INTRODUCTION
With soaring need of wireless power transfer (Green and
Boys, 1994; Boys and Green, 1995; Kurs
et al., 2007; Aristeidis et al., 2008)
and green cars (Bai et al., 2005), electric vehicles
and wireless dynamic power supply technique (Covic et
al., 2007; Madawala and Thrimawithana, 2010;
Seungyoung and Joungho, 2011) have become hot research
areas in recent years. In the electric vehicle wireless dynamic power supply
system, on the one hand, the relative move between power emission unit (primary
part) and power pickup unit (second part) leads to change of coupled parameter
which results in output fluctuation; on the other hand, the nonlinear and higher
order and characters of system which result from the existence of vast nonlinear
switching and energystorage devices, make it hard to build the accurate system
model and control. Neural network (NN) is an algorithm that can deal with higherorder,
nonlinear, strongcoupled, uncertain and complex matter very well (Abdalla
and Deris, 2005; Edriss et al., 2008; Reddy
et al., 2008; Mahi and Izabatene, 2011; Alsaade,
2011). With powerful ability in nonlinear mapped, it is good at selflearning
and selforganizing (Venkatachalam et al., 2008;
Guo et al., 2011). Under NN control, a higherorder,
nonlinear and model hard to build system can be robust.
There are two ways to regulate output power, primary control and secondary
control. Phaseshift control (Yugang et al., 2008;
Yue et al., 2009), primary detuning control (Ping
et al., 2008) and primary power injecting control (Xin
et al., 2011) are the several common methods which ask to send second
part output parameter to primary controller via added communication device such
as infrared, radio frequency and so on. In the dynamic wireless power supply
system for electric vehicles, obviously it is difficult to build an effective
communication system between primary part and second part. In addition, the
realtime transfer of signal cannot be insured. Therefore, for the dynamic wireless
power supply system for electric vehicles, the latter one is more feasible.
Some previous studies have proposed the principle of second part power regulate
(Hu et al., 2000; Sallan
et al., 2009) but an effective control strategy has not been given.
From the above analysis, a constant current control strategy based on BP neural network, used in electric vehicles dynamic wireless power supply is presented in this paper. Using the nonlinear function approximation ability of neural network keeps the output current constant via regulating the duty ratio of power control switch as the pickup and track become misaligned which leads to the coupling parameter change. Then, a simulation model is built in the Simulink to verify that this control strategy is much better than conventional PID control method both in overshoot and setting time.
DYNAMIC WIRELESS POWER SUPPLY SYSTEM FOR ELECTRIC VEHICLES
Principe: The wireless power supply system for electric vehicles mainly
employs inductive coupling (Chaoui et al., 2005;
Hmida et al., 2007), magnetic resonance and microwave,
replacing wires and connectors to transmit electric energy from power supply
to load. Figure 1 shows the fundamental structure of electric
vehicle power supply system based on inductively coupled power transfer technique
(EVPSICPT). Primary power convertor takes power from a conventional singlephase
or threephase power supply to generate a high frequency current in the primary
energy emission unit (underground track or coil array), around which high frequency
magnetic field is formed. In the pickup unit which is located in the high frequency
magnetic field, high frequency current is induced and conditioned by the onboard
converter and controller to produce stable supply to battery charging or motor
driving.
Main circuit: Four basic resonant topologies of ICPT system labeled
as SS, SP, PS and PP can be employed in the inductively coupled power transfer
system (Green and Boys, 1994), where the first S or
P stands for series or parallel compensation of the primary winding and the
second S or P stands for series or parallel compensation of the secondary winding.
Since the seriescompensated secondary reflects no reactance at the nominal
resonant frequency, the primary inductance can be tuned out independent of either
the magnetic coupling or the load by a seriesconnected capacitance in the primary
network. As the parallelcompensated secondary reflects a loadindependent capacitive
reactance at the nominal resonant frequency, series tuning in the primary is
dependent on the magnetic coupling but not the load. Because the reflected impedance
contains a real component representing the load, parallel tuning in the primary
becomes dependent on both the magnetic coupling and the load. What’s more,
SS and SP compensation are more advantageous for highpower transmission. At
lowpower levels, where wire section is not a relevant parameter, PS and PP
compensations make possible working at a larger distance with the same operating
frequency. Theoretically, SS is the best topology, as the primary capacitance
is then independent of either the magnetic coupling or the load and is viable
for highpower transmission. Considering capacitor requirements, however, parallel
compensation implies lower voltages and higher currents than series compensation
and requires lower operating frequency. That is due to the fact that the higher
the required current, the lower the operating frequency (Sallan
et al., 2009).

Fig. 1: 
Block diagram of system 

Fig. 2: 
Main circuit topology 
Therefore, SP topology is also widely used for EVPSICPT application. A typical
main circuit based on SP topology for EVPSICPT is shown in Fig.
2. It shows that the main circuit consists of power emission side (primary
part) and pickup part (second part) settled on car. The primary converter,
composed of S_{1}S_{4}, derives power from DC source E_{dc}
and generates a track current in L_{s} which is loosely coupled to the
pickup winding L_{p}. The onboard rectifier, composed of D_{1}D_{4},
converts induced high frequency ac current to dc current to battery pack charging.
The power controller that consists of D_{r}, S_{a} and D_{r}
can regulate the rank of charging power. C_{s}, R_{s}, R_{r},
C_{p} and R_{p} are the primary compensation capacitor, internal
resistance of primary track, reflected resistance, secondary compensation capacitor
and internal resistance of secondary pickup winding respectively.
The mutual inductance between L_{s} and L_{p} is denoted as M, whose value is given by:
where, k stands for the coupling coefficient between L_{s} and L_{p}.
To transfer maximum power to the load, the system should operate at the point of natural resonant frequency, whose value is determined by:
where, C_{p} is the value of secondary compensation capacitor.

Fig. 3: 
Equivalent circuit as switch S_{a} on and off (a)
S_{a} on (b) S_{a} off 
The value of primary compensation capacitor can be calculate by:
The real part of reflected impedance is given by:
For maximum power transfer purpose, the dc inductance L_{r} is normally designed to be a value determined by Eq. 5 to ensure the continuation of the dc current I_{c} under the steadystate conditions:
where, R_{min} is the equivalent resistance of the maximum load.
Power regulating: Power control is finished by a Booster which consists
of L_{r}, S_{a} and D_{r}. The equivalent circuit as
S_{a} on and off are showed in Fig. 3a and b,
respectively. Supposed t_{on} as the time of S_{a} on and t_{off}
as the time of S_{a} off. Then the output power can be regulated by
changing the ration of t_{on} and t_{off}.
THE ARCHITECTURE AND ALGORITHM OF THE BP NEURAL NETWORK
The BP neural network is one of the most typical neural network models. It
is very good at nonlinear fitting, prediction, generalization and error tolerance
(Mullai and Rene, 2008; Yedjour
et al., 2011). A BP neural network has a layered structure (a single
input layer, a single hidden layer or multi hidden layers, a single output layer).
Each layer consists of units (neurons or nodes) which receive their input from
units from a layer directly above and send their output to units in a layer
directly below the unit. There are no connections among units in the same layer.
A trilayer BP neural network, whose number of neurons of input layer, hidden layer and output layer are p, q and r, respectively, is shown in Fig. 4.
Mark X = [x_{1}, x_{2},…, x_{p}] as the input vector, Y = [y_{1}, y_{2},…, y_{q}] as the output vector, w_{ij} (i = 1, 2,…, p; j = 1, 2,…, q) as the weight between the input layer node i and hidden layer node j, v_{jt} (j = 1, 2,…, q; t = 1, 2,…, r) as the weight between the hidden layer node j and output layer node t, θ_{j} as the threshold of hidden layer node j and γ_{t} as the threshold of output layer node t. Then:
where, S_{j}, b_{j}, f(), L_{t}, y_{t} and g() are the input of hidden node j, the output of hidden node j, the active function of hidden layer, the input of output layer node t, the output of output layer t and the active function of output layer, respectively.
Mark e(k) as the error between actual and expected output and it is given by:
The expression for energy function is:
The BP neural network is a kind of learning algorithm for error correction
built on the basis of gradient descent method which organically combined positive
spread of the input signal with backpropagation of error ones (Mianli
et al., 2010). While learning the new sample, it tends to forget
the old ones, that is to say, it fails to take into account the previous experience.
As a result, the local minimum problem and slow convergence speed will exist.
To solve these issues, three major methods have been introduced:
• 
Change the learning efficiency 
• 
Add momentum factor 
• 
Appropriate transfer function 
Method 1 and 2 are adopted in this paper. Thus, we can get the following expressions:
where, ηε [0,1] and αε [0,1] stands for learning efficiency and momentum factor, respectively.
DESIGN OF THE BP NEURAL NETWORK CONTROLLER
In this study, we use a 3q2 BP neural model, whose number of input layer nodes, hidden layer nodes and output layer nodes are 3, q and 2. The error e between actual output current and reference current, reference current I_{ref} and mutual inductance are the three nodes of input layer. The duty ratio variation Δd of switch S_{a} and reference duty ration d_{0} are the two node of output layer. The number of hidden layer nodes has a huge effect on the ability in function approximation of BP neural network but more hidden layer nodes is not always better. Usually long learning time, bad error tolerance and failed to identify new sample all result from too many hidden layer nodes. An optimized number of hidden layer is given by the following empirical equation:
where, q is the number of hidden layer nodes, p is the number of input layer nodes and r is the number of output layer nodes.
Table 1: 
Partial training data 

Based on Eq. 16, 10 hidden layer nodes
is suitable. And then, a simulation model is built and its primary configuration
parameters as following:
• 
The active function of input layer to hidden layer: double
tangent S function “tansig” 
• 
The active function of hidden layer to output layer: linear function “purelin” 
• 
The train function: reflected propagation algorithm “trainlm” 
• 
Weights correct rule: momentum gradient descent learning function “learndm” 
• 
Learning speed: 0.05 
• 
Maximum train steep: 1000 
• 
Target error: 0.05 
• 
The train sample: includes data when mutual inductance is 2.0, 2.2, 2.4
and 2.6 μH. Partial training data is shown in Table 1 
With the above parameters, the mean square error function curve is shown in Fig. 5.
It is can be seen from Fig. 5 that the work meets the need of aim error after 77 iterations. This indicates that the system is able to converge with a high speed.
SIMULATIONS
In this section, a simulation model whose parameters are shown in Table 2 is built in the MATLAB/Simulink environment to verify the validity of BP neural network control method used in the dynamic wireless power supply system for electric vehicles.
Figure 6 shows the control block diagram. The error e between referenced current and out current, the referenced current Iref and the mutual inductance M are inputted in the BPNN controller which will give out the duty ratio variation Δd of switch S_{a} and reference duty ration d_{0}. The duty ratio d is calculated out by d calculator and used to drive the control circuit.
Figure 7, where, BPNN control is added at 0.02 sec and mutual inductance varies instantaneously from 2.4 to 2.0 μH at 0.08 sec and goes back 2.4 μH at 0.14 sec, demonstrates the control results of BP neural network control. To show the advantages of BP neural network control, the results of conventional PID method are shown in Fig. 8.
Figure 7 and 8 tell us that the regulate
time of BPNN control method is only about 0.005 sec and the overshoot is less
than 0.1 A.

Fig. 6: 
Control block diagram of system 

Fig. 7: 
Waveforms of BP neural network control method (M = 2.0, 2.4
μH) 
Contrastively, the overshoot of PID control method is about 0.24 A (δ≈5%)
and the regulate time is about 0.03 sec when the mutual inductance goes from
2.0 to 2.4 μH. And the overshoot is about 0.3 A (δ≈6.5%) and
the regulate time is also about 0.03 sec when the mutual inductance goes back
2.0 μH.
Figure 9 shows this situation: mutual inductance varies instantaneously from 2.5 to 2.1 μH at 0.08 sec and goes back 2.5 μH at 0.14 sec. It verifies that the effect of BPNN control is also very good despite the input parameter is out of the training sample.

Fig. 8: 
Waveforms of PID control method (M = 2.0, 2.4 μH) 

Fig. 9: 
Waveforms of BP neural network control method (M = 2.1, 2.5
μH) 
CONCLUSIONS
In this study, a constant current control method based on the backpropagation
neural network is proposed to solve the problem of wireless constant current
charging for moving electric vehicles. Simulation results prove this method
to be plausible, even when the input parameter is not in the training sample.
By introducing this control method, the problem of accurately modeling and output
control caused by higherorder nonlinear behavior and multidisturbance factor
can be satisfactorily resolved.
ACKNOWLEDGMENTS
This study is supported by the National Natural Science Foundation of China (No. 50807057) and the central university basic scientific research business project of China (No. CDJXS11172238).