Efficient Resonant Inductive Coupling Energy Transfer Using New Magnetic and Design Criteria S. Valtchev Univ. Nova de Lisboa / IT PORTUGAL
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B. V. Borges Inst. Superior Técnico / IT PORTUGAL
[email protected]
Abstract — This paper describes some theoretical and experimental results obtained in an effort to optimize the Series Resonant Converter (SRC) when used with a loosely coupled transformer for Inductive Coupling Power Transfer (ICPT). The main goal of this work is to define precisely which mode of operation of the power stage is the most efficient. The results also suggest a way to choose the design criteria for the physical parameters (operation frequency, characteristic impedance, transformer ratio, etc.) to achieve that mode of operation. The analysis involves also the investigation of the separated in two halves pot core ferrite transformer, especially the way it changes its magnetizing and leakage fluxes and hence, inductances. It is shown that for the practical values of the separation distance, the leakage inductance remains almost unchanged. Nevertheless the current distribution between the primary and the secondary windings changes drastically due to the large variation of the magnetizing inductance. The analysis has lead to a set of equations with solutions that show graphically the way to an optimized operation of the converter, i.e. higher primary currents and higher transformer ratios to fit in the desired mode.
I.
INTRODUCTION
One application field, where the resonant converters are best suited is the contactless energy transfer. The widely used method, in different variations [1-5], is the Inductive Coupling Power Transfer (ICPT) applied between highfrequency magnetic coils with a relatively low mutual inductance. The presence of resonant processes in this case is unavoidable, not only because of the parasitic reactances involved in the inductive link, but also because the resonant processes are intentionally used to compensate the low coupling coefficient. The knowledge of the resonant conversion is therefore not only extremely advantageous but also indispensable. The problem stated here is to discover and analyze the influence of the loosely coupled inductive elements on the converter performance, optimizing it for the best possible efficiency. II.
IDEALIZED CONVERTER
Fig.1 shows the generic power circuit of the ideal SRC. One of the many possible ways of operation consists in closing each pair of switches Q1/Q4 and Q3/Q2 alternatively at a frequency above the resonant frequency (Fig.1). There are also several other ways of functioning and it can be
K. Brandisky Tech. University of Sofia BULGARIA
[email protected]
J. B. Klaassens Tech. University of Delft THE NETHERLANDS
[email protected]
chosen some other topology as well, but in general terms the intention is to keep the Zero Voltage Switching (ZVS) in all the possible modes of operation. Q1 VIN
Lr
+ -
Q2 A
Q3
iO
Cr
+ B
VO
iL
-
Q4
Fig.1 Basic circuit of an ideal series resonant DC-DC converter
To start the investigation of the above mentioned loosely coupled transformer converter it would be assumed the use of the normalized notation from [6] and [7], where the SRC was analyzed with an ideal transformer. The normalization of voltages, currents, frequency etc. serves well the purpose of obtaining generalized expressions that could be used in any specific converter. The use of the same notation here would be also necessary to start the analysis first with the ideal transformer converter, in order to be compared later to the loosely coupled converter analysis, made in the same terms. In [6] it was shown that the efficiency variations achieved in the SRC depend on some parameters of the circuit: R 1 2 (1), = 1 + loss ρ i η Ro where the efficiency η depends on the relation between Rloss (the equivalent loss resistance of the circuit), and Ro (the load resistance) as well as on the squared relation coefficient between rms and rectified average current in the circuit (current form factor) ρ = I rms / I O .
i
The transformer ratio n, the normalized frequency F = fSW/fRES (the switching frequency fSW divided by the resonant one fRES) and the characteristic impedance Zr =
Lr of the resonant circuit can be designed to get the Cr converter operation in almost any desirable point of its output characteristics, hence also in the best efficiency region. In normalized form the output characteristics are q =
N
f( I 0 ), where q is the normalized output voltage
n * V0 N and I 0 is the normalized form of the average VIN Z * I0 N output current I 0 = r . The output characteristics in VIN
properly the relation F between the switching and resonant frequency and the characteristic impedance Zr.
q=
Fig.2 are plotted at different current form factor
ρ
i
values,
thus showing the most desirable operation zones (the zones with the minimum value of the current form factor). How to reach these efficient zones, it can be answered when a comparison is done with other output characteristics, where the normalized frequency of operation F is used as a fixed value for the graphics (Fig.3), showing here only the SuperResonant operation mode. From these graphics it can be defined the best frequencies of operation in case of Frequency Control (FC), to keep the operation confined to that region, generally for the highest output power operation. It is possible to show similarly the best zone for Pulse Width Modulation (PWM) as in [7] and the zones when current shaping by second inductance is used as in [8] but it will be not a subject of this research. As eq. (1) states, the highest efficiency is obtained for lower values of ρi, which is confirmed by practical solutions as in [6] and [8]. In case of ideal transformer the best zone is at the high q and current up to 3 (normalized) as shown in Fig.2. Combined this result with the knowledge about the maximum obtainable power which by the set of parabolic curves shows the best place as equally distant from the x and
ION
Fig.3. The output characteristics q = f(ION), for an idealized transformer, when the normalized frequency F is given fixed values.
The loosely coupled transformer will change the zones of best operation. In the next section we will investigate the changes in the converter operation that will result from the use of a loosely coupled transformer. III.
ANALYSIS OF THE NONIDEAL TRANSFORMER SLSRC OPERATION
The main problem of the changing transformer parameters can be seen in Fig. 4, where a T-model, derived from the measuring and calculation of a real transformer, permitted to use equations and to obtain the necessary normalized output diagrams. The magnetizing inductance Lm is providing alternative path for the resonant current, thus reducing the + uAB
+
Cr
iL uC
ION
Fig.2. Current form factor distribution on the output characteristics q = f(ION), for an idealized transformer.
y axes, in conclusion it shows as best zone of operation the higher output voltage values. This zone must be considered as the best mode of operation at least for the maximum output power. The operation of the converter with ideally coupled transformer is relatively easy to situate in the zones of more efficient functioning (high output voltage and relative current up to 2.5 or 3.0). It would be necessary to choose the transformer ratio in order to get in the upper part of the characteristics and also it is necessary to choose
Llk
Lr
Llk
im
ilk Lm
+
U0
-
Fig.4. Equivalent Circuit of the Series Resonant DC-DC Converter.
current transferred to the secondary, especially when the output voltage is high. Unfortunately, it was already discovered that the most efficient zone of operation is exactly the highest output voltage zone, where the values of ρ i have their minimum value (Fig.2). A. Magnetic Modelling
Fig. 7. Longitudinal section of the PM62 core, N27 material with nonlinear (more realistic) characteristics, 1.3 mm distance (simulated by 2*1.3 mm air gap).
Fig. 5 Simulation arrangement (MagNet) for the used core (Potcore PM62).
To find the most efficient zone in case of non ideal transformer, measurements and simulations were executed and a small representative part of those results will be shown here. In Fig. 5 the arrangement is shown in its 3D version. To help the more rapidly analysing the different situations the FEMM [10] simulation was also used. Some indication of the changing flux densities in the core is shown graphically in Fig. 6 (linear magnetizing characteristics of N27 material) and Fig. 7 (non linear magnetizing characteristics of the same material).
Fig. 6. Longitudinal section of PM62 core, ferrite material N27, initial μ = 1400, 1.3 mm distance (simulated by 2*1.3 mm air gap).
The simulation obtained with the program FEMM and the measuring of the parameters have given the useful result of almost constant leakage inductance, which means most of the change is the rapidly dropping magnetizing inductance (or mutual inductance M). This can be seen in Fig. 8 and 9.
Fig. 8 Changes in the total value of the inductance L1 and its mutual and leakage component in case of linear magnetic characteristics of the material.
Fig. 9. Changes in the total value of the inductance L1 and its mutual and leakage component in case of non linear magnetic characteristics.
To confirm the simulation results, some measured inductance values are presented in the Table I. This results show that the leakage inductances are almost constant and thus very similar to the ideal case. In case of loosely coupled magnetic connection (growing reluctance) the leakage inductance is also not changing significantly
especially when the distance between the two halves of the magnetic core is above some minimum and especially in case of round shaped like the pot core. To minimize the effect of the leakage inductance some initial value of resonant inductance is provided (used in the calculations as a times higher than the leakage inductance). TABLE I CHANGES IN THE TOTAL AND MAGNETIZING INDUCTANCE, DEPENDING ON THE AIR-GAP DISTANCE No
Airgap [mm]
L1 [μH]
M [μH]
k=M/L1
1
0
5052
5028
0.995
2
2.6
144.5
113.7
0.787
3
7.6
73
34
0.46
4
12.6
64.1
18.74
0.29
5
22.6
59.95
7.386
0.12
6
52.6
59.22
1.0936
0.018
7
102.6
59.11
0.159
0.0027
be divided by two reactances of the same type to a lower value: Lm (3) qT = q * L m + Ll k The secondary current is modeled by another idealized circuit which has the output voltage recalculated to be boosted by the output current to a higher value: 1+ k (4) qT = q * 2*k Lm . with k = L m + Ll k The idealized circuit for the secondary has characteristic impedance k times higher than the circuit of the primary, which needs one final recalculation of the real average value of the current in relation with the original idealized circuit, the one which has k=1. The recalculated average value of the output current is given by:
I 0N = I 0N ( 2) * k * N (2)
where the I 0
a+2 a +1+ k
(5),
value is the one received by the idealized
B. Electrical Circuit Analysis
equations for the secondary.
The resonant current calculation is done dividing the differential equations in several piecewise-correct subequations, separately for the primary and for the secondary. This set of differential equations is bringing some useful results allowing conclusions to be drawn as in which part of the normalized characteristics to operate the converter, depending on the variation of the magnetizing and leakage inductances. In the above mentioned way of reasoning, the differential equations were solved using the transformer coupling coefficient as a parameter. For the both charging and recuperating parts of the normalized time interval xk and x0-xk as marked in [6], the current shape iL can be obtained in generalized form. This involves the manipulation of forth order differential equations, which is not practical. In order to simplify the analysis, and to obtain the value of the normalized output voltage q and the average current in the output easily, a simplification consisting in modifying the original circuit, dividing it into two simplified parts with separated equations was used. Accordingly, the resonant parameters have also been modified. For the primary current the total resonant inductance is calculated as: (2) LrT = ( L + L + Llk * Lm ) r lk Llk + Lm The equations to solve for the primary are the same as for an ideal resonant converter [6], but with the above calculated inductance and the output voltage recalculated to
In order to verify that this approximation is accurate Fig. 10 presents the time diagrams of the currents in the primary and in the secondary simulated using the original circuit and the two separated modified circuits. As it can be verified there is no significant difference between the approximated and real current diagrams .
I L ≈ I L a pro x
I lk ≈ I lkapro x
Fig.10 Comparison of current diagrams using real circuit simulation and the two approximated circuits simulation
The characteristics shown in Fig.11 a) and b) represent the normalized output voltage in function of the normalized output current with F as a parameter, and for k=0.5 and k=0.3 respectively.
factor was calculated relating the output current average and the input current RMS value, Figs. 14 and 15. q
q
ρ = 1.11 F=1.05 F=1.2
F=1.1
F=1.5
ρ = 1.12 ρ = 1.13
F=2 F=5
I 0N a)
ρ = 1.14
I 0N Fig. 13 Output voltage characteristics in function of the normalized output current with ρ as a parameter for k=0.7.
q
F=1.05 F=1.5 F=2 F=5
F=1.1
F=1.2
I 0N b) Fig. 11 Output voltage characteristics in function of the normalized output current with F as a parameter: a) k=0.5, b) k=0.3.
Fig.14. Changes in the output characteristics, taken at constant value of the current form factor ρ for distance between transmitter and receptor magnetic halves, approximately 2mm.
As expected, it can be observed that it is not possible to obtain higher output voltages when the coupling coefficient is too low. The same will happen with the output characteristics considering the form factor ρ of the primary current as a parameter, shown in Fig.12 and 13. q
ρ = 1.12 ρ = 1.13 ρ = 1.14
IN
0 Fig. 12 Output voltage characteristics in function of the normalized output current with ρ as a parameter for k=0.5.
Although the results shown in Figs. 12 and 13 present some reasonably high efficiency it would be not possible to reach the corresponding higher voltages as it is patented in Fig.11. In order to show the correspondence between the output characteristics and the real efficiency, the current form
Fig.15. Changes in the output characteristics, taken at constant value of the normalized frequency of operation for distance between transmitter and receptor magnetic halves, approximately 2mm.
Considering Figs.14 and 15 it is concluded finally that the most efficient zones of operation are where the output voltages are lower. This low value of the output voltage is in reality the transformed (equivalent) value of the average rectified output voltage. This way we would receive the necessary output voltage in real value by changing the transformer ratio to boost the secondary voltage (at the price of greater primary current).
IV.
EXPERIMENTAL EQUIPMENT FOR THE NONIDEAL TRANSFORMER USED IN SERIES LOADED SRC
The experimental equipment was specially prepared to operate in all possible regimes, even in those regulated by Phase-Shift (PS) modulation, which allow wider power regulation, especially for the lowest power levels where the frequency control requires extremely high frequencies (Figs.16 ).
airgap=1
u AB
iL
a)
airgap=0.5 mm
Fig.18. Experimental resonant converter with loosely coupled transformer: Above photo, with receiver block mounted; Below photo, without the receiver block.
u AB
REFERENCES [1]
iL
b) Fig.16. Experimental converter at 1 kW output power and 21 A average output current delt=0 (resonant current iL and voltage uAB (Fig.1)):a) airgap= 1mm; b) airgap=.5mm
The experimental equipment serving to verify the supposed advantage applying high transformation ratio is a modular construction easily adaptable to many different regimes of converter operation (Fig.18). V.
CONCLUSIONS
A detailed study of the SRC when operating in adverse conditions as contactless energy transmission application permit to conclude that this converter is the most proper choice for such an application and opened a new way for future development. It is also demonstrated that the magnetic parameters of a loosely coupled transformer permit the operation to rely on a nearly stable resonant frequency enabling a simplified control. The approximation adopted to solve the circuit equations can also be used in the control strategy independent slow and fast feed back loops related to the secondary and primary sides respectively.
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