Parallel Compensation in Wireless Power Transfer

International Conference on Smart Energy Grid Engineering (SEGE’14), UOIT, Oshawa, ON, 11-13 August, 2014

Parallel Compensation in Wireless Power Transfer Konrad Woronowicz*, and Alireza Safaee Bombardier Transportation Inc., 5095 Taylor-Kidd Bl, Kingston, Ontario Canada K7K2H6 E-mail: [email protected] E-mail: [email protected] *Corresponding author Abstract: With the ever-increasing reliability and cost effectiveness of power electronics components the interest in wireless power transfer to vehicles has grown significantly among academic and industrial professionals. Due to existence of large air gap between the primary (installed on the ground) and the secondary (under the vehicle) there is a need to tune or compensate the significant inductance of the windings. There are two basic approaches reported in literature for transformer secondary side tuning – serial or parallel. In this paper the concept of parallel tuning is analyzed based on a Boucherot Bridge model. The analysis is backed by simulation for which the component values are derived from finite element analysis results, confirming the analytical predictions of the parallel compensation method. Keywords: Inductive power transfer, wireless power transfer, Boucherot Bridge, AC current source, tuning, parallel compensation, series compensation. Reference to this paper should be made as follows: Woronowicz, K. and Safaee, A. (2014) ‘Parallel Compensation in Wireless Power Transfer’, International Conference on Smart Energy Grid Engineering (SEGE’14), Oshawa, ON, Canada 11-13 August, 2014. Biographical notes: Konrad Woronowicz received the B.Sc. and M.Sc. degrees from the Technical University of Szczecin, Szczecin, Poland, and the Ph.D. degree from the West Pomeranian University of Technology, Szczecin. He has been with Bombardier Transportation Inc., Kingston, ON, Canada, since 1995, where he has been involved in various transportation systems and R&D projects and played a key role in the development of LIM-based mass transit systems for New York, Beijing, Vancouver, and Kuala Lumpur among others. He is a Fellow Expert. His current research interests include electromagnetic design for wireless power transfer for electric traction and automotive applications, highperformance linear motors, special permanent magnet motors, and energy storage. Alireza Safaee received the B.Sc. degree in electrical engineering from the Isfahan University of Technology, Isfahan, Iran, the M.Sc. degree in physics from the Sharif University of Technology, Tehran, Iran, and the Ph.D. degree in engineering from the University of Quebec, QC, Canada, in 1997, 1999, and 2009, respectively. He was a Design Engineer and Design Manager with Manabe Taghzyeh Electronic Company, Tehran, from 1997 to 2005, where his teams developed several types of chargers, inverters, stabilizers, and UPS systems for more than 1000 communication sites and power plants. He is currently a Research Assistant with the Queen’s Centre for Energy and Power Electronics Research, Queen’s University, Kingston, ON, Canada, and an Electrical Analyst with Bombardier Transportation Inc., Kingston. His current research interests include power electronics, wireless power transfer, magnetic design, resonant and soft-switching converters, and their control methods toward applications in aviation and renewable energy systems.

Copyright © 2014 Inderscience Enterprises Ltd.

K. Woronowicz and A. Safaee

1

Introduction Wireless Power Transfer (WPT) has recently attracted the attention of many academic scholars and industrial researchers for example (Budhia, Covic and Boys 2011), (Huh, et al. 2011), (Arnold and Gratzfeld 2013). The benefits include convenience, all-weather functionality with no impact from humidity, dust, chemicals or pollution, no electrocution hazard, crash safety, ruggedness and ease of integration to electric and hybrid cars. In addition, there are other advantages such as reducing the battery size and weight, no special training for drivers, lower maintenance, no moving or wearable parts, and minimized vandalism possibility. The concept of WPT is not new, however the recent technology advancements in power electronics have opened new landscapes for cost effective WPT solutions and applications. A standard block diagram of majority of WPT systems is shown in Figure 1. The energy transfer is based on electromagnetic coupling principle. The primary winding is usually installed on the ground fed by a DC-AC inverter converter via a tuning network. The magnetic field induces voltage in the onboard winding, the secondary, which is connected to the vehicle dc bus though a rectifier. The wall-to-battery efficiency of a WPT system, must be at least 90%, to compete with conductive charging (Pickelsimer, et al. 2012)(Vollenwyder, Dickson and Woronowicz 2012) and (Bloom, Niu and Krishnamurthy 2013). This requires at least 96% efficiency for the WPT transformer (Wu, et al. 2011) and (Peschiera and Williamson 2013). Having a robust energy transfer requires the tuning networks to guarantee the tuning for all the operating conditions. A precise and practical analytical method for the tuning is essential for designing a high performance system. Rectifier +

Tuning

+

_

Vehicle side

Vehicle DC bus

_ Secondary

~ +

~

Utility

_

Tuning

DC/AC Inverter

= =

Wayside

Primary

AC/DC Converter

Figure 1: Block diagram of a single-phase WPT system

2

AC Current Source The Boucherot bridge topology, Figure 2, was reported as long ago (Bartlett 1927). It functions as an AC current source where current through Z L, at the frequency for which is determined by the amplitude of the voltage source, , and the value of the resonant circuit characteristic impedance , and its value is equal to or . The impedances and can assume any values as long as they are not equal zero or infinity at the same time. The opposites are allowed and and renders the topology as shown in Figure 3.

Parallel Compensation in Wireless Power Transfer

Us·sin(ωt)

~

IZL

IL

IC

C

IS L

~

C IZL

Z1

ZL

ZL

L

Z2

Figure 2: Boucherot bridge topology

Figure 3: Current source base on Boucherot bridge

If becomes modified by an addition of a series capacitor, as in Figure 4(a), and the value of this capacitor is then the source current has a value of and is clearly in phase with . The terminal resistance, , as seen by the supply source is , Figure 4(b). The entire reactive power is compensated out and the current source is tuned. IC IS

ICL=IRL CL

C IL

~

RSL

L

ZSL=RSL=L/CRL=Z02/RL

US

RL

Us

(a) (b) Figure 4: (a) Current source with RC load, (b) equivalent impedance seen by

3

WPT Transformer - A Current Source The evolution of two coupled inductors with a mutual inductance M, a transformer, into a current source is shown in Figure 5 and also in (Woronowicz and Safaee 2014). The transformer differs from the current source of Figure 4(a) by having the additional two inductors and , which introduce the reactive impedance in the primary and a the secondary sides. L1-M M

L2-M

L1-M

L2-M

L1

-M

-M

L2

M a''

L1

L1

L2

L2

RL

RL

M

M

RL

RL M

RL

b''

Figure 5: Evolution of WPT transformer model (left to right) This reactive power can be removed by adding capacitors selected to be in resonance with the respective inductances at the operating frequency of system. Thus having and , Figure 6(a), the transformer becomes a current source because the impedance of an inductance – is equal to which can be replaced with an equivalent capacitive impedance of where .


C1

L1

a'

-M

-M

L2

-M

a''

-M

a'

Z=0 US

C2

Z=0

ZSL

R

RL

M

Z

b''

b'

RL

M

b'

(a) (b) Figure 6: (a) Series compensated WPT transformer model of Figure 5 In consequence the supply source of such transformer, the power electronic converter, sees the load as purely resistive and, if the harmonics were to be neglected, switches at zero current. This process of removing the reactive power is called, in the wireless power transfer nomenclature, series compensation or series tuning. Without tuning the high frequency of power transfer operatio n would result in considerable voltage drop across and which puts a limit on the transferred power. By analogy to series tuning another method of compensation, parallel tuning, is frequently cited as a means for the efficient power transfer (Zhang, et al. 2014). In this method the secondary capacitor is inserted across transformer terminals in parallel to the load as in Figure 7(a). The value of is determined by and for the assumed input current gives the highest power transfer to the load. At this moment it is still assumed that the primary inductance and capacitance are in resonance as in the case of series tuning. Resistors and are winding self resistances and are included to make the model more realistic and it is shown that they do not affect the analysis of the parallel compensation approach. Such capacitor insertion maximizes power transfer to load and the current through resistor is where is the source current.

C1

R1 a

L1

a'

-M

-M

R2

L2

a'''

a'' Z=0

U S'

US b

RSL'

R''

Z2

M

b''

b'

Zequiv

C2

RL

b'''

(a) C1

R1 a

L1

a'

-M

-M

R2

L2_equiv

a'''

a''

R2_equiv

Z=0 U S'

US b

RSL' b'

R''

M

b''

Z2

Zequiv

b'''

(b) Figure 7: Parallel compensation: (a) impedance

in parallel with load, and (b) equivalent


As opposed to series compensation, the addition of in a configuration shown in Figure 7(a) does not automatically compensate the reactive power stored in and instead the circuit components , and can be shown to have an equivalent impedance of: (1) or (2)

As can be seen, the equivalent impedance in the parallel compensation scheme depends not only on the reactive tuning component values but also on the load resistance itself. Considering that equals and , can be represented with , as mentioned earlier, the part of the circuit enclosed in dashed lines of Figure 7(b) can be replaced by a current source analogous to the one in Figure 4(a) as shown in Figure 8. I2 IS

C

~

C IL

RSL

L

Lequiv Requiv

U2

Us

Figure 8: CLC current sources with inductive impedance load The character of the source current can now be calculated as follows. As shown earlier, because of the current source nature of the circuit as in Figure 8: (3) (4) (5) (6) (7) Because, again,

:

(8)


(9) where (10) is the goodness factor of the parallel compensated secondary. It is now clear that the current in (9) is of capacitive character, the most undesirable for the converter because a capacitive current generate excessive amount of switching loss in the switching actions. The input apparent power is given by: (11) And because

we have: (12)

The reactive part of the apparent power is load dependent. This proves that by using the parallel compensation in the output and a series compensation in the input, , the reactive power cannot be tuned out of the converter. In order to remove the reactive power and achieve Zero Current Switching (ZCS), where both input voltage and input current are in phase, the primary compensating capacitor must obviously have a different value than that from Figure 7, which produces resonance with the primary inductance. In other words: . With reference to Figure 7(a): (13) Where Z is the impedance between points

and

:

(14) Substituting (14) to (13): (15) (16)

The imaginary part of the bracket in (16) must be zero to have Therfeore:

are in phase with


(17)

(18) where is the coupling co-efficient of the transformer. Now, the effective uncompensated reactance of the primary is: (19) The reactive power is removed from the input source but it oscillates between the uncompensated inductive reactance on the primary side and the capacitive component of impedance .

4

Design Example The output voltage and power are the main design inputs for a WPT transformer. The transformer output voltage is determined by the magnetic core geometry, air gap, turns ratio, primary current, etc. The design must also be compliant to standards on public exposure limits (ICNIRP 1998), (ICNIRP 2010). Therefore the coils and ferrite cores usually need shielding material and many iterations are necessary to reach an optimized design. In this section a simple design for a 3700W, 370Vrms transformer is provided with a nominal gap 60 mm between the primary and secondary windings. The design geometry is shown in Figure 9. Finite element analysis software Maxwell3D was applied to calculate magnetic fields, voltages and the inductance matrix. The input parameters for the simulation are given in Table 1.

Figure 9 WPT transformer geometry

A. Series Compensation in Secondary Having 3700W of load power at the secondary voltage of 370Vrms means the nominal load resistance of . Assuming 11 turns for the secondary winding, the finite element electromagnetic in time domain shows that the primary needs to have 5 turns and 89 Arms to induce 370Vrms in the secondary, shown in Figure 10.


Table 1: Simulation parameters Primary input current Secondary current Magnetics Primary coil, X×Y×Z Width of primary copper Secondary coil, X×Y×Z Width of secondary copper Primary to secondary gap Primary ferrite to coil Secondary ferrite to coil Frequency

89 (Arms) / 5 turns 10 (Arms) / 11 turns Ferrite; =3000; linear 198×335×6 (mm) 40.3 (mm) 155×250×4.8 (mm) 20 (mm) 60 (mm) copper to copper 10 (mm) 4 (mm) 85 (kHz)

Figure 10 WPT Secondary voltage at no load, nominal gap and 5 turns / 89 Arms in primary Frequency domain finite element simulation, using ANSYS Maxwell software, is used to calculate the winding resistances and inductance matrix as: (DC resistance) and (20) The series tuning capacitor values, Figure 6(a), are: (21) Figure 11 shows the system implementation in PSIM software. Only first harmonic of Us

V

Is

C1

R1

277n

7.28m

A Us

85k 42.6*sqrt(2)

12.66u

7.84u

R2

C2

3.15m

56n

62.51u

Figure 11 Series compensated WPT system

RL 37

is considered.


Figure 12 illustrates the input current and voltage, as well as the output current waveforms. and are in phase and load current is at right angle to both of them. In this method of compensation there is no phase shift between and by changing the value of . Is

Us

100 50 0 -50 -100 I(RL) 10 0 -10 0.012905

0.01291

0.012915 Time (s)

0.01292

0.012925

0.01293

Figure 12 Input voltage and input/output current waveforms for Figure 11 at full load.

B. Parallel Compensation in Secondary In this type of compensation is calculated from (17) so

has the same value as in previous section, equation (21), however . Figure 13 shows the system.

Us

V

Is

C1

R1

300n

7.28m

7.84u

A Us

85k 47*sqrt(2)

R2 3.15m

12.66u

62.51u

C2 56n

RL 37

Figure 13 Parallel compensated WPT system

Is

Us

100 50 0 -50 -100 I(RL) 10 0 -10 0.012905

0.01291

0.012915 Time (s)

0.01292

0.012925

Figure 14 Input voltage and input/output current waveforms for Figure 13 at full load

0.01293


Figure 14 illustrates the input current and voltage, as well as the output current waveforms. , and the load current is in phase. In this method at full load a of about 10% higher is required compared with the previous method.

5

Conclusion The analysis of the wireless power transfer system based on a parallel compensated output transformer was made. The parallel compensated output was converted into series impedance, which in conjunction with a current source transformer theory (Boucherot bridge topology) led to a quick calculation of source current and input power. It was shown that the parallel compensation is always inductive in its character and is load dependent as long as the primary series compensation capacitor is in resonance with . When reflected to the primary side, the character of the load changes to capacitive due to the current source nature of the mutual inductance-based structure of the transformer. Hence, this parallel compensation will always produce highly undesirable capacitive switching. A different value of is necessary to remove reactive power from the input source and it was calculated as a function of the transformer coupling coefficient. The reactive power oscillates between the uncompensated inductive reactance on the primary side and the capacitive reflected impedance of the secondary. In order to confirm the accuracy of theoretical prediction both the electromagnetic and circuit simulations were performed using true transformer inductance values and corresponding voltages and currents.

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