Experimental Study of the Energy Portions Control in Series Resonant Converters

Stanimir Valtchev1,2, Svilen Valtchev3,4

1Dept. of Electrical Engineering, FCT/UNL and 2UNINOVA of Universidade Nova de Lisboa, Portugal 3Instituto Politécnico de Leiria and 4CEMAT, Instituto Superior Técnico, TU-Lisbon, Portugal

ssv@fct.unl.pt, ssv@math.ist.utl.pt

Abstract− Although the Series Resonant Converter (SRC) is not yet fully explored and widely applied it is becoming more and more important for the contactless charging of the Electric Vehicles (EV) batteries. From the point of view of the modern propulsion batteries the careful and reliable charging is very important and good solutions will be the SRC contactless battery charging and the online resonant energy transfer. To their high efficiency must be added the high stability of an instantaneous method of control. The proposed solution is based on correcting the portion of energy that is sent to the load in each half period through the resonant circuit. Experimental results are shown from the implementation of this idea in the SRC working on a loosely coupled (contactless) magnetic connection. Keywords: Electric/Hybrid Vehicle, Battery, Charging, Contactless Energy Transfer, Series-Loaded Series-Resonant Converter, Energy Portions

I. INTRODUCTION

The most problematic building block of any autonomous electric driven vehicle (including robots) is and will probably remain its electric energy source, i.e. its BATTERY. This block restricts the most important characteristics of the vehicle which are the total available energy (i.e. its autonomy) and the achievable velocity and acceleration (i.e. its maximum instantaneous power, both for propulsion and for braking).

The Li-Ion battery is the most commonly used nowadays and it can guarantee approximately 200 km of autonomy (e.g. a 25 kWh battery) while its weight is at least 150-200 kg and it costs around 12000 Euros. Of course, the volume and price of the batteries improve every day but still a lot of energy is required to bring on the EV. The final and most convenient battery technology is still to be developed but there are solutions that do not weight hundreds of kilograms and do not require highly priced energy storage. One such solution is the Hybrid Electric Vehicle (HEV) and Plug-in HEV (PHEV). In the case of HEV and especially PHEV the battery is much smaller in size and the speed of charge (the charging current is usually limited to the household grid capacity. Another interesting solution, proposed by KAIST (Republic of Korea), is the “on-line” charging system OLEV [1]. By this (OLEV) solution the speed of charge and the battery size are also

diminished thus making the car more accessible for the people, for the electric grid and for the environment. In order to show how important the speed and the depth of discharge of the battery are, two factory-provided diagrams are shown in Fig.1.

The curves are based on measuring real EV batteries in a SAFT factory. As it can be observed, the life expectancy of the battery (defined here as the instant when the capacity of the battery decreases by 20%) is halved if the Depth of Discharge (DOD) of each cycle changes from 50% to 80%. The total charging/discharging cycles then change from 4900 to 2300 cycles. This proves that it would be best if the battery charge will be obtained slowly at the charging socket or even during the voyage.

Applying charging during voyage (on-line) or applying a stationary (parked) charging, equally requires a safe, independent of the weather, and reliable transfer of energy to the car propulsion battery. A good solution for this reliable charging is to apply a contactless (Inductively Coupled) energy transfer which will permit to charge the vehicle in bad weather, or even when less carefully manipulated.

In the case of a bi-directional power flow (a more sophisticated secondary side) the inductive transfer makes the energy management of the grid also possible. One example of dynamically charged EV is shown in Fig. 2 (OLEV project).

Fig. 1. Tests at Depth of Discharge (DOD) 80% and 50% until 20% change in power (W) or in internal resistance (Ri) is reached

827978-1-4673-1653-8/12/$31.00 '2012 IEEE

Fig. 2. Street bus with dynamic charging by underground transmitters (KAIST, Korea)

To achieve a contactless transfer of energy at a reasonable distance will always require applying a resonance, in one or another form.

II. THE SERIES RESONANT TOPOLOGY FOR CONTACTLESS

CHARGING

The main topologies for contactless energy transfer are always resonant, based on Parallel and Series resonance loops. The topologies may include one or two resonant loops, each one series or parallel, differing also by the way the load is connected. Here the main topology will be the series resonant converter. This topology involves a series connection of L and C elements and in terms of resonant frequency stability, this leads to better results [2, 3]. This resonant topology is characterized by higher amplitudes of the resonant current, while the voltage peaks are safely cut. Nevertheless, the modern switching power devices have enough reserve in maximum allowed current value (the breakdown voltage is still a limitation, especially when low voltage drop and high speed at high current are required). The “Trf” in Fig. 3 may be the isolation transformer of a classical SRC or a loosely coupled magnetic element for the contactless energy transfer. In some cases the secondary side is also provided with a similar resonant circuit [4].

Fig. 3. DC-DC series resonant converter with transformer connection to the output rectifier

Fortunately, it is possible to find a similarity between the different SRC topologies and apply a general equivalent circuit as in Fig. 4. This possibility seems easier for the supposed double (primary and secondary) resonant loops:

they will be reduced to one loop by transforming to the other side. To recalculate the converter with a loosely coupled transformer for inductive charging seems more difficult at a first sight but it was already shown in previous publications, e.g. [5] that it is possible to recalculate its parameters too.

Fig. 4. Equivalent circuit of the simplified SLSR power converter

The recalculation as shown in [5] is a convenient way to simplify the state variable control by looking only at one side of the transformer. This model is already seen in some articles, e.g. [6]. It allows considering the primary side of the converter as the only controlled side and permits to calculate (rapidly) the state variables in any instant of the process.

In Fig. 5 the resonant current is shown together with the input and output voltages. The figure shows the conduction of the transistor (interval t1) and the other transistor’s diode (interval t2), which may be expressed as in (1a) and (1b):

max1

max

1 arccos1

c

c

q qvtq v

ω⎛ ⎞− −= ⎜ ⎟− +⎝ ⎠

(1a)

max2

max

1 arccos1

c

c

q qvtq v

ω⎛ ⎞+ += ⎜ ⎟+ +⎝ ⎠

(1b)

It is possible to calculate the output voltage/output current

relation in a normalized form [2] and consequently it is also possible [5, 7] to obtain the recalculated values of the necessary variables in order to correspond to a non-unity magnetic coupling. The resulting output characteristics (in steady state) are shown in Fig. 6 and Fig. 7.

Fig. 5. Super-resonant (FM) operation of SLSR converter

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Fig. 6. Normalized output voltage q as a function of value IN of the rectified resonant current Io for cnormalized switching frequency F

Fig. 7. Normalized output characteristics of the contawith K=0.5 and a=1

In Fig. 6 the advised zone of minimum cρi, i.e. the maximum efficiency zone [2, 3],

In the case of a loosely coupled tcontactless energy transfer, the recalcuoutput voltage q is recalculated into qT bythe magnetic coupling ratio K of the transfothe same time the resonant inductance is ashown in [5]. As a result, the regulation cfrom the primary look are limited in veshown in Fig. 7.

The last two figures illustrate the similariin the ideal converter and in the loosely cothe reason to use the same control methodand non ideal SRC.

III. THE ENERGY PORTIONS REGULAT

In a steady-state operation the energy pin the LC tank is fully discharged at eactank is charged by resonant current (from th= t1) and discharged from t = t1 to t =½Tsw switching. As Fig.5 shows the current incand charges (magnetic) energy to the tankenergy is discharged during t2 until theswitching period. This process is expressed

the normalized average constant values of the

actless power converter,

current form factor is shown as well.

transformer, as in ulated normalized y multiplying q by former (qT =Kq). In also recalculated as characteristics seen ertical direction as

ity of the processes oupled one. This is d both for the ideal

TION OF THE SRC

ortion ΔELC stored h half period. The he instant t = 0 to t each half period of

creases (from zero) k during t1 and this e end of the half d in (2):

1

1

2

1 20

swTt

LC LC r LC rt

V i dt V i dtΔ = + =∫ ∫E

If an increase of the perio

(through the tank) is required, thcircuit operates during a longer than the one for the previouslyhence ΔELC will be positive andthe energy portions is requirdecrease and ΔELC will be negat

At the zero crossing points oresonant tank energy consistsenergy: ½Cvcmax

2, so the capaccan be used to assess the totaexpression (2) it is possible to o

LC 1 1[ ( ) (0)]LC c c r LCV v t v C VΔ = − +E

In a steady state operation

capacitor voltage vc reaches (opposite polarity) in t = 0 and vcmax is used in (4). To express tand final absolute values of thisand vcmax2.

[LC 1 max1 1[ ( )]r LC c cC V v v tΔ = + +E

By rewriting the excitation va

(VLC1=1-q and VLC2=-1-q) the en

NC 1 max1(0, ) 2 ( ) (

2sw

c cT v t q vΔ = − +E

This expression (5) refers to

transistor (or the whole diagonaand provides a method to controtank during transition and durinthe capacitor voltage vc has a cmay be measured and comparprevious amplitude vcmax1 and vcmax2 which corresponds to thsupplied energy portions.

It was shown in [8] that the reconvenient as a control refereconsidered. In steady state themaximum values (alternatively)

0 (2)

odically sent energy portions hen it will be expected that the conduction interval t1 (longer

y maintained steady state), and d not zero. When a decrease in red, then t1 is supposed to tive.

of the current (Fig. 5) the total s of only resonant capacitor citor voltage maximums vcmax al energy [2]. By integrating

obtain:

2 1[ ( )]2sw

C c c rTv v t C⎛ ⎞ −⎜ ⎟

⎝ ⎠ (3)

n of the SRC the resonant the same amplitude values

t =½Tsw, so the absolute value the transient process the initial s voltage are indexed as vcmax1

]2 max 2 1[ ( )]LC c cV v v t− (4)

alues VLC in normalized form nergy is expressed as in (5):

max 2 )cv+

(5)

o the instant t1 in which the al of the bridge) is switched off ol the charging of the resonant

ng a steady state. At the time t1 ertain value vc(t1) which value ed. Equation (5) involves the the next (desired) amplitude

he increase or decrease of the

elation expressed in (5) is very ence when the steady state is e capacitor voltage repeats its ) resulting in equation (6).

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Fig. 8. Switching off of the resonant current in SLSR converter

1 max( )c cv t qv= (6)

The simulation of the instant at which the transistor is

turned off is shown in Fig. 8. The predicted amplitude vcmax2 depends on the previous amplitude of the resonant capacitor voltage vcmax1 and depends on the interval t1 (the time the transistors are kept switched on).

The regulation of the energy will require a pre-multiplication of the normalized output voltage q by the last measured amplitude vcmax1 and the addition or subtraction of some vc quantity in order to regulate immediately the prepared energy portion. The transition process will require several (growing or diminishing) portions of energy to achieve the required level of output power. The amplified error voltage (proportional to the difference between the really obtained and the required output voltage) will define the necessary portions of energy for the transition. Thus by adding the voltage Δvcmax1, proportional to the error voltage (similarly to the Current Mode Control) the instantaneous control is to be achieved (7).

N1 max1 LC max 2 max1 max1( ) ( )c new c c c cv t qv qv q v v= + Δ = ≈ + ΔE (7)

This method was presented in [8] and now the idea is tested

in an experimental construction. The clean measuring of the state variables was not always easy due to the magnetic influence on the devices and the parasitic elements.

IV. EXPERIMENTAL ASSEMBLY

The converter used as a basis for this experiment was a factory made IGBT half-bridge converter, produced by APRONEX Ltd. in Bulgaria, originally intended for piezoelectric actuators rated 2kW. The tests were performed at a lower level of output power, up to 300W. The half bridge power stage is shown in Fig. 9.

Fig. 9. Resonant converter power stage (from APRONEX Ltd.)

The half-bridge structure shows its well known softness as it returns the reactive energy to the opposite supply source. However, the results from the calculations made from the oscilloscope images are close enough to the expected result.

The converter and the electronic load together with the contactless magnetic link (protected by the two aluminum plates) are shown in Fig. 10.

Fig. 10a. Experimental set with APRONEX converter, construction overview

Fig. 10b. Experimental set with APRONEX converter, double pole magnetization

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Fig. 10c. Experimental set with APRONEX convewith Litz wire

In Fig. 11 the waveforms measured in tshow the instant of switching off (the veinductive jump (parasitic in the half bridgeand the instant and levels at which the proff occurs can be observed.

The experiments are conducted at a supV. In this case it means that the voltage on filter capacitors has a value of Vs=115V.secondary side) output voltage is V0 =11.6load confirms in Fig. 12.

The transformer ratio (if it were ideallcorrespond to the number of turns of thedivided by the secondary winding turns, (9:1). Therefore, it should be expected the voltage q to be q=0.907.

Fig. 11. Measured waveforms of the resonant conve(supply) voltage vs in case of K=0.95

Fig. 12. Output voltage and power shown by electron

erter, one pole winding

the resonant circuit ertical arrow). The ) is not an obstacle

rocess of switching

pply voltage of 115 each of the double

V. The (real, in the V as the electronic

ly coupled) should e primary winding here: nine to one normalized output

erter: vc, i(L) and input

nic load

As it was mentioned before, to serve as a contactless magnetproximity between the magnmagnetic coupling is not ideaobtained by the closest approxand the secondary ferrite platesthis case the non-ideal magnnormalized voltage in qT [5, 70.865. Following (6), the resoswitching off instant must be =64V. In fact the instant of oscilloscope) is when the capaexactly 64 V.

Another experiment is shownbetween the transmitter and rece

Fig. 13. Measured waveforms of the (supply) voltage vs in case of K=0.8

The resonant capacitor vomaximum at 52 V and the switcalculated relation between capand the amplitude of the capacdoes not correspond to the ideaThe magnetic coupling K herqT=q.K (applying the recalculatinstead of 0.865, both as a caThe maximum resonant capacimuch lower now and the outpexpression (6) permits to dtransistor (transistors) is (are)steady state). The relative valvoltage for the commutation hasthe corrected output voltage qT.

In order to compare the measresonant capacitor voltages a sisame conditions: supply voltagvoltage V0 =11.6 V. After the reratio and including the schecoupling K = 0.95 and b) maobtained diagrams (Fig.correspondence to the measurealready expected as the simula

the transformer was prepared tic link and even in the closest netic halves (windings) the

al. The maximum coupling is ximation between the primary s and it is roughly K=0.95. In

netic coupling transforms the , 8], i.e. qT=q.K=0.907*0.95=

onant capacitor voltage at the vc(t1)= q.vcmax= 0.865*74V

switching off (shown by the acitor voltage has a value of

n in Fig. 13 at a larger distance eiver coils (K=0.8).

resonant converter: vc, i(L) and input

oltage in Fig. 13 shows a tching off occurs at 38 V. The

pacitor voltage at switching off citor voltage, i.e. 0.865, again al normalized output voltage q. re is equal to 0.8. This time tion by K) is obtained as 0.73

alculated and measured value. itor voltage vcmax has a value put power is also lower. The

define the instant when the ) supposed to turn off (in a lue of the resonant capacitor s been proved to correspond to

sured values with the expected imulation was executed at the

ge Vs = 115V and real output ecalculation by the transformer ematic changes: a) magnetic agnetic coupling K = 0.8 the

14) show almost ideal ed values. The difference was ated circuit uses approximated

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(idealized) electronic elements for simplifying and accelerating the calculations.

Fig. 14. Simulated waveforms for the conditions applied in Fig.11, 12, 13

The simulation of the first measurement described above is shown in the lower set of graphics and the upper set of graphics corresponds to the second measurement described. The resonant capacitor voltage vC has a peak of vCmax=74V (lower graph) and vCmax=52V (upper graph) so the expected switching off voltage is expected to be as calculated and shown in Fig. 14 by dotted lines. The difference in comparison to the predicted switching off instants is very small.

The relation between the resonant capacitor voltage and the switching process is easier to apply in the control of an ideal series resonant converter but here it is shown as an application for a contactless energy transfer converter (loosely coupled magnetic link). The half bridge resonant circuit is somehow easier to apply this voltage measurements although the parasitic here are disturbing the good operation.

V. CONCLUSION

In general this method was presented already in [8]. The main result from the experimentation of the method here is the proof that the resonant capacitor voltage can serve as the measure for the internal energy of the resonant tank. The method has a certain similarity to the Current Mode Control (CMC) of the hard switched converters but it here the attention is aimed at the resonant capacitor voltage (where the current is integrated) instead of measuring the inductor current as in CMC. In CMC the inductor current is the value that is instantly (each half-period) compared to the necessity of the output (i.e. the output voltage error). Here it is the

capacitor voltage. Because of the meaning, given in the past, to the expression “voltage-mode” control, this method will be called “instantaneous” control of the series resonant converter. The experimental results shown above confirm the possibilities that this “instantaneous” control of the SRC offers.

As it is shown in [2] the resonant capacitor voltage is a reliable measure for the integrated resonant current during each half cycle and the prediction of the next amplitude is a way to stabilize the resonant converters operation in practice. The described instantaneous control method will permit the internal processes of the SLSR converter to be regulated faster and with a higher precision.

In case of a contactless energy converter the magnetic coupling will be included in the calculations or special measures will be taken to include the influence of the magnetic coupling in the measured voltage.

ACKNOWLEDGMENT

The conference presentation is supported by the Portuguese Foundation of Science and Technology (FCT).

REFERENCES

[1] S. Lee, J. Huh, C. Park, N. Choi, G. Cho and C. Rim, “On-Line Electric Vehicle Using Inductive Power Transfer System”, in 2010 IEEE Energy Conversion Congress and Exposition (ECCE), pp. 1598-1601.

[2] S. Valtchev and J. B. Klaassens, “Efficient Resonant Power Conversion”, IEEE Trans. IE, vol. 37, No. 6, pp. 490-495, 1990.

[3] S. Valtchev, “Some Regulation Characteristics of Pulse–Width Modulated Series Resonant Power Conversion”, in Power Electronics and Motion International Conference (PEMC), (Budapest, Hungary), pp. 83-87, Oct. 1990.

[4] Y. Jang and M. Jovanović, “A Contactless Electrical Energy Transmission System for Portable-Telephone Battery Charges”, IEEE Trans. IE, vol. 50, No. 3, pp. 520-527, June 2003.

[5] S. Valtchev, K. Brandisky, B. Borges and J. B. Klaassens, “Resonant Contactless Energy Transfer with Improved Efficiency”, IEEE Trans. PE, vol. 24, No. 3, pp. 685-699, 2009.

[6] J. Pereira Dias, H. Kim and D. Jang, “Computer model for railway inductive power supply using Valtchev model”, in 2011 International Conference on Electrical Machines and Systems (ICEMS), DOI: 10.1109/ICEMS.2011.6073510.

[7] S. Valtchev, R. Miletiev, R. Arnaudov and S. Valtchev, “Control strategy for efficient operation of super-resonant SLSR (contactless) converters”, in International Scientific Conference on Information, Communication and Energy Systems and Technologies ICEST'09, pp. 527-530, 2009.

[8] S. Valtchev and S. Valtchev, “Improved Strategy for an Instantaneous Super-Resonant Converter Regulation”, in 12th International Conference on Optimization of Electrical and Electronic Equipment OPTIM 2010, pp. 631-638, 2010

[9] APRONEX Ltd., High Frequency Generator for piezoelectric actuators, (Gabrovo, Bulgaria), 2010.

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