Optimization algorithm and practical implementation for 2-coil wireless

2014 American Control Conference (ACC) June 4-6, 2014. Portland, Oregon, USA

Optimization Algorithm and Practical Implementation for 2-coil Wireless Power Transfer Systems Wenshan Hu, Hong Zhou, Qijun Deng and Xingran Gao 

Abstract— Wireless power transfer based on inductive coupling techniques has attracted a lot of research interest in recent years. It can be potentially applied in many industrial sections. However, the harsh outdoor industrial environment could induce circuit parameter drift. Only small drift may result in huge performance drop, as the circuits are very sensitive to the parameter changes. In order to address the problem, an optimization method to compensate for the effect of drifting parameters and track the maximum performance is introduced in this paper. A switch network which is able to dynamically change the inductance of the Tx coil is designed. When the parameter drift occurs, the tuning algorithm is able to adjust both the exciting frequency and the Tx coil inductance. By measuring the input power only, the best working point can be found out without requiring any measurement on the Rx side. Therefore, the algorithm can be implemented in the controller located on the Tx side without coordination and communication between both sides. In order to verify the effectiveness of the proposed method, a test rig is setup and practical experiments are conducted. The experimental results are also presented in the paper.

I. INTRODUCTION Wireless power transfer (WPT) technology has been an increasing research interest in recent years. There are several WPT techniques being researched presently. Farfield techniques use propagating electromagnetic waves that transfer energy the same way radios transmit signals [1]. Inductive coupling (or near-field) techniques operate at distances less than a wavelength of the signal being transmitted. The early work of inductive coupling [2-4] mainly based on the pure physical theory, which could be difficult for the engineers from electrical background. Recent researches [5-7] start to use circuit and magnetic theory to analyze the principle of the magnetic resonance coupling, which makes the technology more tangible for a wider range of researchers. A key requirement in all of the WPT applications is to deliver sufficient power to the load with high power transfer efficiency (PTE) and relative long distance. There are many configurations of WPT system developed recently including the 2-coil, 3-coil [8] and 4-coil [9] links. The multi-coil structures are able to increase the PTE in some cases but the price is the increasing complexity of the system structure. Each coil has its own parameters such as resistance, Research supported by the National Science Foundation of China under Grant 61374064. W. Hu, H. Zhou, Q. Deng and X. Gao are with Department of Automation, School of Power and Mechanical Engineering, Wuhan University, Wuhan, 430072, China (phone: +86 27 68772267; e-mail: [email protected])

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inductance and capacitance etc. Some parameters may be sensitive to the external environment like temperature, humidity. More coil loops means that more tuning work is required to get all the parameters aligned. It could be difficult to maintain the optimal performance in some harsh environment for the practical applications. Potentially, inductive coupling WPT systems can be used in many industrial applications, such as power supplies for moving sensors and transducers [10], medical implants [11] and wireless electric car charging stations [12] etc. In power industry, due to the importance of High Voltage (HV) cables in the transmission network, on-site condition monitoring is a very important issue [13][14]. However, the power supply is always a major problem for the reliability of the monitoring devices which operate in the outdoor environment with no reliable power sources. Some applications applies the solar and wind power to solve the problem but these power sources are not guaranteed in case of continuous bad weather condition which could occur frequently in some places like the mountain areas in South West China. The inductive coupling could be a potential solution for the problem. A tiny amount of the power can be recovered from the magnetic field around the HV power cables using induction coils and then transferred through the insulator (a few meters distance) to power the monitoring devices installed on the towers. For this kind of applications, robustness and reliabilities are more important issues than the performance. Therefore, the simple 2-coil structure may be the best option. Moreover, the WPT systems must be able to cope with the circuit parameters drift caused by changing weather conditions in the outdoor environment. In this paper, a WPT test rig designed for practical HV power cable monitoring is setup. It is able to deliver 20W power for a distance of 2.2m. Due to relative low working frequency, there is no requirement for high performance power electronics. All the power electric components can be purchased with low costs. In order to track the best performance with the drifting parameters in potential practical applications, a dynamic optimization algorithm is designed and experiments are conducted to verify the proposed methods. II. CIRCUIT AND MAGNETIC PRINCIPLE OF 2-COIL WPT SYSTEMS A. Circuit Model Fig. 1 shows the circuit model of the 2-coil WPT system using magnetically coupled resonator. Both the Tx Coil and Rx Coil have the same resonant frequency. When the Tx

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Coil is energized by the resonant frequency, electric power can be transmitted through the magnetic field between the two coils. On the Tx side, an AC voltage source drives an RLC branch which create high frequency magnetic field around the Tx coil. The Rx coil recovers the energy from the field and drives a load RL. In addition, both the Tx and Rx circuit have the parasitic resistance Rp1 and Rp2.

L1

Rp1

, PO  R L I 22

(4)

The overall wireless transmission efficiency is E 

PO PI

2



RL I2

V s I 1 cos(  V s   I 1 )

(5)

An experimental test rig is setup in the laboratory whose measured circuit parameters are listed in Table I. In order to maximum the power transmission, both Tx and Rx coils are made with the same resonant frequency, which means they have the same inductance and capacitance.

C2

C1

PI  V s I 1 cos(  V s   I 1 )

L2 Rp2

TABLE I.

CIRCUIT PARAMETERS

Parameter

Value

RL

AC

k

L1, L2

298uH

Fig.1. Circuit model of two-coil WPT system

C 1, C 2

200pF

Normally the distance between the two coils can be several times of the coil radius, which makes the coupling coefficient k is a very small value around 0.001 to 0.01. Only a small amount of the flux generated by Tx coil is able to penetrate the Rx coil. However, large amount of magnetic energy can still be transferred through the limited amount of flux with relatively high efficiency (around 30%). This phenomenon can be explained by the circuit of and magnetic theory.

Rp1

7Ω

Rp2

5Ω

Rl

7Ω

k

0.0001 to 0.1

Frequency

620kHz to 680kHz

B. Circuit and Magnetic Principle Kirchhoff’s voltage law (KVL) can be applied to analyze the both two circuit loops as I 1 ( R 1  j L1  I 2 ( R 2  j L 2 

1 j C 1

)  j I 2 M  V s

(1)

)  j I 1 M  0

(2)

1 j C 2

Using the data in Table I, the output power can be plotted in Fig 2, in which Po can be considered as a function of frequency and coupling coefficient k. Frequency splitting can be clearly observed as the value of k is increased. When the coupling between the two coils decreases, the frequency separation decreases until the two peak values converge at is at fs, which is very close to the resonant frequency of the two coils f0 (detailed calculation reveals that fs≠f0 but they are closed enough to be considered as a single value).

where R1=Rp1, R2=RL+Rp2 and the M is the mutual inductance between the Tx and Rx coil. The relationship between the mutual inductance and coupling coefficient is defined as k 

M L1 L 2

In order to simply the two circuit equation (1) and (2), Z1 and Z2 are defined as the impendence of the two circuit loops as Z 1 R 1  j L1 

1 j C 1

, Z 2  R 2  j L 2 

1

Fig. 2. Output power Po as a function of frequency and coupling coefficient k using the parameter given in Table I

j C 2

The two KVL equations (1) and (2) can be solved as I1 

Z 2V s 2

Z1Z 2   M

2

, I2  

j  M 12 V s 2

Z1Z 2   M

2

kc

(3)

Therefore, the input power PI which energizes the Tx coil and output power PO which are consumed on the load RL can be calculated as

As shown in Fig. 2, fs is very close to the resonant frequency f0. From the engineering point of view, f0 can be used as a very close approximation to fs without inducing big calculation errors. Therefore, the WPT system at resonant frequency can be analyzed to find out the optimized operating area. When f=f0, both the power Po and efficiency E against coupling k are plotted in Fig 3. It can be seen that the overall efficiency drops when the coupling k is decreased. However, the output power increases with the

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decreasing coupling k until it reaches the peak value Pmax. Then it drops dramatically.

III. OPTIMIZATION ALGORITHM FOR PRACTICAL APPLICATIONS A. Effects of the Parameter Drift In practical applications, it is very difficult to make two coils with the same resonant frequency. Even if the two coils were adjusted carefully initially, the capacitance and inductance could also change with the changing environment. Without perfect resonant frequency match, the performance of the WPT could degrade greatly.

Fig. 3. Output power and efficiency when f=f0

To simplify the analysis, it is assume both the Tx and Rx loops have the same inductance and capacitance as L=L1=L2, C=C1=C2. The resonant frequency for both two coils is 1

0 

For the sake of simplicity, it is assumed that the capacitance of the two coils is the same but the inductance is slightly different. L2 has a constant value 298uH but L1 changes from 288uH to 308uH. For a given distance (k=0.007), output power is a function of frequency and Rx coil inductance L1, which is plotted in Fig 4.

(6)

LC

When ω=ω0, combine (3)(4) and (6), the output power can be obtained as 1 Po

  0

C

 RL

2

2

k LV s

( R1 R 2 

1 C

(7) 2

k L)

2

In order to get corresponding value of coupling kc at the maximum power, the derivative of (7) is taken with respect to k. By setting the result to zero and solving the equation, kc is obtained as kc 

R1 R 2 C

(8)

L

For the two coils, their series quality factor are defined as Q1 

1

L

R1

C

, Q2 

1

L

R2

C

(9)

Combining (8) and (9), the relationship between kc and the quality factors is kc 

1 Q1Q 2

The coupling k is roughly reversely proportional to the third power of the coil distance. In order to get the maximum power at long distance, kc should be as small as possible, which means Q factors of the both coils are very important parameters for the performance of the WPT. However, high Q coils are very difficult to make with the limitation of coil size, material etc. For the case that the distance is several times of the coil diameter, normally the operating area is around the critical point as shown in the shadowed area in Fig 3.

Fig. 4. Output power as function of the frequency and L2

Only when the resonant frequency of the both coils and the exciting frequency are aligned, the maximum efficiency can be achieved. Only a small deviation of exciting frequency and circuit parameter could result in big performance drop as shown in Fig 4. Therefore, it is very important to develop an optimization algorithm to dynamically track the optimal operating point. By dynamically adjusting the value of L1 and f, the maximum output power can be achieved. However, measurement of output power need to be conducted on the Rx side and the data has to be sent back through wireless communication, which increases the complexity. It would be much easier if the optimized output power tracking could be achieved using the measurement data from a single side. In order to achieve that target, the circuit model on the Tx side are analyzed in details. The circuit formula (1) is separated into several terms as V R  I 1 R 1 V L  jI 1  L 1

VC  

jI 1 j C 1

V M  j I 2 k

L1 L 2

where Vc is the voltage across the capacitor, Vr is the voltage across the resistor, Vl is the voltage across the capacitance, and Vm is the voltage incited by the current I2 on the Rx coil. Fig 5 is the corresponding circuit model in which the mutual

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L1

C1 VC R1

VL +

VR

jI 2 k L1 L2 VS

-

I1

I2

Fig. 5. Circuit model for the Tx coil

B. Tuning of the Frequency It is assumed the resonant frequency of the two coils matches. Without the coupling between the two coils, the coil current I1 maximum at the resonant frequency because the term Vl and Vc compensate for each other. However, with the interaction between the two coils, there are two scenario need to be considered.

the peak value of the output power and resonant frequency. In this case, the frequency fp at the peak of I1p should be selected. C. Tuning of the Tx Coil Resonant Frequency It is assuming L1 is a tunable parameter. By the tuning of L1, the Tx coil resonant frequency can be changed to align the Rx coil. In the case when L1 is not equal to L2, the two coils have different resonant frequency. A peak or bottom (depend on the coupling k) value of I1p can still be detected close to the Tx resonant frequency. However, because the Rx coil is not on its resonant frequency, the incited current I2 is weaker, which results in the “counter force” term Vm on the Tx coil is weaker as well. Therefore, in this case, the peak or bottom value of I1 is bigger than the case when the two resonant frequencies are perfectly matched. 4.2 4

Current I1 (A)

1) The coupling k is big. Fig 6 shows the output power Po and I1 when the coupling k=0.006. In this case, due to the strong coupling, the term Vm is big and it acts as “back EMF” to limit the current at the resonant frequency. Therefore, the output power maximum at the resonant frequency but I1 has two peaks and a bottom. In this case, the frequency fp at the middle bottom I1p curve should be selected. 2.5

25

1.5

15

1

10

0.5

0 6.2

16

3.6

14

3.4

12

3.2

10

3

8

2.8

6

2.6

4

2.9

2.92

2.94

2.96

2.98 L1 (H)

3

3.02

3.04

3.06

2 3.08 -4

x 10

Fig. 8. Output power and Tx coil current peak

Fig 8 shows plot of the output power Po and the input current peak I1p against the changing L1. When the two coils parameters are aligned, the output power reaches the peak and the I1p reach the bottom, which is the optimized operating point for the system.

Output Power (W)

Tx Coil Current (A)

20

18

3.8

2.4 2.88

Tx Coil Current Output Power 2

20 Tx Coil Current Peak Output Power

Output Power (W)

reactance from the Rx coil is considered as a voltage source controlled by the derivative of I2.

5

6.3

6.4

6.5 Coupling k

6.6

D. Tuning Algorithm Based on the analysis of the circuit model in Fig 8, it can be seen the value of the I1 can reflect the output power. By measuring the current I1, the optimization algorithm can be developed. It is assumed that the possible range of L2 is between L2, min to L2, min+ndL with the step size dL and the frequency ranges from fmin to fmax.

0 6.8

6.7

5

x 10

Fig. 6. Current I1 and Efficiency when coupling is strong (0.007) 4

20 Tx Coil Current Ouput Power

2

0 6.2

10

6.3

6.4

6.5 Coupling k

6.6

6.7

2) Keep changing the exciting frequency from fmin to fmax.

Output Power (W)

Tx Coil Current (A)

1) Set L1 to a L1, min. 3) If the current I1 has two peak values, record the value at the bottom between the peaks as I1,p1 and the corresponding frequency fp1 and inductance L1, p1. 4) If the current I1 has a single peak value, the peak current is recorded as I1,p1.

0 6.8 5

x 10

Fig. 7. Current I1 and Efficiency when coupling is weak (0.004)

2) The coupling k is small. Fig 7 shows results when the coupling k=0.004. Because of the smaller coupling, the effect of term Vm decreases greatly. The two peaks and a bottom in Fig 6 merge into a single peak which is align with

5) Set L2 to L2, min+dL and the scan the frequency for the whole range. Record the current I1,p2 and corresponding fp2 and L1,p2. 6) Repeat the fifth step n times until the I1,pn, L1,pn and fpn are obtained.

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7) Compare the value of I1,pi (i=0 to n). If I1,pi is the minimum value, then the corresponding L1,pi and fpi is the optimized parameter for the WPT system.

either the capacitance or inductance. In this paper, a switch network which is able to “digitally” tuning the coil inductance is introduced. The switch network which consists of four switches and four inductors with 1.5uH, 3uH, 6uH and 12uH inductance are connected in serial in the Tx coil loop. With four switches, the following overall inductance of the switch network can be achieved as shown in Table III.

IV. IMPLEMENTATION OF WPT SYSTEM Fig. 9 is the diagram of the practical application of the proposed WPT system. A DDS (Direct Digital Synthesizer) module AD9850 controlled by a MCU (Micro Controller Unit) controller is adopted to generate the accurate the square wave exciting signal. The frequency signal is amplified by a gate driver module and then drives a MOSFET H-bridge to generate a high frequency AC voltage source. The Tx coil is energized by the AC and transmit the power to the Rx coil though the inductive coupling. On the Rx side, the electric energy receive by the coil is rectified to DC by a high speed bridge rectified made of Shockley Diodes. The DC is filtered by capacitors and then drives the load. Even though the H-bridge inverter can only generate square waves rather than sinusoidal ones, only the fundamental frequency which perfectly matches the resonant frequency can pass through the WPT system. Therefore, the theoretical analysis based on the AC source is still applicable for the case of H-bridge inverters.

TABLE II.

S1

D1

S3

SW1

SW2

SW3

SW4

0uH

Off

Off

Off

Off

1.5uH

On

Off

Off

Off

3uH

Off

On

Off

Off

…

…

…

…

…

21uH

Off

On

On

On

22.5uH

On

On

On

On

Using the switch network, the add-on inductance can be tuned digitally from 0uH to 22.5uH with a step size of 1.5uH. On the Rx coils, a compensation inductor with 11uH inductance is also added to the loop. Assuming both the two coils are tuned to have the same resonant frequency, the switch network would give a tunable frequency from -11uH to 11.5uH to cope with the parameter drift. V. EXPERIMENTAL RESULTS In order to verify the proposed optimization algorithm, a WPT test rigs has been setup in the laboratory as shown in Fig 10. The two coils are winded by 19 turns using Litz cable with 500 strands, which form 298uH inductance. Two parallel 100pF high voltage ceramic capacitors are connected in serial as the add-on capacitors. The detailed circuit parameters are listed in Table I.

It is easy to achieve the tuning of the exciting frequency with the DDS technology. However, the tuning of the resonant frequency is very difficult as it require changing

Rp1

Switching Pattern

Inductance

When the system is initially tuned, the resonant frequency of the two coils and the excited AC frequency are aligned. The system has the optimized performance. However, due to the changes of the environment, the coil resonant frequency could drift and result in the dramatic performance drop. Therefore, in order to track the optimal operating point with the changing circuit parameters, both the exciting frequency and the resonant of the coils must be adjusted using the algorithm introduced in Section III.

+

SWITCHING PATTERN AND INDUCTANCE

C2

C1

D3

L1

L2 Rp2

Vd S2

D2

S4

D4

RL

SW1 SW2 SW3 SW4 k

-

Current Sensor

Low Pass Filter

LA1 LA2 LA3 LA4 1.5uH 3uH 6uH 12uH Switch Network

To S2 and S3

Controller

DDS Frequency Generation

To S1 and S4

Fig. 9. Diagram of the practical implementation

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LB

TABLE III.

EXPERIMENTAL RESULTS

both sides is not required in the simplified system. In order to verify the proposed method, practical experiments have been conducted. It shows that with the proposed algorithm, the maximum power and efficiency can be achieved.

Experimental Results

Add-on Inductance

I1p

Frequency

Output Power

Efficiency

…

…

…

…

…

3uH

2.73

641KHz

20.9W

19.1%

4.5uH

1.77

636KHz

21.8W

30.8%

6uH

2.46

632KHz

10.2W

10.4%

7.5uH

2.63

631KHz

8.9W

8.4%

…

…

…

…

…

The radius of the both coils is 20cm and the distance between the two coils is 2.2m, which makes the coupling between the two coils is around 0.006. The photos of the prototype are shown in Fig 10. By switching the SW1 to SW4, the resonant frequency of the Tx coil can be adjusted. The exciting frequency is changed by using the keyboard on the MCU based controller. Both the overall efficiency and the DC bus current on the Tx side are measured and the experimental results are shown in Table III.

In the future, the switch network in the current circuit would be replaced by a relay network which control by MCU controller. A dynamic tuning algorithm will be implemented using a computer program without manual interference. Therefore, the optimization program can be executed automatically to make sure the whole system is working in the optimized condition. REFERENCES [1]

[2] [3] [4]

[5]

[6] (a) [7]

[8]

(b)

(c) Fig. 10. Picture of the WPT system. (a) Coil structure. (b) Power electronics. (c) Test rig

From the experimental results, the maximum DC bus current does reflect the efficiency of the whole system. By selecting the smallest peak current on the resonant frequency, the most optimized operating point can be achieved.

[9]

[10]

[11]

VI. CONCLUSION AND FUTURE WORK In this paper, the design and implementation of a practical 2-coil WPT system have been introduced. In practical applications, the environment change could cause the circuit parameter drift. It is proved that only slight drift could result in great performance drop. In order to address this problem, a dynamic parameter tuning algorithm has been introduced to optimize the performance of the whole system. The proposed algorithm only requires the measurement of the input power on the Tx and the involvement of the Rx side is not necessary. Therefore the communication between the

[12]

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[14]

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