Efficiency and Cost Optimization of a Micro-Inverter Transformer

Umut Güvengir, Mustafa Deniz Electrical Power Technologies Department

TÜB TAK – MAM Energy Institute Ankara, Turkey

umut.guvengir@tubitak.gov.tr

Zaid S. Al-Otaibi, Saeed S. Al-Zahrani, Hisham Y. Shafei, Omar A. Almokaiteeb,

Fahd Saud Alanazi, Abdullah A. Altuwaijry Energy Research Institute,

King Abdulaziz City for Science and Technology (KACST) Riyadh, Saudi Arabia

zalotaibi@kacst.edu.sa

Abstract—The high-frequency transformer design for switch mode power supplies consists of core and winding design. It is necessary to take the cost of power loss and core volume in the long term into consideration during selection of core size, shape and material to produce an efficient transformer. The proximity effect seen in the windings deteriorates the performance of the transformer and can be averted by using Litz wires and sandwich winding structure.

Keywords-component; transformer; core loss; winding loss; efficiency; micro-inverter

I. INTRODUCTION Design of high-frequency transformers for switch mode

power supplies is a complicated task as it involves consideration of many different parameters and their interaction between each other. In order to achieve an efficient transformer operation, it is necessary to inspect the effects of these parameters on a single cost function which gives the cost of power loss in the long term and that of initial expenditure to construct the transformer.

The optimization problem can be constructed by using many methods. For example, area product method has been used in [1-3] while genetic algorithms, squared field derivative method and expert system shells method have been used in [4], [5] and [6] respectively.

Full bridge converters are classified as one of the symmetrical converters. This type of inverters has an even number of switches enabling their transformer for better utilization of the whole B-H curve of the core (first and third quadrants of the B-H curve). This feature gives the transformers the capability of producing more power by increasing the flux density frequency. As a result, smaller cores can be used for certain power requirements which leads to decrease the core losses that inversely proportional to the core volume. On the other hand, primary and secondary number of turns are inversely proportional to the size of the core. Therefore, optimization between both losses is needed and hence the most suitable core can be selected [7,8].

In a conventional microgrid system, series-connected PV modules construct a PV array which is utilized to acquire

sufficient dc-bus voltage in order to produce ac utility line voltage through an inverter. However, it is crucial to avoid the shadows of obstacles around the PV array so that some of the modules in the array are not partially covered and they do not influence the working state of other modules, which may result in a reduction in the total power generated, the total efficiency of the system and the utilization of PV modules. In order to avert these handicaps, a micro-inverter PV module system, in which each PV module has its own dc-ac utility interactive inverter, can be used. The advantages of this system can be listed as small volume, independent control of the maximum power point tracking, decrease in manufacturing and installation costs and increase in total efficiency [9,10].

This paper presents a design of a full bridge high-frequency transformer for a photovoltaic (PV) micro-inverter (Fig. 1). The transformer design optimization of a power converter is an essential research topic since transformers are one of the lossiest components in a converter application in general. Therefore, it is required to consider all the parameters affecting the efficiency of the transformer at the same time within a cost function whose minimum value is to be searched to find optimum operation. For this reason, our approach included consideration of selection of an optimum core size, material and shape to minimize core losses and a winding structure which will avert the bad effects of skin and proximity effects to minimize winding losses. In proximity effect, eddy currents caused by the magnetic fields of currents in adjacent coil layers increase exponentially in amplitude as the number of coil layers increases. Due to skin effect, the resistance of windings is increased since AC currents in conductor generate eddy currents which cause a non-uniform current distribution, resulting in a decrease in effective conductor area. Therefore, a sandwich structure is utilized for the winding design. Apart from these considerations, the effect of core volume selection in the term of micro-inverter operation is investigated with an economic approach which includes a market analysis of the core volume prices. It has been seen that although choosing a maximum size of core results in lower total losses, this is not economically feasible in the long term since excess money spent for a larger core may not refund itself in a reasonable time.

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The specifications of the micro-inverter for which the transformer is designed are listed in Table I. For these specifications, core size, material and shape selection is investigated in Section I, and design of a loss-optimized sandwich winding structure is explained in Section II.

Although the so-called area-product method is suggested by [9] and others as a good initial step for selection of core size, we start by investigating the cost function for several core sizes which includes more parameters than area-product method. The resulting design has been simulated and verified in Ansoft Maxwell program as shown in section III of this paper.

II. TRANSFORMER DESIGN

A. Core Design Advances in power electronics enabled high frequency

operation. Increase in switching frequency decreased core and winding sizes and reduced cost of the transformer prices. In the proposed micro-inverter application, 100 kHz switching frequency is chosen to keep both switching losses and transformer size as low as possible.

In the core size and winding design sections, duty cycle (D) term will be used extensively. Theoretical maximum duty cycle for a transistor of a full bridge converter is 0.5 (Fig. 2). During the power transients at rated power, to have some space for duty cycle increase, duty cycle is chosen as 0.4 at rated power.

Figure 1. Full bridge converter based solar micro-inverter

TABLE I. MICRO-INVERTER SPECIFICATIONS

Input Voltage 20-40VDC Input Power 250W

Output Voltage 220VAC±20% Output Frequency 45-66Hz

Design Life 25 Years

Figure 2. Transformer primary winding voltage waveform and duty cycle

definition.

Figure 3. ETD type trensformer core and the coil former

At 100 kHz frequency, N97, N51, 3C85 and 3C95 ferrite magnetic materials have the lowest core losses. In this design, N97 ferrite material is used. Core size will be optimized by the algorithm developed in the following section. ETD type (Fig. 3) cores are investigated during the optimization since circular center leg eases the winding process and hence better winding area utilization can be achieved.

The design procedure for high frequency transformers starts with determining the specifications of the transformer with respect to the requirements for the operation of the micro-inverter. During the design procedure, total losses and cost function of the transformer is minimized. Total power loss of the transformer can be written as

where is total core loss and is total winding (copper) loss. Total core loss can be approximated by the following equation [7].

(2)

where is constant depending on the core material and operating frequency, is the peak flux density, is a core material dependent value in the range 2 to 3, is core cross-sectional area and is the length of mean magnetic path in the core. From Faradays law, peak flux density can be written as

(3)

where is the voltage time area (Fig. 2) applied to primary winding of the transformer, is the number of turns in primary winding. Equation (3) states that peak flux density is inversely proportional to number of turns. Hence, as peak flux increases, core loss increases and as number of turns decreases, copper loss decreases. While optimizing core losses, copper loss should also be considered. The copper loss can be formulated as

(4)

where is mean length of turn, is winding area, is copper fill factor and is:

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(5)

From (3) and (4), copper loss can be written in terms of peak flux density as,

(6)

Losses due to proximity and skin effect is included in the specific resistivity by multiplying the default value with

.

Total loss versus peak flux curves are obtained for five different core sizes with by using (1) in MATLAB. Fig. 4 shows that with larger core sizes, lowest total losses can be obtained.

Although choosing the largest core results in lowest total power losses, it is not economically feasible. Excess money spent for a larger core may not refund itself in a reasonable time. Upon some market analysis the following function which gives the price of the transformer with respect to core volumes is formulated.

(7)

where is in USD and is the core volume in cm³. Every one watt increase in power loss will result in a cost increase which can be formulated as:

(8)

where is the total operation hour for the minimum expected life time of PV installation which is around 20 years. Operation of the PV system is normalized as 6 hour at rated power per day. is unit price of energy in watt.hour which is taken as 0.00015USD/W.h. For 20 years, total cost of a transformer compared to a priceless ideal transformer can be written as

(9)

Figure 4. Total power loss versus peak flux density for different core sizes

Figure 5. Total cost versus peak flux density for different core sizes

Figure 6. Core, winding and total power losses of the transformer with

ETD39 core

Fig. 5 presents total cost versus peak flux curves for five different core sizes. Lowest total cost is obtained with ETD39 core when peak flux density is 82 mT.

Fig. 6 shows core loss, copper loss and total loss separately. As seen on the figure, lowest total loss is not at the point where copper loss equals to core loss.

B. Winding Design The second phase of the design procedure of the high

frequency transformer is the winding design. In order to determine the number of turns for the primary and secondary windings, Faraday’s Law is utilized.

For a full bridge converter, the input and the output voltages are related with the following equation.

(10)

where Np is the number of primary turns, Ns is the number of secondary turns and D is the duty cycle. For a nominal input voltage of 30 V and a DC link voltage of 350 V at a duty cycle of 0.4, the turns ratio is calculated as

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where is the flux, B is the flux density, Acore area, Ep is the instantaneous primary volcycle, Ts is the switching period.

The winding structure is chosen to be a sas depicted in Fig. 7. This structure aids proximity effect and skin effect seen in the w

Using a conductor with thickness less thhelps to decrease the proximity effect. Litzkind of wire designed to decrease proximmany strands of twisted thin wires to fodistribution and to prevent circulation of cuavailable conduction area, at the cost of deccopper within core window. The secondtransformer is built with Litz wires to achievof the aforementioned reasons.

Round conductors do not utilize the availas good as rectangular conductors. In order this winding area, rectangular foils of coppeprimary side with thickness of half the sswitching frequency. Using such thin fodecrease the proximity effect.

Figure 7. Sectional view of half of the tra

(11)

(12)

(13)

(14)

Ae is the effective ltage, D is the duty

sandwich structure in decreasing the

windings.

han the skin depth z wire is a special

mity loss by using orce equal current urrent through the creased amount of dary side of the e less loss because

lable core window to utilize more of

er are used for the skin depth at the ils also helps to

ansformer

If we neglect the ripple currthe output of the converter, thwinding current can be calculat

which also equals the ac value has no dc component.

The current density was during core selection, which bri

For copper resistivity = 2to incorporate the effects of higmean length of turn (MLT) of resistance of the secondary is ca

The skin depth at 100 kHz iDowell’s curves [10] which gito the dc resistance for differenwires used for secondary side, strand of the wire to the skin dlayer of secondary,

The rms value of the primar

which is also equal to the ac vsince there is no dc componewith 25.7 mm x 0.12 mm rectresults in a current density of 3assumed value of 420 A/cm2; hachieve this value is thought to

For = 2.1x10-8 .m and M

The skin depth at 100 kHsandwich arrangement proposetaken as 1.5 effectively, and for

rent on the dc link inductance at he rms value of the secondary ted as follows.

(15)

of the secondary current since it

(16)

assumed as Jrms = 420 A/cm2 ings about a conductor size of

(17)

2.1x10-8 .m, which is taken so gh operation temperatures, and a 6.9 cm for ETD39 core, the DC alculated as

(18)

is = 7.6/ = 0.024 cm. From ive the ratio of the ac resistance nt layers of conductors. For Litz the ratio of the thickness of one

depth can be taken as 1. For one

(19)

ry winding is

(20)

alue of the primary winding Ipac ent. The primary is constructed tangular foils. This arrangement 311 A/cm2 which is less than the however, using a thinner foil to be less practical.

MLT = 6.9 cm,

(21)

Hz is = 0.024 cm. For the ed, the number of layers can be r this value,

(22)

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Therefore the winding losses can be calfor the primary and the secondary sides.

where and are the primary and sDC losses, respectively; and aresecondary winding AC losses, respectively;primary and secondary total winding losses, the total winding loss; and is the ttransformer.

In (30), is the core loss found from Mas 0.384W. In MATLAB optimization it is Research is ongoing to solve the inconsimulation result and calculated result. Forresistance of the core can be found from the e

where Aw is the window area of the cortemperature rise of the core can be calculated

III. SIMULATION RESULT

The designed transformer has been simMaxwell program to verify calculated resultfrom Fig. 7, only one half of the transforsimplicity since the increased number of solution time. Therefore, the solution istransformer assuming it is cylindrical anecessary settings in the program are adjustThe number of meshes are increased beforeaccurate results in the regions such as twindings. The solution is step is chosen toinstantaneous core and winding losses aprogram is shown in Fig. 8 and Table II shofthe mean core and winding losses acquirand MATLAB. As can be seen from the acquired from the program are in accocalculations presented before. An experimebeing tested to further verify the results.

culated as follows

(23)

(24)

(25)

(26)

(27)

(28)

(29)

(30)

secondary winding e the primary and ; and are the respectively; is total loss of the

Maxwell simulation found as 0.552W.

nsistency between r ETD39, thermal empirical formula,

(31)

re. Therefore, the d as,

(32)

TS mulated in Ansoft ts. As can be seen rmer is drawn for

meshes increases s applied to the about z-axis and ted in accordance. ehand to get more the core and the o be 100 ns. The cquired from the

hows a comparison red from Maxwell

table, the values ordance with the ental prototype is

TABLE II. MEAN CORE AN

Core Loss (mFrom

Maxwell 384.46

From MATLAB 552

Figure 8. Instantaneou

IV. CO

An efficient and cost-optimfor a full bridge micro-invertesystem has been designed and taddressed. It has been obserchoosing a maximum size of cthis is not economically feasexcess money spent for a largereasonable time.

The designed transformer iprogram to verify the results anfrom MATLAB and Maxwecorrelation.

Although only optimizationhas been considered in this papfor transformers in other topdesign. The analysis presentedtake some other parameters, selection optimization, into acc

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721

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ONCLUSION mized high-frequency transformer

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er core may not refund itself in a

is simulated in Ansoft Maxwell nd the acquired figures and data

ell is presented showing good

n of the full bridge transformer per, same approach can be used pologies and also for inductor d here can also be extended to

such as switching frequency ount.

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