C
C.1 dc-dc Converter Design
There are different types of circuit topologies has been reported for bidirectional dc to dc Buck- Boost (BB) converter [195–199]. A simple dc-dc converter topology is used in the BCCS unit. Fig.
C.1 (a) shows the circuit diagram for bidirectional BB converter with two switches (S13and S14) and two diodes (D13 and D14). This circuit diagram has the ability to provide an output voltage higher or lower than the input voltage and also it can transfer power in both directions. Moreover, this circuit diagram has few number of switches are used for bidirectional power flow. This circuit topology selected due to its simple structure, well-known dynamic behavior, pulse by pulse currant limitation and instantaneous shutdown. The output voltage is controlled in either direction by controlling the duty (D) ratio of the S13or S14.
C.1.1 Modes of Operation
During G2V operation the switch S13and diode D14 will conduct and V2G operation switch S14 and diode D14would conduct.
The BB converter operates by storing the energy in the inductor (Lb) during the interval of Switch S13in turned on (ton). The stored energy is transferred to load or distributed energy source when the switch S13is turned o f f (to f f). During this operating interval, the Lb provides a least resistance path.
Hence, the maximum current flows through the Lb. The capacitor Cb2is used to remove the ripples in the output voltage. Fig. C.1(b) and Fig. C.1 (c) shows the equivalent circuit diagram for G2V modes operation and corresponding waveforms. When the S13is turned on, the energy is stored into the Lb, the inductor current (Ib1) is reaching to the maximum (Imax) after a time interval kT which is shown in Fig C.1 (c). The voltage across the switch S13is low and the current provided from the source (Idc) to load is maximum. The switch S13 is turned o f f , then the current falls to zero but the Ib2 starts to flow through the load and diode D14. The stored energy in the Lbwill transfer to the load. The Ib2 is decreased, then the switch S13 would be turned on again in the next cycle.
The net impedance (Znet) of the output side is calculated from Eq. (C.1).
Znet = Vc/d2
Pcs (C.1)
Load
(a) Circuit diagram
Load Load
(b) Modes of operation Mode : 1
Mode : 2
kT T
kT
kT
kT
T
T
T
T kT
t
t
t
t t T+kT
T+kT
T+kT
T+kT
T+kT 2T
2T
2T 2T 0 2T
1
D13 D14
S13 S14
Lb Cb2
Vdc
Ib
ICb2
Vt
I
D14
Lb Cb2
Ib
ICb2
Vt D13
S13
Lb Cb2
Vdc
Ib
ICb2
Vt
I
I
Imax
Imax
Ib
Imax
VCb2
I Imin
Imax
Imin
Imax
VCb2max
VCb2min
∆Ib
∆VCb2
to f f
ton ton to f f
Figure C.1: Buck-boost converter circuit diagram, modes of operation and waveforms.
where Vc/d is the battery terminal voltage or output voltage of the dc-dc converter and Pcs is the maximum power handling capacity of the BCCS unit. The peak to peak ripple current (∆Ib) is calculated from Eq. (C.2).
∆Ib = Vdc
f Lb (C.2)
where Vdc is the supply voltage or input voltage of the BB converter and f is the switching fre- quency. The peak to peak ripple voltage (∆VCb2) is calculated from Eq. (C.3).
∆VCb2 = Ik
f Cb2 (C.3)
where k is the duty cycle. The output voltage of the BB converter is given in Eq. (C.4).
Vc/d = −Vdck
1−k (C.4)
The equation for Lband Cb2is derived from Eq. (C.2) and Eq. (C.3) which is given below. Assume the peak to peak ripple voltage is 3% of the maximum voltage and the ripple current is 3% of the rated
current.
Lb = Vdck
f∆Ib (C.5)
Cb2 = Ik f∆VCb2
(C.6)
C.2 Contactless Power Transfer System
The inductive power transfer (IPT) system consists of the primary and the secondary sides. Pri- mary side consists of a converter that converts dc supply into high-frequency ac signal and passes on to the primary coil. The primary coil is coupled with the secondary coil. The high-frequency current passing through the primary coil induces a voltage into the secondary coil and hence the power is transferred.
C.2.1 Self and Mutual Inductance Calculation
Although spiral circular geometry is the one having better coupling [94], the geometry used here is square or rectangular with planar coil distribution. They show better tolerance to misalignment, which is one of the important characteristics for EV applications. The calculation of L1 and L2 for rectangular winding and planar coil distribution can be approximated using neuman’s formula, which is given in Eq. (C.7). The rectangular winding with N1 and N2 turns and their equivalent radius r is given by
L= µo 4πN2
I
r1
I
r2
dl.dl′
r (C.7)
y
z e x
r1
r2 a1
b1
b2
c a2
h
Figure C.2: Parameters of the rectangular coils for any dimension and any relative position between them [2]
The Eq. (C.7), applied to the system shown in Fig. C.2, gives
L= µo π Ni2
ai.ln 2aibi
ri(ai+√
ai2+bi2 +bi.ln 2aibi
ri(bi+√
ai2+bi2
−2(ai+bi− p
ai2+bi2) +0.25(ai+bi)
(C.8)
Where riis the equivalent radius of the winding, defined as ri =
rNiSi
π (C.9)
Winding resistance Ri is given by the following expression:
Ri = ρCuNi2(ai+bi)
Si (C.10)
Where in Eq. (C.8) - Eq. (C.10), i = 1 should be used for the primary winding and i = 2 for the secondary winding. To consider the possibility of having winding of different sizes and significant misalignment can occur while transferring the power from primary side to secondary side via contact- less coil. Therefore, an general expression for mutual inductance of the primary and secondary side coil is given in Eq. (C.11).
M = µ0
4πN1N2 I
r1
I
r2
dl.dl′
r (C.11)
Fig. C.3 shows the induced and reflected voltages, which are specified in terms of mutual induc- tance M, the operational frequencyωo and Ip, Is, Vp, Vs are the primary and secondary current and voltages. The mutual inductance is related to the magnetic coupling coefficient, k and is given by
k= M
pLpLs (C.12)
C.2.2 Electrical Circuit Parameter Calculation
Fig. C.3 shows the series-series compensation circuit topology and mutual inductance coupling model of a series compensated contactless coil.
The voltage induced at the secondary side of the contactless coil is given in Eq. (C.13).
Vs = jωMIp (C.13)
Reflected impedance at the primary side can be expressed as the ratio of the reflected voltage and