different (Fig. 4). The implemented equations (33) and (34) present the simplified relation between the on-resistance and the transformer turns ratio n. Combining equations (14), (16), (33), (34) we conclude to the conduction losses ratio given by eq. (35) and eq. (36).

2.48

8 dcmaxDS1 acp

acp

VR (n) 5.29 10 1.5V n 0.0166V

= + +

(33)

2.4

8 dcmaxDS2 acp

acp

VR (n) 3.784 10 1.2V 2nV

= +

(34)

L DS2 p w dcCL1 w dc

PV,w

16g (n)R (n)d (n,P ,V )P (n,P ,V )P 9

= (35)

dc L DS2 p w dcCL2 w dc

PV,w acp

2nV g (n)R (n)d (n,P ,V )P (n,P ,V )P 3V

= (36)

The diode conduction losses can be calculated by multiplying the average current by the diode voltage drop Vd forming the power loss ratio that is given by eq. (36).

d d

PV,w acp

P 4VP V

= (37)

Optimization example By summing the power loss formulas (22), (25), (30), (35), (36) and (37) the total power loss ratio appears. The optimization is based in minimizing the total power loss ratio. As it is mentioned earlier

Fig. 4: The relation between the on-resistance and the mosfet secondary voltage

the procedure to optimize the efficiency starts by taking into account the input specifications. By computing the loss formulas the algorithm calculates the optimum weighted-efficiency for all design parameters. By keeping only as independent variable the fs and finding the optimum efficiency for all the others variables (only the current density was kept steady J=4 A/mm2) the diagram of figure 5 appears. By repeating the same sequence but keeping as independent variable only the transformer ratio, the diagram of figure 6 is extracted. These curves where printed taking into account as input specifications: Pnom=100W, Vdcmin=25V and Vdcmax=40 for a utility voltage of 230V/50Hz. The algorithm calculated that the smaller possible ETD core that can be used is ETD44.

Fig. 5: Optimum European Efficiency versus fs Fig. 6: Optimum European Efficiency versus n

As it can be easily understood to obtain the maximum efficiency the inverter must have n=0.26 and fs=22kHz.

Experimental results The design parameters of the implemented inverter are presented in table II. The calculated losses for the transformer and semiconductor losses are described in figure 7. These calculations were conducted for the minimum input voltage Vdcmin=25V. The analysis of these losses can be seen in figures 8 and 9.

Table II: Implemented inverter parameters

Fig. 7: Power losses of the two main components

P=IXFH60N20 S1,S2=IXFX26N120 fs=22.2kHz NDC=20 n=0.263 r=0.15mm J=4A/mm2 Primary Strands=24 Secondary Strands=4 Core type: ETD44 Material: 3f3

The leakage inductance of the transformer was measured at 2.5% of the main inductance. The energy stored in the leakage inductance is lost so the transformer has an extra power loss ratio of 2.5% at any output power ratio. The calculated efficiency can be seen in figure 10. In figure 11 the actual measured efficiency is presented.

Fig. 8: Semiconductors losses analysis Fig. 9: Transformer losses analysis

Fig. 10: Calculated Efficiency versus power ratio

Fig. 11: Measured Efficiency Versus power ratio

In figures 12 and 13 the output current for two different power levels is presented. In figure 12 the current is measured before the output filter and in figure 13 the operation of the filter that eliminates the high frequency component can be observed.

Fig. 12: Output current before the filter Fig. 13: Output current injected to the mains

Conclusions

This paper defines a design methodology for the flyback inverter that clearly specifies the appropriate design parameters to obtain the maximum weighted efficiency. Taking into consideration the input

specifications, these consist of the voltage and nominal power of the PV module, the optimization algorithm selects among all the feasible designs that of the maximum weighted efficiency. Feasible design is a set of all the design parameters that satisfy the constraints. The constraints are a set of equations that ensure the proper operation of the flyback under DCM control scheme. The optimal solution corresponds to design parameters from which all other topology variables can be determined. In order to validate the performance of our methodology an inverter prototype was implemented. As is it already presented the measured efficiency is very close to the calculated values. The presented losses equations can be used not only to optimize the efficiency but also to fulfill extra targets. By using the same equations many different objective functions can be optimized. For example, for a given input voltage and transformer volume the maximum feasible nominal power can be determined.

References [1] Gow J., Manning C., Photovoltaic converter system suitable for use in small scale stand-alone or grid-connected applications, IEE Proceedings-Electric Power Applications, Vol. 147, No. 6, pp. 535-543, November 2000. [2] Soeren Baekhoej Kjaer, John K. Pedersen and Frede Blaabjerg.: A Review of Single-Phase Grid-Connected Inverters for Photovoltaic Modules, IEEE Trans. on Industry Applications, Vol. 41, No. 5, pp. 1292-1306, September/October 2005. [3] Wills R.H., Hall F.E.: Strong S. J., The AC photovoltaic module, in Proc. IEEE PSC96, Washington DC (USA), 13-17 May, 1996, pp. 1231-1234. [4] Kyritsis, A.Ch.; Tatakis, E.C.; Papanikolaou, N.P.: Optimum Design of the Current-Source Flyback Inverter for Decentralized Grid-Connected Photovoltaic Systems, Energy Conversion, IEEE Transactions on , vol.23, no.1, pp.281-293, March 2008. [5] Kasa N., Iida, T., Chen L.: Flyback Inverter Controlled by Sensorless Current MPPT for Photovoltaic Power System, Industrial Electronics, IEEE Transactions on , vol.52, no.4, pp. 1145- 1152, Aug. 2005. [6] Young-Hyok Ji, Doo-Yong Jung, Jae-Hyung Kim, Chung-Yuen Won, Dong-Sung Oh.: Dual mode switching strategy of flyback inverter for photovoltaic AC modules, Power Electronics Conference (IPEC), 2010 International , vol., no., pp.2924-2929, 21-24 June 2010. [7] Roshen W.: A. A Practical, Accurate and Very General Core Loss Model for Nonsinusoidal Waveforms, Power Electronics, IEEE Transactions on , vol.22, no.1, pp.30-40, Jan. 2007. [8] Jieli Li, Abdallah T., Sullivan C.R.: Improved calculation of core loss with nonsinusoidal waveforms, Industry Applications Conference, 2001. Thirty-Sixth IAS Annual Meeting. Conference Record of the 2001 IEEE, vol.4, no., pp.2203-2210 vol.4, 30 Sep-4 Oct 2001. [9] Reinert, J. Brockmeyer, A. De Doncker.: R.W.A.A.; , Calculation of losses in ferro- and ferrimagnetic materials based on the modified Steinmetz equation, Industry Applications, IEEE Transactions on , vol.37, no.4, pp.1055-1061, Jul/Aug 2001 [10] Venkatachalam K., Sullivan C.R., Abdallah T., Tacca, H.: Accurate prediction of ferrite core loss with nonsinusoidal waveforms using only Steinmetz parameters, Computers in Power Electronics, 2002. Proceedings. 2002 IEEE Workshop on, vol., no., pp. 36- 41, 3-4 June 2002. [11] Dimitrakakis G.S., Tatakis E.C., Rikos E.J.: , A Semiempirical Model to Determine HF Copper Losses in Magnetic Components With Nonlayered Coils, Power Electronics, IEEE Transactions on , vol.23, no.6, pp.2719-2728, Nov. 2008. [12] Yali Xiong, Shan Sun, Hongwei Jia, Shea, P.: Shen, Z.J., New Physical Insights on Power MOSFET Switching Losses, Power Electronics, IEEE Transactions on, vol.24, no.2, pp.525-531, Feb. 2009. [13] Duncan A. Grant, John Gowar.: Power Mosfets, Theory and Applications, Wiley-Interscience, 1989, ch. 4.

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